Statistical Machine Learning Problems

There are 4 basics problems in machine learning community: density estimation, clustering, classification and regression.

These problem can also be formulated in statistical framework.

Regression: $p({\bf y}|{\bf x})=p({\bf y,x})/p({\bf x})=p({\bf y,x})/\int p({\bf y,x})d{\bf y}$
Classification: $p(c|{\bf x})=p(c,{\bf x})/p({\bf x})=p(c,{\bf x})/\sum_c p(c,{\bf x})$
Clustering: $p(c|{\bf x})=p(c,{\bf x})/p({\bf x})$,  $c$ is unobserved
Density Estimation:  $p({\bf y}|{\bf x})=p({\bf y,x})/p({\bf x})$, $\bf x$ is unobserved