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verticapy.machine_learning.model_selection.cross_validate

verticapy.machine_learning.model_selection.cross_validate(estimator: VerticaModel, input_relation: str | vDataFrame, X: str | list[str], y: str, metrics: None | str | list[str] = None, cv: int = 3, average: Literal['binary', 'micro', 'macro', 'weighted'] = 'weighted', pos_label: bool | float | str | timedelta | datetime | None = None, cutoff: int | float | Decimal = -1, show_time: bool = True, training_score: bool = False, **kwargs) → TableSample

Computes the K-Fold cross validation of an estimator.

estimator: object

Vertica estimator with a fit method.

input_relation: SQLRelation

Relation used to train the model.

X: SQLColumns

list of the predictor columns.

y: str

Response Column.

metrics: str | list, optional

Metrics used to do the model evaluation. It can also be a list of metrics. If empty, most of the estimator metrics are computed.

For Classification:

• accuracy:

  Accuracy.

  \[Accuracy = \frac{TP + TN}{TP + TN + FP + FN}\]

• auc:

  Area Under the Curve (ROC).

  \[AUC = \int_{0}^{1} TPR(FPR) \, dFPR\]

• ba:

  Balanced Accuracy.

  \[BA = \frac{TPR + TNR}{2}\]

• bm:

  Informedness

  \[BM = TPR + TNR - 1\]

• csi:

  Critical Success Index

  \[index = \frac{TP}{TP + FN + FP}\]

• f1:

  F1 Score .. math:

  F_1 Score = 2 \times 
  

rac{Precision times Recall}{Precision + Recall}

• fdr:

  False Discovery Rate

  \[FDR = 1 - PPV\]

• fm:

  Fowlkes-Mallows index

  \[FM = \sqrt{PPV * TPR}\]

• fnr:

  False Negative Rate

  \[FNR = \frac{FN}{FN + TP}\]

• for:

  False Omission Rate

  \[FOR = 1 - NPV\]

• fpr:

  False Positive Rate

  \[FPR = \frac{FP}{FP + TN}\]

• logloss:

  Log Loss

  \[Loss = -\frac{1}{N} \sum_{i=1}^{N} \left( y_i \log(p_i) + (1 - y_i) \log(1 - p_i) \right)\]

• lr+:

  Positive Likelihood Ratio.

  \[LR+ = \frac{TPR}{FPR}\]

• lr-:

  Negative Likelihood Ratio.

  \[LR- = \frac{FNR}{TNR}\]

• dor:

  Diagnostic Odds Ratio.

  \[DOR = \frac{TP \times TN}{FP \times FN}\]

• mcc:

  Matthews Correlation Coefficient

• mk:

  Markedness

  \[MK = PPV + NPV - 1\]

• npv:

  Negative Predictive Value

  \[NPV = \frac{TN}{TN + FN}\]

• prc_auc:

  Area Under the Curve (PRC)

  \[AUC = \int_{0}^{1} Precision(Recall) \, dRecall\]

• precision:

  Precision

  \[TP / (TP + FP)\]

• pt:

  Prevalence Threshold.

  \[\frac{\sqrt{FPR}}{\sqrt{TPR} + \sqrt{FPR}}\]

• recall:

  Recall.

  \[TP / (TP + FN)\]

• specificity:

  Specificity.

  \[TN / (TN + FP)\]

For Regression:

• max:

  Max Error.

  \[ME = \max_{i=1}^{n} \left| y_i - \hat{y}_i \right|\]

• mae:

  Mean Absolute Error.

  \[MAE = \frac{1}{n} \sum_{i=1}^{n} \left| y_i - \hat{y}_i \right|\]

• median:

  Median Absolute Error.

  \[MedAE = \text{median}_{i=1}^{n} \left| y_i - \hat{y}_i \right|\]

• mse:

  Mean Squared Error.

  \[MSE = \frac{1}{n} \sum_{i=1}^{n} \left( y_i - \hat{y}_i \right)^2\]

• msle:

  Mean Squared Log Error.

  \[MSLE = \frac{1}{n} \sum_{i=1}^{n} (\log(1 + y_i) - \log(1 + \hat{y}_i))^2\]

• r2:

  R squared coefficient.

  \[R^2 = 1 - \frac{\sum_{i=1}^{n} (y_i - \hat{y}_i)^2}{\sum_{i=1}^{n} (y_i - \bar{y})^2}\]

• r2a:

  R2 adjusted

  \[\text{Adjusted } R^2 = 1 - \frac{(1 - R^2)(n - 1)}{n - k - 1}\]

• var:

  Explained Variance.

  \[VAR = 1 - \frac{Var(y - \hat{y})}{Var(y)}\]

• rmse:

  Root-mean-squared error

  \[RMSE = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2}\]

cv: int, optional

Number of folds.

average: str, optional

The method used to compute the final score for multiclass-classification.

