[Mixture Models] An Introduction to Mixture Models
[Mixture Models] An Introduction to Mixture Models

We have discussed many machine learning algorithms, including linear regression, linear classification, neural network models and e.t.c, till now. However, most of them are supervised learning, which means a teacher is leading the models to bias to a certain task

[Linear Classification] From Linear Regression to Linear Classification
[Linear Classification] From Linear Regression to Linear Classification

In the posts 'Introduction to Linear Regression', 'Simple Linear Regression' and 'Polynomial Regression and Features-Extension of Linear Regression', we had discussed the regression task. The goal of regression is to find out a function or hypothesis that given an input $\boldsymbol{x}$, the hypothesis can make a prediction $\hat{y}$ which should be as close to the target $y$ as possible.

[Linear Regression] Maximum Likelihood Estimation
[Linear Regression] Maximum Likelihood Estimation

To any input $\boldsymbol{x}$, our goal in a regression task is to give a prediction $\hat{y}=y(\boldsymbol{x})$ to approximate target $t$ where the function $y$ is the chosen hypothesis. And the difference between $t$ and $\hat{y}$ can be called 'error' or more precisely 'loss'.