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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