Transforms that captures the local patterns
Level set can be used in ML
For a convolution $$ f*h(x) = \sum_{s+t=x} f(s) h(t), $$ the dilated version of it is1 $$ f*_l h(x) …
Convolution and Fourier transform
Useful when centering a vector around its mean
Very useful in calculating the partition function
Gaussian integral is one of the most useful things if one could write it down.
Jensen’s inequality shows that $$ f(\mathbb E(X)) \leq \mathbb E(f(X)) $$ for a concave …
A bag is a set in which duplicate elements are allowed. An ordered bag is a list that we use in …
The conditional probability table is also called CPT
Diagnolizing a matrix is a transformation using its eigen space.
Distance between a point and a distribution by measuring the distance between the point and the mean of the distribution using the coordinate system defined by the principal components.
Also known as the second central moment is a measurement of the spread.
Bayes’ Theorem is stated as $$ P(A\mid B) = \frac{P(B \mid A) P(A)}{P(B)} $$ $P(A\mid B)$: …
Canonical decomposition
Decomposing a matrix into two
$$ \mathbf{A} \ast \mathbf{B} = \left(\mathbf{A}_{ij} \otimes \mathbf{B}_{ij}\right)_{ij} $$
Simple decomposition of tensors
Given a matrix $\mathbf X \to X_{m}^{\phantom{m}n}$, we can decompose it into three matrices $$ …
Tucker decomposition of a generalization of SVD to higher ranks