AN INTRODUCTION TO NEURAL NETWORKS. Scott Kuindersma November 12, 2009
|
|
- Abigail Morris
- 5 years ago
- Views:
Transcription
1 AN INTRODUCTION TO NEURAL NETWORKS Scott Kuindersma November 12, 2009
2
3 SUPERVISED LEARNING We are given some training data: We must learn a function If y is discrete, we call it classification If it is continuous, we call it regression
4 ARTIFICIAL NEURAL NETWORKS Artificial neural networks are one technique that can be used to solve supervised learning problems Very loosely inspired by biological neural networks real neural networks are much more complicated, e.g. using spike timing to encode information Neural networks consist of layers of interconnected units
5 PERCEPTRON UNIT The simplest computational neural unit is called a perceptron The input of a perceptron is a real vector x The output is either 1 or -1 Therefore, a perceptron can be applied to binary classification problems Whether or not it will be useful depends on the problem... more on this later...
6 PERCEPTRON UNIT[MITCHELL 1997]
7 SIGN FUNCTION
8 EXAMPLE Suppose we have a perceptron with 3 weights: On input x1 = 0.5, x2 = 0.0, the perceptron outputs: where x0 = 1
9 LEARNING RULE Now that we know how to calculate the output of a perceptron, we would like to find a way to modify the weights to produce output that matches the training data This is accomplished via the perceptron learning rule for an input pair where, again, x0 = 1 Loop through the training data until (nearly) all examples are classified correctly
10 MATLAB EXAMPLE
11 LIMITATIONS OF THE PERCEPTRON MODEL Can only distinguish between linearly separable classes of inputs Consider the following data:
12 PERCEPTRONS AND BOOLEAN FUNCTIONS Suppose we let the values (1,-1) correspond to true and false, respectively Can we describe a perceptron capable of computing the AND function? What about OR? NAND? NOR? XOR? Let s think about it geometrically
13 BOOLEAN FUNCS CONT D AND OR NAND NOR
14 EXAMPLE: AND Let pand(x1,x2) be the output of the perceptron with weights w0 = -0.3, w1 = 0.5, w2 = 0.5 on input x1, x2 x1 x2 pand(x1,x2)
15 XOR
16 XOR XOR cannot be represented by a perceptron, but it can be represented by a small network of perceptrons, e.g., x1 x2 x1 x2 OR NAND AND
17 PERCEPTRON CONVERGENCE The perceptron learning rule is not guaranteed to converge if the data is not linearly separable We can remedy this situation by considering linear unit and applying gradient descent The linear unit is equivalent to a perceptron without the sign function. That is, its output is given by: where x0 = 1
18 LEARNING RULE DERIVATION Goal: a weight update rule of the form First we define a suitable measure of error Typically we choose a quadratic function so we have a global minimum
19 ERROR SURFACE [MITCHELL 1997]
20 LEARNING RULE DERIVATION The learning algorithm should update each weight in the direction that minimizes the error according to our error function That is, the weight change should look something like
21 GRADIENT DESCENT
22 GRADIENT DESCENT Good: guaranteed to converge to the minimum error weight vector regardless of whether the training data are linearly separable (given that α is sufficiently small) Bad: still can only correctly classify linearly separable data
23 NETWORKS In general, many-layered networks of threshold units are capable of representing a rich variety of nonlinear decision surfaces However, to use our gradient descent approach on multi-layered networks, we must avoid the non-differentiable sign function Multiple layers of linear units can still only represent linear functions Introducing the sigmoid function...
24 SIGMOID FUNCTION
25 SIGMOID UNIT [MITCHELL 1997]
26 EXAMPLE Suppose we have a sigmoid unit k with 3 weights: On input x1 = 0.5, x2 = 0.0, the unit outputs:
27 NETWORK OF SIGMOID UNITS o 2 o 3 o output layer w hidden layer w 31 x 0 x 1 x 2 x 3
28 EXAMPLE x 0 x1 x 2
29 EXAMPLE output x 0 x1 x x x1 1 2
30 BACK-PROPAGATION Really just applying the same gradient descent approach to our network of sigmoid units We use the error function:
31 BACKPROP ALGORITHM
32 BACKPROP CONVERGENCE Unfortunately, there may exist many local minima in the error function Therefore we cannot guarantee convergence to an optimal solution as in the single linear unit case Time to convergence is also a concern Nevertheless, backprop does reasonably well in many cases
