# LinearRegression¶

Linear regression.

This estimator supports learning with mini-batches. On top of the single instance methods, it provides the following methods: learn_many, predict_many, predict_proba_many. Each method takes as input a pandas.DataFrame where each column represents a feature.

It is generally a good idea to scale the data beforehand in order for the optimizer to converge. You can do this online with a preprocessing.StandardScaler.

## Parameters¶

• optimizer (optim.Optimizer) – defaults to None

The sequential optimizer used for updating the weights. Note that the intercept updates are handled separately.

• loss (optim.losses.RegressionLoss) – defaults to None

The loss function to optimize for.

• l2 – defaults to 0.0

Amount of L2 regularization used to push weights towards 0.

• intercept_init – defaults to 0.0

Initial intercept value.

• intercept_lr (Union[optim.schedulers.Scheduler, float]) – defaults to 0.01

Learning rate scheduler used for updating the intercept. A optim.schedulers.Constant is used if a float is provided. The intercept is not updated when this is set to 0.

• clip_gradient – defaults to 1000000000000.0

Clips the absolute value of each gradient value.

• initializer (optim.initializers.Initializer) – defaults to None

Weights initialization scheme.

## Attributes¶

• weights (dict)

The current weights.

## Examples¶

>>> from river import datasets
>>> from river import evaluate
>>> from river import linear_model
>>> from river import metrics
>>> from river import preprocessing

>>> dataset = datasets.TrumpApproval()

>>> model = (
...     preprocessing.StandardScaler() |
...     linear_model.LinearRegression(intercept_lr=.1)
... )
>>> metric = metrics.MAE()

>>> evaluate.progressive_val_score(dataset, model, metric)
MAE: 0.555971

>>> model['LinearRegression'].intercept
35.617670


You can call the debug_one method to break down a prediction. This works even if the linear regression is part of a pipeline.

>>> x, y = next(iter(dataset))
>>> report = model.debug_one(x)
>>> print(report)
0. Input
--------
gallup: 43.84321 (float)
ipsos: 46.19925 (float)
morning_consult: 48.31875 (float)
ordinal_date: 736389 (int)
rasmussen: 44.10469 (float)
you_gov: 43.63691 (float)
<BLANKLINE>
1. StandardScaler
-----------------
gallup: 1.18810 (float)
ipsos: 2.10348 (float)
morning_consult: 2.73545 (float)
ordinal_date: -1.73032 (float)
rasmussen: 1.26872 (float)
you_gov: 1.48391 (float)
<BLANKLINE>
2. LinearRegression
-------------------
Name              Value      Weight      Contribution
Intercept    1.00000    35.61767       35.61767
ipsos    2.10348     0.62689        1.31866
morning_consult    2.73545     0.24180        0.66144
gallup    1.18810     0.43568        0.51764
rasmussen    1.26872     0.28118        0.35674
you_gov    1.48391     0.03123        0.04634
ordinal_date   -1.73032     3.45162       -5.97242
<BLANKLINE>
Prediction: 32.54607


## Methods¶

clone

Return a fresh estimator with the same parameters.

The clone has the same parameters but has not been updated with any data. This works by looking at the parameters from the class signature. Each parameter is either - recursively cloned if it's a River classes. - deep-copied via copy.deepcopy if not. If the calling object is stochastic (i.e. it accepts a seed parameter) and has not been seeded, then the clone will not be idempotent. Indeed, this method's purpose if simply to return a new instance with the same input parameters.

debug_one

Debugs the output of the linear regression.

Parameters

• x (dict)
• decimals – defaults to 5

Returns

str: A table which explains the output.

learn_many

Update the model with a mini-batch of features X and boolean targets y.

Parameters

• X (pandas.core.frame.DataFrame)
• y (pandas.core.series.Series)
• w (Union[float, pandas.core.series.Series]) – defaults to 1

Returns

MiniBatchRegressor: self

learn_one

Fits to a set of features x and a real-valued target y.

Parameters

• x (dict)
• y (numbers.Number)
• w – defaults to 1.0

Returns

Regressor: self

predict_many

Predict the outcome for each given sample.

Parameters --------- X A dataframe of features.

Parameters

• X

Returns

The predicted outcomes.

predict_one

Predicts the target value of a set of features x.

Parameters

• x

Returns

The prediction.