CPS331 Lecture: Resemblance-Based Learning last revised November 8, 2018
|
|
|
- Dayna Evans
- 5 years ago
- Views:
Transcription
1 CPS331 Lecture: Resemblance-Based Learning last revised November 8, 2018 Objectives: 1. To introduce support vector machines 2. To introduce the notion of linear separability 3. To introduce the "kernel trick" Materials: 1. Story from p. 177 of Domingos to read 2. Projectable of Komondor dog 3. Projectable of example data points 4. Projectable of the above with multiple separators 5. Projectable of the above showing notion of margin I. Introduction A.Pedro Domingos begins his chapter on resemblance-based learning with the following story READ Story from p. 177 B. The story I just read suggested a general problem-solving strategy: from the set of descriptions of problems solved in the past, find the one that most-closely resembles the problem being solved, and use or adapt the solution for that piece of data. C. This is a strategy that we use in everyday life. Consider the following picture: PROJECT picture of Komondor 1. What kind of animal is this? 1
2 ASK It's a Komondor - an unusual-looking dog. 2. I assume none of you knows how to recognize a Komondor. How did you recognize it as a dog? ASK 3. Presumably you recognized this as a dog because it is more similar to other dogs you have seen that it is to other creatures like cats or squirrels or... D.Resemblance-based reasoning is used in lots of places. Examples: 1. Law 2. Medical diagnosis 3. Auto mechanics fixing a car E. As a learning strategy, we use a set of training data representing previously-solved / classified problems, and learn an efficient way of identifying the one(s) that serve as precedents. II.Support-Vector Machines A.One class of approaches that is widely used for supervised learnng is called support-vector machines (or SVM's). In fact, there are "off-theshelf" SVM packages that can be applied to a given data set without the user having to understand the underlying mathematics. 2
3 B. In its basic form, an SVM is used for two-way classification i.e. a given instance belongs to one or the other of two classes. Often, this takes the form of a decision problem - i.e. for any given description, decide whether or not it belongs to a particular category (a yes-no, boolean result). An SVM finds a function that has the following behavior: Description of instance Fits Classification Learned Mapping Where the description of the instance is in the form of what is called a feature vector. C. SVM's learn what is called a "maximum margin" mapping. To see what that is, consider the following: Suppose our training data consists of entities described by a feature vector with two values. Suppose, if we were to plot all the data on a single graph, we would get the following, where the x's represent data points for one classification and the o's data points for the other classification. o oo o o o oo au o o ooooo oo o x x o oooo o o ooooo o o o xx x ooooooo o oo oooooo x xxxx x ooo oooo oooo oooooo ooooo xxx x x oo o oooooo oo ooo oo x xxxx xxx ooo oooo oooooooooooo x xxxx x xxxxx xx PROJECT 1. This data is linearly-separable - i.e. it is possible to draw a single line that separates the two categories. (If the feature vector has more than two elements - as is generally the case - we would have a multi-dimension graph and the separator would be a hyper-plane.) 3
4 2. In fact, though, in a case like this there are multiple possibilities for the separator: o oo o o o oo au o o ooooo o o x x o oooo o o ooooo o o o? xx x ooooooo o oo oooooo x xxxx x ooo oooo oooo oooooo ooooo xxx x x oo o oooooo oo ooo oo x xxxx xxx ooo oooo oooooooooooo x xxxx x xxxxx xx PROJECT 3. We call the descriptions of the data points that are nearest the separator line (the underlined ones) the support vectors. The mapping ultimately discovered will depend only on these - they support the mapping. 4. Which separator is the most desirable? a) In two cases, the separator is so close to some of the data points that a new data point that belongs to one of the categories might be misclassified (e.g. the point labeled?, which probably should be classified as an o but will be classified instead as an x if the leftmost separator is used. b) The most desirable separator is the middle one. We call this the maximum-margin separator, because it has the largest margins between it and the actual data points - shown below as the spaces between the separator and the dashed lines. o oo o o o oo au o o ooooo oo o x x o oooo o o ooooo o o o xx x ooooooo o oo oooooo x xxxx x ooo oooo oooo oooooo ooooo xxx x x oo o oooooo oo ooo oo x xxxx xxx ooo oooo oooooooooooo x xxxx x xxxxx xx PROJECT 4
5 5. An SVM can also be learned with data that is not linearly separable. Consider the following two-dimensional data: y x Where the +'s are at (0, 1) and (1, 0), and the -'s are at (0, 0) and (1,1) (Hopefully, you recognize that this is essentially the exclusive or function: something is classified as a "+" if x xor y is 1. ) 6. Clearly, there is no way to draw a single line that separates the +'s and -'s. (This corresponds to the xor-problem we looked at with neural networks) 7. Suppose we replace the original variables with two new variables calculated from the original ones: w = (x-y) 2 z = xy. Then we could graph the points in terms of these new variables as follows 1 ++ (double point) w z Clearly, this function is linearly separable. 5
6 8. Such a way of replacing variables (and perhaps adding additional ones) is called the kernel trick. a) It can be done ahead of time as a preprocessing step if it is known that the function is not linearly separable; there are several well-known transformations that can be used in cases like this. b) It can be used by SVM's to convert non-linearly separable ones into the equivalent of linearly separable ones. 6
Lecture 3: Linear Classification
Lecture 3: Linear Classification Roger Grosse 1 Introduction Last week, we saw an example of a learning task called regression. There, the goal was to predict a scalar-valued target from a set of features.
Chakra Chennubhotla and David Koes
MSCBIO/CMPBIO 2065: Support Vector Machines Chakra Chennubhotla and David Koes Nov 15, 2017 Sources mmds.org chapter 12 Bishop s book Ch. 7 Notes from Toronto, Mark Schmidt (UBC) 2 SVM SVMs and Logistic
Lecture #11: The Perceptron
Lecture #11: The Perceptron Mat Kallada STAT2450 - Introduction to Data Mining Outline for Today Welcome back! Assignment 3 The Perceptron Learning Method Perceptron Learning Rule Assignment 3 Will be
1-Nearest Neighbor Boundary
Linear Models Bankruptcy example R is the ratio of earnings to expenses L is the number of late payments on credit cards over the past year. We would like here to draw a linear separator, and get so a
Robot Learning. There are generally three types of robot learning: Learning from data. Learning by demonstration. Reinforcement learning
Robot Learning 1 General Pipeline 1. Data acquisition (e.g., from 3D sensors) 2. Feature extraction and representation construction 3. Robot learning: e.g., classification (recognition) or clustering (knowledge
Support Vector Machines
Support Vector Machines RBF-networks Support Vector Machines Good Decision Boundary Optimization Problem Soft margin Hyperplane Non-linear Decision Boundary Kernel-Trick Approximation Accurancy Overtraining
Applying Supervised Learning
Applying Supervised Learning When to Consider Supervised Learning A supervised learning algorithm takes a known set of input data (the training set) and known responses to the data (output), and trains
Supervised vs. Unsupervised Learning. Supervised vs. Unsupervised Learning. Supervised vs. Unsupervised Learning. Supervised vs. Unsupervised Learning
Overview T7 - SVM and s Christian Vögeli cvoegeli@inf.ethz.ch Supervised/ s Support Vector Machines Kernels Based on slides by P. Orbanz & J. Keuchel Task: Apply some machine learning method to data from
5 Learning hypothesis classes (16 points)
5 Learning hypothesis classes (16 points) Consider a classification problem with two real valued inputs. For each of the following algorithms, specify all of the separators below that it could have generated
Kernels + K-Means Introduction to Machine Learning. Matt Gormley Lecture 29 April 25, 2018
10-601 Introduction to Machine Learning Machine Learning Department School of Computer Science Carnegie Mellon University Kernels + K-Means Matt Gormley Lecture 29 April 25, 2018 1 Reminders Homework 8:
Machine Learning for NLP
Machine Learning for NLP Support Vector Machines Aurélie Herbelot 2018 Centre for Mind/Brain Sciences University of Trento 1 Support Vector Machines: introduction 2 Support Vector Machines (SVMs) SVMs
LECTURE 5: DUAL PROBLEMS AND KERNELS. * Most of the slides in this lecture are from
LECTURE 5: DUAL PROBLEMS AND KERNELS * Most of the slides in this lecture are from http://www.robots.ox.ac.uk/~az/lectures/ml Optimization Loss function Loss functions SVM review PRIMAL-DUAL PROBLEM Max-min
Support Vector Machines
Support Vector Machines RBF-networks Support Vector Machines Good Decision Boundary Optimization Problem Soft margin Hyperplane Non-linear Decision Boundary Kernel-Trick Approximation Accurancy Overtraining
Practice EXAM: SPRING 2012 CS 6375 INSTRUCTOR: VIBHAV GOGATE
Practice EXAM: SPRING 0 CS 6375 INSTRUCTOR: VIBHAV GOGATE The exam is closed book. You are allowed four pages of double sided cheat sheets. Answer the questions in the spaces provided on the question sheets.
3 Perceptron Learning; Maximum Margin Classifiers
Perceptron Learning; Maximum Margin lassifiers Perceptron Learning; Maximum Margin lassifiers Perceptron Algorithm (cont d) Recall: linear decision fn f (x) = w x (for simplicity, no ) decision boundary
ECG782: Multidimensional Digital Signal Processing
ECG782: Multidimensional Digital Signal Processing Object Recognition http://www.ee.unlv.edu/~b1morris/ecg782/ 2 Outline Knowledge Representation Statistical Pattern Recognition Neural Networks Boosting
Lecture 9. Support Vector Machines
Lecture 9. Support Vector Machines COMP90051 Statistical Machine Learning Semester 2, 2017 Lecturer: Andrey Kan Copyright: University of Melbourne This lecture Support vector machines (SVMs) as maximum
Support Vector Machines
Support Vector Machines . Importance of SVM SVM is a discriminative method that brings together:. computational learning theory. previously known methods in linear discriminant functions 3. optimization
Data mining with Support Vector Machine
Data mining with Support Vector Machine Ms. Arti Patle IES, IPS Academy Indore (M.P.) artipatle@gmail.com Mr. Deepak Singh Chouhan IES, IPS Academy Indore (M.P.) deepak.schouhan@yahoo.com Abstract: Machine
.. Spring 2017 CSC 566 Advanced Data Mining Alexander Dekhtyar..
.. Spring 2017 CSC 566 Advanced Data Mining Alexander Dekhtyar.. Machine Learning: Support Vector Machines: Linear Kernel Support Vector Machines Extending Perceptron Classifiers. There are two ways to
Introduction to Support Vector Machines
Introduction to Support Vector Machines CS 536: Machine Learning Littman (Wu, TA) Administration Slides borrowed from Martin Law (from the web). 1 Outline History of support vector machines (SVM) Two classes,
More on Classification: Support Vector Machine
More on Classification: Support Vector Machine The Support Vector Machine (SVM) is a classification method approach developed in the computer science field in the 1990s. It has shown good performance in
Support Vector Machines
Support Vector Machines Michael Tagare De Guzman May 19, 2012 Support Vector Machines Linear Learning Machines and The Maximal Margin Classifier In Supervised Learning, a learning machine is given a training
Support vector machines. Dominik Wisniewski Wojciech Wawrzyniak
Support vector machines Dominik Wisniewski Wojciech Wawrzyniak Outline 1. A brief history of SVM. 2. What is SVM and how does it work? 3. How would you classify this data? 4. Are all the separating lines
CIS192 Python Programming
CIS192 Python Programming Machine Learning in Python Robert Rand University of Pennsylvania October 22, 2015 Robert Rand (University of Pennsylvania) CIS 192 October 22, 2015 1 / 18 Outline 1 Machine Learning
Naïve Bayes for text classification
Road Map Basic concepts Decision tree induction Evaluation of classifiers Rule induction Classification using association rules Naïve Bayesian classification Naïve Bayes for text classification Support
The Boundary Graph Supervised Learning Algorithm for Regression and Classification
The Boundary Graph Supervised Learning Algorithm for Regression and Classification! Jonathan Yedidia! Disney Research!! Outline Motivation Illustration using a toy classification problem Some simple refinements
CPS222 Lecture: Sets. 1. Projectable of random maze creation example 2. Handout of union/find code from program that does this
CPS222 Lecture: Sets Objectives: last revised April 16, 2015 1. To introduce representations for sets that can be used for various problems a. Array or list of members b. Map-based representation c. Bit
ABSTRACT INTRODUCTION
Raster-Vector Conversion Methods for Automated Cartography With Applications in Polygon Maps and Feature Analysis Shin-yi Hsu Xingyuan Huang Department of Geography Department of Geography SUNY-Binghamton
CS6375: Machine Learning Gautam Kunapuli. Mid-Term Review
Gautam Kunapuli Machine Learning Data is identically and independently distributed Goal is to learn a function that maps to Data is generated using an unknown function Learn a hypothesis that minimizes
Hsiaochun Hsu Date: 12/12/15. Support Vector Machine With Data Reduction
Support Vector Machine With Data Reduction 1 Table of Contents Summary... 3 1. Introduction of Support Vector Machines... 3 1.1 Brief Introduction of Support Vector Machines... 3 1.2 SVM Simple Experiment...
