A note for the eigenvector used in the Markov Steady Status: using or P to calculate eigenvector? Last night, a classmate of my friend asks a good question about the eigenvector used for the Markov Steady status. Do we use Markov probability transition matrix to calculate its eigenvalue, or use its transpose to calculate? Why? Here is an example. The P matrix below is the Markov probability transition matrix: sum of each row probability is 1.  You can image the 3 nodes with transition graph as below: We can computeRead More

Start from idiot example: 4 sample data:  +(1,0), +(2,0), -(-1,0),-(-2,0), what is the SVM boundary and support vectors? It is easy to know that the most closest positive (+) example and negative (-) example are (1,0) and (-1,0) accordingly.  It is easy to know the SVM boundary should be x=0. Ok, how can we use math analytic to get it via SVM concept, i.e. max the width between closet positive/negative samples. Set the SVM boundary is ax+by+c=0 The support vector are ax+by+c=d and is ax+by+c=-d.   (d>0) Set the twoRead More

Ref:   http://setosa.io/ev/principal-component-analysis/ https://matthew-brett.github.io/teaching/pca_introduction.html https://blog.statsbot.co/singular-value-decomposition-tutorial-52c695315254 http://www.bluebit.gr/matrix-calculator/calculate.aspx PCA is the major method to reduce features/variables before you train your data in the machine learning. It uses the top K most variance transformed features to represent the original N features (assume N>>K). For example, we have food consumption of 17 types of food in grams per person per week for every country in the UK.   Maybe even after you view the above table for 5 minutes, you are hardly to get some patterns. But if you use PCA to extract theRead More

Reference  LikelyhoodFunction_The world is a complex place.pdf Example Likelihood:  when an event......

This note is to describe the Junction Tree local consistency and global consistency (text book:  P109, Example 6.1) Reference: pgm_Princeton_COS513 Foundations of Probabilistic Modelinglecture7.pdf gouws_python_2010: a master thesis on how to implement graphical model with python Text: Bayesian Reasoning and Machine Learning Junction tree property(JTP): For each pair U, V of cliques with intersection S, all cliques on the path between U and V contain S. (from gouws_python_2010.pdf, a master thesis on how to implement graphical model with python) Example 1 to reflect the property Add Separators in diagram b), you may findRead More

The note is to generate the Junction Tree step by step, with two examples, one is simple BN, another is complex BN. Reference: PGM_CS 731 Advanced methods in artificial intelligence, with biomedical applications (Fall 2009): http://pages.cs.wisc.edu/~dpage/cs731/lecture5.ppt Text: Bayesian Reasoning and Machine Learning https://en.wikipedia.org/wiki/Kruskal%27s_algorithm Sample 1: Below is a full procedure on how to generate a Junction tree with complete potential and separators from simple Bayes model Problem: Turn it into Cliques graph: moralized, and triangulated Here is the cliques set:   {ABC}   {BCD}  {CDE}  {DEF}  Turn it into aRead More