Insight by Mathematics and Intuition for understanding Pattern Recognition
Waleed A. Yousef Faculty of Computers and Information, Helwan University. February 27, 2010
Basics of Statistics: A random variable (or vector) is denoted by upper case letters, e.
This Thisintroductionisadaptedfrom Bishopsslides
Probability ProbabilityTheory
Apples andOranges
Probability ProbabilityTheory
p ( xi , y j ) = 1
i j
MarginalProbability
JointProbability
ConditionalProbability
Probability ProbabilityTheory
SumRule
Produc
Please review the law of total probability, conditional probability, and Bayes rule before solving the first two problems. 1An electronic fuse is produced by five production lines in a manufacturing operation. The fuses are costly, are quite reliable, and
Assignment 3 (Computer Exercise)
Faculty of Computers and Information Faculty
Department of Computer Science Pattern Recognition
A First Simulation Example on Designing and Assessing Classiers
Generate two small (10 observations per class) training data
(Computer Exercise)
Faculty of Computers and Information Faculty
Department of Computer Science Pattern Recognition
1 1. Prove that in the centered model, i.e., Xc = X1 n JX1 ,
1 Xc = 0. 2. For the centered model, prove that (X X)
1
=
1/n 0 0 (Xc Xc )1
3.
(Computer Exercise)
Faculty of Computers and Information Faculty
Department of Computer Science Pattern Recognition
A complete real-life problem on linear regression: A reproduction to the prostate cancer example.
Download the prostate cancer dataset fro
(Computer Exercise)
Faculty of Computers and Information Faculty
Department of Computer Science Pattern Recognition
A First Simulation Example on Designing and Assessing a Regression Function (cont.)
Similar to the previous simulation on linear model, th
(Computer Exercise)
Faculty of Computers and Information Faculty
Department of Computer Science Pattern Recognition
A First Simulation Example on Designing and Assessing a Regression Function
Generate one small (10 observations) training dataset from bin
Assignement
Faculty of Computers and Information Faculty
Department of Computer Science Pattern Recognition
Simulation
Generate two large datasets from two bivariate normals with identity covariance matrix and mean vectors 1 = (0, 0) and 2 = (1, 1) ; eac
Assignment 2 (Computer Exercise)
Faculty of Computers and Information Faculty
Department of Computer Science Pattern Recognition
1. Assume that the daily temperature in Cairo in Summer time is normally distributed with = 37 and = 2. Using mathematics, nd
Insight by Mathematics and Intuition for understanding Pattern Recognition
Waleed A. Yousef Faculty of Computers and Information, Helwan University. May 8, 2010
Ch4. Linear Models for Classication
Before modeling a linear model for classication, what is t
Insight by Mathematics and Intuition for understanding Pattern Recognition
Waleed A. Yousef Faculty of Computers and Information, Helwan University. April 4, 2010
Ch3. Linear Models for Regression
We saw that the best regression function is Y = E [Y |X ]
Insight by Mathematics and Intuition for understanding Pattern Recognition
Waleed A. Yousef Faculty of Computers and Information, Helwan University. March 13, 2010
Ch2. Introduction and Statistical Decision Theory
Types of Variables and Important Notation
Insight by Mathematics and Intuition for understanding Pattern Recognition
Waleed A. Yousef Faculty of Computers and Information, Helwan University. February 20, 2010
Chapter 1
Introduction
Learning: is the process of estimating an unknown input-output de