logistic sigmoid function

Preliminaries ‘An Introduction to Probabilistic Generative Models for Linear Classification’ Idea of logistic regression1 Logistic sigmoid function(logistic function for short) had been introduced in post ‘An Introduction to Probabilistic Generative Models for Linear Classification’. It has an elegant form: \[ \delta(a)=\frac{1}{1+e^{-a}}\tag{1} \] and when \(a=0\), \(\delta(a)=\frac{1}{2}\) and this is just the half of the range of logistic function. This gives us a strong implication that we can set \(a\) equals to some functions \(y(\mathbf{x})\), and then...

Preliminaries Probability Bayesian Formular Calculus Probabilistic Generative Models1 The generative model used for making decisions contains an inference step and a decision step: Inference step is to calculate \(\Pr(\mathcal{C}_k|\mathbf{x})\) which means the probability of \(\mathbf{x}\) belonging to the class \(\mathcal{C}_k\) given \(\mathbf{x}\) Decision step is to make a decision based on \(\Pr(\mathcal{C}_k|\mathbf{x})\) which was calculated in step 1 In this post, we just give an introduction and a framework for the probabilistic generative model in classification....