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Machine Learning and Neural Networks Professor Tony Martinez Computer Science Department Brigham Young University http:/

Machine Learning and Neural Networks Professor Tony Martinez Computer Science Department Brigham Young University http://axon.cs.byu.edu/~martinez. Tutorial Overview. Introduction and Motivation Neural Network Model Descriptions Perceptron Backpropagation Issues Overfitting Applications

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Machine Learning and Neural Networks Professor Tony Martinez Computer Science Department Brigham Young University http:/

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  1. Machine Learning and Neural NetworksProfessor Tony MartinezComputer Science DepartmentBrigham Young Universityhttp://axon.cs.byu.edu/~martinez Machine Learning Tutorial – UIST 2002

  2. Tutorial Overview • Introduction and Motivation • Neural Network Model Descriptions • Perceptron • Backpropagation • Issues • Overfitting • Applications • Other Models • Decision Trees, Nearest Neighbor/IBL, Genetic Algorithms, Rule Induction, Ensembles Machine Learning Tutorial – UIST 2002

  3. More Information • You can download this presentation from: ftp://axon.cs.byu.edu/pub/papers/NNML.ppt • An excellent introductory text to Machine Learning: Machine Learning, Tom M. Mitchell, McGraw Hill, 1997 Machine Learning Tutorial – UIST 2002

  4. What is Inductive Learning • Gather a set of input-output examples from some application: Training Set i.e. Speech Recognition, financial forecasting • Train the learning model (Neural network, etc.) on the training set until it solves it well • The Goal is to generalize on novel data not yet seen • Gather a further set of input-output examples from the same application: Test Set • Use the learning system on actual data Machine Learning Tutorial – UIST 2002

  5. Motivation • Costs and Errors in Programming • Our inability to program "subjective" problems • General, easy-to use mechanism for a large set of applications • Improvement in application accuracy - Empirical Machine Learning Tutorial – UIST 2002

  6. Example Application - Heart Attack Diagnosis • The patient has a set of symptoms - Age, type of pain, heart rate, blood pressure, temperature, etc. • Given these symptoms in an Emergency Room setting, a doctor must diagnose whether a heart attack has occurred. • How do you train a machine learning model solve this problem using the inductive learning model? • Consistent approach • Knowledge of ML approach not critical • Need to select a reasonable set of input features Machine Learning Tutorial – UIST 2002

  7. Examples and Discussion • Loan Underwriting • Which Input Features (Data) • Divide into Training Set and Test Set • Choose a learning model • Train model on Training set • Predict accuracy with the Test Set • How to generalize better? • Different Input Features • Different Learning Model • Issues • Intuition vs. Prejudice • Social Response Machine Learning Tutorial – UIST 2002

  8. UC Irvine Machine Learning Data BaseIris Data Set 4.8,3.0,1.4,0.3, Iris-setosa 5.1,3.8,1.6,0.2, Iris-setosa 4.6,3.2,1.4,0.2, Iris-setosa 5.3,3.7,1.5,0.2, Iris-setosa 5.0,3.3,1.4,0.2, Iris-setosa 7.0,3.2,4.7,1.4, Iris-versicolor 6.4,3.2,4.5,1.5, Iris-versicolor 6.9,3.1,4.9,1.5, Iris-versicolor 5.5,2.3,4.0,1.3, Iris-versicolor 6.5,2.8,4.6,1.5, Iris-versicolor 6.0,2.2,5.0,1.5, Iris-viginica 6.9,3.2,5.7,2.3, Iris-viginica 5.6,2.8,4.9,2.0, Iris-viginica 7.7,2.8,6.7,2.0, Iris-viginica 6.3,2.7,4.9,1.8, Iris-viginica Machine Learning Tutorial – UIST 2002

