101 lines
3.1 KiB
Python
101 lines
3.1 KiB
Python
# -*- coding: utf-8 -*-
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from __future__ import absolute_import
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from sklearn.utils.validation import check_X_y, check_array
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import numpy as np
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from numpy.linalg import lstsq
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from ..base import BaseSimpleEstimator
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__all__ = [
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'SimpleLinearRegression'
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]
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class SimpleLinearRegression(BaseSimpleEstimator):
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"""Simple linear regression.
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This class provides a very simple example of straight forward OLS
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regression with an intercept. There are no tunable parameters, and
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the model fit happens directly on class instantiation.
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Parameters
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----------
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X : array-like, shape=(n_samples, n_features)
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The array of predictor variables. This is the array we will use
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to regress on ``y``.
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y : array-like, shape=(n_samples,)
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This is the target array on which we will regress to build
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our model.
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Attributes
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----------
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theta : array-like, shape=(n_features,)
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The least-squares solution (the coefficients)
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rank : int
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The rank of the predictor matrix, ``X``
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singular_values : array-like, shape=(n_features,)
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The singular values of ``X``
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X_means : array-like, shape=(n_features,)
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The column means of the predictor matrix, ``X``
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y_mean : float
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The mean of the target variable, ``y``
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intercept : float
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The intercept term
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"""
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def __init__(self, X, y):
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# First check X, y and make sure they are of equal length, no NaNs
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# and that they are numeric
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X, y = check_X_y(X, y, y_numeric=True,
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accept_sparse=False) # keep it simple
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# Next, we want to scale all of our features so X is centered
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# We will do the same with our target variable, y
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X_means = np.average(X, axis=0)
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y_mean = y.mean(axis=0)
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# don't do in place, so we get a copy
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X = X - X_means
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y = y - y_mean
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# Let's compute the least squares on X wrt y
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# Least squares solves the equation `a x = b` by computing a
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# vector `x` that minimizes the Euclidean 2-norm `|| b - a x ||^2`.
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theta, _, rank, singular_values = lstsq(X, y, rcond=None)
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# finally, we compute the intercept values as the mean of the target
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# variable MINUS the inner product of the X_means and the coefficients
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intercept = y_mean - np.dot(X_means, theta.T)
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# ... and set everything as an instance attribute
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self.theta = theta
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self.rank = rank
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self.singular_values = singular_values
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# we have to retain some of the statistics around the data too
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self.X_means = X_means
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self.y_mean = y_mean
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self.intercept = intercept
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def predict(self, X):
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"""Compute new predictions for X"""
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# copy, make sure numeric, etc...
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X = check_array(X, accept_sparse=False, copy=False) # type: np.ndarray
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# make sure dims match
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theta = self.theta
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if theta.shape[0] != X.shape[1]:
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raise ValueError("Dim mismatch in predictors!")
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# creates a copy
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return np.dot(X, theta.T) + self.intercept
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