• binary:

  considers one of the classes as positive and use the binary confusion matrix to compute the score.

• micro:

  positive and negative values globally.

• macro:

  average of the score of each class.

• weighted:

  weighted average of the score of each class.

pos_label: PythonScalar, optional

The main class to be considered as positive (classification only).

cutoff: PythonNumber, optional

The model cutoff (classification only).

show_time: bool, optional

If set to True, the time and the average time are added to the report.

training_score: bool, optional

If set to True, the training score is computed with the validation score.

TableSample

result of the cross validation.

We import verticapy:

import verticapy as vp

Hint

By assigning an alias to verticapy, we mitigate the risk of code collisions with other libraries. This precaution is necessary because verticapy uses commonly known function names like “average” and “median”, which can potentially lead to naming conflicts. The use of an alias ensures that the functions from verticapy are used as intended without interfering with functions from other libraries.

For this example, we will use the Wine Quality dataset.

import verticapy.datasets as vpd

data = vpd.load_winequality()

	123 fixed_acidity Numeric(8)	123 volatile_acidity Numeric(9)	123 citric_acid Numeric(8)	123 residual_sugar Numeric(9)	123 chlorides Float(22)	123 free_sulfur_dioxide Numeric(9)	123 total_sulfur_dioxide Numeric(9)	123 density Float(22)	123 pH Numeric(8)	123 sulphates Numeric(8)	123 alcohol Float(22)	123 quality Integer	123 good Integer	Abc color Varchar(20)
1	3.8	0.31	0.02	11.1	0.036	20.0	114.0	0.99248	3.75	0.44	12.4	6	0	white
2	3.9	0.225	0.4	4.2	0.03	29.0	118.0	0.989	3.57	0.36	12.8	8	1	white
3	4.2	0.17	0.36	1.8	0.029	93.0	161.0	0.98999	3.65	0.89	12.0	7	1	white
4	4.2	0.215	0.23	5.1	0.041	64.0	157.0	0.99688	3.42	0.44	8.0	3	0	white
5	4.4	0.32	0.39	4.3	0.03	31.0	127.0	0.98904	3.46	0.36	12.8	8	1	white
6	4.4	0.46	0.1	2.8	0.024	31.0	111.0	0.98816	3.48	0.34	13.1	6	0	white
7	4.4	0.54	0.09	5.1	0.038	52.0	97.0	0.99022	3.41	0.4	12.2	7	1	white
8	4.5	0.19	0.21	0.95	0.033	89.0	159.0	0.99332	3.34	0.42	8.0	5	0	white
9	4.6	0.445	0.0	1.4	0.053	11.0	178.0	0.99426	3.79	0.55	10.2	5	0	white
10	4.6	0.52	0.15	2.1	0.054	8.0	65.0	0.9934	3.9	0.56	13.1	4	0	red
11	4.7	0.145	0.29	1.0	0.042	35.0	90.0	0.9908	3.76	0.49	11.3	6	0	white
12	4.7	0.335	0.14	1.3	0.036	69.0	168.0	0.99212	3.47	0.46	10.5	5	0	white
13	4.7	0.455	0.18	1.9	0.036	33.0	106.0	0.98746	3.21	0.83	14.0	7	1	white
14	4.7	0.6	0.17	2.3	0.058	17.0	106.0	0.9932	3.85	0.6	12.9	6	0	red
15	4.7	0.67	0.09	1.0	0.02	5.0	9.0	0.98722	3.3	0.34	13.6	5	0	white
16	4.7	0.785	0.0	3.4	0.036	23.0	134.0	0.98981	3.53	0.92	13.8	6	0	white
17	4.8	0.13	0.32	1.2	0.042	40.0	98.0	0.9898	3.42	0.64	11.8	7	1	white
18	4.8	0.17	0.28	2.9	0.03	22.0	111.0	0.9902	3.38	0.34	11.3	7	1	white