  9. Voting Records Data Base democrat,n,y,y,n,y,y,n,n,n,n,n,n,y,y,y,y democrat,n,y,n,y,y,y,n,n,n,n,n,n,?,y,y,y republican,n,y,n,y,y,y,n,n,n,n,n,n,y,y,?,y republican,n,y,n,y,y,y,n,n,n,n,n,y,y,y,n,y democrat,y,y,y,n,n,n,y,y,y,n,n,n,n,n,?,? republican,n,y,n,y,y,n,n,n,n,n,?,?,y,y,n,n republican,n,y,n,y,y,y,n,n,n,n,y,?,y,y,?,? democrat,n,y,y,n,n,n,y,y,y,n,n,n,y,n,?,? democrat,y,y,y,n,n,y,y,y,?,y,y,?,n,n,y,? republican,n,y,n,y,y,y,n,n,n,n,n,y,?,?,n,? republican,n,y,n,y,y,y,n,n,n,y,n,y,y,?,n,? democrat,y,n,y,n,n,y,n,y,?,y,y,y,?,n,n,y democrat,y,?,y,n,n,n,y,y,y,n,n,n,y,n,y,y republican,n,y,n,y,y,y,n,n,n,n,n,?,y,y,n,n Machine Learning Tutorial – UIST 2002

  10. Machine Learning Sketch History • Neural Networks - Connectionist - Biological Plausibility • Late 50’s, early 60’s, Rosenblatt, Perceptron • Minsky & Papert 1969 - The Lull, symbolic expansion • Late 80’s - Backpropagation, Hopfield, etc. - The explosion • Machine Learning - Artificial Intelligence - Symbolic - Psychological Plausibility • Samuel (1959) - Checkers evaluation strategies • 1970’s and on - ID3, Instance Based Learning, Rule induction, … • Currently – Symbolic and connectionist lumped under ML • Genetic Algorithms - 1970’s • Originally lumped in connectionist • Now an exploding area – Evolutionary Algorithms Machine Learning Tutorial – UIST 2002

  11. Inductive Learning - Supervised • Assume a set T of examples of the form (x,y) where x is a vector of features/attributes and y is a scalar or vector output • By examining the examples postulate a hypothesis H(x) => y for arbitrary x • Spectrum of Supervised Algorithms • Unsupervised Learning • Reinforcement Learning Machine Learning Tutorial – UIST 2002

  12. Other Machine Learning Areas • Case Based Reasoning • Analogical Reasoning • Speed-up Learning • Inductive Learning is the most studied and successful to date • Data Mining • COLT – Computational Learning Theory Machine Learning Tutorial – UIST 2002

  13. Machine Learning Tutorial – UIST 2002

  14. Perceptron Node – Threshold Logic Unit x1 w1 x2 Z w2 xn wn Machine Learning Tutorial – UIST 2002

  15. x2 x2 T .8 .3 1 .4 .1 0 Learning Algorithm x1 .4 Z .1 x2 -.2 Machine Learning Tutorial – UIST 2002

  16. .8 .3 x2 x2 T .8 .3 1 .4 .1 0 First Training Instance .4 Z =1 .1 -.2 Net = .8*.4 + .3*-.2 = .26 Machine Learning Tutorial – UIST 2002

  17. .4 .1 x2 x2 T .8 .3 1 .4 .1 0 Second Training Instance .4 Z =1 .1 -.2 Net = .4*.4 + .1*-.2 = .14 Dwi = (T - Z) * C * Xi Machine Learning Tutorial – UIST 2002

  18. Delta Rule Learning Dwij = C(Tj – Zj)xi • Create a network with n input and m output nodes • Each iteration through the training set is an epoch • Continue training until error is less than some epsilon • Perceptron Convergence Theorem: Guaranteed to find a solution in finite time if a solution exists • As can be seen from the node activation function the decision surface is an n-dimensional hyper plane Machine Learning Tutorial – UIST 2002

  19. Linear Separability Machine Learning Tutorial – UIST 2002

  20. Linear Separability and Generalization When is data noise vs. a legitimate exception Machine Learning Tutorial – UIST 2002

  21. Limited Functionality of Hyperplane Machine Learning Tutorial – UIST 2002

  22. Gradient Descent Learning Error Landscape TSS: Total Sum Squared Error 0 Weight Values Machine Learning Tutorial – UIST 2002

  23. Deriving a Gradient Descent Learning Algorithm • Goal to decrease overall error (or other objective function) each time a weight is changed • Total Sum Squared error = S (Ti – Zi)2 • Seek a weight changing algorithm such that is negative • If a formula can be found then we have a gradient descent learning algorithm • Perceptron/Delta rule is a gradient descent learning algorithm • Linearly-separable problems have no local minima Machine Learning Tutorial – UIST 2002

