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※ https://theaiacademy.blogspot.com/2020/05/understanding-conditional-variational.html Vanilla VAE The variational autoencoder or VAE is a directed graphical generative model which has obtained excellent results and is among the state of the art approaches to generative modeling (저자가 이 글을 작성한 날짜가 2020년 5월 20일이다). It assumes that the data is generated by some random process, involving an unobserv..

※ https://www.youtube.com/watch?v=a-wydhEuAm0&t=1182s Idea We want to generate more samples from the peaks of the probability density than in the tails of the density. We want to sample each location in exact proportion to its height so whilst we don't sample very often from the tails, in the shoulders we sample slightly more and in the head we sample even more than that. For the clarity this is..

※ https://bayesianbrad.github.io/posts/2019_hmc.html In this post I will go through a powerful Markov Chain Monte Carlo (MCMC) algorithm called Hamiltonian Monte Carlo (HMC) (MC's be in da house) and demonstrate how to implement the algorithm within the pytorch framework. Let us start with a super nice gif demonstrating the conservation of momentum in action: Why is momentum important? Well, it ..

※ https://people.duke.edu/~ccc14/sta-663-2018/notebooks/S10D_MCMC.html Introduction to MCMC In regular Markov chain models, we are usually interested in finding the equilibrium distribution Tπ at which for a given transition kernel T. MCMC inverts this thinking - we fix the equilibrium distribution to be the posterior distribution and look for a transition kernel that will converge to this equil..

※ Taboga, Marco (2021). "Metropolis-Hastings algorithm", Lectures on probability theory and mathematical statistics. Kindle Direct Publishing. Online appendix. https://www.statlect.com/fundamentals-of-statistics/Metropolis-Hastings-algorithm The Metropolis-Hastings algorithm is one of the most popular Markov Chain Monte Carlo (MCMC) algorithms. Like other MCMC methods, the Metropolis-Hastings al..

※ https://medium.com/@liuec.jessica2000/importance-sampling-explained-end-to-end-a53334cb330b Importance sampling is a useful technique when it's infeasible for us to sample from the real distribution p, when we want to reduce variance of the current Monte Carlo estimator, or when we only know p up to a multiplicative constant. I found it confusing when I first learned about importance sampling ..