Credit Card Fraud

In this example, we use VerticaPy to detect fraudulent credit card transactions. You can download the Jupyter notebook here.

The Credit Card Fraud Detection dataset contains credit card transactions from September 2013 by European cardholders. It contains numerical input variables from a principal component analysis (PCA) transformation.

To preserve the cardholders' confidentiality, we cannot access the original features and background information about the data.

"Time" and "Amount" are the only features that have not been transformed with PCA.

  • V1, V2,..., V28 : principal components from PCA
  • Time : Number of seconds elapsed between this transaction and the first transaction in the dataset
  • Amount : Transaction amount
  • Class : Response variable, where a value of 1 indicates fraudulent activity

"Amount" will be useful for example-dependent cost-sensitive learning.

We will follow the entire Data Science cycle (Data Exploration, Data Preparation, Data Modeling, Model Evaluation, Model Deployment) to solve this problem.

Initialization

This example uses the following version of VerticaPy:

In [1]:
import verticapy as vp
vp.__version__
Out[1]:
'0.9.0'

Connect to Vertica. This example uses an existing connection called "VerticaDSN." For details on how to create a connection, use see the connection tutorial.

In [2]:
vp.connect("VerticaDSN")

Let's create a Virtual DataFrame of the dataset.

In [3]:
creditcard = vp.read_csv('data/creditcard.csv', 
                         parse_nrows = 1000)
display(creditcard)
123
Time
Int
123
V1
Float
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V2
Float
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V3
Float
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V4
Float
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V5
Float
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V6
Float
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V7
Float
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V8
Float
123
V9
Float
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V10
Float
123
V11
Float
123
V12
Float
123
V13
Float
123
V14
Float
123
V15
Float
123
V16
Float
123
V17
Float
123
V18
Float
123
V19
Float
123
V20
Float
123
V21
Float
123
V22
Float
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V23
Float
123
V24
Float
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V25
Float
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V26
Float
123
V27
Float
123
V28
Float
123
Amount
Numeric(9,3)
123
Class
Int
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93601.107029376948430.2164410003713510.5383781497082331.47639799266774-0.251941920499494-0.3406797069124960.154091744631261-0.08650254563322860.144420201120718-0.157374627687008-0.1075602976940881.06632565737920.620788366839222-0.0708893376688794-0.203857982828647-0.8534794193307680.336478013774869-1.17953172110404-0.501729107425755-0.111852535538935-0.06003745010764930.0598841227860989-0.04752636647783270.4439924186361190.640295758747984-0.3376571306685210.04210848389191540.02426471000685826.720
9462-1.035105817766890.9960131278175142.19247013559677-0.170445302779918-0.302319738525738-0.1422557677002870.2234317744485960.2890434101184210.0941408906153459-0.157858732844487-0.386373549409945-0.628633662180404-1.023958211220710.09843387469763141.562288761964390.168577701728536-0.148826411284152-0.285927210472601-0.4833638941512240.180287626805096-0.098000008392506-0.17024584412346-0.137227527043150.05522827893583530.07934755420630780.3020326021134110.3913773499747970.1965998806652895.990
9564-0.6583049340956840.406790567371532.03746063876455-0.2912979744171950.147909808593845-0.3508572919580210.945373213135361-0.1725600167339780.0251333984849018-0.778134723733662-0.1962898019372620.6329552618263730.374025171567011-0.531597207426503-0.615062565100624-0.5180784591851660.00388089531948063-1.2889540744158-0.7978044852172220.0641328738661188-0.156095760618683-0.2388049648914450.08987717739851130.421195367129561-0.3524871342279070.0747827424634443-0.0941921697507859-0.092493130400881354.990
96640.959601658512230.3707113046139330.8886133700455652.343244103022470.3524908410847551.36551460619135-0.2777707304627410.516053179747465-0.7009290450550260.4682162393672580.7456115099471320.373531002993358-0.2239182858666670.4174381420698961.67840014345469-0.5157016002371870.662478668271888-2.5142351135941-2.5896875748614-0.298404520795831-0.155547160729115-0.4032393156847710.356504034074842-0.696881458915448-0.198717970162506-0.2202679155151420.06854619613585830.02079731541614097.550
97641.21251089095254-0.0990542956039435-1.192094094634260.2863235615097552.160516251832093.61631350966622-0.404206898066650.8423309516479930.169360420742526-0.0305221765721243-0.5419572580231060.237212014866616-0.2181296487032740.197436520971338-0.147850245921019-0.0978301417256899-0.51005250120389-0.07093928064214850.3551705836531590.0147774396345371-0.167496336516951-0.494694569848075-0.1497854509684641.011226554671010.883547704730387-0.3294338105920750.0203701456794310.017037086350501234.70
9867-1.494667840742710.8372413999636292.628210617906073.14541437889465-0.6090983888544240.258495000688512-0.01218861335878050.102136035246365-0.2861635968242871.19855632464938-0.550295668711412-0.1068459885207450.208014288229433-0.6805104027696350.507763583158711-0.2602640225587780.2466313239022870.008855504384242280.899415801359582-0.0283519350532205-0.1400473580571390.3550441838116020.3327199884352280.718192517148152-0.2193660461143240.118926551385282-0.317485702168288-0.34078339765064328.280
9967-0.6534446272949950.1602250768520381.592255555240821.296832283575650.997174923623236-0.3430003024091340.469936930779834-0.132470081994361-0.197794077439788-0.105005538081425-0.5436622109269710.3022330226359640.141211078726449-0.2078804435531010.0241083998795536-1.206876591915640.39483638189259-0.7509556302064260.4405584811704080.2259203469185410.03836296797903680.336449012374641-0.01488283283567180.102959010243-0.265322060067868-0.348636686626220.0112384491290326-0.049478339972149219.850
10068-0.7701963826479880.4835724164120241.90107177893088-0.001876250116188520.0242447851356973-1.171903181582750.666483360897814-0.0946029012075535-0.136665621886762-0.842507532652561-0.4082350970881010.503046644959921-0.010588597193309-0.200012764882671-0.908689458907517-0.323594882408827-0.0221036727295719-0.796683932841244-0.479505428522999-0.0338308901120332-0.0573359108181297-0.1558012807637610.01810780200743670.941555368544963-0.1685818411260970.05617099692751760.05897936129031080.13418792127799622.360
Rows: 1-100 | Columns: 31

Data Exploration

Let's explore the data by displaying descriptive statistics of all the columns.

In [4]:
creditcard.describe()

Out[4]:
count
mean
std
min
approx_25%
approx_50%
approx_75%
max
"Time"28480694813.841365702747488.22832975130.053836.351912568384348.356547619139145.62236534172792.0
"V1"2848064.94593944284826e-061.9586974640224-56.407509631329-0.922687561939835-0.004023521563535611.315890444824242.45492999121121
"V2"2848065.70457762978566e-061.65130867214891-72.7157275629303-0.5957557556492920.06488872801405330.80634597197939322.0577289904909
"V3"284806-8.9455359328619e-061.51625015150494-48.3255893623954-0.8897478621394210.1797950030480911.027902405428869.38255843282114
"V4"284806-1.35415518936858e-061.4158708761878-5.68317119816995-0.850673053289735-0.02276909609958510.74216249847936916.8753440335975
"V5"284806-1.76537738534109e-061.38024883562916-113.743306711146-0.692237575696747-0.0541469873155910.61268391143762134.8016658766686
"V6"284806-1.78084282248157e-061.33227308968888-26.1605059358433-0.767764777497726-0.2720730111341110.39740972899175973.3016255459646
"V7"2848066.12498031875639e-061.23709145154523-43.5572415712451-0.5538828475189340.03981456264679790.570420541346974120.589493945238
"V8"284806-2.67056953047529e-061.19435414910998-73.2167184552674-0.2087661827582030.0220061628565510.32847087188162820.0072083651213
"V9"284806-1.05394689850686e-051.09861961972555-13.4340663182301-0.641658431375348-0.05166901173298820.5959896806161515.5949946071278
"V10"2848064.08381472133854e-061.08884949581936-24.5882624372475-0.535699872562504-0.09292037159809670.45328255250960223.7451361206545
"V11"284806-1.38169915208807e-061.02071455331551-4.79747346479757-0.763765051282868-0.03382187485375190.73984174842771112.0189131816199
"V12"2848066.93843535334324e-060.999196282625864-18.6837146333443-0.4043222887970750.1419286303375090.6187311497957377.8483920756446
"V13"284806-8.12075363651004e-070.995275883057862-5.79188120632084-0.649459842407078-0.01334910490294320.6614371689126657.12688295859376
"V14"284806-1.84962341608303e-060.95859678593258-19.2143254902614-0.4267411848911070.05116431665091320.49276491045535310.5267660517847
"V15"2848061.13497169209891e-050.91529757725878-4.49894467676621-0.5830265047062520.04647603158499510.6497512300068888.87774159774277
"V16"284806-7.66515009784341e-080.876254424770488-14.1298545174931-0.4675522387000860.06626739121742440.52342780734466717.3151115176278
"V17"284806-1.82546167118454e-060.849337996047683-25.1627993693248-0.483346901949957-0.06605825142364860.3994048505087349.25352625047285
"V18"284806-3.95506512618923e-060.838175023391719-9.49874592104677-0.499033588630568-0.003262777455159320.5005742148118095.04106918541184
"V19"284806-2.80927640719469e-070.81404191608048-7.21352743017759-0.4548850313037110.003652402667366090.4586940743659245.59197142733558
"V20"284806-7.33947797666482e-070.770926278808211-54.497720494566-0.211671047672314-0.06249770509640540.13334617592955339.4209042482199
"V21"284806-7.64172187575889e-070.734525190677675-34.8303821448146-0.2286085901976-0.02938689104486870.18606448848130427.2028391573154
"V22"284806-2.66232723466359e-060.725701443601768-10.933143697655-0.5421584039904380.006747921053238860.52840312158958410.5030900899454
"V23"284806-9.87528822847108e-070.624461169497999-44.8077352037913-0.161700875369553-0.0111335096927520.14775835082307922.5284116897749
"V24"284806-2.58634991744588e-060.605646558279992-2.83662691870341-0.3534686481854890.04096385948910910.4388432916332714.58454913689817
"V25"2848062.60318278485781e-060.521277134452016-10.2953970749851-0.3173985280137780.01697338816639960.3498730114756877.51958867870916
"V26"284806-8.96574869783747e-070.482227622472413-2.60455055280817-0.327442353708538-0.05385973923824510.241233936262753.5173456116238
"V27"284806-4.98388964024732e-070.403633115942523-22.5656793207827-0.07102288983282510.001439592508895260.091310343991825931.6121981061363
"V28"284806-8.01132016653443e-070.330083566760313-15.4300839055349-0.0529499817329360.01126499591763050.078347660770601833.8478078188831
"Amount"28480688.3497556582376250.1205377537440.05.6372294372294422.001091370558477.028498293515425691.16
"Class"2848060.001727491696101910.04152726241384280.00.00.00.01.0
Rows: 1-31 | Columns: 9

It'll be difficult to work on the principal components (V1 through V28) without knowing what they mean. The only features we can work on are Time and Amount.