  24. Multi-layer Perceptron • Can compute arbitrary mappings • Assumes a non-linear activation function • Training Algorithms less obvious • Backpropagation learning algorithm not exploited until 1980’s • First of many powerful multi-layer learning algorithms Machine Learning Tutorial – UIST 2002

  25. Responsibility Problem Output 1 Wanted 0 Machine Learning Tutorial – UIST 2002

  26. Multi-Layer Generalization Machine Learning Tutorial – UIST 2002

  27. Backpropagation • Multi-layer supervised learner • Gradient Descent weight updates • Sigmoid activation function (smoothed threshold logic) • Backpropagation requires a differentiable activation function Machine Learning Tutorial – UIST 2002

  28. Multi-layer Perceptron Topology Input Layer Hidden Layer(s) Output Layer Machine Learning Tutorial – UIST 2002

  29. Backpropagation Learning Algorithm • Until Convergence (low error or other criteria) do • Present a training pattern • Calculate the error of the output nodes (based on T - Z) • Calculate the error of the hidden nodes (based on the error of the output nodes which is propagated back to the hidden nodes) • Continue propagating error back until the input layer is reached • Update all weights based on the standard delta rule with the appropriate error function d Dwij = CdjZi Machine Learning Tutorial – UIST 2002

  30. Activation Function and its Derivative • Node activation function f(net) is typically the sigmoid • Derivate of activation function is critical part of algorithm 1 .5 0 -5 0 5 Net .25 0 -5 5 0 Net Machine Learning Tutorial – UIST 2002

  31. i k i j k i k i Backpropagation Learning Equations Machine Learning Tutorial – UIST 2002

  32. Backpropagation Summary • Excellent Empirical results • Scaling – The pleasant surprise • Local Minima very rare is problem and network complexity increase • Most common neural network approach • User defined parameters lead to more difficulty of use • Number of hidden nodes, layers, learning rate, etc. • Many variants • Adaptive Parameters, Ontogenic (growing and pruning) learning algorithms • Higher order gradient descent (Newton, Conjugate Gradient, etc.) • Recurrent networks Machine Learning Tutorial – UIST 2002

  33. Inductive Bias • The approach used to decide how to generalize novel cases • Occam’s Razor – The simplest hypothesis which fits the data is usually the best – Still many remaining options A B C -> Z A B’ C -> Z A B C’ -> Z A B’ C’ -> Z A’ B’ C’ -> Z’ • Now you receive the new input A’ B C What is your output? Machine Learning Tutorial – UIST 2002

  34. Overfitting Noise vs. Exceptions revisited Machine Learning Tutorial – UIST 2002

  35. The Overfit Problem • Newer powerful models can have very complex decision surfaces which can converge well on most training sets by learning noisy and irrelevant aspects of the training set in order to minimize error (memorization in the limit) • This makes them susceptible to overfit if not carefully considered TSS Validation/Test Set Training Set Epochs Machine Learning Tutorial – UIST 2002

  36. Avoiding Overfit • Inductive Bias – Simplest accurate model • More Training Data (vs. overtraining - One epoch limit) • Validation Set (requires separate test set) • Backpropagation – Tends to build from simple model (0 weights) to just large enough weights (Validation Set) • Stopping criteria with any constructive model (Accuracy increase vs Statistical significance) – Noise vs. Exceptions • Specific Techniques • Weight Decay, Pruning, Jitter, Regularization • Ensembles Machine Learning Tutorial – UIST 2002

  37. Ensembles • Many different Ensemble approaches • Stacking, Gating/Mixture of Experts, Bagging, Boosting, Wagging, Mimicking, Combinations • Multiple diverse models trained on same problem and then their outputs are combined • The specific overfit of each learning model is averaged out • If models are diverse (uncorrelated errors) then even if the individual models are weak generalizers, the ensemble can be very accurate Combining Technique M1 M2 M3 Mn Machine Learning Tutorial – UIST 2002

  38. Application Issues • Choose relevant features • Normalize features • Can learn to ignore irrelevant features, but will have to fight the curse of dimensionality • More data (training examples) the better • Slower training acceptable for complex and production applications if accuracy improvement, (“The week phenomenon”) • Execution normally fast regardless of training time Machine Learning Tutorial – UIST 2002

