Jump to navigation Jump to search
1,153 bytes added ,  08:49, 4 December 2019
* KL is always >= 0
* KL is not symmetric
* Jensen-Shannon Divergence
** <math>JSD(P \Vert Q) = \frac{1}{2}KL(P \Vert Q) + \frac{1}{2}KL(Q \Vert P)</math>
** This is symmetric
The main idea is to ensure the that discriminator is lipschitz continuous and to limit the lipschitz constant (i.e. the derivative) of the discriminator.<br>
If the correct answer is 1.0 and the generator produces 1.0001, we don't want the discriminator to give us a very high loss.<br>
====Earth mover's distance====
{{main | wikipedia:earth mover's distance}}
The minimum cost of converting one pile of dirt to another.<br>
Where cost is the cost of moving (amount * distance)<br>
Given a set <math>P</math> with m clusters and a set <math>Q</math> with n clusters:<br>
<math>EMD(P, Q) = \frac{\sum_{i=1}^{m}\sum_{j=1}^{n}f_{i,j}d_{i,j}}{\sum_{i=1}^{m}\sum_{j=1}^{n}f_{i,j}}</math><br>
* Also known as Wasserstein metric
==Dimension Reduction==
Goal: Reduce the dimension of a dataset.<br>
If each example <math>x \in \mathbb{R}^n</math>, we want to reduce each example to be in <math>\mathbb{R}^r</math> where <math>r < n</math>
Principal Component Analysis<br>
Preprocessing: Subtract the sample mean from each example so that the new sample mean is 0.<br>
Goal: Find a vector <math>v_1</math> such that the projection <math>v_1 \cdot x</math> has maximum variance.<br>
These principal components are the eigenvectors of <math>X^TX</math>.<br>
===Kernel PCA===

Navigation menu