PanYaa

Sunday, August 1, 2010

Estimating Pi with Monte Carlo Integration

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There are several tutorials on how to perform this calculation. I like to add the technique I use with MATLAB recently. Basically, Imagine y...
Saturday, July 10, 2010

Likelihood Function in Machine Learning

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The (log) probability function $p({\bf x}|\theta)$ assigns a probability (density) to any joint configuration of variables $\bf x$ given fix...

Statistical Machine Learning Problems

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There are 4 basics problems in machine learning community: density estimation , clustering , classification and regression . These problem...
Saturday, June 19, 2010

Akaike and Bayesian Information Criteria

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Usually, when we have data, we want to know what (parametric) model did the data come from. In other words, we want to do model fitting to t...

Log Likelihood Function

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In maximum likelihood estimation (MLE), if we let $Y_1,...,Y_n$ be n independent random variables (r.v.'s) with probability functions ...
Tuesday, June 15, 2010

Model-based Clustering

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Model-Based Clustering ( MBC ) assumes that the data comes from several subpopulations, each is model separately by $g_k({\bf x}; {\bf \the...
Saturday, June 12, 2010

False Alarm Probability to Likelihood Ratio Threshold

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Let's start from something easier to understand. We know from the " likelihood ratio approach to classification " that \[P({...
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Khirin
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