Lect26 - Announcements • Final 7-8:15 PM Wed 12/15 here...

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

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

Unformatted text preview: Announcements • Final 7-8:15 PM, Wed. 12/15 here • Q/A session 11-noon Mon. 12/13 2405SC • Projects (for 4 credits) due Tue. 12/7 – Code – Sample I/O (if it doesn’t work, say so) – Paper discussing • What you did & why • What you learned • How you would do it differently given… 1 VC Dimension of a Concept Class • Can be challenging to prove • Can be non-intuitive • Signum(sin( x)) on the real line • Convex polygons in the plane 2 Learnability • Often the hypothesis space (or concept class) is syntactically parameterized n-Conjuncts, k-DNF, k- CNF, m of n, MLP w/ k units,… • The concept class is PAC learnable if there exists an algorithm whose running time grows no faster than polynomially in the natural complexity parameters: 1/ , 1/ , others • Clearly, polynomially-bounded growth in the minimum number of training examples is a necessary condition. 3 Suppose… • All h H are very low accuracy, say < 0.1% correct • VC(H) is 100 • Training set S contains 80 labeled examples What’s the probability that an arbitrary h gets the first training example right? What is the best some h H can possibly do on all 80 elements of S? Will this h work well in general? 4 log(labelings) vs. |S| |S| labelings(|S|) 1 100 10,000 1,000,000 5 10 20 15 All Labelings (exponential growth) Labelings Possible by H (polynomial growth after VC(H) Sauer’s Lemma) VC(H) 5 Back to Perceptrons (linear threshold units, linear discriminators) • If there is one perceptron, there are many • Are some better? • Is one best? • Can we tell? • Can we find it? 6 What’s the Best Separating Hyperplane? +------- + + + + + 7 What’s the Best Separating Hyperplane? +------- + + + + + 8 What’s the Best Separating Hyperplane? +------- + + + + + 9 What’s the Best Separating Hyperplane?...
View Full Document

This note was uploaded on 10/13/2011 for the course CS 440 taught by Professor Levinson,s during the Fall '08 term at University of Illinois, Urbana Champaign.

Page1 / 28

Lect26 - Announcements • Final 7-8:15 PM Wed 12/15 here...

This preview shows document pages 1 - 11. Sign up to view the full document.

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