Let's convert the number of seconds elapsed to the correct date and time. We know that the records were ingested in September 2013, so we'll use that to create the new feature.

In [5]:
creditcard["Time"].apply("TIMESTAMPADD(second, {}::int, '2013-09-01 00:00:00'::timestamp)")
Out[5]:
📅
Time
Datetime
123
V1
Float
123
V2
Float
123
V3
Float
123
V4
Float
123
V5
Float
123
V6
Float
123
V7
Float
123
V8
Float
123
V9
Float
123
V10
Float
123
V11
Float
123
V12
Float
123
V13
Float
123
V14
Float
123
V15
Float
123
V16
Float
123
V17
Float
123
V18
Float
123
V19
Float
123
V20
Float
123
V21
Float
123
V22
Float
123
V23
Float
123
V24
Float
123
V25
Float
123
V26
Float
123
V27
Float
123
V28
Float
123
Amount
Numeric(9,3)
123
Class
Int
12013-09-01 00:00:00-1.3598071336738-0.07278117330984972.536346737969141.37815522427443-0.3383207699425180.4623877777622920.2395985540612570.09869790126105070.3637869696112130.0907941719789316-0.551599533260813-0.617800855762348-0.991389847235408-0.3111693536998791.46817697209427-0.4704005252594780.2079712419292420.02579058019855910.4039929602557330.251412098239705-0.0183067779441530.277837575558899-0.1104739101887670.06692807491467310.128539358273528-0.1891148438888240.133558376740387-0.0210530534538215149.620
22013-09-01 00:00:001.191857111314860.266150712059630.166480113353210.4481540784609110.0600176492822243-0.0823608088155687-0.07880298333231130.0851016549148104-0.255425128109186-0.1669744140046141.612726661054791.065235311372870.48909501589608-0.1437722964415190.6355580932582080.463917041022171-0.114804663102346-0.183361270123994-0.145783041325259-0.0690831352230203-0.225775248033138-0.6386719527718510.101288021253234-0.3398464755291270.1671704044181430.125894532368176-0.008983099143228130.01472416919249272.690
32013-09-01 00:00:01-1.35835406159823-1.340163074736091.773209342631190.379779593034328-0.5031981333181931.800499380792630.7914609564504220.247675786588991-1.514654322605830.2076428652166960.6245014594248950.0660836852688310.717292731410831-0.1659459227635542.34586494901581-2.890083194442311.10996937869599-0.121359313195888-2.261857095304140.5249797252244040.2479981534697540.7716794019172290.909412262347719-0.689280956490685-0.327641833735251-0.139096571514147-0.0553527940384261-0.0597518405929204378.660
42013-09-01 00:00:01-0.966271711572087-0.1852260080828981.79299333957872-0.863291275036453-0.01030887960308231.247203167524860.237608939771780.377435874652262-1.38702406270197-0.0549519224713749-0.2264872638354010.1782282258773030.507756869957169-0.28792374549456-0.631418117709045-1.0596472454325-0.6840927863454791.96577500349538-1.2326219700892-0.208037781160366-0.1083004520355450.00527359678253453-0.190320518742841-1.175575331863210.647376034602038-0.2219288444584070.06272284872930330.0614576285006353123.50
52013-09-01 00:00:02-1.158233093495230.8777367548484511.5487178465110.403033933955121-0.4071933773116530.09592146246842560.592940745385545-0.2705326771922820.8177393082352940.753074431976354-0.8228428779463630.538195550149951.3458515932154-1.119669834717310.175121130008994-0.451449182813529-0.237033239362776-0.03819478703528420.8034869249601750.408542360392758-0.009430697132329190.79827849458971-0.1374580796190630.141266983824769-0.2060095876197560.5022922241815690.2194222295133480.21515314749920669.990
62013-09-01 00:00:02-0.4259658844124540.9605230448829851.14110934232219-0.1682520797603020.42098688077219-0.02972755166397420.4762009487200270.260314333074874-0.56867137571251-0.3714071968344711.341261980019570.359893837038039-0.358090652573631-0.1371337002176120.5176168065557420.401725895589603-0.05813282336401310.0686531494425432-0.03319378778762820.0849676720682049-0.208253514656728-0.559824796253248-0.0263976679795373-0.371426583174346-0.2327938167370340.1059147790979570.2538442247393370.08108025692294433.670
72013-09-01 00:00:041.229657634507930.1410035070493260.04537077358994491.202612736735940.1918809885976450.272708122899098-0.005159002882509830.08121293988308940.464959994783886-0.0992543211289237-1.41690724314928-0.153825826253651-0.751062715562620.167371962521750.0501435942254188-0.4435867979167270.00282051247234708-0.61198733994012-0.0455750446637976-0.21963255278686-0.167716265815783-0.270709726172363-0.154103786809305-0.7800554150046710.75013693580659-0.2572368459171390.03450742974384130.005167768906249164.990
82013-09-01 00:00:07-0.894286082202820.286157196276544-0.113192212729871-0.2715261300886042.66959865959863.721818061127510.3701451276769160.851084443200905-0.392047586798604-0.410430432848439-0.705116586646536-0.110452261733098-0.2862536324705830.0743553603016731-0.328783050303565-0.210077268148783-0.4997679688002670.1187648610042170.570328167465360.0527356691149697-0.0734251001059225-0.268091632235551-0.2042326699478781.01159180187850.373204680146282-0.3841573077022940.01174735645819960.1424043299214793.20
92013-09-01 00:00:07-0.6442694423481461.417963545473851.0743803763556-0.4921990184950150.9489340947641570.4281184628330891.12063135838353-3.807864238735890.6153747306670271.24937617815176-0.6194677961219130.2914743530887051.75796421396042-1.323865219705260.686132504394383-0.0761269994382006-1.2221273453247-0.3582215698690780.324504731321494-0.1567418524882851.94346533978412-1.015454709799710.057503529867291-0.649709005559993-0.415266566234811-0.0516342969262494-1.20692108094258-1.0853391883237740.80
102013-09-01 00:00:09-0.338261752425751.119593376415661.04436655157316-0.2221872767382960.49936080649727-0.246761100619910.6515832064899720.0695385865186387-0.736727316364109-0.3668456392065411.017614467832620.8363895703070291.00684351373408-0.4435228168761420.1502191014226350.739452777052119-0.5409799219430590.476677260042820.4517729643941250.203711454727929-0.246913936910008-0.633752642406113-0.12079408408185-0.385049925313426-0.06973304604169230.09419883395149610.2462193046199260.08307564934733263.680
112013-09-01 00:00:100.384978215180950.616109459176472-0.874299702595052-0.09401862596791152.924584378388173.317027168261560.4704546718058790.53824722837695-0.5588946124284410.30975539423728-0.259115563735702-0.326143233995877-0.09004672270206480.3628323685697930.928903660629178-0.129486811402759-0.8099789259635890.3599853902199810.707663826446480.125991575615420.0499236858889710.2384215122251030.009129868612628660.996710209581086-0.767314827174801-0.4922082953400170.042472441919027-0.05433738837321229.990
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722013-09-01 00:00:461.00658858258061-0.07110535735928640.3476137101292681.32968404626518-0.1932395405580010.1554182209515820.008573550045375380.1465377011585320.1038443034999970.03183002484319951.070980866594950.940664826248853-0.7294737772203350.380114784646787-0.729126304640312-0.4934024646755410.0435558761530204-0.405289649578765-0.092584543842081-0.091366856699256-0.0202386866152166-0.0188806243664369-0.1209661872342670.02738178851882540.59386362410547-0.3346879219757770.02136801040040560.015080401274455167.970
732013-09-01 00:00:471.197838599049520.2368276177020660.5096050016335640.657658659875326-0.365487846531556-0.7451010672193340.079497447992953-0.130535519206068-0.0522631188334045-0.1100578976672510.3071314747412180.6706644292320840.4379736094178590.2690262352431891.12741944172679-0.1969225708856770.00770367393603528-1.12264047790795-0.590917690926777-0.120981428275126-0.149875596688501-0.3742106675970010.1455159858079020.4149839213149970.2121560106649030.181724249919295-0.01640213406122880.01599420898811693.630
742013-09-01 00:00:48-1.793406244227861.854603990828380.9795139766444811.11226152645262-0.206402962131258-0.1995456680924450.61664240423530.06418035317757050.6902715323418371.55172381714636-0.161964841677680.4242130609822460.0159444010110314-0.4058328183146970.271930432913219-1.423020648645360.676324382969801-0.9110483000367040.4618454981126060.667846871696291-0.1807225256916810.235138169654476-0.09144157132609250.4176544738315250.122733846237321-0.2329850411907460.8118798414783010.61856831193962226.720
752013-09-01 00:00:48-0.5806289650162570.4826839330971821.33312308028373-0.253080022676203-0.0284689398233383-0.5191657003195270.5032494608097050.1177734828960210.117112238017822-0.4204875387932110.449718913713424-0.0178648303429265-1.983823179410230.321663489232864-1.425301879591290.125194163398465-0.4044094516188860.0977768572186709-0.0205312679140408-0.298750730213523-0.0421423262477711-0.1487072755659710.001451164977144520.302764487325416-0.680714199200363-0.0155539239808445-0.006307004342134830.16422220534353221.660
762013-09-01 00:00:49-0.5496261447980350.4189491535255971.729833252355970.203065373845713-0.1870123876104910.2538775518852130.5008937777715980.251255794962937-0.227984854678695-0.576169419891261.102031894004260.823707807488722-0.5695098835710020.00871007349263582-1.04141380966471-0.6034030995567280.225483728892329-0.3521325999227450.1949463808554420.01697037066626380.1150624655482370.418528728119492-0.06513278824540820.2649807850820180.003958220341818250.3959688889892730.0271821022392780.043505755709894859.990
772013-09-01 00:00:490.921543679723553-0.06708375422575630.07746102757870930.9536382170223130.06741246291082270.01615246495475120.320451556953410.0385340276125158-0.3915126650811470.03156024523976771.391691180106711.079363219968690.1062677116839970.6659852513348080.442253557748870.122646354959781-0.492391586114359-0.535140313996294-0.07808183411136340.120050785637899-0.333929581340575-1.299919566743420.0843109903360168-0.3703978711988170.155101565371628-0.8344903650331980.0009090651979645090.035546875724878135.510
782013-09-01 00:00:491.098608346146420.2024235638291010.5254559719457531.32343627201394-0.1304864212044760.03992430707661490.02837941590282380.0728410708847139-0.09786935198068610.01951299516864231.474413320900631.689674217584350.5067805232645670.125136664522659-0.89270971177356-0.6216791333177810.0443402665913568-0.642093954200622-0.161986891000608-0.128040892456864-0.02497167844621070.154264260038072-0.06314674325475980.2532053071387930.629405434975953-0.3453446553872180.04046933787118260.01026375002675713.180
792013-09-01 00:00:50-0.6717085477410520.594502594388030.216415943954576-0.8673106388542762.966908301100923.632494873738090.5632950747404770.673025596986071-0.188766143762422-0.404378291830518-0.699710626192874-0.184142608712838-0.426813033653942-0.183001108223398-0.747731683219242-0.0377075788937061-0.866459638474451-0.00725732026000804-0.160432044223361-0.00278433437563492-0.136440966831564-0.300362025601945-0.3316916234166020.9963824708686040.502469492348796-0.51804304841771-0.208275755084745-0.11604840639451614.80
