fun with hyperplanes fall 2006

40 %
60 %
Information about fun with hyperplanes fall 2006
Entertainment

Published on December 21, 2007

Author: Jacqueline

Source: authorstream.com

Fun with Hyperplanes: Perceptrons, SVMs, and Friends:  Fun with Hyperplanes: Perceptrons, SVMs, and Friends Ryan Gabbard From CSE 391, Spring 2006 Universal Machine Learning Diagram:  Universal Machine Learning Diagram Generative v. Discriminative Models:  Generative v. Discriminative Models Generative question: “How can we model the joint distribution of the classes and the features?” Why waste energy on stuff we don’t care about? Let’s optimize the job we’re trying to do directly! Discriminative question: “What features distinguish the classes from one another?” Example:  Example Modeling what sort of bizarre distribution produced these training points is hard, but distinguishing the classes is a piece of cake! chart from MIT tech report #507, Tony Jebara Linear Classification:  Linear Classification Representing Lines:  Representing Lines How do we represent a line? In general a hyperplane is defined by Why bother with this weird representation? Projections:  Projections alternate intuition: recall the dot product of two vectors is simply the product of their lengths and the cosine of the angle between them Now classification is easy!:  Now classification is easy! But... how do we learn this mysterious model vector? Perceptron Learning Algorithm :  Perceptron Learning Algorithm Perceptron Update Example I:  Perceptron Update Example I Perceptron Update Example II:  Perceptron Update Example II Properties of the Simple Perceptron:  Properties of the Simple Perceptron You can prove that if it’s possible to separate the data with a hyperplane (i.e. if it’s linearly separable), the algorithm will converge to that hyperplane. But what if it isn’t? Then perceptron is very unstable and bounces all over the place. Voted Perceptron:  Voted Perceptron Works just like a regular perceptron, except you keep track of all the intermediate models you created. When you want to classify something, you let each of the (many, many) models vote on the answer and take the majority. Properties of Voted Perceptron:  Properties of Voted Perceptron Simple! Much better generalization performance than regular perceptron (almost as good as SVMs) Can use the ‘kernel trick’ Training as fast as regular perceptron But run-time is slower. Averaged Perceptron:  Averaged Perceptron Extremely simple! Return as your final model the average of all your intermediate models. Approximation to voted perceptron. Nearly as fast to train and exactly as fast to run as regular perceptron. What’s wrong with these hyperplanes?:  What’s wrong with these hyperplanes? They’re unjustifiably biased!:  They’re unjustifiably biased! A less biased choice:  A less biased choice Margin:  Margin The margin is the distance to closest point in the training data. We tend to get better generalization to unseen data if we choose the separating hyperplane which maximizes the margin. Support Vector Machines:  Support Vector Machines Another learning method which explicitly calculates the maximum margin hyperplane by solving a gigantic quadratic programming problem. Generally considered the highest-performing current machine learning technique. But it’s relatively slow and very complicated. Margin-Infused Relaxed Algorithm (MIRA):  Margin-Infused Relaxed Algorithm (MIRA) Multiclass; each class has a prototype vector Classify an instance by choosing the class whose prototype vector has the greatest dot product with the instance During training, when updating make the ‘smallest’ (in a sense) change to the prototype vectors which guarantees correct classification by a minimum margin Pays attention to the margin directly What if it isn’t separable?:  What if it isn’t separable? Project it to someplace where it is!:  Project it to someplace where it is! Kernel Trick:  If our data isn’t linearly separable, we can define a projection to map it into a much higher dimensional feature space where it is. For some algorithms where everything can be expressed as the dot products of instances (SVM, voted perceptron, MIRA) this can be done efficiently using something called the `kernel trick’ Kernel Trick

Add a comment

Related presentations

Related pages

“Real Analysis” “A First Course in Optimization Theory ...

Fall 2006 Instructor: Yusufcan Masatlioglu ... It might even be fun. ... # 11 Nov 15 Hyperplanes,
Read more

HyperPlanesDrifter: Rockies Rock - Summer 2006

... 2006. Rockies Rock ... Falling there with no protection on the undercling would result in a very unpleasant swinging fall into the ... Fun climbing ...
Read more

Classification with support hyperplanes - dl.acm.org

... SHs consider the set of all hyperplanes that do not make classification ... 2006-09-18 (yyyy-mm ... Learning to have fun: Jonathan Schaeffer: ...
Read more

Methodology Multiclass microarray data classification ...

Multiclass microarray data classification based on ... (2006) compared the ... instances were classified according to the side of the hyperplane they fall ...
Read more

Magazine (Pacific Institute for the Mathematical Sciences ...

Magazine (Pacific Institute for the Mathematical Sciences)... Open Collections. ... vol. 10, [issue 1] Fall 2006: Alternate Title: PIMS magazine
Read more

HyperPlanesDrifter: Bugaboos 2006

... 2006. Bugaboos 2006 ... Rock fall every hour or so, ... Catching up with work on Tuesday/Wednesday/Thursday was fun, ...
Read more

Robert (Bob) Bosch | Arts and Sciences | Oberlin College

Bob Bosch, Biggs Professor of ... "Maximizing Fun at an Amusement Park" ... "Separating Hyperplanes and the Authorship of the Disputed Federalist Papers" ...
Read more

Stefan Langerman's Publications - McGill University

Papers Accepted in Refereed Journals. 1 ... Fall 2006. 58 J ... Special issue of selected papers from the 3rd International Conference on Fun with ...
Read more