Download pdf - High-Dimensional Lecture 9 (09/27/21) Fall 2021

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Page 1: High-Dimensional Lecture 9 (09/27/21) Fall 2021

High-DimensionalProbability and Statistics

MATH/STAT/ECE 888: Topics in Mathematical Data ScienceSebastien Roch (Math+Stat)

UW-MadisonFall 2021

Lecture 9 (09/27/21)

Page 2: High-Dimensional Lecture 9 (09/27/21) Fall 2021

Today’s slides based on Williams (but results can befound in any graduate-level probability textbook)

See e.g. https://people.math.wisc.edu/~roch/grad-prob/

https://people.math.wisc.edu/~roch/grad-prob/

Page 3: High-Dimensional Lecture 9 (09/27/21) Fall 2021

Facts About Conditional Expectation

Page 4: High-Dimensional Lecture 9 (09/27/21) Fall 2021

Conditional Expectation: Definition

Page 5: High-Dimensional Lecture 9 (09/27/21) Fall 2021

Conditional Expectation: Definition cont’d

Page 6: High-Dimensional Lecture 9 (09/27/21) Fall 2021

Conditional Expectation: Definition cont’d

Page 7: High-Dimensional Lecture 9 (09/27/21) Fall 2021

Independence

Page 8: High-Dimensional Lecture 9 (09/27/21) Fall 2021

Conditional expectation as least squares

Page 9: High-Dimensional Lecture 9 (09/27/21) Fall 2021

Conditional Expectation Cheat Sheet

Page 10: High-Dimensional Lecture 9 (09/27/21) Fall 2021

Conditional Expectation Cheat Sheet cont’d

Page 11: High-Dimensional Lecture 9 (09/27/21) Fall 2021

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