Conditional Expectation
Lucas Schiffer
January 20, 2016
Data Analysis for the Life Sciences
Today's Topics
Introduction
Conditional Probability / Conditional Expectation
Galton Height Data
Regression as Machine Learning
Conditional Expectation / Optimal Prediction
Exercises
Introduction
Conditional probability and conditional expectation are slightly different
Both are often useful as machine learning techniques
Helpful in solving classification and prediction problems
Generally useful for categorical and continuous outcomes
Conditional Probability / Conditional Expectation
Conditional probability
What is the probability that the next marble is green given that the first was yellow?
\[ f_{k}(x)=Pr(Y=k\ |\ X = x) \]
Conditional Expectation
Given that the first marble was yellow, what color is expected next?
\[ E[(\hat{Y}-Y)^2|X=x] \]
Galton Height Data
Francis Galton created a height dataset (1885)
Useful for conditional expectation practice
Regression as Machine Learning
Suppose we want to predict a random son's height
Suppose we want to predict a son's height who's father is 71 inches tall
\[ E[(\hat{Y}-Y)^2|X=71] \]
Conditional Expectation / Optimal Prediction
Exercises
The Exercises <-
http://rpubs.com/schifferl/cee