802013-09-01 00:00:50-0.5715207499617471.071600449398151.280110249611420.5427800030524580.574438986516567-0.2593592658304571.0611484151742-0.410971967925814-0.179130181138251.003500657648871.062382268494360.159422388058099-0.28986031374680.005804746354828560.46044095320685-0.22103526461389-0.7758524545457760.6570233150082060.807582918688910.3547306347658550.003558520080444980.561240486431022-0.1992867196920430.00138738938225278-0.179529951929609-0.3741157257533050.0716414539902948-0.1755104686980039.790
812013-09-01 00:00:511.259873135650040.254239576458420.514788628251950.620924297433486-0.475930098771269-0.9922858392020210.0664165097996613-0.2092750580746550.0355715653783499-0.0676158213568395-0.2041072636871510.4025966906978740.3766476943514490.2271350132947151.024996121322910.29953171476471-0.426046050892739-0.550315065603572-0.119898968647883-0.0889700937046651-0.256530535925767-0.7392116924878210.1357323808721380.381989866208370.2193018917501540.0942906925877441-0.02868666772080690.0191975910878781.980
822013-09-01 00:00:52-3.005236722414592.600138202194611.48369073726212-2.418472955136820.306326406574465-0.8245745319394182.0654256392882-1.829346589380924.009258516657256.051521350772732.572500181942680.0668507400137308-0.353574309497439-2.837135998308940.292226879668893-0.303773839706442-1.94230314485255-0.435449716450276-0.9340161151891542.45672404561526-0.852308858371298-0.181268483843722-0.1637465040792370.5158205258001350.136318431995170.460053967482399-0.251258637837596-1.105751157085521.460
832013-09-01 00:00:521.147368927029220.05903464455358560.2636323414017741.21102345823936-0.04409557882633870.30106650133832-0.1329598556873630.2278851362514610.2521912372268310.0839039381173390.6450464509092540.413361748049543-1.468036029302190.502861187887764-0.626936022547138-0.369716051829749-0.0317992395701179-0.2153421738034870.0550196503583034-0.255923874900886-0.0878134178536766-0.110756406773342-0.0977707247600232-0.3233741782374580.633278881348768-0.3053278191069350.0273941237350875-0.0005804646888181916.670
842013-09-01 00:00:53-1.19896767411718-1.474100470942111.8403259873066-4.515824354881050.327567428246331-0.1744692828348480.959725705478786-1.02645622795451.70043458447966-0.07894176120449581.662667144935980.485619299748722-0.93302495795613-1.118786564879320.14125304079379-2.81188754821512-0.5047458098701210.891222663154531-1.51202243652326-0.769854286810439-0.4531694169735250.334614040441455-0.364541412466894-0.310185782073785-0.30259949355198-1.24392415371264-1.12345654520885-0.7343510858163389.170
852013-09-01 00:00:541.202398328079050.3217113866070540.2812108944880010.643688582463962-0.148668596204498-0.5897386669930220.0484125495667614-0.0933612495778056-0.042934036363588-0.3432456623178940.2351060505128590.5698819154997730.676330388590739-0.3512497460036091.295130058562630.1648597823325480.246413935319911-0.804462522225513-0.561740542791253-0.0707505670634631-0.251113124454264-0.6801551650435490.1481625265264880.04706150087370340.1570497458852380.121934641489905-0.004607898335311260.02941810909107567.530
862013-09-01 00:00:55-4.57509260816239-4.429183774748763.402585003798280.9039146799043333.00222377368078-0.491077708080676-2.705393163041140.6664513021564691.92221617202329-0.6143120273803960.3849265769875951.1944034523469-1.02071845428099-1.24682940571382-2.34867343715332-0.213437533486602-0.100221744823898-0.406073073481075-1.63757251876291-0.960962933953718-0.04736502892315170.853359934678944-0.971600429208365-0.1148616394046990.408300391838859-0.3045764658877890.547784788743973-0.456296829036198200.010
872013-09-01 00:00:55-0.7734500004581890.853112494368190.818253541761677-0.2360701612179330.803462538724049-1.438728331707190.799479364773059-0.00798899962925418-0.761089558526749-1.044464033500441.50413489421274-0.291634167856543-1.61543302342075-0.665286835592656-0.2929830458229840.8031060541875930.4621493668839270.83464109457954-0.65179683321786-0.100858489502690.0353615493510926-0.116890316122963-0.1789263467604910.400155137444786-0.02623068390643350.165155683503030.0277618003921970.1329797884966020.760
882013-09-01 00:00:56-0.8479983655984531.043459330280731.267368892188161.135529490126370.02136210259874260.3369141041328280.3984797427978490.317399165838859-0.02865794535935010.5340331924724640.811280074910828-0.0710028675857182-1.969051595412820.450006443181567-0.263173073378825-0.9683614129491940.4592537236625080.00377119214263821.000716251831990.128621717056598-0.02404610574564740.215006397493466-0.131981589595316-0.00741562681325391-0.136578135429545-0.2429607782066560.382930846823310.27641693566338420.220
892013-09-01 00:00:560.0869961905163749-0.0519887420255876-0.497882441560081-3.15190785651412.55840036235552.796670969782550.4702832707901460.2653328029436430.919513460198576-0.7355856879811520.2087249487434410.0171306492463427-0.110866963820059-0.04267686950739131.65414036352275-0.392648022607194-0.8759602173661430.1839461891870071.259380027870670.167231088284993-0.239425579903453-0.4373421437194050.01842576812320371.01303776342658-0.258926558625905-0.293189252573023-0.394955581242805-0.43599559315079210.840
902013-09-01 00:00:59-0.773292609110981-4.1460072502577-0.9320375670760450.0270936838890165-1.698307321791810.4601878052254410.737344474460422-0.314215581514513-0.842672538454470.0172757940177998-0.617560331727886-0.1975035354765671.59495759349141-0.2598787971287831.221025465605871.324639512244730.120540185550046-1.24864887121931-0.005069791085224882.442781774004850.8909777793368710.0261225750123657-1.1347693370818-0.6549582499523890.0983862618989874-0.209149914074031-0.1717091563836530.2080566411588631142.020
912013-09-01 00:00:590.921024018835922-0.16244686110781-0.09433136738690690.474083926327042-0.0214859605972665-0.3975063066852790.482642978539503-0.117495974844976-0.577836031422653-0.01860713714006671.837579183031731.450671064387870.6797439728420610.5937184499238650.249734697673045-0.0843672205235-0.25970727981991-0.894995460456715-0.01037394168546550.214510447897743-0.209381106373359-0.9301072963770230.02850991079318450.03268200910991040.1551304951094730.133250470013276-0.07353423081608520.0223491449446096149.90
922013-09-01 00:01:001.069141384895190.04378592516723040.3098672908506731.31669399295505-0.462393623949898-0.8578876042696920.207903690796087-0.1912699419893710.05639789890128890.041567455076056-0.507358124813112-0.108666220084406-0.4732573482579370.4520458899715591.005674810398810.185441397662765-0.439975752389420.0125391476665563-0.498587992492488-0.001998251424376050.1157754499158340.164781092368047-0.1775640545301980.3918905697482690.624681738099145-0.288376427654957-0.001311833579605220.035811519293162489.40
932013-09-01 00:01:001.107029376948430.2164410003713510.5383781497082331.47639799266774-0.251941920499494-0.3406797069124960.154091744631261-0.08650254563322860.144420201120718-0.157374627687008-0.1075602976940881.06632565737920.620788366839222-0.0708893376688794-0.203857982828647-0.8534794193307680.336478013774869-1.17953172110404-0.501729107425755-0.111852535538935-0.06003745010764930.0598841227860989-0.04752636647783270.4439924186361190.640295758747984-0.3376571306685210.04210848389191540.02426471000685826.720
942013-09-01 00:01:02-1.035105817766890.9960131278175142.19247013559677-0.170445302779918-0.302319738525738-0.1422557677002870.2234317744485960.2890434101184210.0941408906153459-0.157858732844487-0.386373549409945-0.628633662180404-1.023958211220710.09843387469763141.562288761964390.168577701728536-0.148826411284152-0.285927210472601-0.4833638941512240.180287626805096-0.098000008392506-0.17024584412346-0.137227527043150.05522827893583530.07934755420630780.3020326021134110.3913773499747970.1965998806652895.990
952013-09-01 00:01:04-0.6583049340956840.406790567371532.03746063876455-0.2912979744171950.147909808593845-0.3508572919580210.945373213135361-0.1725600167339780.0251333984849018-0.778134723733662-0.1962898019372620.6329552618263730.374025171567011-0.531597207426503-0.615062565100624-0.5180784591851660.00388089531948063-1.2889540744158-0.7978044852172220.0641328738661188-0.156095760618683-0.2388049648914450.08987717739851130.421195367129561-0.3524871342279070.0747827424634443-0.0941921697507859-0.092493130400881354.990
962013-09-01 00:01:040.959601658512230.3707113046139330.8886133700455652.343244103022470.3524908410847551.36551460619135-0.2777707304627410.516053179747465-0.7009290450550260.4682162393672580.7456115099471320.373531002993358-0.2239182858666670.4174381420698961.67840014345469-0.5157016002371870.662478668271888-2.5142351135941-2.5896875748614-0.298404520795831-0.155547160729115-0.4032393156847710.356504034074842-0.696881458915448-0.198717970162506-0.2202679155151420.06854619613585830.02079731541614097.550
972013-09-01 00:01:041.21251089095254-0.0990542956039435-1.192094094634260.2863235615097552.160516251832093.61631350966622-0.404206898066650.8423309516479930.169360420742526-0.0305221765721243-0.5419572580231060.237212014866616-0.2181296487032740.197436520971338-0.147850245921019-0.0978301417256899-0.51005250120389-0.07093928064214850.3551705836531590.0147774396345371-0.167496336516951-0.494694569848075-0.1497854509684641.011226554671010.883547704730387-0.3294338105920750.0203701456794310.017037086350501234.70
982013-09-01 00:01:07-1.494667840742710.8372413999636292.628210617906073.14541437889465-0.6090983888544240.258495000688512-0.01218861335878050.102136035246365-0.2861635968242871.19855632464938-0.550295668711412-0.1068459885207450.208014288229433-0.6805104027696350.507763583158711-0.2602640225587780.2466313239022870.008855504384242280.899415801359582-0.0283519350532205-0.1400473580571390.3550441838116020.3327199884352280.718192517148152-0.2193660461143240.118926551385282-0.317485702168288-0.34078339765064328.280
992013-09-01 00:01:07-0.6534446272949950.1602250768520381.592255555240821.296832283575650.997174923623236-0.3430003024091340.469936930779834-0.132470081994361-0.197794077439788-0.105005538081425-0.5436622109269710.3022330226359640.141211078726449-0.2078804435531010.0241083998795536-1.206876591915640.39483638189259-0.7509556302064260.4405584811704080.2259203469185410.03836296797903680.336449012374641-0.01488283283567180.102959010243-0.265322060067868-0.348636686626220.0112384491290326-0.049478339972149219.850
1002013-09-01 00:01:08-0.7701963826479880.4835724164120241.90107177893088-0.001876250116188520.0242447851356973-1.171903181582750.666483360897814-0.0946029012075535-0.136665621886762-0.842507532652561-0.4082350970881010.503046644959921-0.010588597193309-0.200012764882671-0.908689458907517-0.323594882408827-0.0221036727295719-0.796683932841244-0.479505428522999-0.0338308901120332-0.0573359108181297-0.1558012807637610.01810780200743670.941555368544963-0.1685818411260970.05617099692751760.05897936129031080.13418792127799622.360
Rows: 1-100 | Columns: 31