19	4.8	0.21	0.21	10.2	0.037	17.0	112.0	0.99324	3.66	0.48	12.2	7	1	white
20	4.8	0.225	0.38	1.2	0.074	47.0	130.0	0.99132	3.31	0.4	10.3	6	0	white
21	4.8	0.26	0.23	10.6	0.034	23.0	111.0	0.99274	3.46	0.28	11.5	7	1	white
22	4.8	0.29	0.23	1.1	0.044	38.0	180.0	0.98924	3.28	0.34	11.9	6	0	white
23	4.8	0.33	0.0	6.5	0.028	34.0	163.0	0.9937	3.35	0.61	9.9	5	0	white
24	4.8	0.34	0.0	6.5	0.028	33.0	163.0	0.9939	3.36	0.61	9.9	6	0	white
25	4.8	0.65	0.12	1.1	0.013	4.0	10.0	0.99246	3.32	0.36	13.5	4	0	white
26	4.9	0.235	0.27	11.75	0.03	34.0	118.0	0.9954	3.07	0.5	9.4	6	0	white
27	4.9	0.33	0.31	1.2	0.016	39.0	150.0	0.98713	3.33	0.59	14.0	8	1	white
28	4.9	0.335	0.14	1.3	0.036	69.0	168.0	0.99212	3.47	0.46	10.4666666666667	5	0	white
29	4.9	0.335	0.14	1.3	0.036	69.0	168.0	0.99212	3.47	0.46	10.4666666666667	5	0	white
30	4.9	0.345	0.34	1.0	0.068	32.0	143.0	0.99138	3.24	0.4	10.1	5	0	white
31	4.9	0.345	0.34	1.0	0.068	32.0	143.0	0.99138	3.24	0.4	10.1	5	0	white
32	4.9	0.42	0.0	2.1	0.048	16.0	42.0	0.99154	3.71	0.74	14.0	7	1	red
33	4.9	0.47	0.17	1.9	0.035	60.0	148.0	0.98964	3.27	0.35	11.5	6	0	white
34	5.0	0.17	0.56	1.5	0.026	24.0	115.0	0.9906	3.48	0.39	10.8	7	1	white
35	5.0	0.2	0.4	1.9	0.015	20.0	98.0	0.9897	3.37	0.55	12.05	6	0	white
36	5.0	0.235	0.27	11.75	0.03	34.0	118.0	0.9954	3.07	0.5	9.4	6	0	white
37	5.0	0.24	0.19	5.0	0.043	17.0	101.0	0.99438	3.67	0.57	10.0	5	0	white
38	5.0	0.24	0.21	2.2	0.039	31.0	100.0	0.99098	3.69	0.62	11.7	6	0	white
39	5.0	0.24	0.34	1.1	0.034	49.0	158.0	0.98774	3.32	0.32	13.1	7	1	white
40	5.0	0.255	0.22	2.7	0.043	46.0	153.0	0.99238	3.75	0.76	11.3	6	0	white
41	5.0	0.27	0.32	4.5	0.032	58.0	178.0	0.98956	3.45	0.31	12.6	7	1	white
42	5.0	0.27	0.32	4.5	0.032	58.0	178.0	0.98956	3.45	0.31	12.6	7	1	white
43	5.0	0.27	0.4	1.2	0.076	42.0	124.0	0.99204	3.32	0.47	10.1	6	0	white
44	5.0	0.29	0.54	5.7	0.035	54.0	155.0	0.98976	3.27	0.34	12.9	8	1	white
45	5.0	0.3	0.33	3.7	0.03	54.0	173.0	0.9887	3.36	0.3	13.0	7	1	white
46	5.0	0.31	0.0	6.4	0.046	43.0	166.0	0.994	3.3	0.63	9.9	6	0	white
47	5.0	0.33	0.16	1.5	0.049	10.0	97.0	0.9917	3.48	0.44	10.7	6	0	white
48	5.0	0.33	0.16	1.5	0.049	10.0	97.0	0.9917	3.48	0.44	10.7	6	0	white
49	5.0	0.33	0.16	1.5	0.049	10.0	97.0	0.9917	3.48	0.44	10.7	6	0	white
50	5.0	0.33	0.18	4.6	0.032	40.0	124.0	0.99114	3.18	0.4	11.0	6	0	white
51	5.0	0.33	0.23	11.8	0.03	23.0	158.0	0.99322	3.41	0.64	11.8	6	0	white
52	5.0	0.35	0.25	7.8	0.031	24.0	116.0	0.99241	3.39	0.4	11.3	6	0	white
53	5.0	0.35	0.25	7.8	0.031	24.0	116.0	0.99241	3.39	0.4	11.3	6	0	white
54	5.0	0.38	0.01	1.6	0.048	26.0	60.0	0.99084	3.7	0.75	14.0	6	0	red
55	5.0	0.4	0.5	4.3	0.046	29.0	80.0	0.9902	3.49	0.66	13.6	6	0	red
56	5.0	0.42	0.24	2.0	0.06	19.0	50.0	0.9917	3.72	0.74	14.0	8	1	red
57	5.0	0.44	0.04	18.6	0.039	38.0	128.0	0.9985	3.37	0.57	10.2	6	0	white
58	5.0	0.455	0.18	1.9	0.036	33.0	106.0	0.98746	3.21	0.83	14.0	7	1	white
59	5.0	0.55	0.14	8.3	0.032	35.0	164.0	0.9918	3.53	0.51	12.5	8	1	white
