Monthly Archives: April 2016

Adaptive Regularization of Weight Vectors — Mathematical derivation

In this post I am showing my understanding about the paper Adaptive Regularization of Weight Vectors: http://papers.nips.cc/paper/3848-adaptive-regularization-of-weight-vectors.pdf The paper aims to address the negatives of a previous algorithm called confidence weighted (CW) learning by introducing the algorithm Adaptive Regularization Of Weights (AGOW). CW and AGOW are both online learning algorithms, meaning updates happen after observing each …

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Math Derivation for Bayesian Probabilistic Matrix Factorization Model

In this paper I am trying to derive the mathematical formulas that appear in the paper Bayesian Probabilistic Matrix Factorization using Markov Chain Monte Carlo. We will use exactly the same notations as in the paper. The part that I am interested in is the Inference part (Section 3.3). Sample $latex U_i$ In Gibbs sampling, …

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Estimate best K for K-Means in parallel

Gap statistic is often used to determine the best number of clusters. Please see a local version implementation for gap statistic here: https://github.com/echen/gap-statistic. It is often desired to parallelize such tedious job to boost the speed. I implement a parallelized version basd on the source code: library(plyr) library(ggplot2) # Calculate log(sum_i(within-cluster_i sum of squares around cluster_i …

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How to make match prediction using TrueSkill?

TrueSkill [1] is a widely accepted algorithm for matchmaking, in which player skills are initialized with a random variable following Gaussian distribution and then get updated through team-based match outcomes. Eventually, with sufficient amount of matches, player skill random variables will converge to some means with very small variance. There are multiple open sourced libraries …

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