Let's take the data over two days and split them into a training set (first day) and test set (second day).

In [6]:
creditcard["Time"].describe()
Out[6]:
value
name"Time"
dtypedatetime
count284806
min2013-09-01 00:00:00
max2013-09-02 23:59:52
Rows: 1-5 | Columns: 2

Fraudulent activity probably isn't uniform across all hours of the day, so we'll extract the hour from the time and see how that influences the prediction.

In [7]:
import verticapy.stats as st
creditcard["hour"] = st.hour(creditcard["Time"])
creditcard[["Time", "hour"]]
Out[7]:
📅
Time
Datetime
123
hour
Integer
12013-09-01 00:00:000
22013-09-01 00:00:000
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82013-09-01 00:00:070
92013-09-01 00:00:070
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1002013-09-01 00:01:080
Rows: 1-100 | Columns: 2

We can visualize the frequency of fraudulent transactions throughout the day with a histogram.

In [8]:
creditcard["hour"].hist(method="avg", of="Class")
Out[8]:
<AxesSubplot:xlabel='"hour"', ylabel='avg'>

It seems like most fraudulent activity happens at night.

The transaction amount also likely differs between fraudulent and genuine transactions, so we'll look at that relationship with a bar chart. Notice that fraudulent transactions tend to be larger purchases.

In [9]:
creditcard["Class"].bar(method = "avg", 
                        of = "Amount")
Out[9]:
<AxesSubplot:xlabel='AVG("Amount")', ylabel='"Class"'>

Let's create some new features and move forward from there.

Features Engineering

Since all data (besides Time and Amount) are encoded, we're somewhat limited in creating features.

One way to work with this limitation for time series is with moving windows.

In lieu of customer IDs, we'll aggregate on the transaction amount over some partitions. Let's compute some features to analyze the transaction amount and frequencies across different windows: 5 hours preceding, 5 minutes preceding, and 5 seconds preceding. Choosing these windows is pretty subjective, but we can close in on the most relevant windows after some more extensive testing.

In [10]:
creditcard.rolling(name="nb_same_transactions_mn_5h", 
                   func="COUNT", 
                   columns="Amount",
                   window=("- 5 hours", "0 hour"),
                   by=["Amount"],
                   order_by=["Time"],)
creditcard.rolling(name="nb_same_transactions_mn_5m", 
                   func="COUNT", 
                   columns="Amount",
                   window=("- 5 minutes", "0 minute"),
                   by=["Amount"],
                   order_by=["Time"],)
creditcard.rolling(name="nb_same_transactions_mn_5s", 
                   func="COUNT", 
                   columns="Amount",
                   window=("- 5 seconds", "0 second"),
                   by = ["Amount"],
                   order_by = ["Time"],)
Out[10]:
📅
Time
Datetime
123
V1
Float
123
V2
Float
123
V3
Float
123
V4
Float
123
V5
Float
123
V6
Float
123
V7
Float
123
V8
Float
123
V9
Float
123
V10
Float
123
V11
Float
123
V12
Float
123
V13
Float
123
V14
Float
123
V15
Float
123
V16
Float
123
V17
Float
123
V18
Float
123
V19
Float
123
V20
Float
123
V21
Float
123
V22
Float
123
V23
Float
123
V24
Float
123
V25
Float
123
V26
Float
123
V27
Float
123
V28
Float
123
Amount
Numeric(9,3)
123
Class
Int
123
hour
Integer
123
nb_same_transactions_mn_5h
Integer
123
nb_same_transactions_mn_5m
Integer
123
nb_same_transactions_mn_5s
Integer
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832013-09-01 03:01:501.084898592560530.1993585351282061.60691623672192.88089313423186-0.6881786674042670.62788617069338-0.8444090535786990.3203991538232631.650858764486180.129207331514003-0.077701598220752-3.16564615837033-0.05237857952891341.38892202206499-0.6008458668699310.3794011495388190.693252240036643-0.166050337345302-1.39210231102881-0.3485210093211-0.229154915480322-0.3063685800729190.107861357632864-0.03227130537023670.144010584102172-0.04677164286390490.02150458994974450.02223739869747940.0038321
842013-09-01 03:05:53-0.4018961438583850.9020529356378062.960560448366482.28779528789042-0.03167994528660780.2838433799603760.140211215067913-0.04702708065331820.958767135487564-0.104688163781482-0.0862278584893869-2.749378238711071.567424553519990.714822484596932-1.220440221197790.4012229657775870.2354647638898320.222484477836387-0.87484711726326-0.053805327024949-0.201845703016314-0.073923672972158-0.1417686916988290.302592917373657-0.218362791487778-0.151553777978881-0.0975212981619207-0.1512158235376640.0038421
852013-09-01 03:07:05-0.3194729632733131.143915235628431.926443320186032.9075219042780.6689145232730650.2414438286405520.1262593739320350.0544757077217116-0.4953705188887140.5130029018671281.99799602476017-1.773975124473462.755055752884031.69963823594122-0.2657589445707860.3025569132903890.2410670818822750.659074291209211.052333430231980.216685670549315-0.245719132186787-0.5564076963779630.142773382615279-0.0712179899492115-0.908682165768198-0.2293803968753910.1591038942071860.1768018850308840.0038521
862013-09-01 03:08:44-0.7719222060966421.037221938215352.457278148291221.257142142323680.7401267829159111.563389534538090.02725948246826990.4623027410627380.646801259938004-0.477165499498217-0.157360996360568-2.825640783987741.24898409909691.06548431389713-2.142528420218361.46306681923631-0.7469548357293171.28538048636127-0.594104292936294-0.163635776775283-0.254585698027431-0.487168227191215-0.496858142511257-1.494759277321620.462470509657279-0.07517392941457280.02434926622626470.04192425777054090.0038631
872013-09-01 03:08:46-0.5744116342294211.077250703023892.946749147648482.5969459941663-0.07203266738567220.900387032215987-0.134659083864950.3033390764452360.617273503268949-0.2457346558375860.135332783259484-2.557476404494061.772674392125870.975639760543272-0.6253926311188-0.08778824568928660.869049675147082-0.129551087520276-0.546276532344251-0.0562631465706766-0.1194335076459140.0722151018660031-0.1258452645788880.0247878874825628-0.2707475107554970.02560158111671350.1312895396491720.1163216838948330.0038742
882013-09-01 03:11:34-1.169743852965590.4628775162014371.58757912327917-1.25255989437011.01281739344023-0.9184125358364650.817632446548305-0.5228039864503761.38824716825758-0.0224494240832962.19601645201901-1.824537958376912.018640970366141.0829956899864-1.051438788650830.454417380292377-0.468231576313130.146580100118293-0.342892608298760.280455162260437-0.418851207093186-0.546607316105327-0.0421438220210644-0.0212689058377677-0.2839791600542030.556660650458781-0.191722193195158-0.07177272321696640.0038841
892013-09-01 03:21:33-4.696795224445042.69386747884008-4.475132712591535.4676845487781-1.55675807549758-1.54942028904253-4.104214872785260.553934075416293-1.49846813107494-4.594951762850095.27550585077254-11.34902855009150.374549235103921-8.138694884347730.548570894168134-6.65359434741365-10.2467554066001-4.191066266554910.991486122257293-0.1589705486606110.573898081112651-0.08016277539815710.318407817148194-0.2458622026508530.3382384315641410.0322706213908033-1.508457933632190.6080746825901010.0138911
902013-09-01 03:23:02-0.1874679925625760.8930387137058012.443297365491831.870029557985490.1843941137291950.08401505146742560.315892236394514-0.1570571547702611.08080097798804-0.17555624005224-0.0763064321758883-2.062806355009512.61388298710460.48815556657775-1.96879178507850.621044993024558-0.1875312716389170.018082857093576-1.71585640806577-0.15043558423607-0.08352178367088740.3460320925484780.09678719876714320.34143898772198-1.2165402123676-0.4718771056476780.07470448211334550.0253527972386090.0039021
912013-09-01 03:25:261.167826095510070.327340080469650.9344057634259162.10306374298121-0.1913342878754910.213219903664585-0.274590398524983-0.02141108141677131.1154524964629-0.03878156841716430.365188990863-1.903221977050512.208821283509451.07865659544523-1.37963587788655-0.2032574669923480.938990791734884-1.000001760121-0.885902614570564-0.168706873840079-0.234445121569277-0.16720758960890.0007158563061090160.1097796895982910.35243669060770.998417430329332-0.0674632077242019-0.003192987950745230.0039131
922013-09-01 03:28:42-3.58219216453489-3.15718651858782.215613415089911.557263531070944.71917979125558-1.93246959696005-1.870640667438810.4388624965927580.500591634965006-0.02806412480769331.98378299478933-2.446828512549680.02958003281051691.89357249137872-1.70843800295856-0.1153945278198960.63377795236539-0.610103496848815-1.746130058511780.7755323249625420.174725659996541-0.3133227279385420.402521780868763-0.3384399847465580.4654250468451070.876260033706203-0.394009526047803-0.1325707354108210.0039221
932013-09-01 03:29:341.062376435180550.2751023157522151.765981724094662.95076888412909-0.7699326980252460.455029934516271-0.7737630166643510.2452633340949831.488990794872910.1017683037755220.372195389601147-2.566314538724560.8127196680486051.22516523328833-0.7267962763716830.2403253329210060.759747995471775-0.386521218914549-1.52169060494071-0.300559170184297-0.19695713623966-0.1695761225327050.1365070405782740.3063981464961560.131279935739828-0.06948884466750260.0280572718368770.02740154314070590.0039331
942013-09-01 03:30:00-2.13033560918075-0.3085636416796471.960456176473792.566007903128661.285829527419671.04568850724476-0.188935400215488-0.1963085288704871.147373588400880.9673926162023190.731859401321798-2.072321184107922.715533762906810.432466615321326-1.400609606095430.775076794291224-0.4357160879128471.042252301023050.78126789642629-1.11631108135107-0.515056332076440.2564052464685690.753569645112509-0.972319323739425-0.272540837936764-0.0280610497381203-0.112772821611776-0.3486861065904170.0039441
952013-09-01 03:33:56-1.294414562858070.3533414232463692.414413426574362.890917302140221.082939916810640.460519344528452-1.08077142912233-0.6134945538618660.7483114405987450.130782584917957-0.630935797206847-2.181359029375143.075933436660080.748101550939601-0.7477862073646140.3084781582543370.3847685187372620.4818603687021490.423383431758413-0.240704256501250.539478790445257-0.325389981612828-0.244364270887563-0.466850390993672-0.3240405407280260.06701720173773110.3464273657014850.09697478985461510.0039531
962013-09-01 03:36:131.042686968610570.2240558156067551.651553807685032.75648799605323-0.5414251187569030.970706300592251-0.8758587362051640.4068134847569731.234201628099140.2676910278250131.7968829398642-1.924194115297820.9019340265195451.37889324417228-1.415995971502990.5270937431393770.3829246475488190.201760495743565-1.10913960121824-0.271378280740515-0.165517974449411-0.10807747331470.082058705826471-0.07271614909285720.148948094483859-0.06696866185505410.02456914608271420.01414220491233630.0039621
972013-09-01 03:45:05-0.564637608480581.150080103470412.896179303501782.35620502615992-0.4598435855266090.127907163891802-0.004725114075254260.1166456133156290.874582407896479-0.212263481004740.0971716308530224-2.653016263306831.35647684770850.939497353890981-1.252530206066480.3846841280186340.4615252708744860.153842930387312-1.00123449295571-0.180206501641516-0.117954732325565-0.0493405134705883-0.07111910900357330.628489935968084-0.258518585101223-0.156375629523735-0.07045255763295890.07156421153248530.0039711
982013-09-01 03:49:061.109824130873560.3313515984261631.560525944511992.71955568163731-0.4835546529869580.712092997049856-0.7416793598647150.2362676205112931.119022360423820.2848338335050831.43917894704333-1.621292919123441.914700793470731.1446326523948-1.746316554977150.872179780583861-0.06915702617760280.643919457760809-0.632373121321768-0.16899370200811-0.20414687956603-0.2068282392227370.00041614775001936-0.06735036040111810.297569426041841-0.07928170510945170.0137645432748470.01620622669519730.0039821
992013-09-01 03:49:491.176946472838670.4558491450450860.6672766932656141.662556207685390.1679019560205720.360022975413173-0.2198105583532560.04370194041518620.3634726135988920.2907398693271262.25113579453457-1.527960631855672.449104408521241.67410612977367-0.6668422935954930.6949049004707640.0792745081734653-0.173522594769222-0.863169574665242-0.11412664437267-0.180051362194958-0.2673336952537720.0370602379879596-0.3066857594700780.1784907714058120.868661752476268-0.0869047147275453-0.01216474151809240.0039931
1002013-09-01 03:55:23-1.81207017758376-2.323481732882422.05550308781535-1.650283845341141.41764679398422-1.07164730318686-2.022478427897760.5312974920275521.00666402407914-0.3677218409437491.3681186713173-3.000820390610270.4472000178366971.0717156533887-1.955263682018631.707652620362420.376583549484098-0.411846189637525-1.290016517151920.2602494536284940.5088212515427251.043305215992270.249979936329487-0.384754342792913-0.540387320781441-0.4894931569766540.08849547578370720.1983652621189440.00310011
Rows: 1-100 of 284806 | Columns: 35

