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verticapy.machine_learning.vertica.linear_model.LinearRegression

class verticapy.machine_learning.vertica.linear_model.LinearRegression(name: str = None, overwrite_model: bool = False, tol: float = 1e-06, max_iter: int = 100, solver: Literal['newton', 'bfgs'] = 'newton', fit_intercept: bool = True)

Creates a LinearRegression object using the Vertica Linear Regression algorithm.

Parameters

name: str, optional

Name of the model. The model is stored in the database.

overwrite_model: bool, optional

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

tol: float, optional

Determines whether the algorithm has reached the specified accuracy result.

max_iter: int, optional

Determines the maximum number of iterations the algorithm performs before achieving the specified accuracy result.

solver: str, optional

The optimizer method used to train the model.

  • newton:

    Newton Method.

  • bfgs:

    Broyden Fletcher Goldfarb Shanno.

fit_intercept: bool, optional

boolean, specifies whether the model includes an intercept. If set to False, no intercept is used in training the model. Note that setting fit_intercept to False does not work well with the BFGS optimizer.

Attributes

Many attributes are created during the fitting phase.

coef_: numpy.array

The regression coefficients. The order of coefficients is the same as the order of columns used during the fitting phase.

intercept_: float

The expected value of the dependent variable when all independent variables are zero, serving as the baseline or constant term in the model.

features_importance_: numpy.array

The importance of features is computed through the model coefficients, which are normalized based on their range. Subsequently, an activation function calculates the final score. It is necessary to use the features_importance() method to compute it initially, and the computed values will be subsequently utilized for subsequent calls.

Note

All attributes can be accessed using the get_attributes() method.

Note

Several other attributes can be accessed by using the get_vertica_attributes() method.

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)
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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.

You can easily divide your dataset into training and testing subsets using the vDataFrame.train_test_split() method. This is a crucial step when preparing your data for machine learning, as it allows you to evaluate the performance of your models accurately.

data = vpd.load_winequality()
train, test = data.train_test_split(test_size = 0.2)

Warning

In this case, VerticaPy utilizes seeded randomization to guarantee the reproducibility of your data split. However, please be aware that this approach may lead to reduced performance. For a more efficient data split, you can use the vDataFrame.to_db() method to save your results into tables or temporary tables. This will help enhance the overall performance of the process.

Model Initialization

First we import the LinearRegression model:

from verticapy.machine_learning.vertica import LinearRegression

Then we can create the model:

model = LinearRegression(
    tol = 1e-6,
    max_iter = 100,
    solver = 'newton',
    fit_intercept = True,
)

Hint

In verticapy 1.0.x and higher, you do not need to specify the model name, as the name is automatically assigned. If you need to re-use the model, you can fetch the model name from the model’s attributes.

Important

The model name is crucial for the model management system and versioning. It’s highly recommended to provide a name if you plan to reuse the model later.

Model Training

We can now fit the model:

model.fit(
    train,
    [
        "fixed_acidity",
        "volatile_acidity",
        "citric_acid",
        "residual_sugar",
        "chlorides",
        "density",
    ],
    "quality",
    test,
)



=======
details
=======
   predictor    |coefficient|std_err | t_value |p_value 
----------------+-----------+--------+---------+--------
   Intercept    | 142.55628 | 6.83038|20.87091 | 0.00000
 fixed_acidity  |  0.14577  | 0.01236|11.79777 | 0.00000
volatile_acidity| -0.73644  | 0.08665|-8.49900 | 0.00000
  citric_acid   | -0.06035  | 0.09560|-0.63122 | 0.52793
 residual_sugar |  0.04128  | 0.00384|10.75581 | 0.00000
   chlorides    | -0.18007  | 0.36608|-0.49190 | 0.62281
    density     |-138.46779 | 6.94721|-19.93142| 0.00000


==============
regularization
==============
type| lambda 
----+--------
none| 1.00000


===========
call_string
===========
linear_reg('"public"."_verticapy_tmp_linearregression_v_demo_1529433e55a411ef880f0242ac120002_"', '"public"."_verticapy_tmp_view_v_demo_153a749c55a411ef880f0242ac120002_"', '"quality"', '"fixed_acidity", "volatile_acidity", "citric_acid", "residual_sugar", "chlorides", "density"'
USING PARAMETERS optimizer='newton', epsilon=1e-06, max_iterations=100, regularization='none', lambda=1, alpha=0.5, fit_intercept=true)

===============
Additional Info
===============
       Name       |Value
------------------+-----
 iteration_count  |  1  
rejected_row_count|  0  
accepted_row_count|5196 

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.

