The log-likelihood function for logistic function is $$l(\theta) = \sum_{i=1}^m(y^{(i)}\log h(x^{(i)}) + (1-y^{(i)})\log(1 - h(x^{(i)})))$$, where $$h(x^{(i)}) = \frac{1}{1 + e^{-\theta^Tx^{(i)}}}$$. And according to maximum likelihood estimation, I implemented the LR model fitting using Newton's method, and I encountered 2 problems:

1. I try to fit the model to my data, but during the iterations, singular Hessian matrix is encountered, what do I do with this kind of problem?

2. With different initial guess $\theta$, will the model converge to different results?

The log-likelihood function for logistic function is $$l(\theta) = \sum_{i=1}^m(y^{(i)}\log h(x^{(i)}) + (1-y^{(i)})\log(1 - h(x^{(i)})))$$, where $$h(x^{(i)}) = \frac{1}{1 + e^{-\theta^Tx^{(i)}}}\,.$$

In order to obtain maximum likelihood estimation, I implemented fitting the logistic regression model using Newton's method. I encountered 2 problems:

1. I try to fit the model to my data, but during the iterations, a singular Hessian matrix is encountered, what do I do with this kind of problem?

2. With different initial guess $\theta$, will the model converge to different results?