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Pitt CS 2710 - Learning

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1CS 2710 Foundations of AICS 2710 Foundations of AILecture 20-bMilos [email protected] Sennott SquareLearningCS 2710 Foundations of AIMachine Learning• The field of machine learning studies the design of computer programs (agents) capable of learning from past experience or adapting to changes in the environment• The need for building agents capable of learning is everywhere – Predictions in medicine, text classification, speech recognition, image/text retrieval, commercial software • Machine learning is not only the deduction but induction of rules from examples that facilitate prediction and decision making2CS 2710 Foundations of AILearningLearning process:Learner (a computer program) takes data D representing past experiences and tries to either:– to develop an appropriate response to future data, or – describe in some meaningful way the data seen Example:Learner sees a set of past patient cases (patient records) with corresponding diagnoses. It can either try:– to predict the presence of a disease for future patients– describe the dependencies between diseases, symptoms (e.g. builds a Bayesian network for them) CS 2710 Foundations of AITypes of learning• Supervised learning– Learning mapping between inputs x and desired outputs y– Teacher gives me y’s for the learning purposes• Unsupervised learning– Learning relations between data components– No specific outputs given by a teacher• Reinforcement learning– Learning mapping between inputs x and desired outputs y– Critic does not give me y’s but instead a signal (reinforcement) of how good my answer was• Other types of learning:– Concept learning, explanation-based learning, etc.3CS 2710 Foundations of AISupervised learningData: a set of n examples is input vector, and y is desired output (given by a teacher)Objective: learn the mapping s.t.Two types of problems:• Regression: X discrete or continuousY is continuous• Classification: X discrete or continuousY is discrete},..,,{21 ndddD =>=<iiiyd ,xixYXf →:nixfyii,..,1allfor)(=≈CS 2710 Foundations of AISupervised learning examples• Regression: Y is continuousDebt/equityEarnings company stock priceFuture product orders• Classification: Y is discreteHandwritten digit (array of 0,1s)Label “3”4CS 2710 Foundations of AIUnsupervised learning• Data:vector of valuesNo target value (output) y •Objective:– learn relations between samples, components of samplesTypes of problems:• ClusteringGroup together “similar” examples, e.g. patient cases•Density estimation– Model probabilistically the population of samples, e.g. relations between the diseases, symptoms, lab tests etc.},..,,{21 ndddD =iid x=CS 2710 Foundations of AIUnsupervised learning example. • Density estimation. We want to build the probability model of a population from which we draw samples -2 -1.5 -1 -0.5 0 0.5 1 1.5 2-1-0.500.511.522.53iid x=5CS 2710 Foundations of AIUnsupervised learning. Density estimation• A probability density of a point in the two dimensional space– Model used here: Mixture of GaussiansCS 2710 Foundations of AIReinforcement learning• We want to learn:• We see samples of x but not y • Instead of y we get a feedback (reinforcement) from a criticabout how good our output was • The goal is to select output that leads to the best reinforcementLearnerinput sampleoutputCriticreinforcementYXf →:6CS 2710 Foundations of AILearning• Assume we see examples of pairs (x , y) and we want to learn the mapping to predict future ys for values of x• We get the data what should we do?YXf →:-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2-10-8-6-4-20246810xyCS 2710 Foundations of AILearning bias• Problem: many possible functions exists for representing the mapping between x and y • Which one to choose? Many examples still unseen!YXf →:-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2-10-8-6-4-20246810xy7CS 2710 Foundations of AILearning bias• Problem is easier when we make an assumption about the model, say,• Restriction to a linear model is an example of the learning biasbaxxf+=)(-2.5 -2 -1. 5 -1 -0. 5 0 0.5 1 1.5 2-10-8-6-4-20246810xyCS 2710 Foundations of AILearning bias• Bias provides the learner with some basis for choosing among possible representations of the function.•Forms of bias: constraints, restrictions, model preferences•Important: There is no learning without a bias!-2.5 -2 -1. 5 -1 -0. 5 0 0.5 1 1.5 2-10-8-6-4-20246810xy8CS 2710 Foundations of AILearning bias• Choosing a parametric model or a set of models is not enough Still too many functions– One for every pair of parameters a, bbaxxf+=)(-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1. 5 2-10-8-6-4-20246810xyCS 2710 Foundations of AIFitting the data to the modelWe are interested in finding the best set of model parametersHow is the best set defined? Our goal is to have the parameters that:• reduce the misfit between the model and data• Or, (in other words) that explain the data the best Error function:Gives a measure of misfit between the data and the model• Examples of error functions:– Mean square error– Misclassification error21))((1iinixfyn−∑=Average # of misclassified cases )(iixfy≠9CS 2710 Foundations of AIFitting the data to the model• Linear regression – Least squares fit with the linear model – minimizes-2.5 -2 -1 .5 -1 -0 .5 0 0.5 1 1.5 2-10-8-6-4-20246810xy21))((1iinixfyn−∑=CS 2710 Foundations of AITypical learningThree basic steps:• Select a model or a set of models (with parameters)E.g.•Select the error function to be optimizedE.g.•Find the set of parameters optimizing the error function– The model and parameters with the smallest error represent the best fit of the model to the dataBut there are problems one must be careful about …baxy


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Pitt CS 2710 - Learning

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