Trending Technology Machine Learning, Artificial Intelligent, Block Chain, IoT, DevOps, Data Science

Recent Post

Codecademy Code Foundations

Search This Blog

Bayesian Learning in Machine Learning

Probability for Learning

Probability for classification and modeling concepts.
Bayesian probability
 - Notion of probability interpreted as partial belief
Bayesian Estimation
 - It calculate the validity of a proposition
           - Based on prior estimate of its probability
           - and New relevant evidence

Bayes Theorem 

Goal: To determine the most probable hypothesis, given the data D plus any initial knowledge about the prior probabilities of the various hypotheses in H.

Bayes Rule :
                      P(h|D) = P(D|h)P(h)/P(D)

P(h) = prior probability of hypothesis h
P(D) = prior probability of training data D
P(h|D) = probability of h given D (posterior density)
P(D|h) = probability of D given h (likelihood of D given h)

An Example

Does patient have cancer or not ?
  A patient takes a lab test and the result comes back positive. The test returns a correct positive result in only 98% of the cases in which the disease is actually present, and a correct negative result in only 97%  of the cases in which disease is not present. Furthermore, .008 of the entire population have this cancer.

Maximum A Posteriori (MAP) Hypothesis

P(h|D) = P(D|h)P(h)/P(D)

The Goal of Bayesian Learning: the most probable hypothesis given the training data (Maximum A Posteriori hypothesis)

Compute ML Hypo

Bayes Optimal Classifier

Question: Given new instance x, what is its most probable classification?
 hMAP (x) is not the most probable classification!
Example: Let P(h1|D) = .4,
                       P(h2|D) = .3,
                       P(h3|D) = .3
 Given new data x, we have h1(x)=+, h2(x) = -, h3 = -
 What is the most probable classification of x?

Bayes optimal classification:

Where V is the set of all the values a classification can take and vj is one possible such classification.

No comments:

Post a Comment

Popular Articles