1CS 188: Artificial IntelligenceFall 2008Lecture 22: Naïve Bayes11/18/2008Dan Klein – UC BerkeleyMachine Learning Up until now: how to reason in a model and how to make optimal decisions Machine learning: how to select a model on the basis of data / experience Learning parameters (e.g. probabilities) Learning structure (e.g. BN graphs) Learning hidden concepts (e.g. clustering)Example: Spam Filter Input: email Output: spam/ham Setup: Get a large collection of example emails, each labeled “spam” or “ham” Note: someone has to hand label all this data! Want to learn to predict labels of new, future emails Features: The attributes used to make the ham / spam decision Words: FREE! Text Patterns: $dd, CAPS Non-text: SenderInContacts …Dear Sir.First, I must solicit your confidence in this transaction, this is by virture of its nature as being utterly confidencial and top secret. …TO BE REMOVED FROM FUTURE MAILINGS, SIMPLY REPLY TO THIS MESSAGE AND PUT "REMOVE" IN THE SUBJECT.99 MILLION EMAIL ADDRESSESFOR ONLY $99Ok, Iknow this is blatantly OT but I'm beginning to go insane. Had an old Dell Dimension XPS sitting in the corner and decided to put it to use, I know it was working pre being stuck in the corner, but when I plugged it in, hit the power nothing happened.Example: Digit Recognition Input: images / pixel grids Output: a digit 0-9 Setup: Get a large collection of example images, each labeled with a digit Note: someone has to hand label all this data! Want to learn to predict labels of new, future digit images Features: The attributes used to make the digit decision Pixels: (6,8)=ON Shape Patterns: NumComponents, AspectRatio, NumLoops …0121??Other Classification Tasks In classification, we predict labels y (classes) for inputs x Examples: Spam detection (input: document, classes: spam / ham) OCR (input: images, classes: characters) Medical diagnosis (input: symptoms, classes: diseases) Automatic essay grader (input: document, classes: grades) Fraud detection (input: account activity, classes: fraud / no fraud) Customer service email routing … many more Classification is an important commercial technology!Important Concepts Data: labeled instances, e.g. emails marked spam/ham Training set Held out set Test set Features: attribute-value pairs which characterize each x Experimentation cycle Learn parameters (e.g. model probabilities) on training set (Tune hyperparameters on held-out set) Compute accuracy of test set Very important: never “peek” at the test set! Evaluation Accuracy: fraction of instances predicted correctly Overfitting and generalization Want a classifier which does well on test data Overfitting: fitting the training data very closely, but not generalizing well We’ll investigate overfitting and generalization formally in a few lecturesTrainingDataHeld-OutDataTestData2Bayes Nets for Classification One method of classification: Use a probabilistic model! Features are observed random variables Fi Y is the query variable Use probabilistic inference to compute most likely Y You already know how to do this inferenceSimple Classification Simple example: two binary featuresMS Fdirect estimateBayes estimate (no assumptions)Conditional independence+General Naïve Bayes A general naive Bayes model: We only specify how each feature depends on the class Total number of parameters is linear in nYF1FnF2|Y| parametersn x |F| x |Y| parameters|Y| x |F|nparametersInference for Naïve Bayes Goal: compute posterior over causes Step 1: get joint probability of causes and evidence Step 2: get probability of evidence Step 3: renormalize+General Naïve Bayes What do we need in order to use naïve Bayes? Inference (you know this part) Start with a bunch of conditionals, P(Y) and the P(Fi|Y) tables Use standard inference to compute P(Y|F1…Fn) Nothing new here Estimates of local conditional probability tables P(Y), the prior over labels P(Fi|Y) for each feature (evidence variable) These probabilities are collectively called the parameters of the model and denoted by θθθθ Up until now, we assumed these appeared by magic, but… …they typically come from training data: we’ll look at this nowA Digit Recognizer Input: pixel grids Output: a digit 0-93Naïve Bayes for Digits Simple version: One feature Fijfor each grid position <i,j> Possible feature values are on / off, based on whether intensity is more or less than 0.5 in underlying image Each input maps to a feature vector, e.g. Here: lots of features, each is binary Naïve Bayes model: What do we need to learn?Examples: CPTs1 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.10 0.11 0.012 0.053 0.054 0.305 0.806 0.907 0.058 0.609 0.500 0.801 0.052 0.013 0.904 0.805 0.906 0.907 0.258 0.859 0.600 0.80Parameter Estimation Estimating distribution of random variables like X or X | Y Empirically: use training data For each outcome x, look at the empirical rate of that value: This is the estimate that maximizes the likelihood of the data Elicitation: ask a human! Usually need domain experts, and sophisticated ways of eliciting probabilities (e.g. betting games) Trouble calibratingr g gA Spam Filter Naïve Bayes spam filter Data: Collection of emails, labeled spam or ham Note: someone has to hand label all this data! Split into training, held-out, test sets Classifiers Learn on the training set (Tune it on a held-out set) Test it on new emailsDear Sir.First, I must solicit your confidence in this transaction, this is by virture of its nature as being utterly confidencial and top secret. …TO BE REMOVED FROM FUTURE MAILINGS, SIMPLY REPLY TO THIS MESSAGE AND PUT "REMOVE" IN THE SUBJECT.99 MILLION EMAIL ADDRESSESFOR ONLY $99Ok, Iknow this is blatantly OT but I'm beginning to go insane. Had an old Dell Dimension XPS sitting in the corner and decided to put it to use, I know it was working pre being stuck in the corner, but when I plugged it in, hit the power nothing happened.Naïve Bayes for Text Bag-of-Words Naïve Bayes: Predict unknown class label (spam vs. ham) Assume evidence features (e.g. the words) are independent Warning: subtly different assumptions than before! Generative model Tied distributions and
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