cs6501: PoKER Class 3: Probabilistic Reasoning Spring 2010 University of Virginia David Evans Plan • One-line Proof of Bayes’ Theorem • Inductive Learning Home Game this Thursday, 7pm! (Game start: 7:15pm) This is not an official course activity. Email me by Wednesday afternoon if you are coming. Bayes’ Theorem Bayes’ Theorem Proof
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cs6501: PoKER
Class 3:
Probabilistic
Reasoning
Spring 2010
University of Virginia
David Evans
Plan
• One-line Proof of Bayes’ Theorem
• Inductive Learning
Home Game this Thursday, 7pm! (Game start: 7:15pm)
This is not an official course activity.
Email me by Wednesday afternoon if you are coming.
Bayes’ Theorem Bayes’ Theorem Proof
Machine
Learning
Inductive Learning“Learning from Examples”
Learner
Input:
Output:
Limits of Induction
It was the summer of 1919 that I began to feel more and more
dissatisfied with these three theories—the Marxist theory of
history, psycho-analysis, and individual psychology; and I began
to feel dubious about their claims to scientific status. My
problem perhaps first took the simple form, “What is wrong with
Marxism, psycho-analysis, and individual psychology? Why are
they so different from physical theories, from Newton's theory,
and especially from the theory of relativity?”
To make this contrast clear I should explain that few of us at the
time would have said that we believed in the truth of Einstein's
theory of gravitation. This shows that it was not my doubting the
truth of those three other theories which bothered me, but
something else.
One can sum up all this by saying that the criterion of the scientific
status of a theory is its falsifiability, or refutability, or testability.
Karl Popper, Science as Falsification, 1963.
Deciding on h
• Many hypotheses fit the training data
• Depends on hypothesis space: what types of
functions
• Pick between simple hypothesis function (that
may not fit exactly) and complex one
• How many functions are there for
X: n bits, Y: 1 bit ?
Forms of Inductive Learning
Supervised Learning
Given:
Output: hypothesis function
Unsupervised Learning (no explicit outputs)
Given:
Output: clustering
Reinforcement Learning
Given:
Output:
Feedback:
No feedback for individual decisions (output), but overall feedback.
First Reinforcement Learner (?)Arthur Samuel. Some Studies in Machine Learning
Using the Game of Checkers. IBM Journal, 1959.
Earlier inductive learning paper:
R. J. Solomonoff. An Inductive Inference Machine, 1956.