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Bayesian His2011

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Mohammad Shazri Shahrir

1. Bayesian methods can be used to approximate the probability of B given A (P(B|A)) by treating it as a function (f(A;w)) of the exemplars A and weights w, where the weights are unknown. 2. A Bayesian model is set up where the model/basis shapes are normally distributed, the confidence weights are independent, and there are precision tuners on the basis and weights. 3. Complexity control through regularization adds a penalty term (E_w) to the standard regression error term (E_d) controlled by a hyperparameter (lambda) to solve overfitting.

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Bayesian Methods in Machine Learning Mohammad Shazri mshazri@gmail.com shazri.shahrir@extolcorp.com
Sources Papers from Michael Tipping -Bayesian Inference: An introduction to Principles in Machine Learning Youtube from mathematicalmonk
approximate P(B|A) P(B|A)=f(A;w) .. A is the exemplars and w is the weights.|given A, what is B?. B and A usually relates as D= {A_n,B_n} from n=1 to N. Prior statements, possible to over-fit.
Initial statement Given A , what is the likelihood of B. P(B|A) Then to approximate P(B|A)
Setup and Model Setup; it is a supervised learning situation (1) Models/Basis* shape are normally distributed (2) confidence weights/tuneVar are independent. (3) there are precision tuners on basis+weights. Var and alpha (4) all are known except weights.
Usual vs MAP Usual ; over-fitting MAP ; solves over-fitting but there is no interpretation of BR. ______________________________________ Confidence-Level/Interpretation of the unknown
Complexity Control : Regularization E(w)= E_d(w)+lambda*E_w(w) E_d is the standard regression model, liner, sigmoid etc. E_w is the penalty Lamda is a hyperparameter
Error model -Note there is no x
Log of error model
Tune Shape Confidence on w + shape of error contribution
Interpretation
Lastly -Correspondence to NN -How we honestly manage complexity in Extol
Questions.. thanks

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Bayesian His2011