As an aside, we could also create some features that represent different parts of the day, but won't be useful for our use case since we're only working with data for two days' worth of data.

Let's look at the correlation matrix and see which features influence our prediction.

In [11]:
creditcard.corr(focus="Class")
creditcard.corr()
Out[11]:
"V1"
"V2"
"V3"
"V4"
"V5"
"V6"
"V7"
"V8"
"V9"
"V10"
"V11"
"V12"
"V13"
"V14"
"V15"
"V16"
"V17"
"V18"
"V19"
"V20"
"V21"
"V22"
"V23"
"V24"
"V25"
"V26"
"V27"
"V28"
"Amount"
"Class"
"hour"
"nb_same_transactions_mn_5h"
"nb_same_transactions_mn_5m"
"nb_same_transactions_mn_5s"
"V1"1.0-2.48444192942183e-064.24296182351879e-066.87825715222241e-079.19843170418736e-079.61315517136252e-07-3.56070922100461e-061.60806790647091e-066.89929948071414e-06-2.69731578057294e-069.73515347230113e-07-4.99395188999346e-065.86795091619122e-071.38765327307279e-06-8.91777137708676e-066.29106337671093e-081.54570204970557e-063.39353663199689e-062.48188310839069e-076.84677317443555e-077.48200768593993e-072.63837829506253e-061.13730764875215e-063.07115436982447e-06-3.59144819139119e-061.33711295484153e-068.88004657509551e-071.74547568068598e-06-0.227709261538788-0.101347495968755-0.005219022427602890.06119268623726990.04269588651424180.0472934003641123
"V2"-2.48444192942183e-061.05.80474202796654e-069.4100559922698e-071.2584257256026e-061.31516351413525e-06-4.87136093092507e-062.19997722070319e-069.43884373879601e-06-3.69016336244496e-061.33185394616816e-06-6.83216196984572e-068.0278689047611e-071.89843076675341e-06-1.22002894290408e-058.60672381199213e-082.11465528455406e-064.64265424121466e-063.39543264938587e-079.36698315984261e-071.02360394086788e-063.60953173896088e-061.55593610730875e-064.20160717435644e-06-4.9134145240299e-061.82928720208352e-061.21486786077321e-062.38796304744298e-06-0.5314104015281140.09128866205634580.007795721975568310.09762832119088610.02741797183626020.0116527988935146
"V3"4.24296182351879e-065.80474202796654e-061.0-1.60706144246859e-06-2.14915560995973e-06-2.24605313146269e-068.31937273539253e-06-3.75714934136276e-06-1.61197785144215e-056.30210836429911e-06-2.2745572677627e-061.16680539227091e-05-1.37100975707797e-06-3.24216443529464e-062.08358109147335e-05-1.46986732639043e-07-3.61143544403125e-06-7.92878451464591e-06-5.79876349617743e-07-1.59970540755538e-06-1.74812395184857e-06-6.16440464307054e-06-2.65724766328053e-06-7.17555867258572e-068.39119240319819e-06-3.12408016770587e-06-2.07476692871922e-06-4.07819394535443e-06-0.210880613110927-0.192961538675933-0.0215578163868944-0.05122652130632610.02060111397909860.0280807335045743
"V4"6.87825715222241e-079.4100559922698e-07-1.60706144246859e-061.0-3.48399198240531e-07-3.64107236075953e-071.34865189263834e-06-6.09070746814796e-07-2.61317415560212e-061.02163355921981e-06-3.68728035907606e-071.89150594780525e-06-2.2225412453863e-07-5.25586644471265e-073.37768924751585e-06-2.38279903444195e-08-5.85449097298247e-07-1.2853337128394e-06-9.40036423971279e-08-2.59327931459649e-07-2.83388033212681e-07-9.99310435273731e-07-4.30765900645478e-07-1.16322841773707e-061.36029456604378e-06-5.06444027731259e-07-3.36340063558392e-07-6.61115225736419e-070.09873183191040250.133447543813193-0.0350613652813372-0.0168576354481181-0.0482568977107855-0.0352615068084596
"V5"9.19843170418736e-071.2584257256026e-06-2.14915560995973e-06-3.48399198240531e-071.0-4.86927933030668e-071.80357932022656e-06-8.14522568089834e-07-3.49465038269906e-061.36625111884572e-06-4.93107421498449e-072.52954896873744e-06-2.97224913805939e-07-7.02877597991695e-074.51705180325678e-06-3.18656501239528e-08-7.82932858351176e-07-1.71890263847597e-06-1.25712962585169e-07-3.46804461867274e-07-3.78980519644249e-07-1.33639795564565e-06-5.760719066627e-07-1.55560877338775e-061.81914929702961e-06-6.77277789021642e-07-4.49794332770325e-07-8.84122696293118e-07-0.386356163868081-0.0949742681987903-0.03513223080116230.0725254335233830.000262219813011165-0.0152492611048474
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"V28"1.74547568068598e-062.38796304744298e-06-4.07819394535443e-06-6.61115225736419e-07-8.84122696293118e-07-9.23984537623645e-073.42243540924017e-06-1.54562144926085e-06-6.63137745231968e-062.59257031943305e-06-9.35710609676386e-074.80002064876936e-06-5.64007946371038e-07-1.33376622291671e-068.57146558075383e-06-6.04676113366978e-08-1.48567745918545e-06-3.26175466955293e-06-2.38550360363385e-07-6.58089089948252e-07-7.19145721814866e-07-2.53592156557841e-06-1.09314232666191e-06-2.95189155107061e-063.4519806873781e-06-1.2851885510994e-06-8.53520573849219e-071.00.01025860191462110.00953614990797394-0.007487599415303860.003753285123679050.00235777535622701-0.00825995143308286
"Amount"-0.227709261538788-0.531410401528114-0.2108806131109270.0987318319104025-0.3863561638680810.2159814519491970.397311912920897-0.103078826095225-0.044244693622819-0.1015029309739730.000104187309905036-0.009542946654258530.00529353649050950.0337514907872742-0.00298783965945414-0.003909513296176790.007309381030182280.0356511881923284-0.05615073695880620.3394036106026890.105999110058921-0.0648002034857503-0.1126323528831430.00514689431072122-0.0478378107566908-0.003207750080822820.02882566269191380.01025860191462111.00.00563173057564682-0.00666770577076545-0.133209630870605-0.0682229029844123-0.0513831957789587
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"nb_same_transactions_mn_5m"0.04269588651424180.02741797183626020.0206011139790986-0.04825689771078550.000262219813011165-0.0333694451054732-0.0327632826626872-0.0002208951340574930.130424793202479-0.0749124826643940.0360411048508409-0.00538838573719724-0.02744330146971860.02759307489902710.0655088772715180.00410209093172362-0.009334709781995440.03364449336030440.0280139940598116-0.0199728645287429-0.005497979153359420.0350686846958245-0.009717426728393120.01446863862253880.054852258717222-0.08700352693267420.02260396480615360.00235777535622701-0.0682229029844123-0.0008348463328019670.01977336249908160.5586536421700671.00.627143968944717
"nb_same_transactions_mn_5s"0.04729340036411230.01165279889351460.0280807335045743-0.0352615068084596-0.0152492611048474-0.0232324241825098-0.0322799326799646-0.004296943115789780.138588518083758-0.04798324800031010.0480448881618955-0.08428957764967870.01849266242270080.07410987187260490.03727574731984890.0108371484016456-0.002897008962909030.01513352371985640.0349589290972023-0.01522923759632830.001526854522142880.0424155561878907-0.009441633471479940.008434634738117230.0422053100859362-0.08156278351912380.00711198299460737-0.00825995143308286-0.0513831957789587-0.00129388713798246-0.05421481167603840.3338091910766470.6271439689447171.0
Rows: 1-34 | Columns: 35

Our new features aren't linearly correlated with our response, but some of the components seem to have a large influence on our prediction. We'll use these when we create our model.

