Lecture24 - CS440/ECE448: Intro to Articial Intelligence!...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
Lecture 24: Perceptrons Prof. Julia Hockenmaier juliahmr@illinois.edu http://cs.illinois.edu/fa11/cs440 CS440/ECE448: Intro to ArtiFcial Intelligence
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Regression
Background image of page 2
Linear regression Given some data {(x,y)…}, with x, y ˥ R, fnd a Function F(x) = w 1 x + w 0 such that F(x) = y. o o o o o
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Squared Loss We want to fnd a weight vector w which minimizes the loss (error) on the training data {(x 1 ,y 1 )…(x N , y N )} 4 CS440/ECE448: Intro AI L ( w ) = L 2 ( f w ( x i ), i = 1 N ! y i ) = ( y i " f w ( x i ) i = 1 N ! ) 2
Background image of page 4
Linear regression We need to minimize the loss on the training data: w = argmin w Loss(f w ) We need to set partial derivatives of Loss(f w ) with respect to w1, w0 to zero. This has a closed-form solution for linear regression (see book).
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Gradient descent In general, we won ʼ t be able to fnd a closed- Form solution, so we need an iterative (local search) algorithm. We will start with an initial weight vector w, and update each element iteratively in the direction oF its gradient: w i := w i ! d/dw i Loss( w ) 6 CS440/ECE448: Intro AI
Background image of page 6
Binary classifcation with Naïve Bayes For each item x = (x 1…. x d ) , we compute f k ( x ) = P( x | C k )P(C k ) = P(C k ) " i P(x i |C k ) for both class C 1 and C 2 We assign class C 1 to x if f 1 ( x ) > f 2 ( x ) Equivalently, we can de±ne a ʻ discriminant function ʼ f( x ) = f 1 ( x ) - f 2 ( x ) and assign class C 1 to x if f( x ) > 0 7 CS440/ECE448: Intro AI
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 20

Lecture24 - CS440/ECE448: Intro to Articial Intelligence!...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online