机器学习--逻辑回归模型

逻辑回归是一种用于二分类任务的广义线性模型，通过sigmoid函数将线性组合映射到概率空间：

h θ ( x ) = σ ( θ T x ) = 1 1 + e − θ T x h_\theta(x) = \sigma(\theta^T x) = \frac{1}{1 + e^{-\theta^T x}} hθ​(x)=σ(θTx)=1+e−θTx1​

其中：

J ( θ ) = − 1 m ∑ i = 1 m [ y ( i ) log ⁡ ( h θ ( x ( i ) ) ) + ( 1 − y ( i ) ) log ⁡ ( 1 − h θ ( x ( i ) ) ) ] J(\theta) = -\frac{1}{m} \sum_{i=1}^m [y^{(i)} \log(h_\theta(x^{(i)})) + (1-y^{(i)}) \log(1-h_\theta(x^{(i)}))] J(θ)=−m1​i=1∑m​[y(i)log(hθ​(x(i)))+(1−y(i))log(1−hθ​(x