Multi-class Logistic Regression from scratch

问题

I am trying to implement from scratch the multiclass logistic regression but my implementation returns bad results. I believe the definition of the gradient function and the cost function is fine. Maybe there is a problem with how these functions are interacting with the minimize function. I have tried it but I could not find out what is wrong. Could you please cast some light?

You can add the estimator 'myLR': myLR(**par_dict), with paramters

par_dict= {'alpha': 0.1, 'maxit': 2000, 'opt_method': 'bfgs', 'positive': False, 'penalty': None, 'verbose': True, 'seed': 3}

in this example or in any of these examples to test it.

import numpy as np
from scipy.optimize import minimize
from sklearn import preprocessing


class myLR():

    def __init__(self, alpha=0.1, reltol=1e-8, maxit=1000, opt_method=None, verbose=True, seed=0):
        
        self.alpha = alpha
        self.maxit = maxit
        self.reltol = reltol
        self.seed = seed
        self.verbose = verbose
        self.opt_method = opt_method

        self.lbin = preprocessing.LabelBinarizer()

    def w_2d(self, w, n_classes):
        return np.reshape(w, (-1, n_classes), order='F')

    def softmax(self, W, X):
        a = np.exp(X @ W)
        o = a / np.sum(a, axis=1, keepdims=True)
        return o

    def cost_wraper(self, W):
        return self.cost(W, self.X, self.T, self.n_samples, self.n_classes)

    def cost(self, W, X, T, n_samples, n_classes):
        W = self.w_2d(W, n_classes)
        log_O = np.log(self.softmax(W, X))
        reg = self.apha * np.linalg.norm(W, ord='fro')
        c = -np.sum([np.vdot(T[[i]], log_O[[i]]) for i in range(n_samples)]) / n_samples + reg
        return c

    def gradient_wraper(self, W):

        return self.gradient(W, self.X, self.T, self.n_samples, self.n_classes)

    def gradient(self, W, X, T, n_samples, n_classes):
        W = self.w_2d(W, n_classes)
        O = self.softmax(W, X)
        reg = self.alpha * W
        grad = -X.T.dot(T - O) / n_samples + reg
        return grad.flatten()

    def fit(self, X, y=None):

        self.n_classes = len(np.unique(y))
        self.n_samples, n_features = X.shape

        if self.n_classes == 2:
            self.T = np.zeros((self.n_samples, self.n_classes), dtype=np.float64)
            for i, cls in enumerate(range(self.n_classes)):
                self.T[y == cls, i] = 1
        else:
            self.T = self.lbin.fit_transform(y)

        self.X = X
         
        np.random.seed(self.seed)
        W_0 = np.random.random(n_features * self.n_classes)        

        options = {'disp': self.verbose, 'maxiter': self.maxit}
        f_min = minimize(fun=self.cost_wraper, x0=W_0,
                         method=self.opt_method,
                         jac=self.gradient_wraper,
                         options=options)

        self.coef_ = self.w_2d(f_min.x, self.n_classes)
        self.W_ = self.coef_

        return self

    def predict_proba(self, X):

        O = self.softmax(self.coef_, X)

        return O

    def predict(self, X):

        sigma = self.predict_proba(X)
        y_pred = np.argmax(sigma, axis=1)
        return y_pred

Edit: Regularization term is included.

回答1:

I think it is now working with the following code.

import numpy as np
from scipy.optimize import minimize
from sklearn import preprocessing


class myLR():

def __init__(self, reltol=1e-8, maxit=1000, opt_method=None, verbose=True, seed=0):

    self.maxit = maxit
    self.reltol = reltol
    self.seed = seed
    self.verbose = verbose
    self.opt_method = opt_method

    self.lbin = preprocessing.LabelBinarizer()

def w_2d(self, w, n_classes):
    return np.reshape(w, (n_classes, -1))


def softmax(self, W, X):
    a = np.exp(X @ W.T)
    o = a / np.sum(a, axis=1, keepdims=True)
    return o

def squared_norm(self, x):
    x = np.ravel(x, order='K')
    return np.dot(x, x)

def cost(self, W, X, T, n_samples, n_classes):
    W = self.w_2d(W, n_classes)
    log_O = np.log(self.softmax(W, X))
    c = -(T * log_O).sum()
    return c / n_samples

def gradient(self, W, X, T, n_samples, n_classes):
    W = self.w_2d(W, n_classes)
    O = self.softmax(W, X)
    grad = -(T - O).T.dot(X)
    return grad.ravel() / n_samples

def fit(self, X, y=None):   
    n_classes = len(np.unique(y))
    n_samples, n_features = X.shape

    if n_classes == 2:
        T = np.zeros((n_samples, n_classes), dtype=np.float64)
        for i, cls in enumerate(np.unique(y)):
            T[y == cls, i] = 1
    else:
        T = self.lbin.fit_transform(y)

     np.random.seed(self.seed)
     W_0 = np.random.random((self.n_classes, self.n_features))
        
    options = {'disp': self.verbose, 'maxiter': self.maxit}
    f_min = minimize(fun=self.cost, x0=W_0,
                     args=(X, T, n_samples, n_classes),
                     method=self.opt_method,
                     jac=self.gradient,
                     options=options)

    self.coef_ = self.w_2d(f_min.x, n_classes)
    self.W_ = self.coef_

    return self

def predict_proba(self, X):
    O = self.softmax(self.W_, X)
    return O

def predict(self, X):
    sigma = self.predict_proba(X)
    y_pred = np.argmax(sigma, axis=1)
    return y_pred

来源：https://stackoverflow.com/questions/65765309/multi-class-logistic-regression-from-scratch