To simplify things, let's save the dataset into a new table.

In [12]:
vp.drop("creditcard_clean", relation_type="table")
creditcard.to_db("creditcard_clean", 
                 relation_type="table",
                 inplace=True,)
Out[12]:
📅
Time
Timestamp
123
V1
Float
123
V2
Float
123
V3
Float
123
V4
Float
123
V5
Float
123
V6
Float
123
V7
Float
123
V8
Float
123
V9
Float
123
V10
Float
123
V11
Float
123
V12
Float
123
V13
Float
123
V14
Float
123
V15
Float
123
V16
Float
123
V17
Float
123
V18
Float
123
V19
Float
123
V20
Float
123
V21
Float
123
V22
Float
123
V23
Float
123
V24
Float
123
V25
Float
123
V26
Float
123
V27
Float
123
V28
Float
123
Amount
Numeric(9,3)
123
Class
Int
123
hour
Int
123
nb_same_transactions_mn_5h
Int
123
nb_same_transactions_mn_5m
Int
123
nb_same_transactions_mn_5s
Int
12013-09-01 00:04:42-0.3564661898956330.7254175152223391.971748888806990.8313427151031230.369681434554579-0.1077762626372380.75160990401556-0.120166260063708-0.420674967946903-0.0599432188183031-0.5082702317900230.4255060430411550.414309244458954-0.698375266726369-1.46534865127239-0.119008625259757-0.144735012716226-1.33222124868776-1.54744049309526-0.1336021203359570.02080378969470350.424311754701893-0.0159891286058440.466754445207633-0.8099620071976320.657334415234234-0.0431501856619478-0.04640139514513720.000111
22013-09-01 00:06:20-1.299836790376260.88181746380941.4528418792573-1.29369833187415-0.025104981110272-1.1701026264140.861610195375755-0.1939335163870030.5920009465645650.2419788579342860.144973301434815-0.58389128427118-1.595345314905490.03261288574827410.752833857365528-0.0942863738983986-0.16342701943749-1.11117601351647-1.12402458988570.0659790095339547-0.272562732384431-0.3608530384852730.2239112148329930.598929622195593-0.3977046379465070.6371407810647690.2348722844668630.02137879304088030.000221
32013-09-01 00:06:431.237412804002930.5123648299198110.6877455596274261.69387239409344-0.236322621630244-0.6502317397828020.118066209111006-0.230545315655817-0.808522532194650.511283784239812-0.1781588483970170.7629090909472041.70092326051437-0.1338606244759920.4024177533670220.684668257160155-0.609395281881646-0.704276523095046-0.720725513423142-0.00671619887222853-0.0775430475419849-0.1782196581737060.03872219018551880.4712181499147270.2892486881105150.871803080279644-0.06688386496018370.01298637930946790.000331
42013-09-01 00:06:46-2.31222654232631.95199201064158-1.609850732297693.9979055875468-0.522187864667764-1.42654531920595-2.537387306245791.39165724829804-2.77008927719433-2.772272144659153.20203320709635-2.89990738849473-0.595221881324605-4.289253782442170.389724120274487-1.14074717980657-2.83005567450437-0.01682246818082570.4169557050379070.1269105590614740.517232370861764-0.0350493686052974-0.4652110761823880.3201981985145260.04451916747317240.1778397982844010.261145002567677-0.1432758746989190.010442
52013-09-01 00:07:10-1.86025769215298-0.6298589200587750.966570447762290.8446320763117160.759982662401822-1.48117290348222-0.5096814522041360.540722084608081-0.733623387939623-0.3716215044664330.8597411624896790.37260884000575-1.240184765905770.998391328880186-0.34638712534557-0.3916785825390510.3482894322992790.282124765524721.165893165344640.320449625226850.2680277959085050.125515236056546-0.2250285354240170.586664442562558-0.03159808211372670.570168024306224-0.0430074855159307-0.2237394795252450.000551
62013-09-01 00:11:51-0.4313493441817421.02769436869642.670816225896532.08478703855765-0.2745673457155110.2868560360753430.1521097493054250.20087166142106-0.5965052905360880.0222241406011005-0.9936743341548620.2446814240953080.711845591884474-0.666973041865272-0.6002667161286980.480204121812359-0.438581795947928-0.119474666881166-0.6815386138625-0.05788637859790580.001241337547490510.154170368665755-0.1415325397657320.384610194681868-0.147132473946542-0.08710014287353670.1011168842673880.07794387047789340.000621
72013-09-01 00:13:241.18169674230131-0.00790838253075205-0.06684538694892991.532223018203951.728831642143264.40988461711759-1.138815799730171.1646445000658-0.02057844633212270.554215865529178-0.729227342877205-0.0106978368353561-0.0135860907766805-0.272330444031316-0.1148226745010810.947450987027758-0.9146551285051810.245244225308704-0.469550433499195-0.0403823736964867-0.139919854652528-0.3995630362332320.01020002455054450.9922354142055130.457014725945733-0.02792357113759670.04527339187559180.02886817603161460.000721
82013-09-01 00:13:40-0.9374813085137890.4016488004434621.88268869393492-0.3620009064131920.751088403396458-0.8992623384432370.880557364828084-0.18165031297733-0.211657089897852-0.666698857826818-0.343745846388087-0.429063633477079-1.325857371446350.100212925740607-0.143886427405123-0.6134344620362670.130665354538906-0.988969032794731-0.829911523115769-0.0564090721918242-0.001757499771624360.0973792151772486-0.3240503179222260.4365211019677690.5096736181332240.454116159819843-0.201804278541049-0.1754390145826130.000831
92013-09-01 00:15:121.083002822209750.2015888059422631.49766367312642.66192199724507-0.6212558068865850.618553696447846-0.6441402472330620.3109189300344390.1259640358630160.45323987238862-0.755020410799430.184040526414531-0.107568748226366-0.361091286955654-0.03724729361768610.334321189452785-0.129614597351314-0.633847755580659-1.19957779935243-0.203726141752987-0.06043324585948230.009647268476610010.07707210597322340.07214124353205640.220746648040652-0.01348302555615420.05859641498810310.03205390658501420.000941
102013-09-01 00:19:531.130645713639230.6253908086324390.8379871349605082.50654261118492-0.107115844107941-0.2455479355201340.099603142140642-0.0414565895316853-0.8673193086275920.623164773210170.1115908824110650.5031492195423290.7273294900412080.1743577723404760.6848832186259570.2934123207263-0.288419298134927-0.952502636687351-1.49158969766224-0.153059843881975-0.017153643660555-0.01431113663464210.08655948662445650.3934961233816260.332062276297816-0.0663780125223530.01385823368629350.02538193716541150.0001021
112013-09-01 00:24:031.076699649347380.1363186992239541.459567588469952.75420529991268-0.6428234624464410.681681495683721-0.643585168066860.3543086186843240.3257199723337750.406610208672651-0.9998372089900720.00102691175192051-0.770442752780127-0.354094413831894-0.5737105617411810.07897537201820860.12216634382473-0.812831361258335-0.962203729624461-0.253816150364729-0.182605449318902-0.302743288420010.1035334090692350.05474627987266080.22555209844086-0.0593106322540810.05524265278609420.02881533901867680.0001121
122013-09-01 00:24:04-0.9604027659141021.355315886403722.501171336496553.03648845550012-0.7128195023659821.05734348513293-0.5189107568280610.92723539282841-0.6566387920581690.277072240976983-1.10968171014067-0.273956037777502-0.653900910465794-0.06502001294881320.185245716464043-0.5593720190660280.954904217582213-0.4084613463540680.8555850483123630.0806193513506753-0.127067725772183-0.131586666448414-0.1142789982783560.07017065649774420.00756984274837280.2450454538698350.2618858251932410.09320259721890360.0001343
132013-09-01 00:24:041.040957731979550.216091879237361.535953390522342.53650724069426-0.4814352740413870.966521940522117-0.686046488640280.407032298300565-0.2699517736556050.5956400123767861.094723301090741.350939159482180.709278892520704-0.343987755042817-0.8363487774871690.489318051591067-0.432900196538757-0.248073106230272-0.915052368215916-0.1348232488564960.001437086589243820.195375108476390.05345809818638790.04063745983399550.221507406264301-0.033785160406710.06066462395093860.02378201711891070.0001343
142013-09-01 00:27:261.28612164488794-0.01702238466805130.184088350535741-0.258991166864363-0.391869392678392-0.689619653025552-0.100592418563675-0.04952838735685080.0520858890831794-0.01343343877453591.10674609739150.530833571392091-0.5028211757152030.556565932124940.4313268278263290.531113723544923-0.604196906446870.006973669309362440.586531632994946-0.0913212178833729-0.209443705324552-0.6568896023644060.06686512733762940.03730180362679740.1680113175976140.85211428403787-0.0946691397534299-0.01098009180639180.0001441
152013-09-01 00:30:39-3.766354956875650.001152410093159311.291388559607043.63539310654681-0.118166550944944-0.0671626510827364-2.286446504768721.75597338210586-0.3853741737990120.633255126651698-1.312410476456130.254941881079809-0.3861384558639510.490435375607150.321687233733395-0.2282327717780191.28587781553884-0.4457237765132290.842838178384914-0.307880926767925-0.253191545396841-0.413501604685424-1.085178595677960.184933907901855-0.08947934415313140.2554454530944580.790232347057114-0.6160058972511990.0001521
162013-09-01 00:30:40-4.102362680747920.8098071780874040.6671091801360473.49495603680674-1.521750875782070.58158851060692-1.498208835724292.13184694031426-0.4995530118166170.508821792328595-1.436215319027250.270510145996615-0.3162622052966950.6550792785624110.272116912466589-0.07209755473823921.38251524390765-0.3470727768056840.855960781495459-0.376651540115215-0.303160904907221-0.2017392800468290.5094065719104950.1036393339432410.3656107562704780.3050376327800920.750671416960727-0.696266658038050.0001632
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782013-09-01 02:46:59-1.053957924138361.347766614137123.401139005557463.16720189690557-0.1708052586633010.644893907135058-0.0386908650739715-1.243417879940260.8324116422098220.82778342781220.724831999283981-2.116625515658282.88832874769150.293874333991389-0.331562681102554-0.5042380691329430.8617217447724520.1192065171614380.6935540921518180.05042212453324350.554093537151372-0.122618921154248-0.09597379703617020.692757652721293-0.08353653715739040.0916596744466658-0.585233080841678-0.2978358306001620.0027831
792013-09-01 02:54:17-0.5786416202134520.894593981061162.556048508953962.14277538393592-0.07400241643326960.768205599169102-0.211932186256270.3366232523852150.776075487360116-0.0007271076438588041.14159300574627-2.410418545204380.9374964136390071.1749779644097-1.844061717804050.814997207690026-0.01060691582094640.915076635995028-0.476435058225513-0.198708938740377-0.129871175015201-0.110309170848017-0.0488906771776075-0.0834038909918407-0.163707306384934-0.126847121495154-0.09131830108825040.009036842558964520.0027911
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812013-09-01 02:56:23-1.20259751221030.6357018817233373.377879543900352.234869211454350.2376571162160020.4240866632397020.06823447817377110.03517755868700730.5221479094066640.05542165082604451.93302792632427-1.728726539515422.052140046298280.766450542154629-1.898678717527550.4827664816912710.05374856555783430.592503157051873-0.542945563871723-0.0402677061210182-0.1660824792064610.06033900604114570.06127146162961720.4714876120641840.193197314912081-0.10862787996815-0.205586330468282-0.1705427877054610.0028131
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842013-09-01 03:05:53-0.4018961438583850.9020529356378062.960560448366482.28779528789042-0.03167994528660780.2838433799603760.140211215067913-0.04702708065331820.958767135487564-0.104688163781482-0.0862278584893869-2.749378238711071.567424553519990.714822484596932-1.220440221197790.4012229657775870.2354647638898320.222484477836387-0.87484711726326-0.053805327024949-0.201845703016314-0.073923672972158-0.1417686916988290.302592917373657-0.218362791487778-0.151553777978881-0.0975212981619207-0.1512158235376640.0038421
852013-09-01 03:07:05-0.3194729632733131.143915235628431.926443320186032.9075219042780.6689145232730650.2414438286405520.1262593739320350.0544757077217116-0.4953705188887140.5130029018671281.99799602476017-1.773975124473462.755055752884031.69963823594122-0.2657589445707860.3025569132903890.2410670818822750.659074291209211.052333430231980.216685670549315-0.245719132186787-0.5564076963779630.142773382615279-0.0712179899492115-0.908682165768198-0.2293803968753910.1591038942071860.1768018850308840.0038521
862013-09-01 03:08:44-0.7719222060966421.037221938215352.457278148291221.257142142323680.7401267829159111.563389534538090.02725948246826990.4623027410627380.646801259938004-0.477165499498217-0.157360996360568-2.825640783987741.24898409909691.06548431389713-2.142528420218361.46306681923631-0.7469548357293171.28538048636127-0.594104292936294-0.163635776775283-0.254585698027431-0.487168227191215-0.496858142511257-1.494759277321620.462470509657279-0.07517392941457280.02434926622626470.04192425777054090.0038631
872013-09-01 03:08:46-0.5744116342294211.077250703023892.946749147648482.5969459941663-0.07203266738567220.900387032215987-0.134659083864950.3033390764452360.617273503268949-0.2457346558375860.135332783259484-2.557476404494061.772674392125870.975639760543272-0.6253926311188-0.08778824568928660.869049675147082-0.129551087520276-0.546276532344251-0.0562631465706766-0.1194335076459140.0722151018660031-0.1258452645788880.0247878874825628-0.2707475107554970.02560158111671350.1312895396491720.1163216838948330.0038742
882013-09-01 03:11:34-1.169743852965590.4628775162014371.58757912327917-1.25255989437011.01281739344023-0.9184125358364650.817632446548305-0.5228039864503761.38824716825758-0.0224494240832962.19601645201901-1.824537958376912.018640970366141.0829956899864-1.051438788650830.454417380292377-0.468231576313130.146580100118293-0.342892608298760.280455162260437-0.418851207093186-0.546607316105327-0.0421438220210644-0.0212689058377677-0.2839791600542030.556660650458781-0.191722193195158-0.07177272321696640.0038841
892013-09-01 03:21:33-4.696795224445042.69386747884008-4.475132712591535.4676845487781-1.55675807549758-1.54942028904253-4.104214872785260.553934075416293-1.49846813107494-4.594951762850095.27550585077254-11.34902855009150.374549235103921-8.138694884347730.548570894168134-6.65359434741365-10.2467554066001-4.191066266554910.991486122257293-0.1589705486606110.573898081112651-0.08016277539815710.318407817148194-0.2458622026508530.3382384315641410.0322706213908033-1.508457933632190.6080746825901010.0138911
902013-09-01 03:23:02-0.1874679925625760.8930387137058012.443297365491831.870029557985490.1843941137291950.08401505146742560.315892236394514-0.1570571547702611.08080097798804-0.17555624005224-0.0763064321758883-2.062806355009512.61388298710460.48815556657775-1.96879178507850.621044993024558-0.1875312716389170.018082857093576-1.71585640806577-0.15043558423607-0.08352178367088740.3460320925484780.09678719876714320.34143898772198-1.2165402123676-0.4718771056476780.07470448211334550.0253527972386090.0039021
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922013-09-01 03:28:42-3.58219216453489-3.15718651858782.215613415089911.557263531070944.71917979125558-1.93246959696005-1.870640667438810.4388624965927580.500591634965006-0.02806412480769331.98378299478933-2.446828512549680.02958003281051691.89357249137872-1.70843800295856-0.1153945278198960.63377795236539-0.610103496848815-1.746130058511780.7755323249625420.174725659996541-0.3133227279385420.402521780868763-0.3384399847465580.4654250468451070.876260033706203-0.394009526047803-0.1325707354108210.0039221
932013-09-01 03:29:341.062376435180550.2751023157522151.765981724094662.95076888412909-0.7699326980252460.455029934516271-0.7737630166643510.2452633340949831.488990794872910.1017683037755220.372195389601147-2.566314538724560.8127196680486051.22516523328833-0.7267962763716830.2403253329210060.759747995471775-0.386521218914549-1.52169060494071-0.300559170184297-0.19695713623966-0.1695761225327050.1365070405782740.3063981464961560.131279935739828-0.06948884466750260.0280572718368770.02740154314070590.0039331
942013-09-01 03:30:00-2.13033560918075-0.3085636416796471.960456176473792.566007903128661.285829527419671.04568850724476-0.188935400215488-0.1963085288704871.147373588400880.9673926162023190.731859401321798-2.072321184107922.715533762906810.432466615321326-1.400609606095430.775076794291224-0.4357160879128471.042252301023050.78126789642629-1.11631108135107-0.515056332076440.2564052464685690.753569645112509-0.972319323739425-0.272540837936764-0.0280610497381203-0.112772821611776-0.3486861065904170.0039441
952013-09-01 03:33:56-1.294414562858070.3533414232463692.414413426574362.890917302140221.082939916810640.460519344528452-1.08077142912233-0.6134945538618660.7483114405987450.130782584917957-0.630935797206847-2.181359029375143.075933436660080.748101550939601-0.7477862073646140.3084781582543370.3847685187372620.4818603687021490.423383431758413-0.240704256501250.539478790445257-0.325389981612828-0.244364270887563-0.466850390993672-0.3240405407280260.06701720173773110.3464273657014850.09697478985461510.0039531
962013-09-01 03:36:131.042686968610570.2240558156067551.651553807685032.75648799605323-0.5414251187569030.970706300592251-0.8758587362051640.4068134847569731.234201628099140.2676910278250131.7968829398642-1.924194115297820.9019340265195451.37889324417228-1.415995971502990.5270937431393770.3829246475488190.201760495743565-1.10913960121824-0.271378280740515-0.165517974449411-0.10807747331470.082058705826471-0.07271614909285720.148948094483859-0.06696866185505410.02456914608271420.01414220491233630.0039621
972013-09-01 03:45:05-0.564637608480581.150080103470412.896179303501782.35620502615992-0.4598435855266090.127907163891802-0.004725114075254260.1166456133156290.874582407896479-0.212263481004740.0971716308530224-2.653016263306831.35647684770850.939497353890981-1.252530206066480.3846841280186340.4615252708744860.153842930387312-1.00123449295571-0.180206501641516-0.117954732325565-0.0493405134705883-0.07111910900357330.628489935968084-0.258518585101223-0.156375629523735-0.07045255763295890.07156421153248530.0039711
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1002013-09-01 03:55:23-1.81207017758376-2.323481732882422.05550308781535-1.650283845341141.41764679398422-1.07164730318686-2.022478427897760.5312974920275521.00666402407914-0.3677218409437491.3681186713173-3.000820390610270.4472000178366971.0717156533887-1.955263682018631.707652620362420.376583549484098-0.411846189637525-1.290016517151920.2602494536284940.5088212515427251.043305215992270.249979936329487-0.384754342792913-0.540387320781441-0.4894931569766540.08849547578370720.1983652621189440.00310011
Rows: 1-100 | Columns: 35

