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Geoff Gordon—10-701 Machine Learning—Fall 2013
Recitation
• First recitation tomorrow 5–6:30 here
• Linear algebra
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Geoff Gordon—10-701 Machine Learning—Fall 2013
Probability
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P(a) = P(u) =
P(~a) =
Geoff Gordon—10-701 Machine Learning—Fall 2013
Conventions
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Geoff Gordon—10-701 Machine Learning—Fall 2013
Union, intersection
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Geoff Gordon—10-701 Machine Learning—Fall 2013
Conditioning
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Geoff Gordon—10-701 Machine Learning—Fall 2013
Law of total probability
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Geoff Gordon—10-701 Machine Learning—Fall 2013
Marginals
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Geoff Gordon—10-701 Machine Learning—Fall 2013
Finite vs. infinite |u|
• http://www.amazon.com/Probability-Measure-Wiley-Series-Statistics/dp/1118122372
• http://en.wikipedia.org/wiki/Regular_conditional_probability• http://en.wikipedia.org/wiki/Borel%E2%80%93Kolmogorov_paradox
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Geoff Gordon—10-701 Machine Learning—Fall 2013
How I learned to stop worrying and love the density function…
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Expectation: average value, mean, 1st moment:
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Moments
Variance: the spread, 2nd moment:
Uniform Distribution
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CDF PDF CDF PDF 1√2πσ
exp(− 12 (x− µ)2/σ2)
1b−a a ≤ x ≤ b0 o/w
Geoff Gordon—10-701 Machine Learning—Fall 2013
Multivariate densities
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Geoff Gordon—10-701 Machine Learning—Fall 2013
Random variables
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Probability space (σ-algebra)
Geoff Gordon—10-701 Machine Learning—Fall 2013
Bayes rule
• recall def of conditional: ‣ P(a|b) = P(a^b) / P(b) if P(b) != 0
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