Learn probabilistic theories of the world from experience

**STATISTICAL LEARNING METHODS**

Learn
probabilistic theories of the world from experience

â™¦
We focus on the learning of Bayesian networks

â™¦
More specifically, input data (or evidence), learn
probabilistic theories of the world (or hypotheses)

View
learning as Bayesian updating of a probability distribution over the hypothesis
space

H is the
hypothesis variable, values h1, h2, . . ., prior P(H) jth observation dj gives
the outcome of random variable Dj training data d = d1, . . . , dN

Given the
data so far, each hypothesis has a posterior probability:

P(hi|d) =
Î±P(d|hi)P(hi)

where
P(d|hi) is called the likelihood

Predictions
use a likelihood-weighted average over all hypotheses:

P(X|d) =
Î£i P(X|d, hi)P(hi|d) = Î£i P(X|hi)P(hi|d)

Example

Suppose
there are five kinds of bags of candies: 10% are h1: 100% cherry candies

20% are
h2: 75% cherry candies + 25% lime candies 40% are h3: 50% cherry candies + 50%
lime candies 20% are h4: 25% cherry candies + 75% lime candies 10% are h5: 100%
lime candies

Then we
observe candies drawn from some bag:

What kind
of bag is it? What flavour will the next candy be?

1.The true
hypothesis eventually dominates the Bayesian prediction given that the true
hypothesis is in the prior

2.The
Bayesian prediction is optimal, whether the data set be small or large[?] On
the other hand

1.
The hypothesis space is usually very large or
infinite summing over the hypothesis space is often intractable.

2.
Overfitting when the hypothesis space is too
expressive such that some hypotheses fit the date set well.

3.
Use prior to penalize complexity.

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Artificial Intelligence : Statistical Learning Methods |

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