Data Modeling

Train/Test sets

Since we're dealing with time series data, we have to maintain time linearity. Our goal is to use the past to predict the future, so a k-fold cross-validation, for example, wouldn't make much sense here.

We will split the dataset into a train (day 1) and a test (day 2).

In [13]:
train = creditcard.search("Time  < '2013-09-02 00:00:00'")
test  = creditcard.search("Time >= '2013-09-02 00:00:00'")

Supervision

Supervising would make this pretty easy since it would just be a binary classification problem. We can use different algorithms to optimize the prediction. Our dataset is unbalanced, so the AUC might be a good metric to evaluate the model. The PRC AUC would also be a relevant metric.

Logistic Regression

Logistic regression works well with monotonic relationships. Since we have a lot of independent features that correlate with the response, it should be a good first model to use.

In [14]:
from verticapy.learn.linear_model import LogisticRegression

predictors = creditcard.get_columns(exclude_columns=["Class", "Time"])
response = 'Class'
model = LogisticRegression("fraud_model", 
                           penalty = 'L2', 
                           tol = 1e-6, 
                           max_iter = 1000, 
                           solver = "BFGS")
model.fit(train, predictors, response, test)
model.classification_report()
Out[14]:
value
auc0.9534713388092546
prc_auc0.6414466848625406
accuracy0.9990001428367377
log_loss0.00205422248377388
precision0.7204968944099379
recall0.5497630331753555
f1_score0.6236559139784947
mcc0.6288858739383378
informedness0.5494411654844342
markedness0.7198176388740052
csi0.453125
cutoff0.5
Rows: 1-12 | Columns: 2

Based on the report, our model is very good at detecting non-fraudulent events; the AUC is high and the PRC AUC is decent. We can use this model to filter obvious events and to get some insight on the importance of each feature.

