leastsquares.py

import numpy as np
from ..base import BaseClassifier,BaseRegressor
from itertools import combinations_with_replacement


class BaseLeastSquares:
    def __init__(self,degree=2):
        self.beta = 0
        self.degree = degree
    
    def X_to_poly(self,X):
        X_poly = X
        if self.degree >= 2 :
            for deg in range(2,self.degree):
                for com in combinations_with_replacement(range(X.shape[1]), deg):
                    Xd = np.ones(X.shape[0])
                    for c in com :
                        Xd = Xd * X[:,c]
                    X_poly = np.concatenate((X_poly,Xd.reshape(-1,1)),axis=1)
           
        X_poly = np.concatenate((np.ones((X.shape[0],1)),X_poly),axis=1) # add column of 1 for the bias
        return X_poly
    
    def fit(self,X,y):
        X_poly = self.X_to_poly(X)
        self.beta = np.linalg.pinv(X_poly.T @ X_poly) @ X_poly.T @ y

    def predict(self,X):
        X_poly = self.X_to_poly(X)
        return (X_poly @ self.beta)

class PolynomialRegression(BaseLeastSquares,BaseRegressor):
    ''' Polynomial Least Square Regressor
    Parameters
    ----------
    degree : int >=1
             degrees of features to consider,ex for 2 features x1,x2 with degree =2,
             the input features are going to be x1,x2,x1x2,x1^2,x2^2
    '''
    pass

class PolynomialClassification(BaseLeastSquares,BaseClassifier):
    ''' Polynomial Least Square Classifier
    Parameters
    ----------
    degree : int >=1
             degrees of features to consider,ex for 2 features x1,x2 with degree =2,
             the input features are going to be x1,x2,x1^2,x2^2
    '''

    def fit(self,X,y):
        self.labels = np.unique(y)
        assert len(self.labels) == 2, "Only 2 class can be given to this classifier"

        # Renamed labels as 1 and -1
        y_new = np.zeros(y.shape)
        y_new[y == self.labels[0]] = 1
        y_new[y == self.labels[1]] = -1

        super().fit(X,y_new)
    
    def predict(self,X): 
        pred = super().predict(X)
        y_hat  = np.where(pred >0,self.labels[0],self.labels[1])
        return y_hat
    
class LinearRegression(PolynomialRegression):
    '''Least Square Linear Regressor'''
    def __init__(self):
        self.beta = 0
        self.degree = 1

class LinearClassification(PolynomialClassification):
    '''Least Square Linear Classifier'''
    def __init__(self):
        self.beta = 0
        self.degree = 1