60	5.0	0.61	0.12	1.3	0.009	65.0	100.0	0.9874	3.26	0.37	13.5	5	0	white
61	5.0	0.74	0.0	1.2	0.041	16.0	46.0	0.99258	4.01	0.59	12.5	6	0	red
62	5.0	1.02	0.04	1.4	0.045	41.0	85.0	0.9938	3.75	0.48	10.5	4	0	red
63	5.0	1.04	0.24	1.6	0.05	32.0	96.0	0.9934	3.74	0.62	11.5	5	0	red
64	5.1	0.11	0.32	1.6	0.028	12.0	90.0	0.99008	3.57	0.52	12.2	6	0	white
65	5.1	0.14	0.25	0.7	0.039	15.0	89.0	0.9919	3.22	0.43	9.2	6	0	white
66	5.1	0.165	0.22	5.7	0.047	42.0	146.0	0.9934	3.18	0.55	9.9	6	0	white
67	5.1	0.21	0.28	1.4	0.047	48.0	148.0	0.99168	3.5	0.49	10.4	5	0	white
68	5.1	0.23	0.18	1.0	0.053	13.0	99.0	0.98956	3.22	0.39	11.5	5	0	white
69	5.1	0.25	0.36	1.3	0.035	40.0	78.0	0.9891	3.23	0.64	12.1	7	1	white
70	5.1	0.26	0.33	1.1	0.027	46.0	113.0	0.98946	3.35	0.43	11.4	7	1	white
71	5.1	0.26	0.34	6.4	0.034	26.0	99.0	0.99449	3.23	0.41	9.2	6	0	white
72	5.1	0.29	0.28	8.3	0.026	27.0	107.0	0.99308	3.36	0.37	11.0	6	0	white
73	5.1	0.29	0.28	8.3	0.026	27.0	107.0	0.99308	3.36	0.37	11.0	6	0	white
74	5.1	0.3	0.3	2.3	0.048	40.0	150.0	0.98944	3.29	0.46	12.2	6	0	white
75	5.1	0.305	0.13	1.75	0.036	17.0	73.0	0.99	3.4	0.51	12.3333333333333	5	0	white
76	5.1	0.31	0.3	0.9	0.037	28.0	152.0	0.992	3.54	0.56	10.1	6	0	white
77	5.1	0.33	0.22	1.6	0.027	18.0	89.0	0.9893	3.51	0.38	12.5	7	1	white
78	5.1	0.33	0.22	1.6	0.027	18.0	89.0	0.9893	3.51	0.38	12.5	7	1	white
79	5.1	0.33	0.22	1.6	0.027	18.0	89.0	0.9893	3.51	0.38	12.5	7	1	white
80	5.1	0.33	0.27	6.7	0.022	44.0	129.0	0.99221	3.36	0.39	11.0	7	1	white
81	5.1	0.35	0.26	6.8	0.034	36.0	120.0	0.99188	3.38	0.4	11.5	6	0	white
82	5.1	0.35	0.26	6.8	0.034	36.0	120.0	0.99188	3.38	0.4	11.5	6	0	white
83	5.1	0.35	0.26	6.8	0.034	36.0	120.0	0.99188	3.38	0.4	11.5	6	0	white
84	5.1	0.39	0.21	1.7	0.027	15.0	72.0	0.9894	3.5	0.45	12.5	6	0	white
85	5.1	0.42	0.0	1.8	0.044	18.0	88.0	0.99157	3.68	0.73	13.6	7	1	red
86	5.1	0.42	0.01	1.5	0.017	25.0	102.0	0.9894	3.38	0.36	12.3	7	1	white
87	5.1	0.47	0.02	1.3	0.034	18.0	44.0	0.9921	3.9	0.62	12.8	6	0	red
88	5.1	0.51	0.18	2.1	0.042	16.0	101.0	0.9924	3.46	0.87	12.9	7	1	red
89	5.1	0.52	0.06	2.7	0.052	30.0	79.0	0.9932	3.32	0.43	9.3	5	0	white
90	5.1	0.585	0.0	1.7	0.044	14.0	86.0	0.99264	3.56	0.94	12.9	7	1	red
91	5.2	0.155	0.33	1.6	0.028	13.0	59.0	0.98975	3.3	0.84	11.9	8	1	white
92	5.2	0.155	0.33	1.6	0.028	13.0	59.0	0.98975	3.3	0.84	11.9	8	1	white
93	5.2	0.16	0.34	0.8	0.029	26.0	77.0	0.99155	3.25	0.51	10.1	6	0	white
94	5.2	0.17	0.27	0.7	0.03	11.0	68.0	0.99218	3.3	0.41	9.8	5	0	white
95	5.2	0.185	0.22	1.0	0.03	47.0	123.0	0.99218	3.55	0.44	10.15	6	0	white
96	5.2	0.2	0.27	3.2	0.047	16.0	93.0	0.99235	3.44	0.53	10.1	7	1	white
97	5.2	0.21	0.31	1.7	0.048	17.0	61.0	0.98953	3.24	0.37	12.0	7	1	white
98	5.2	0.22	0.46	6.2	0.066	41.0	187.0	0.99362	3.19	0.42	9.73333333333333	5	0	white
99	5.2	0.24	0.15	7.1	0.043	32.0	134.0	0.99378	3.24	0.48	9.9	6	0	white
100	5.2	0.24	0.45	3.8	0.027	21.0	128.0	0.992	3.55	0.49	11.2	8	1	white

