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verticapy.machine_learning.vertica.neighbors.KernelDensity

class verticapy.machine_learning.vertica.neighbors.KernelDensity(name: str = None, overwrite_model: bool = False, bandwidth: int | float | Decimal = 1.0, kernel: Literal['gaussian', 'logistic', 'sigmoid', 'silverman'] = 'gaussian', p: int = 2, max_leaf_nodes: int | float | Decimal = 1000000000.0, max_depth: int = 5, min_samples_leaf: int = 1, nbins: int = 5, xlim: list | None = None, **kwargs)

[Beta Version] Creates a KernelDensity object. This object uses pure SQL to compute the final score.

Parameters

name: str, optional

Name of the model. This is not a built-in model, so this name is used to build the final table.

overwrite_model: bool, optional

If set to True, training a model with the same name as an existing model overwrites the existing model.

bandwidth: PythonNumber, optional

The bandwidth of the kernel.

kernel: str, optional

The kernel used during the learning phase.

• gaussian:

  Gaussian Kernel.

• logistic:

  Logistic Kernel.

• sigmoid:

  Sigmoid Kernel.

• silverman:

  Silverman Kernel.

p: int, optional

The p of the p-distances (distance metric used during the model computation).

max_leaf_nodes: PythonNumber, optional

The maximum number of leaf nodes, an integer between 1 and 1e9, inclusive.

max_depth: int, optional

The maximum tree depth, an integer between 1 and 100, inclusive.

min_samples_leaf: int, optional

The minimum number of samples each branch must have after splitting a node, an integer between 1 and 1e6, inclusive. A split that results in fewer remaining samples is discarded.

nbins: int, optional

The number of bins used to discretize the input features.

xlim: list, optional

list of tuples used to compute the kernel window.

Attributes

Several attributes are computed during the fitting phase, and in the case of kernel density estimation (KDE), a RandomForestRegressor` is employed to approximate the k-nearest neighbors (KNN) computation. This reliance on RandomForestRegressor` enhances the efficiency and accuracy of the KDE algorithm.

Examples

The following examples provide a basic understanding of usage. For more detailed examples, please refer to the Machine Learning or the Examples section on the website.

Load data for machine learning

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 winequality 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.

Model Initialization

First we import the KernelDensity model:

from verticapy.machine_learning.vertica import KernelDensity

Then we can create the model:

model = KernelDensity(
    kernel = 'gaussian',
    p = 2,
)

Important

As this model is not native, it solely relies on SQL statements to compute various attributes, storing them within the object. No data is saved in the database.

Model Training

We can now fit the model:

model.fit(data, X = ["sulphates"])

Important

To train a model, you can directly use the vDataFrame or the name of the relation stored in the database. The test set is optional and is only used to compute the test metrics. In verticapy, we don’t work using X matrices and y vectors. Instead, we work directly with lists of predictors and the response name.

Hint

For clustering and anomaly detection, the use of predictors is optional. In such cases, all available predictors are considered, which can include solely numerical variables or a combination of numerical and categorical variables, depending on the model’s capabilities.

Important

As this model is not native, it solely relies on SQL statements to compute various attributes, storing them within the object. No data is saved in the database.

KDE Plots

Plots highlighting the KDE can be easily drawn using:

model.plot()

Important

Please refer to Density for more examples.

Parameter Modification

In order to see the parameters:

model.get_params()
Out[5]: 
{'nbins': 5,
 'p': 2,
 'bandwidth': 1.0,
 'kernel': 'gaussian',
 'max_leaf_nodes': 1000000000,
 'max_depth': 5,
 'min_samples_leaf': 1,
 'xlim': []}

And to manually change some of the parameters:

model.set_params({'p': 3})

Model Register

As this model is not native, it does not support model management and versioning. However, it is possible to use the SQL code it generates for deployment.

__init__(name: str = None, overwrite_model: bool = False, bandwidth: int | float | Decimal = 1.0, kernel: Literal['gaussian', 'logistic', 'sigmoid', 'silverman'] = 'gaussian', p: int = 2, max_leaf_nodes: int | float | Decimal = 1000000000.0, max_depth: int = 5, min_samples_leaf: int = 1, nbins: int = 5, xlim: list | None = None, **kwargs) → None

Must be overridden in the child class

Methods

__init__([name, overwrite_model, bandwidth, ...])	Must be overridden in the child class
contour([nbins, chart])	Draws the model's contour plot.
deploySQL([X])	Returns the SQL code needed to deploy the model.
does_model_exists(name[, raise_error, ...])	Checks whether the model is stored in the Vertica database.
drop()	Drops the model from the Vertica database.
export_models(name, path[, kind])	Exports machine learning models.
features_importance([tree_id, show, chart])	Computes the model's features importance.
fit(input_relation[, X, return_report])	Trains the model.
get_attributes([attr_name])	Returns the model attributes.
get_match_index(x, col_list[, str_check])	Returns the matching index.
get_params()	Returns the parameters of the model.
get_plotting_lib([class_name, chart, ...])	Returns the first available library (Plotly, Matplotlib, or Highcharts) to draw a specific graphic.
get_score([tree_id])	Returns the feature importance metrics for the input tree.
get_tree([tree_id])	Returns a table with all the input tree information.
get_vertica_attributes([attr_name])	Returns the model Vertica attributes.
import_models(path[, schema, kind])	Imports machine learning models.
plot([chart])	Draws the Model.
plot_tree([tree_id, pic_path])	Draws the input tree.
predict(vdf[, X, name, inplace])	Predicts using the input relation.
register(registered_name[, raise_error])	Registers the model and adds it to in-DB Model versioning environment with a status of 'under_review'.
regression_report([metrics])	Computes a regression report
report([metrics])	Computes a regression report
score([metric])	Computes the model score.
set_params([parameters])	Sets the parameters of the model.
summarize()	Summarizes the model.
to_binary(path)	Exports the model to the Vertica Binary format.
to_graphviz([tree_id, classes_color, ...])	Returns the code for a Graphviz tree.
to_pmml(path)	Exports the model to PMML.
to_python([return_proba, ...])	Returns the Python function needed for in-memory scoring without using built-in Vertica functions.
to_sql([X, return_proba, ...])	Returns the SQL code needed to deploy the model without using built-in Vertica functions.
to_tf(path)	Exports the model to the Frozen Graph format (TensorFlow).

Attributes

object_type