Motivation Word2Vec is a very famous method that I heard of since the freshman year in college (yeah it comes out in 2013). Recently, some reviewer reminds us of the similarity of the “analogy” learnt by the vector representation of words and the vector analogy of image space in GAN or VAE.
Problem Statement Given a bunch of noisy data, you want a smooth curve going through the cloud. As the points are noisy, there is no need to going through each point.
Note on Neural Tuning and Information Given a stimuli with $D$ intrinsic dimensions, we consider how one neuron or a population of neurons is informative about this stimulus space. Specific Information (Mutual Information) Setup for specific information computation is easy given a certain response $r$ , compute the reduction of entropy of stimuli $\mathbb s$ .
TOC {:toc} Philosophy The spirit of Variational Inference is to solve Bayesian inference problem with optimization. In the scenario of latent factor It’s not trying to use Bayes rule directly, but to fit this distribution within a class of distributions $q(z;\nu)$, by minimizing the KL-divergence between the 2 models.
Note on Gaussian Process Gaussian Process can be thought of as a Gaussian distribution in function space (or infinite dimension vector). One of its major usage is to tackle nonlinear regression problem and provide mean estimate and errorbar around it.
Note on Bayesian Optimization Related to Gaussain Process model Philosophy Bayesian Optimization applies to black box functions and it employs the active learning philosophy. Use Case and Limitation BO is preferred in such cases
TOC {:toc} Motivation Sometimes the matrix (samples) to be correlated is too large, then you need to compute the correlation when the data is pouring in, i.e. online computing correlation.
Note on MiniMax (Updating) Motivation This is a very traditional way of solving turn based game like chess or tic-tac-toc. It’s climax is Deep Blue AI in playing chess. Note, some people think about GAN training procedure as a min-max game between G and D, which is also interesting.
Note on Laplacian-Beltrami (Diffusion) Operator Motivation Laplacian on graph and on discrete geometry (mesh) are very useful tools. One core intuition, just like Laplacian in $\R^n$ space, it’s related to diffusion and heat equation. Recall the diffusion equation is
Notes on Cortical Waves Methods