正则项不影响Logistic回归损失函数凸性

Last updated Sep 11, 2021 Edit Source

• All
• Machine learning
• Logistic regression
• Regularization
• Convex optimization
• Cost function

Tags: #MachineLearning #LogisticRegression #Regularization #ConvexOptimization #CostFunction

$$\begin{align} J(\theta)&=P(\theta)+\frac\lambda{2m}\sum^n_{i=1}\theta_i^2 \end{align}$$

$$\begin{aligned} \frac{\partial^2}{\partial \theta_{j}^2} \left(\frac\lambda{2m}\sum^n_{i=1}\theta_i^2\right)&= \frac{\lambda}{m}\frac{\partial}{\partial \theta_{j}} \theta_{j}\\ &=\frac{\lambda}{m}>0 \end{aligned}$$ 所以损失函数还是凸的