  39. Decision Trees - ID3/C4.5 • Top down induction of decision trees • Highly used and successful • Attribute Features - discrete nominal (mutually exclusive) – Real valued features are discretized • Search for smallest tree is too complex (always NP hard) • C4.5 use common symbolic ML philosophy of a greedy iterative approach Machine Learning Tutorial – UIST 2002

  40. Decision Tree Learning • Mapping by Hyper-Rectangles A1 A2 Machine Learning Tutorial – UIST 2002

  41. ID3 Learning Approach • C is the current set of examples • A test on attribute A partitions C into {Ci, C2,...,Cw} where w is the number of values of A C Red Green Attribute:Color Purple C1 C2 C3 Machine Learning Tutorial – UIST 2002

  42. Decision Tree Learning Algorithm • Start with the Training Set as C and test how each attribute partitions C • Choose the bestA for root • The goodness measure is based on how well attribute A divides C into different output classes – A perfect attribute would divide C into partitions that contain only one output class each – A poor attribute (irrelevant) would leave each partition with the same ratio of classes as in C • 20 questions analogy – good questions quickly minimize the possibilities • Continue recursively until sets unambiguously classified or a stopping criteria is reached Machine Learning Tutorial – UIST 2002

  43. ID3 Example and Discussion • 14 Examples. Uses Information Gain. Attributes which best discriminate between classes are chosen • If the same ratios are found in partitioned set, then gain is 0 Temperature Humidity • P N P N • Hot 2 2 High 3 4 • Mild 4 2 Normal 6 1 • Cool 3 1 • Gain: .029 Gain: .151 Machine Learning Tutorial – UIST 2002

  44. ID3 - Conclusions • Good Empirical Results • Comparable application robustness and accuracy with neural networks - faster learning (though NNs are more natural with continuous features - both input and output) • Most used and well known of current symbolic systems - used widely to aid in creating rules for expert systems Machine Learning Tutorial – UIST 2002

  45. Nearest Neighbor Learners • Broad Spectrum • Basic K-NN, Instance Based Learning, Case Based Reasoning, Analogical Reasoning • Simply store all or some representative subset of the examples in the training set • Generalize on the fly rather than use pre-acquired hypothesis - faster learning, slower execution, information retained, memory intensive Machine Learning Tutorial – UIST 2002

  46. Nearest Neighbor Algorithms Machine Learning Tutorial – UIST 2002

  47. Nearest Neighbor Variations • How many examples to store • How do stored example vote (distance weighted, etc.) • Can we choose a smaller set of near-optimal examples (prototypes/exemplars) • Storage reduction • Faster execution • Noise robustness • Distance Metrics – non-Euclidean • Irrelevant Features – Feature weighting Machine Learning Tutorial – UIST 2002

  48. Evolutionary Computation/AlgorithmsGenetic Algorithms • Simulate “natural” evolution of structures via selection and reproduction, based on performance (fitness) • Type of Heuristic Search - Discovery, not inductive in isolation • Genetic Operators - Recombination (Crossover) and Mutation are most common 1 1 0 2 3 1 0 2 2 1 (Fitness = 10) 2 2 0 1 1 3 1 1 0 0 (Fitness = 12) 2 2 0 1 3 1 0 2 2 1 (Fitness = calculated or f(parents)) Machine Learning Tutorial – UIST 2002

  49. Evolutionary Algorithms • Start with initialized population P(t) - random, domain- knowledge, etc. • Population usually made up of possible parameter settings for a complex problem • Typically have fixed population size (like beam search) • Selection • Parent_Selection P(t) - Promising Parents used to create new children • Survive P(t) - Pruning of unpromising candidates • Evaluate P(t) - Calculate fitness of population members. Ranges from simple metrics to complex simulations. Machine Learning Tutorial – UIST 2002

  50. Evolutionary Algorithm Procedure EA t = 0; Initialize Population P(t); Evaluate P(t); Until Done{ /*Sufficiently “good” individuals discovered*/ t = t+1; Parent_Selection P(t); Recombine P(t); Mutate P(t); Evaluate P(t); Survive P(t);} Machine Learning Tutorial – UIST 2002

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