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

Info icon This preview shows pages 1–12. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Image of page 1

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

View Full Document Right Arrow Icon
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
Image of page 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
Image of page 3

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

View Full Document Right Arrow Icon
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
Image of page 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
Image of page 5

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

View Full Document Right Arrow Icon
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
Image of page 6
What’s the Best Separating Hyperplane? + - - - - - - - + + + + + 7
Image of page 7

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

View Full Document Right Arrow Icon
What’s the Best Separating Hyperplane? + - - - - - - - + + + + + 8
Image of page 8
What’s the Best Separating Hyperplane? + - - - - - - - + + + + + 9
Image of page 9

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

View Full Document Right Arrow Icon
What’s the Best Separating Hyperplane? + - - - - - - - + + + + + The larger the margin, the lower the capacity But we can have any margin we want by expanding the space… Need to normalize 10
Image of page 10
What’s the Best Separating Hyperplane?
Image of page 11

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

View Full Document Right Arrow Icon
Image of page 12
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern