Multilayer Perceptrons

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Presentation transcript:

Multilayer Perceptrons

Neural Networks Networks of processing units (neurons) with connections (synapses) between them Large number of neurons: 1010 Large connectitivity: 105 Parallel processing Distributed computation/memory Robust to noise, failures Lecture Notes for E Alpaydın 2004 Introduction to Machine Learning © The MIT Press (V1.1)

Understanding the Brain Levels of analysis (Marr, 1982) Computational theory Representation and algorithm Hardware implementation Reverse engineering: From hardware to theory Parallel processing: SIMD vs MIMD Neural net: SIMD with modifiable local memory Learning: Update by training/experience Lecture Notes for E Alpaydın 2004 Introduction to Machine Learning © The MIT Press (V1.1)

Perceptron (Rosenblatt, 1962) Lecture Notes for E Alpaydın 2004 Introduction to Machine Learning © The MIT Press (V1.1)

What a Perceptron Does y y y s w0 w0 w w x w0 x x x0=+1 Regression: y=wx+w0 Classification: y=1(wx+w0>0) y y y s w0 w0 w w x w0 x x x0=+1 Lecture Notes for E Alpaydın 2004 Introduction to Machine Learning © The MIT Press (V1.1)

K Outputs Regression: Lecture Notes for E Alpaydın 2004 Introduction to Machine Learning © The MIT Press (V1.1)

Training Online (instances seen one by one) vs batch (whole sample) learning: No need to store the whole sample Problem may change in time Wear and degradation in system components Stochastic gradient-descent: Update after a single pattern Generic update rule (LMS rule): Lecture Notes for E Alpaydın 2004 Introduction to Machine Learning © The MIT Press (V1.1)

Training a Perceptron: Regression Regression (Linear output): Lecture Notes for E Alpaydın 2004 Introduction to Machine Learning © The MIT Press (V1.1)

Multilayer Perceptrons (Rumelhart et al., 1986) Lecture Notes for E Alpaydın 2004 Introduction to Machine Learning © The MIT Press (V1.1)

Backpropagation Lecture Notes for E Alpaydın 2004 Introduction to Machine Learning © The MIT Press (V1.1)

Regression x Backward Forward Lecture Notes for E Alpaydın 2004 Introduction to Machine Learning © The MIT Press (V1.1)

Regression with Multiple Outputs yi vih zh whj xj Lecture Notes for E Alpaydın 2004 Introduction to Machine Learning © The MIT Press (V1.1)

Lecture Notes for E Alpaydın 2004 Introduction to Machine Learning © The MIT Press (V1.1)

Lecture Notes for E Alpaydın 2004 Introduction to Machine Learning © The MIT Press (V1.1)

whx+w0 vhzh zh Lecture Notes for E Alpaydın 2004 Introduction to Machine Learning © The MIT Press (V1.1)