我在 Python 中使用正则化损失函数实现逻辑回归，如下所示：

但是梯度算法效果不好。请先阅读粗体字！只需逐个单元格粘贴代码

import numpy as np, scipy as sp, sklearn as sl
from scipy import special as ss
from sklearn.base import ClassifierMixin, BaseEstimator
from sklearn.datasets import make_classification
import theano.tensor as T

这是损失函数：（scipy 是“剪裁”对数的 arg near1）

def lossf(w, X, y, l1, l2):
     w.resize((w.shape[0],1))
     y.resize((y.shape[0],1))

     lossf1 = np.sum(ss.log1p(1 + ss.expm1(np.multiply(-y, np.dot(X, w)))))
     lossf2 = l2 * (np.dot(np.transpose(w), w))
     lossf3 = l1 * sum(abs(w))
     lossf = np.float(lossf1 + lossf2 + lossf3)
     return lossf

这是梯度函数：(??PROBLEM HERE?? - 见最后）

def gradf(w, X, y, l1, l2):
    w.resize((w.shape[0],1))
    y.resize((y.shape[0],1))

    gradw1 = l2 * 2 * w 
    gradw2 = l1 * np.sign(w)
    gradw3 = np.multiply(-y,(2 + ss.expm1(np.multiply(-y, np.dot(X, w)))))
    gradw3 = gradw3 / (2 + (ss.expm1((np.multiply(-y, np.dot(X, w))))))
    gradw3 = np.sum(np.multiply(gradw3, X), axis=0)
    gradw3.resize(gradw3.shape[0],1)
    gradw = gradw1 + gradw2 + gradw3
    gradw.resize(gradw.shape[0],)
    return np.transpose(gradw)

这是我的 LR 课程：

class LR(ClassifierMixin, BaseEstimator):
    def __init__(self, lr=0.0001, l1=0.1, l2=0.1, num_iter=100, verbose=0):
        self.l1 = l1
        self.l2 = l2
        self.w = None
        self.lr = lr
        self.verbose = verbose
        self.num_iter = num_iter

def fit(self, X, y):        
    n, d = X.shape 
    self.w = np.zeros(shape=(d,))
    for i in range(self.num_iter):
        g = gradf(self.w, X, y, self.l1, self.l2)
        g.resize((g.shape[0],1))
        self.w = self.w - g
        print "Loss: ", lossf(self.w, X, y, self.l1, self.l2)
    return self

def predict_proba(self, X):
    probs = 1/(2 + ss.expm1(np.dot(-X, self.w)))
    return probs 

def predict(self, X):
    probs = self.predict_proba(X)
    probs = np.sign(2 * probs - 1)
    probs.resize((probs.shape[0],))
    return probs 

以下是测试：

X, y = make_classification(n_features=100, n_samples=100)
y = 2 * (y - 0.5)
clf = LR(lr=0.000001, l1=0.1, l2=0.1, num_iter=10, verbose=0)
clf = clf.fit(X, y)
yp = clf.predict(X)
yp.resize((100,1))
accuracy = int(sum(y == yp))/len(y)

这不收敛。但是如果我gradw3用 theano 替换我的：

gradw3 = get_gradw3(w,X,y)

在哪里：

w,X,y = T.matrices("wXy") 
logloss = T.sum(T.log1p(1 + T.expm1(-y* T.dot(X, w)))) 
get_gradw3 = theano.function([w,X,y],T.grad(logloss,w).reshape(w.shape))

它收敛到 100% 的准确率。这意味着，我的 gradw3 实现错误，但我找不到错误。