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- 1. Introduction to Machine Learning course 67577 fall 2007 <ul><li>Lecturer: Amnon Shashua </li></ul><ul><li>Teaching Assistant: Yevgeny Seldin </li></ul><ul><li>School of Computer Science and Engineering </li></ul><ul><li>Hebrew University </li></ul>
- 2. What is Machine Learning? <ul><li>Inference engine (computer program) that when given sufficient data (examples) computes a function that matches as close as possible the process generating the data. </li></ul><ul><li>Make accurate prediction based on observed data </li></ul><ul><li>Algorithms to optimize a performance criterion based on observed data </li></ul><ul><li>Learning to do better in the future based on what was experienced in the past </li></ul><ul><li>Programming by examples: instead of writing a program to solve a task directly, machine learning seeks methods by which the computer will come up with its own program based on training examples. </li></ul>
- 3. Why Machine Learning? <ul><li>Data-driven algorithms are able examine large amounts of data. A human expert on the other hand is likely to be guided by subjective impressions or by examining a relatively small number of examples. </li></ul><ul><li>Humans often have trouble expressing what they know but have no difficulty in labeling data </li></ul><ul><li>Machine learning is effective in domains where declarative (rule based) knowledge is difficult to obtain yet generating training data is easy </li></ul>
- 4. Typical Examples <ul><li>Visual recognition (say, detect faces in an image): the amount of variability in appearance introduce challenges that are beyond the capacity of direct programming </li></ul><ul><li>Spam filtering: data-driven programming can adapt to changing tactics by spammers </li></ul><ul><li>Extract topics from documents: categorize news articles whether they are about politics, sports, science, etc. </li></ul><ul><li>Natural language understanding: from spoken words to text; categorize the meaning of spoken sentences </li></ul><ul><li>Optical character recognition (OCR) </li></ul><ul><li>Medical diagnosis: from symptoms to diagnosis </li></ul><ul><li>Credit card transaction fraud detection </li></ul><ul><li>Wealth prediction </li></ul>
- 5. Fundamental Issues <ul><li>Over-fitting: doing well on a training set does not guarantee accuracy on new examples </li></ul><ul><li>What is the resource we wish to optimize? For a given accuracy, use the smallest size training set </li></ul><ul><li>Examples are drawn from some (fixed) distribution D over X x Y (instance space x output space). Does the learner actually need to recover D during the learning process? </li></ul><ul><li>How does the learning process depend on the complexity of the family of learning functions (concept class C)? How does one define complexity of C? </li></ul><ul><li>When the goal is to learn the joint distribution D then the problem is computationally unwieldy because the joint distribution table is exponentially large. What assumptions can be made to simplify the task? </li></ul>
- 6. Supervised vs. Un-supervised Multiclass classification. K=2 is normally of most interest. Supervised Learning Models: where X is the instance (data) space and Y is the output space Regression. Predict the price of a used car given brand, year, mileage.. Kinematics of a robot arm; navigate by determining steering angle from image input.. Un-supervised Learning Models: Find regularities in the input data assuming there is some structure in the input space <ul><li>Density estimation </li></ul><ul><li>Clustering (non-parametric density estimation): divide customers to groups which have similar attributes.. </li></ul><ul><li>Latent class models: extract topics from documents </li></ul><ul><li>Compression: represent the input space with fewer parameters; projection to lower-dimensional spaces </li></ul>
- 7. Notations X is the instance space : space from which observations are drawn. Examples, input instance , a single observation. Examples, Y is the output space : set of possible outcomes that can be associated with a measurement. Examples, An example is an instance-label pair (x,y). If |Y|=2 one typically uses {0,1} or {-1,1}. We say that an example (x,y) is positive if y=1 and otherwise we call it a negative example A training set Z consists of m instance-label pairs: In some cases we refer to the training set without labels:
- 8. Notations Separating hyperplanes : a concept h(x) is specified by a vector and a scalar b such that: Conjunction learning : a conjunction is a special case of a Boolean formula. A literal Is a variable or its negation and a term is a conjunction of literals, i.e. A target function is a term which consists of a subset of literals. In this case and Each is called a concept or hypothesis or classifier. Example, if A concept (hypothesis) class C is a set (not necessarily finite) of functions of the form: Other examples: then C might be: Decision trees : when then any boolean function can be described by a binary tree. Thus, C consists of decision trees ( )
- 9. The Formal Learning Model Probably Approximate Correct (PAC) <ul><li>Distribution invariant: Learner does not need to estimate the joint distribution D over X x Y. Assumptions are that examples arrive i.i.d. and that D exists and is fixed. </li></ul><ul><li>The training sample complexity (size of the training set Z) depends only the desired accuracy and confidence parameters - does not depend on D. </li></ul><ul><li>Not all concept classes D are PAC-learnable. But some interesting classes are. </li></ul>
- 10. Unrealizable case: when and the training set is and D is over XxY Realizable case: when a target concept is known to lie inside C. In this case, the training set is sampled randomly and independently (i.i.d) according to some (unknown) Distribution D, i.e., S is distributed according to the product distribution Given a concept function is the probability that an instance x sampled according to D will be labeled incorrectly by h(x) PAC Model Definitions
- 11. given to the learner specifies desired accuracy, i.e. Note: in realizable case because given to the learner specifies desired confidence, i.e. The learner is allowed to deviate occasionally from the desired accuracy but only rarely so.. PAC Model Definitions
- 12. We will say that an algorithm L learns C if for every and for every D over XxY, L generates a concept function such that the probability that is at least PAC Model Definitions
- 13. from the set of all training examples to C with the following property: given any there is an integer such that if then, for any probability distribution D on XxY, if Z is a training set of length m drawn randomly according to , then with probability of at least then hypothesis is such that Formal Definition of PAC Learning A learning algorithm L is a function: We say that C is learnable (or PAC-learnable) if there is a learning algorithm for C
- 14. Formal Definition of PAC Learning does not depend on D, i.e., PAC model is distribution invariant The class C determines the sample complexity. For “simple” classes would be small compared to more “complex” classes. Notes:
- 15. Course Syllabus 3 x PAC: 2 x Separating Hyperplanes: Support Vector Machine, Kernels, Linear Discriminant Analysis 3 x Unsupervised Learning: Dimensionality Reduction (PCA), Density Estimation, Non-parametric Clustering (spectral methods) 5 x Statistical Inference: Maximum Likelihood, Conditional Independence, Latent Class Models, Expectation-Maximization Algorithm, Graphical Models

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