Features Importance

We can conveniently get the features importance:

result = model.features_importance()

Note

For LinearModel, feature importance is computed using the coefficients. These coefficients are then normalized using the feature distribution. An activation function is applied to get the final score.

Metrics

We can get the entire report using:

result = model.report()
value
explained_variance0.180747705070455
max_error3.14583807237076
median_absolute_error0.541169332796727
mean_absolute_error0.621826428418051
mean_squared_error0.646209084591811
root_mean_squared_error0.803871310964517
r20.180681251562433
r2_adj0.176882246546494
aic-553.8960365438
bic-517.862230187252
Rows: 1-10 | Columns: 2

Important

Most metrics are computed using a single SQL query, but some of them might require multiple SQL queries. Selecting only the necessary metrics in the report can help optimize performance. E.g. model.report(metrics = ["mse", "r2"]).

For LinearModel, we can easily get the ANOVA table using:

result = model.report(metrics = "anova")
Df
SS
MS
F
p_value
Regression6154.32420718129925.72070119688316639.588288337413622.1726466324715088e-44
Residual1294840.7180190539460.6497048060695101
Total13001026.11837048424
Rows: 1-3 | Columns: 6

You can also use the LinearModel.score function to compute the R-squared value:

model.score()
Out[2]: 0.180681251562433

Prediction

Prediction is straight-forward:

model.predict(
    test,
    [
        "fixed_acidity",
        "volatile_acidity",
        "citric_acid",
        "residual_sugar",
        "chlorides",
        "density",
    ],
    "prediction",
)
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)
123
prediction
Float(22)
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Rows: 1-100 | Columns: 15

Note

Predictions can be made automatically using the test set, in which case you don’t need to specify the predictors. Alternatively, you can pass only the vDataFrame to the predict() function, but in this case, it’s essential that the column names of the vDataFrame match the predictors and response name in the model.

Plots

If the model allows, you can also generate relevant plots. For example, regression plots can be found in the Machine Learning - Regression Plots.

model.plot()

Important

The plotting feature is typically suitable for models with fewer than three predictors.

Contour plot is another useful plot that can be produced for models with two predictors.

model.contour()

Machine learning models with two predictors can usually benefit from their own contour plot. This visual representation aids in exploring predictions and gaining a deeper understanding of how these models perform in different scenarios. Please refer to Contour Plot for more examples.

Parameter Modification

In order to see the parameters:

model.get_params()
Out[3]: {'tol': 1e-06, 'max_iter': 100, 'solver': 'newton', 'fit_intercept': True}

And to manually change some of the parameters:

model.set_params({'tol': 0.001})

Model Register

In order to register the model for tracking and versioning:

model.register("model_v1")

Please refer to Model Tracking and Versioning for more details on model tracking and versioning.

Model Exporting

To Memmodel

model.to_memmodel()

Note

MemModel objects serve as in-memory representations of machine learning models. They can be used for both in-database and in-memory prediction tasks. These objects can be pickled in the same way that you would pickle a scikit-learn model.

The following methods for exporting the model use MemModel, and it is recommended to use MemModel directly.

To SQL

You can get the SQL code by:

model.to_sql()
Out[5]: '142.556276427116 + 0.145769130194822 * "fixed_acidity" + -0.73644455007161 * "volatile_acidity" + -0.0603450323997095 * "citric_acid" + 0.0412796262611437 * "residual_sugar" + -0.180072475028282 * "chlorides" + -138.467794908676 * "density"'

To Python

To obtain the prediction function in Python syntax, use the following code:

X = [[4.2, 0.17, 0.36, 1.8, 0.029, 0.9899]]

model.to_python()(X)
Out[7]: array([6.02139803])

Hint

The to_python() method is used to retrieve predictions, probabilities, or cluster distances. For specific details on how to use this method for different model types, refer to the relevant documentation for each model.

__init__(name: str = None, overwrite_model: bool = False, tol: float = 1e-06, max_iter: int = 100, solver: Literal['newton', 'bfgs'] = 'newton', fit_intercept: bool = True) None

Methods

__init__([name, overwrite_model, tol, ...])

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([show, chart])

Computes the model's features importance.

fit(input_relation, X, y[, test_relation, ...])

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_vertica_attributes([attr_name])

Returns the model Vertica attributes.

import_models(path[, schema, kind])

Imports machine learning models.

plot([max_nb_points, chart])

Draws the model.

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_memmodel()

Converts the model to an InMemory object that can be used for different types of predictions.

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