33 MATLAB EXAMPLE Quadratic decision boundary Single linear unit vs. Three-sigmoid unit backprop network... GO!
34 BACK TO ALVINN ALVINN was a 1989 project at CMU in which an autonomous vehicle learned to drive by watching a person drive ALVINN's architecture consists of a single hidden layer backpropagation network The input layer of the network is a 30x32 unit two dimensional "retina" which receives input from the vehicles video camera The output layer is a linear representation of the direction the vehicle should travel in order to keep the vehicle on the road
35 ALVINN
36 REPRESENTATIONAL POWER OF NEURAL NETWORKS Every boolean function can be represented by a network with two layers of units Every bounded continuous function can be approximated to arbitrarily accuracy by a two-layer network of sigmoid hidden units and linear output units Any function can be approximated to arbitrarily accuracy by a three layer network sigmoid hidden units and linear output units
37 READING SUGGESTIONS Mitchell, Machine Learning, Chapter 4 Russell and Norvig, AI a Modern Approach, Chapter 20
Unit 8: Introduction to neural networks. Perceptrons
Unit 8: Introduction to neural networks. Perceptrons D. Balbontín Noval F. J. Martín Mateos J. L. Ruiz Reina A. Riscos Núñez Departamento de Ciencias de la Computación e Inteligencia Artificial Universidad
More informationIntroduction to Machine Learning
Introduction to Machine Learning Neural Networks Varun Chandola x x 5 Input Outline Contents February 2, 207 Extending Perceptrons 2 Multi Layered Perceptrons 2 2. Generalizing to Multiple Labels.................
More informationLecture 4: Perceptrons and Multilayer Perceptrons
Lecture 4: Perceptrons and Multilayer Perceptrons Cognitive Systems II - Machine Learning SS 2005 Part I: Basic Approaches of Concept Learning Perceptrons, Artificial Neuronal Networks Lecture 4: Perceptrons
More informationMultilayer Neural Networks. (sometimes called Multilayer Perceptrons or MLPs)
Multilayer Neural Networks (sometimes called Multilayer Perceptrons or MLPs) Linear separability Hyperplane In 2D: w x + w 2 x 2 + w 0 = 0 Feature x 2 = w w 2 x w 0 w 2 Feature 2 A perceptron can separate
More informationCourse 395: Machine Learning - Lectures
Course 395: Machine Learning - Lectures Lecture 1-2: Concept Learning (M. Pantic) Lecture 3-4: Decision Trees & CBC Intro (M. Pantic & S. Petridis) Lecture 5-6: Evaluating Hypotheses (S. Petridis) Lecture
More informationCMSC 421: Neural Computation. Applications of Neural Networks
CMSC 42: Neural Computation definition synonyms neural networks artificial neural networks neural modeling connectionist models parallel distributed processing AI perspective Applications of Neural Networks
More informationNeural Networks biological neuron artificial neuron 1
Neural Networks biological neuron artificial neuron 1 A two-layer neural network Output layer (activation represents classification) Weighted connections Hidden layer ( internal representation ) Input
More informationNeural Networks. Bishop PRML Ch. 5. Alireza Ghane. Feed-forward Networks Network Training Error Backpropagation Applications
Neural Networks Bishop PRML Ch. 5 Alireza Ghane Neural Networks Alireza Ghane / Greg Mori 1 Neural Networks Neural networks arise from attempts to model human/animal brains Many models, many claims of
More informationFeed-forward Networks Network Training Error Backpropagation Applications. Neural Networks. Oliver Schulte - CMPT 726. Bishop PRML Ch.
Neural Networks Oliver Schulte - CMPT 726 Bishop PRML Ch. 5 Neural Networks Neural networks arise from attempts to model human/animal brains Many models, many claims of biological plausibility We will
More informationArtificial Neural Networks
Artificial Neural Networks Oliver Schulte - CMPT 310 Neural Networks Neural networks arise from attempts to model human/animal brains Many models, many claims of biological plausibility We will focus on
More informationMultilayer Neural Networks. (sometimes called Multilayer Perceptrons or MLPs)
Multilayer Neural Networks (sometimes called Multilayer Perceptrons or MLPs) Linear separability Hyperplane In 2D: w 1 x 1 + w 2 x 2 + w 0 = 0 Feature 1 x 2 = w 1 w 2 x 1 w 0 w 2 Feature 2 A perceptron
More informationArtificial Neural Networks
Artificial Neural Networks 鮑興國 Ph.D. National Taiwan University of Science and Technology Outline Perceptrons Gradient descent Multi-layer networks Backpropagation Hidden layer representations Examples
More informationInput layer. Weight matrix [ ] Output layer
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.034 Artificial Intelligence, Fall 2003 Recitation 10, November 4 th & 5 th 2003 Learning by perceptrons
More informationARTIFICIAL INTELLIGENCE. Artificial Neural Networks
INFOB2KI 2017-2018 Utrecht University The Netherlands ARTIFICIAL INTELLIGENCE Artificial Neural Networks Lecturer: Silja Renooij These slides are part of the INFOB2KI Course Notes available from www.cs.uu.nl/docs/vakken/b2ki/schema.html
More informationLab 5: 16 th April Exercises on Neural Networks
Lab 5: 16 th April 01 Exercises on Neural Networks 1. What are the values of weights w 0, w 1, and w for the perceptron whose decision surface is illustrated in the figure? Assume the surface crosses the
More informationSPSS, University of Texas at Arlington. Topics in Machine Learning-EE 5359 Neural Networks
Topics in Machine Learning-EE 5359 Neural Networks 1 The Perceptron Output: A perceptron is a function that maps D-dimensional vectors to real numbers. For notational convenience, we add a zero-th dimension
More informationArtificial Neural Networks
Artificial Neural Networks Threshold units Gradient descent Multilayer networks Backpropagation Hidden layer representations Example: Face Recognition Advanced topics 1 Connectionist Models Consider humans:
More informationNeural Networks. CSE 6363 Machine Learning Vassilis Athitsos Computer Science and Engineering Department University of Texas at Arlington
Neural Networks CSE 6363 Machine Learning Vassilis Athitsos Computer Science and Engineering Department University of Texas at Arlington 1 Perceptrons x 0 = 1 x 1 x 2 z = h w T x Output: z x D A perceptron
More information(Feed-Forward) Neural Networks Dr. Hajira Jabeen, Prof. Jens Lehmann
(Feed-Forward) Neural Networks 2016-12-06 Dr. Hajira Jabeen, Prof. Jens Lehmann Outline In the previous lectures we have learned about tensors and factorization methods. RESCAL is a bilinear model for
More informationArtificial Neural Networks. MGS Lecture 2
Artificial Neural Networks MGS 2018 - Lecture 2 OVERVIEW Biological Neural Networks Cell Topology: Input, Output, and Hidden Layers Functional description Cost functions Training ANNs Back-Propagation
More informationCSC321 Lecture 5: Multilayer Perceptrons
CSC321 Lecture 5: Multilayer Perceptrons Roger Grosse Roger Grosse CSC321 Lecture 5: Multilayer Perceptrons 1 / 21 Overview Recall the simple neuron-like unit: y output output bias i'th weight w 1 w2 w3
More informationMachine Learning. Neural Networks. (slides from Domingos, Pardo, others)
Machine Learning Neural Networks (slides from Domingos, Pardo, others) For this week, Reading Chapter 4: Neural Networks (Mitchell, 1997) See Canvas For subsequent weeks: Scaling Learning Algorithms toward
More informationARTIFICIAL NEURAL NETWORK PART I HANIEH BORHANAZAD
ARTIFICIAL NEURAL NETWORK PART I HANIEH BORHANAZAD WHAT IS A NEURAL NETWORK? The simplest definition of a neural network, more properly referred to as an 'artificial' neural network (ANN), is provided
More informationMachine Learning
Machine Learning 10-601 Maria Florina Balcan Machine Learning Department Carnegie Mellon University 02/10/2016 Today: Artificial neural networks Backpropagation Reading: Mitchell: Chapter 4 Bishop: Chapter
More informationCOMP-4360 Machine Learning Neural Networks
COMP-4360 Machine Learning Neural Networks Jacky Baltes Autonomous Agents Lab University of Manitoba Winnipeg, Canada R3T 2N2 Email: jacky@cs.umanitoba.ca WWW: http://www.cs.umanitoba.ca/~jacky http://aalab.cs.umanitoba.ca
More informationIntroduction To Artificial Neural Networks
Introduction To Artificial Neural Networks Machine Learning Supervised circle square circle square Unsupervised group these into two categories Supervised Machine Learning Supervised Machine Learning Supervised
More informationNeural Networks. Nicholas Ruozzi University of Texas at Dallas
Neural Networks Nicholas Ruozzi University of Texas at Dallas Handwritten Digit Recognition Given a collection of handwritten digits and their corresponding labels, we d like to be able to correctly classify
More informationAnswers Machine Learning Exercises 4
Answers Machine Learning Exercises 4 Tim van Erven November, 007 Exercises. The following Boolean functions take two Boolean features x and x as input. The features can take on the values and, where represents
More informationMultilayer Perceptron
Outline Hong Chang Institute of Computing Technology, Chinese Academy of Sciences Machine Learning Methods (Fall 2012) Outline Outline I 1 Introduction 2 Single Perceptron 3 Boolean Function Learning 4
More informationMachine Learning. Neural Networks
Machine Learning Neural Networks Bryan Pardo, Northwestern University, Machine Learning EECS 349 Fall 2007 Biological Analogy Bryan Pardo, Northwestern University, Machine Learning EECS 349 Fall 2007 THE
More informationMultilayer Perceptrons (MLPs)
CSE 5526: Introduction to Neural Networks Multilayer Perceptrons (MLPs) 1 Motivation Multilayer networks are more powerful than singlelayer nets Example: XOR problem x 2 1 AND x o x 1 x 2 +1-1 o x x 1-1
More informationWhat Do Neural Networks Do? MLP Lecture 3 Multi-layer networks 1
What Do Neural Networks Do? MLP Lecture 3 Multi-layer networks 1 Multi-layer networks Steve Renals Machine Learning Practical MLP Lecture 3 7 October 2015 MLP Lecture 3 Multi-layer networks 2 What Do Single
More informationNonlinear Classification
Nonlinear Classification INFO-4604, Applied Machine Learning University of Colorado Boulder October 5-10, 2017 Prof. Michael Paul Linear Classification Most classifiers we ve seen use linear functions
More informationNeural Networks (Part 1) Goals for the lecture
Neural Networks (Part ) Mark Craven and David Page Computer Sciences 760 Spring 208 www.biostat.wisc.edu/~craven/cs760/ Some of the slides in these lectures have been adapted/borrowed from materials developed
More informationLinear discriminant functions
Andrea Passerini passerini@disi.unitn.it Machine Learning Discriminative learning Discriminative vs generative Generative learning assumes knowledge of the distribution governing the data Discriminative
More informationLast update: October 26, Neural networks. CMSC 421: Section Dana Nau
Last update: October 26, 207 Neural networks CMSC 42: Section 8.7 Dana Nau Outline Applications of neural networks Brains Neural network units Perceptrons Multilayer perceptrons 2 Example Applications
More informationArtificial Intelligence
Artificial Intelligence Jeff Clune Assistant Professor Evolving Artificial Intelligence Laboratory Announcements Be making progress on your projects! Three Types of Learning Unsupervised Supervised Reinforcement
More informationArtificial Neural Networks Examination, June 2004
Artificial Neural Networks Examination, June 2004 Instructions There are SIXTY questions (worth up to 60 marks). The exam mark (maximum 60) will be added to the mark obtained in the laborations (maximum
More information100 inference steps doesn't seem like enough. Many neuron-like threshold switching units. Many weighted interconnections among units
Connectionist Models Consider humans: Neuron switching time ~ :001 second Number of neurons ~ 10 10 Connections per neuron ~ 10 4 5 Scene recognition time ~ :1 second 100 inference steps doesn't seem like
More informationMultilayer Neural Networks
Multilayer Neural Networks Multilayer Neural Networks Discriminant function flexibility NON-Linear But with sets of linear parameters at each layer Provably general function approximators for sufficient
More informationMultilayer Neural Networks
Multilayer Neural Networks Introduction Goal: Classify objects by learning nonlinearity There are many problems for which linear discriminants are insufficient for minimum error In previous methods, the
More informationAI Programming CS F-20 Neural Networks
AI Programming CS662-2008F-20 Neural Networks David Galles Department of Computer Science University of San Francisco 20-0: Symbolic AI Most of this class has been focused on Symbolic AI Focus or symbols
More informationy(x n, w) t n 2. (1)
Network training: Training a neural network involves determining the weight parameter vector w that minimizes a cost function. Given a training set comprising a set of input vector {x n }, n = 1,...N,
More informationNeural networks. Chapter 19, Sections 1 5 1
Neural networks Chapter 19, Sections 1 5 Chapter 19, Sections 1 5 1 Outline Brains Neural networks Perceptrons Multilayer perceptrons Applications of neural networks Chapter 19, Sections 1 5 2 Brains 10
More informationMachine Learning. Neural Networks. Le Song. CSE6740/CS7641/ISYE6740, Fall Lecture 7, September 11, 2012 Based on slides from Eric Xing, CMU
Machine Learning CSE6740/CS7641/ISYE6740, Fall 2012 Neural Networks Le Song Lecture 7, September 11, 2012 Based on slides from Eric Xing, CMU Reading: Chap. 5 CB Learning highly non-linear functions f:
More informationNeural networks. Chapter 20. Chapter 20 1
Neural networks Chapter 20 Chapter 20 1 Outline Brains Neural networks Perceptrons Multilayer networks Applications of neural networks Chapter 20 2 Brains 10 11 neurons of > 20 types, 10 14 synapses, 1ms
More informationCSE 190 Fall 2015 Midterm DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO START!!!!
CSE 190 Fall 2015 Midterm DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO START!!!! November 18, 2015 THE EXAM IS CLOSED BOOK. Once the exam has started, SORRY, NO TALKING!!! No, you can t even say see ya
More informationChapter 2 Single Layer Feedforward Networks
Chapter 2 Single Layer Feedforward Networks By Rosenblatt (1962) Perceptrons For modeling visual perception (retina) A feedforward network of three layers of units: Sensory, Association, and Response Learning
More informationMachine Learning. Neural Networks. (slides from Domingos, Pardo, others)
Machine Learning Neural Networks (slides from Domingos, Pardo, others) For this week, Reading Chapter 4: Neural Networks (Mitchell, 1997) See Canvas For subsequent weeks: Scaling Learning Algorithms toward
More informationMachine Learning (CSE 446): Neural Networks
Machine Learning (CSE 446): Neural Networks Noah Smith c 2017 University of Washington nasmith@cs.washington.edu November 6, 2017 1 / 22 Admin No Wednesday office hours for Noah; no lecture Friday. 2 /
More informationCSC321 Lecture 4 The Perceptron Algorithm
CSC321 Lecture 4 The Perceptron Algorithm Roger Grosse and Nitish Srivastava January 17, 2017 Roger Grosse and Nitish Srivastava CSC321 Lecture 4 The Perceptron Algorithm January 17, 2017 1 / 1 Recap:
More informationArtificial Neural Networks" and Nonparametric Methods" CMPSCI 383 Nov 17, 2011!
Artificial Neural Networks" and Nonparametric Methods" CMPSCI 383 Nov 17, 2011! 1 Todayʼs lecture" How the brain works (!)! Artificial neural networks! Perceptrons! Multilayer feed-forward networks! Error
More informationEngineering Part IIB: Module 4F10 Statistical Pattern Processing Lecture 5: Single Layer Perceptrons & Estimating Linear Classifiers
Engineering Part IIB: Module 4F0 Statistical Pattern Processing Lecture 5: Single Layer Perceptrons & Estimating Linear Classifiers Phil Woodland: pcw@eng.cam.ac.uk Michaelmas 202 Engineering Part IIB:
More informationMachine Learning and Data Mining. Multi-layer Perceptrons & Neural Networks: Basics. Prof. Alexander Ihler
+ Machine Learning and Data Mining Multi-layer Perceptrons & Neural Networks: Basics Prof. Alexander Ihler Linear Classifiers (Perceptrons) Linear Classifiers a linear classifier is a mapping which partitions
More information2015 Todd Neller. A.I.M.A. text figures 1995 Prentice Hall. Used by permission. Neural Networks. Todd W. Neller
2015 Todd Neller. A.I.M.A. text figures 1995 Prentice Hall. Used by permission. Neural Networks Todd W. Neller Machine Learning Learning is such an important part of what we consider "intelligence" that
More informationData Mining Part 5. Prediction
Data Mining Part 5. Prediction 5.5. Spring 2010 Instructor: Dr. Masoud Yaghini Outline How the Brain Works Artificial Neural Networks Simple Computing Elements Feed-Forward Networks Perceptrons (Single-layer,
More informationLecture 10. Neural networks and optimization. Machine Learning and Data Mining November Nando de Freitas UBC. Nonlinear Supervised Learning
Lecture 0 Neural networks and optimization Machine Learning and Data Mining November 2009 UBC Gradient Searching for a good solution can be interpreted as looking for a minimum of some error (loss) function
More informationMidterm: CS 6375 Spring 2015 Solutions
Midterm: CS 6375 Spring 2015 Solutions The exam is closed book. You are allowed a one-page cheat sheet. Answer the questions in the spaces provided on the question sheets. If you run out of room for an
More informationModule 12. Machine Learning. Version 2 CSE IIT, Kharagpur
Module 12 Machine Learning Lesson 39 Neural Networks - III 12.4.4 Multi-Layer Perceptrons In contrast to perceptrons, multilayer networks can learn not only multiple decision boundaries, but the boundaries
More informationRevision: Neural Network
Revision: Neural Network Exercise 1 Tell whether each of the following statements is true or false by checking the appropriate box. Statement True False a) A perceptron is guaranteed to perfectly learn
More information) (d o f. For the previous layer in a neural network (just the rightmost layer if a single neuron), the required update equation is: 2.
1 Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.034 Artificial Intelligence, Fall 2011 Recitation 8, November 3 Corrected Version & (most) solutions
More informationNeural Networks and the Back-propagation Algorithm
Neural Networks and the Back-propagation Algorithm Francisco S. Melo In these notes, we provide a brief overview of the main concepts concerning neural networks and the back-propagation algorithm. We closely
More informationCOMP 551 Applied Machine Learning Lecture 14: Neural Networks
COMP 551 Applied Machine Learning Lecture 14: Neural Networks Instructor: Ryan Lowe (ryan.lowe@mail.mcgill.ca) Slides mostly by: Class web page: www.cs.mcgill.ca/~hvanho2/comp551 Unless otherwise noted,
More informationFeedforward Neural Nets and Backpropagation
Feedforward Neural Nets and Backpropagation Julie Nutini University of British Columbia MLRG September 28 th, 2016 1 / 23 Supervised Learning Roadmap Supervised Learning: Assume that we are given the features
More informationIntroduction to feedforward neural networks
. Problem statement and historical context A. Learning framework Figure below illustrates the basic framework that we will see in artificial neural network learning. We assume that we want to learn a classification
More informationMachine Learning
Machine Learning 10-315 Maria Florina Balcan Machine Learning Department Carnegie Mellon University 03/29/2019 Today: Artificial neural networks Backpropagation Reading: Mitchell: Chapter 4 Bishop: Chapter
More informationLecture 6. Notes on Linear Algebra. Perceptron
Lecture 6. Notes on Linear Algebra. Perceptron COMP90051 Statistical Machine Learning Semester 2, 2017 Lecturer: Andrey Kan Copyright: University of Melbourne This lecture Notes on linear algebra Vectors
More informationMultilayer Perceptron
Aprendizagem Automática Multilayer Perceptron Ludwig Krippahl Aprendizagem Automática Summary Perceptron and linear discrimination Multilayer Perceptron, nonlinear discrimination Backpropagation and training
More informationCSC321 Lecture 4: Learning a Classifier
CSC321 Lecture 4: Learning a Classifier Roger Grosse Roger Grosse CSC321 Lecture 4: Learning a Classifier 1 / 28 Overview Last time: binary classification, perceptron algorithm Limitations of the perceptron
More informationNeural Networks: Introduction
Neural Networks: Introduction Machine Learning Fall 2017 Based on slides and material from Geoffrey Hinton, Richard Socher, Dan Roth, Yoav Goldberg, Shai Shalev-Shwartz and Shai Ben-David, and others 1
More informationNeural Networks, Computation Graphs. CMSC 470 Marine Carpuat
Neural Networks, Computation Graphs CMSC 470 Marine Carpuat Binary Classification with a Multi-layer Perceptron φ A = 1 φ site = 1 φ located = 1 φ Maizuru = 1 φ, = 2 φ in = 1 φ Kyoto = 1 φ priest = 0 φ
More informationSimple Neural Nets For Pattern Classification
CHAPTER 2 Simple Neural Nets For Pattern Classification Neural Networks General Discussion One of the simplest tasks that neural nets can be trained to perform is pattern classification. In pattern classification
More informationNeed for Deep Networks Perceptron. Can only model linear functions. Kernel Machines. Non-linearity provided by kernels
Need for Deep Networks Perceptron Can only model linear functions Kernel Machines Non-linearity provided by kernels Need to design appropriate kernels (possibly selecting from a set, i.e. kernel learning)
More informationArtificial Neural Networks. Q550: Models in Cognitive Science Lecture 5
Artificial Neural Networks Q550: Models in Cognitive Science Lecture 5 "Intelligence is 10 million rules." --Doug Lenat The human brain has about 100 billion neurons. With an estimated average of one thousand
More informationIntroduction to Artificial Neural Networks
Facultés Universitaires Notre-Dame de la Paix 27 March 2007 Outline 1 Introduction 2 Fundamentals Biological neuron Artificial neuron Artificial Neural Network Outline 3 Single-layer ANN Perceptron Adaline
More informationThe Perceptron. Volker Tresp Summer 2016
The Perceptron Volker Tresp Summer 2016 1 Elements in Learning Tasks Collection, cleaning and preprocessing of training data Definition of a class of learning models. Often defined by the free model parameters
More informationLogistic Regression & Neural Networks
Logistic Regression & Neural Networks CMSC 723 / LING 723 / INST 725 Marine Carpuat Slides credit: Graham Neubig, Jacob Eisenstein Logistic Regression Perceptron & Probabilities What if we want a probability
More informationArtifical Neural Networks
Neural Networks Artifical Neural Networks Neural Networks Biological Neural Networks.................................. Artificial Neural Networks................................... 3 ANN Structure...........................................
More information17 Neural Networks NEURAL NETWORKS. x XOR 1. x Jonathan Richard Shewchuk
94 Jonathan Richard Shewchuk 7 Neural Networks NEURAL NETWORKS Can do both classification & regression. [They tie together several ideas from the course: perceptrons, logistic regression, ensembles of
More informationNONLINEAR CLASSIFICATION AND REGRESSION. J. Elder CSE 4404/5327 Introduction to Machine Learning and Pattern Recognition
NONLINEAR CLASSIFICATION AND REGRESSION Nonlinear Classification and Regression: Outline 2 Multi-Layer Perceptrons The Back-Propagation Learning Algorithm Generalized Linear Models Radial Basis Function
More informationML4NLP Multiclass Classification
ML4NLP Multiclass Classification CS 590NLP Dan Goldwasser Purdue University dgoldwas@purdue.edu Social NLP Last week we discussed the speed-dates paper. Interesting perspective on NLP problems- Can we
More informationLearning and Neural Networks
Artificial Intelligence Learning and Neural Networks Readings: Chapter 19 & 20.5 of Russell & Norvig Example: A Feed-forward Network w 13 I 1 H 3 w 35 w 14 O 5 I 2 w 23 w 24 H 4 w 45 a 5 = g 5 (W 3,5 a
More informationIntroduction to Natural Computation. Lecture 9. Multilayer Perceptrons and Backpropagation. Peter Lewis
Introduction to Natural Computation Lecture 9 Multilayer Perceptrons and Backpropagation Peter Lewis 1 / 25 Overview of the Lecture Why multilayer perceptrons? Some applications of multilayer perceptrons.