Rows: 1-100 | Columns: 14

Note

VerticaPy offers a wide range of sample datasets that are ideal for training and testing purposes. You can explore the full list of available datasets in the Datasets, which provides detailed information on each dataset and how to use them effectively. These datasets are invaluable resources for honing your data analysis and machine learning skills within the VerticaPy environment.

Next, we can initialize a LogisticRegression model:

from verticapy.machine_learning.vertica import LogisticRegression

model = LogisticRegression()

Now we can conveniently use the cross_validate() function to evaluate our model.

from verticapy.machine_learning.model_selection import cross_validate

cross_validate(
    model,
    input_relation = data,
    X = [
        "fixed_acidity",
        "volatile_acidity",
        "citric_acid",
        "residual_sugar",
        "chlorides",
        "density",
    ],
    y = "good",
    cv = 3,
    metric = "auc",
)

	auc	prc_auc	accuracy	log_loss	precision	recall	f1_score	mcc	informedness	markedness	csi	time
1-fold	0.7460738219425275	0.38845411268065855	0.8066451315182279	0.187106965673493	0.5161290322580645	0.07600950118764846	0.13250517598343686	0.1396113446619113	0.058827370603455886	0.3313309324955942	0.07095343680709534	0.27753233909606934
2-fold	0.7530065210901536	0.3937780115991304	0.8106235565819861	0.185217243999051	0.5606060606060606	0.08851674641148326	0.1528925619834711	0.16511522812151755	0.0719168608934524	0.37909105345980043	0.08277404921700224	0.2949562072753906
3-fold	0.748312016176155	0.3955376965141281	0.7936288088642659	0.191542403943617	0.4090909090909091	0.04100227790432802	0.07453416149068323	0.0739385720262932	0.025947269218746127	0.21069317110787433	0.03870967741935484	0.28208184242248535
avg	0.7491307864029454	0.39258994026463906	0.80363249898816	0.18795553787205366	0.4952753339850114	0.06850950850115324	0.11997729981919707	0.126221714936574	0.05223050023855147	0.3070383856877563	0.06414572114781747	0.28485679626464844
std	0.002888871507594039	0.0030114144078077294	0.007257746600157978	0.002651033529677691	0.0635891386606889	0.020109593019294266	0.03319357862435575	0.03840796178149291	0.019338043052376	0.07086163780194722	0.01862213664528516	0.007378937240650716

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Note

VerticaPy Cross-Validation involves splitting the dataset into multiple folds, training the model on subsets of the data, and evaluating its performance on the remaining data. This process is repeated for each fold, and the overall model performance is averaged across all folds. Cross-Validation helps assess how well a model generalizes to new, unseen data and provides more robust performance metrics. In VerticaPy, cross-validation is a valuable technique for model evaluation and parameter tuning, contributing to the reliability and effectiveness of machine learning models.

For example, grid_search_cv(), randomized_search_cv() and some other model validation functions are using Cross-Validation techniques.

See also

grid_search_cv() : Computes the k-fold grid search of an estimator.

randomized_search_cv() : Computes the K-Fold randomized search of an estimator.