In [15]:
model.features_importance()
Out[15]:
importance
sign
nb_same_transactions_mn_5s10.35-1
v148.26-1
v277.86-1
v106.96-1
v206.44-1
nb_same_transactions_mn_5m6.13-1
v215.761
v54.66-1
amount4.261
v44.211
v94.18-1
v283.42-1
v63.38-1
v123.341
v33.271
v72.67-1
v222.561
v82.19-1
v131.92-1
v161.461
v261.071
v110.85-1
nb_same_transactions_mn_5h0.851
v230.73-1
v240.73-1
v150.661
v250.57-1
v20.491
v170.25-1
v190.241
hour0.11-1
v180.1-1
v10.061
Rows: 1-33 | Columns: 3

Some PCA components seem to be very relevant and will be essential for finding anomalies. Notice that one of our new features, nb_same_transactions_mn_5s, is the most important one. It seems that repetitive transactions of the same amount are unlikely to be fraud. Generally speaking, fraudulent events seem to be large, nonrepetitive transactions.

AutoML

AutoML is a powerful function in VerticaPy that tests many different models, compares their performance, and settles on the most well-performing model.

We can expect many collective and contextual outliers, so a tree-based models will probably work well. AutoML can help find suitable algorithms for the dataset.

In [16]:
from verticapy.learn.delphi import AutoML

model = AutoML("creditcard_autoML",
               estimator="native",
               metric="prc_auc",
               estimator_type="binary",
               preprocess_data=False,
               lmax=3,
               stepwise=False)
model.fit(creditcard, 
          X=predictors,
          y=response,)
Starting AutoML

Testing Model - LogisticRegression

Model: LogisticRegression; Parameters: {'tol': 1e-06, 'max_iter': 100, 'penalty': 'none', 'solver': 'bfgs'}; Test_score: 0.68349151048877; Train_score: 0.6714592668018413; Time: 30.67182230949402;
Model: LogisticRegression; Parameters: {'tol': 1e-06, 'max_iter': 100, 'penalty': 'l1', 'solver': 'cgd', 'C': 1.0}; Test_score: 0.500880041328; Train_score: 0.5008555851569509; Time: 1.8258856932322185;
Model: LogisticRegression; Parameters: {'tol': 1e-06, 'max_iter': 100, 'penalty': 'l2', 'solver': 'bfgs', 'C': 1.0}; Test_score: 0.6868969140778011; Train_score: 0.713449210327742; Time: 30.38058606783549;

Grid Search Selected Model
LogisticRegression; Parameters: {'solver': 'bfgs', 'penalty': 'l2', 'max_iter': 100, 'C': 1.0, 'tol': 1e-06}; Test_score: 0.6868969140778011; Train_score: 0.713449210327742; Time: 30.38058606783549;

Testing Model - NaiveBayes

Model: NaiveBayes; Parameters: {'alpha': 0.01}; Test_score: 0.4289489751555001; Train_score: 0.4292646712826215; Time: 1.051988999048869;
Model: NaiveBayes; Parameters: {'alpha': 1.0}; Test_score: 0.42869693348870896; Train_score: 0.4304368841688505; Time: 1.0004164377848308;
Model: NaiveBayes; Parameters: {'alpha': 10.0}; Test_score: 0.438844889453718; Train_score: 0.42504630650758835; Time: 1.0843093395233154;

Grid Search Selected Model
NaiveBayes; Parameters: {'alpha': 10.0, 'nbtype': 'auto'}; Test_score: 0.438844889453718; Train_score: 0.42504630650758835; Time: 1.0843093395233154;

Testing Model - LinearSVC

Model: LinearSVC; Parameters: {'tol': 1e-06, 'fit_intercept': True, 'intercept_mode': 'unregularized', 'max_iter': 100}; Test_score: 0.7380361270228938; Train_score: 0.7792798207101952; Time: 32.016225258509316;
Model: LinearSVC; Parameters: {'tol': 1e-06, 'fit_intercept': True, 'intercept_mode': 'regularized', 'max_iter': 100}; Test_score: 0.7319196076911149; Train_score: 0.7781129275480732; Time: 37.25153398513794;
Model: LinearSVC; Parameters: {'tol': 1e-06, 'C': 1.0, 'fit_intercept': True, 'intercept_mode': 'regularized', 'max_iter': 100}; Test_score: 0.7738477419894275; Train_score: 0.7586906685904172; Time: 31.643476565678913;

Grid Search Selected Model
LinearSVC; Parameters: {'tol': 1e-06, 'C': 1.0, 'max_iter': 100, 'fit_intercept': True, 'intercept_scaling': 1.0, 'intercept_mode': 'regularized', 'class_weight': [1, 1]}; Test_score: 0.7738477419894275; Train_score: 0.7586906685904172; Time: 31.643476565678913;

Testing Model - RandomForestClassifier

Model: RandomForestClassifier; Parameters: {'max_features': 'max', 'max_leaf_nodes': 1000, 'max_depth': 5, 'min_samples_leaf': 1, 'min_info_gain': 0.0, 'nbins': 32}; Test_score: 0.8451952459888945; Train_score: 0.856277396984151; Time: 11.70705803235372;
Model: RandomForestClassifier; Parameters: {'max_features': 'max', 'max_leaf_nodes': 64, 'max_depth': 5, 'min_samples_leaf': 1, 'min_info_gain': 0.0, 'nbins': 32}; Test_score: 0.8054457876917553; Train_score: 0.8559976287559075; Time: 10.56883692741394;
Model: RandomForestClassifier; Parameters: {'max_features': 'max', 'max_leaf_nodes': 32, 'max_depth': 4, 'min_samples_leaf': 2, 'min_info_gain': 0.0, 'nbins': 32}; Test_score: 0.822903124120293; Train_score: 0.8473299727249203; Time: 8.73043696085612;

Grid Search Selected Model
RandomForestClassifier; Parameters: {'n_estimators': 10, 'max_features': 'max', 'max_leaf_nodes': 1000, 'sample': 0.632, 'max_depth': 5, 'min_samples_leaf': 1, 'min_info_gain': 0.0, 'nbins': 32}; Test_score: 0.8451952459888945; Train_score: 0.856277396984151; Time: 11.70705803235372;

Final Model

RandomForestClassifier; Best_Parameters: {'n_estimators': 10, 'max_features': 'max', 'max_leaf_nodes': 1000, 'sample': 0.632, 'max_depth': 5, 'min_samples_leaf': 1, 'min_info_gain': 0.0, 'nbins': 32}; Best_Test_score: 0.8451952459888945; Train_score: 0.856277396984151; Time: 11.70705803235372;


Out[16]:
model_type
avg_score
avg_train_score
avg_time
score_std
score_train_std
1RandomForestClassifier0.84519524598889450.85627739698415111.707058032353720.0168258230553300770.013542560067366049
2RandomForestClassifier0.8229031241202930.84732997272492038.730436960856120.0238208277078791230.019748899475342592
3RandomForestClassifier0.80544578769175530.855997628755907510.568836927413940.020556120431675360.01113579610131046
4LinearSVC0.77384774198942750.758690668590417231.6434765656789130.035144374575994930.01663379561833417
5LinearSVC0.73803612702289380.779279820710195232.0162252585093160.0287393384618709270.01215325640831707
6LinearSVC0.73191960769111490.778112927548073237.251533985137940.0274542170278700220.009676864258223752
7LogisticRegression0.68689691407780110.71344921032774230.380586067835490.044651712272843630.036436079125010096
8LogisticRegression0.683491510488770.671459266801841330.671822309494020.074001629187549070.02623235520865952
9LogisticRegression0.5008800413280.50085558515695091.82588569323221857.33181084951666e-053.661380220521307e-05
10NaiveBayes0.4388448894537180.425046306507588351.08430933952331540.0038027577869705240.003142192012759833
11NaiveBayes0.42894897515550010.42926467128262151.0519889990488690.022078648353479880.011195900389691432
12NaiveBayes0.428696933488708960.43043688416885051.00041643778483080.0142269204424175350.00790643087362655
Rows: 1-12 | Columns: 8
In [17]:
model.plot()
Out[17]:
<AxesSubplot:xlabel='time', ylabel='score'>

As expected, RandomForest models seem to be the best for this problem.

Generally speaking, working with anomalies means working with unsupervised models, so you can't expect to catch every anomaly. Supervised learning techniques are useful for dealing with already-identified anomalies, but what can we do in cases where the anomalies aren't already labeled? For this, we turn to unsupervised learning techniques.

Unsupervised Learning

There are many unsupervised learning techniques, but not all of them will be useful for detecting anomalies. Since there's no rigid mathematical definition for what an outlier is, finding anomalies becomes somewhat subjective.

To solve this problem, we have to evaluate our constraints and needs. Do we need to find anomalies in real-time? Do we have a time constraint?

  • Real-time: We don't have access to historical data, so we need an easy way to preprocess the data that is wholly independent from historical data, and the model must be simple to deploy at the source of the data stream. For example, we might use simple preprocessing techniques like normalization, standardization or One-Hot Encoding instead of more complex ones like windows, interpolation, or intersection. Isolation forests, k-means, robust PCA, or global outlier detection using z-score would be ideal, whereas local outlier factor, DBSCAN, or other hard-to-deploy methods cannot be used.
  • Near Real-time: We have access to historical data and our preprocessing method must be fast. The model has to be simple to score with. We can use any preprocessing technique as long as it is fast enough, which of course varies. Since this is still a real-time use case, we should still avoid any hard-to-deploy algorithms like DBSCAN or local outlier factor.
  • No time constraint: We can use any techniques we want.

Due to the complexity of the computations, anomalies are difficult to detect in the context of "Big Data." We have three efficient methods for that case:

  • Machine Learning : We need to use easily-deployable algorithms to perform real-time fraud detection. Isolation forests and k-means can be easily deployed and they work well for detecting anomalies.
  • Rules & Thresholds : The z-score can be an efficient solution for detecting global outliers.
  • Decomposition : Robust PCA is another technique for detecting outliers.

Before using these techniques, let's draw some scatter plots to get a better idea of what kind of anomalies we can expect.

In [18]:
creditcard.scatter(['V12','V17'], 
                   catcol='Class', 
                   max_nb_points=5000000)
creditcard.scatter(['V12','V17','V10'], 
                   catcol="Class")
Out[18]:
<Axes3DSubplot:xlabel='"V12"', ylabel='"V17"'>