More informationSingle layer NN. Neuron Model
Single layer NN We consider the simple architecture consisting of just one neuron. Generalization to a single layer with more neurons as illustrated below is easy because: M M The output units are independent
More informationArtificial Neural Networks Examination, June 2005
Artificial Neural Networks Examination, June 2005 Instructions There are SIXTY questions. (The pass mark is 30 out of 60). For each question, please select a maximum of ONE of the given answers (either
More informationLecture 5: Logistic Regression. Neural Networks
Lecture 5: Logistic Regression. Neural Networks Logistic regression Comparison with generative models Feed-forward neural networks Backpropagation Tricks for training neural networks COMP-652, Lecture
More informationSections 18.6 and 18.7 Artificial Neural Networks
Sections 18.6 and 18.7 Artificial Neural Networks CS4811 - Artificial Intelligence Nilufer Onder Department of Computer Science Michigan Technological University Outline The brain vs artifical neural networks
More informationMachine Learning. Neural Networks. (slides from Domingos, Pardo, others)
Machine Learning Neural Networks (slides from Domingos, Pardo, others) Human Brain Neurons Input-Output Transformation Input Spikes Output Spike Spike (= a brief pulse) (Excitatory Post-Synaptic Potential)
More informationNeural Networks. Chapter 18, Section 7. TB Artificial Intelligence. Slides from AIMA 1/ 21
Neural Networks Chapter 8, Section 7 TB Artificial Intelligence Slides from AIMA http://aima.cs.berkeley.edu / 2 Outline Brains Neural networks Perceptrons Multilayer perceptrons Applications of neural
More informationMachine Learning and Data Mining. Linear classification. Kalev Kask
Machine Learning and Data Mining Linear classification Kalev Kask Supervised learning Notation Features x Targets y Predictions ŷ = f(x ; q) Parameters q Program ( Learner ) Learning algorithm Change q
More informationCS:4420 Artificial Intelligence
CS:4420 Artificial Intelligence Spring 2018 Neural Networks Cesare Tinelli The University of Iowa Copyright 2004 18, Cesare Tinelli and Stuart Russell a a These notes were originally developed by Stuart
More informationIn the Name of God. Lecture 11: Single Layer Perceptrons
1 In the Name of God Lecture 11: Single Layer Perceptrons Perceptron: architecture We consider the architecture: feed-forward NN with one layer It is sufficient to study single layer perceptrons with just
More informationNeural Networks Lecture 4: Radial Bases Function Networks
Neural Networks Lecture 4: Radial Bases Function Networks H.A Talebi Farzaneh Abdollahi Department of Electrical Engineering Amirkabir University of Technology Winter 2011. A. Talebi, Farzaneh Abdollahi
More informationCSC321 Lecture 4: Learning a Classifier
CSC321 Lecture 4: Learning a Classifier Roger Grosse Roger Grosse CSC321 Lecture 4: Learning a Classifier 1 / 31 Overview Last time: binary classification, perceptron algorithm Limitations of the perceptron
More informationNumerical Learning Algorithms
Numerical Learning Algorithms Example SVM for Separable Examples.......................... Example SVM for Nonseparable Examples....................... 4 Example Gaussian Kernel SVM...............................
More informationNeural Networks. Intro to AI Bert Huang Virginia Tech
Neural Networks Intro to AI Bert Huang Virginia Tech Outline Biological inspiration for artificial neural networks Linear vs. nonlinear functions Learning with neural networks: back propagation https://en.wikipedia.org/wiki/neuron#/media/file:chemical_synapse_schema_cropped.jpg
More informationSections 18.6 and 18.7 Artificial Neural Networks
Sections 18.6 and 18.7 Artificial Neural Networks CS4811 - Artificial Intelligence Nilufer Onder Department of Computer Science Michigan Technological University Outline The brain vs. artifical neural
More informationCSC 411 Lecture 10: Neural Networks
CSC 411 Lecture 10: Neural Networks Roger Grosse, Amir-massoud Farahmand, and Juan Carrasquilla University of Toronto UofT CSC 411: 10-Neural Networks 1 / 35 Inspiration: The Brain Our brain has 10 11
More informationMIDTERM: CS 6375 INSTRUCTOR: VIBHAV GOGATE October,
MIDTERM: CS 6375 INSTRUCTOR: VIBHAV GOGATE October, 23 2013 The exam is closed book. You are allowed a one-page cheat sheet. Answer the questions in the spaces provided on the question sheets. If you run
More informationSections 18.6 and 18.7 Analysis of Artificial Neural Networks
Sections 18.6 and 18.7 Analysis of Artificial Neural Networks CS4811 - Artificial Intelligence Nilufer Onder Department of Computer Science Michigan Technological University Outline Univariate regression
More information