SUPPORT VECTOR MACHINES
SUPPORT VECTOR MACHINES Today Reading AIMA 8.9 (SVMs) Goals Finish Backpropagation Support vector machines Backpropagation. Begin with randomly initialized weights 2. Apply the neural network to each training
Week 3: Perceptron and Multi-layer Perceptron
Week 3: Perceptron and Multi-layer Perceptron Phong Le, Willem Zuidema November 12, 2013 Last week we studied two famous biological neuron models, Fitzhugh-Nagumo model and Izhikevich model. This week,
Supervised Learning (contd) Linear Separation. Mausam (based on slides by UW-AI faculty)
Supervised Learning (contd) Linear Separation Mausam (based on slides by UW-AI faculty) Images as Vectors Binary handwritten characters Treat an image as a highdimensional vector (e.g., by reading pixel
Data Mining: Concepts and Techniques. Chapter 9 Classification: Support Vector Machines. Support Vector Machines (SVMs)
Data Mining: Concepts and Techniques Chapter 9 Classification: Support Vector Machines 1 Support Vector Machines (SVMs) SVMs are a set of related supervised learning methods used for classification Based
( ) =cov X Y = W PRINCIPAL COMPONENT ANALYSIS. Eigenvectors of the covariance matrix are the principal components
Review Lecture 14 ! PRINCIPAL COMPONENT ANALYSIS Eigenvectors of the covariance matrix are the principal components 1. =cov X Top K principal components are the eigenvectors with K largest eigenvalues
Neural Networks. Single-layer neural network. CSE 446: Machine Learning Emily Fox University of Washington March 10, /10/2017
3/0/207 Neural Networks Emily Fox University of Washington March 0, 207 Slides adapted from Ali Farhadi (via Carlos Guestrin and Luke Zettlemoyer) Single-layer neural network 3/0/207 Perceptron as a neural
Infographics and Visualisation (or: Beyond the Pie Chart) LSS: ITNPBD4, 1 November 2016
Infographics and Visualisation (or: Beyond the Pie Chart) LSS: ITNPBD4, 1 November 2016 Overview Overview (short: we covered most of this in the tutorial) Why infographics and visualisation What s the
Support Vector Machines
Support Vector Machines SVM Discussion Overview. Importance of SVMs. Overview of Mathematical Techniques Employed 3. Margin Geometry 4. SVM Training Methodology 5. Overlapping Distributions 6. Dealing
Machine Learning in Biology
Università degli studi di Padova Machine Learning in Biology Luca Silvestrin (Dottorando, XXIII ciclo) Supervised learning Contents Class-conditional probability density Linear and quadratic discriminant
Fall 09, Homework 5
5-38 Fall 09, Homework 5 Due: Wednesday, November 8th, beginning of the class You can work in a group of up to two people. This group does not need to be the same group as for the other homeworks. You
Classification by Support Vector Machines
Classification by Support Vector Machines Florian Markowetz Max-Planck-Institute for Molecular Genetics Computational Molecular Biology Berlin Practical DNA Microarray Analysis 2003 1 Overview I II III
PARALLEL CLASSIFICATION ALGORITHMS
PARALLEL CLASSIFICATION ALGORITHMS By: Faiz Quraishi Riti Sharma 9 th May, 2013 OVERVIEW Introduction Types of Classification Linear Classification Support Vector Machines Parallel SVM Approach Decision
Neural Networks. CE-725: Statistical Pattern Recognition Sharif University of Technology Spring Soleymani
Neural Networks CE-725: Statistical Pattern Recognition Sharif University of Technology Spring 2013 Soleymani Outline Biological and artificial neural networks Feed-forward neural networks Single layer
Support Vector Machines.
Support Vector Machines srihari@buffalo.edu SVM Discussion Overview. Importance of SVMs. Overview of Mathematical Techniques Employed 3. Margin Geometry 4. SVM Training Methodology 5. Overlapping Distributions
PV211: Introduction to Information Retrieval
PV211: Introduction to Information Retrieval http://www.fi.muni.cz/~sojka/pv211 IIR 15-1: Support Vector Machines Handout version Petr Sojka, Hinrich Schütze et al. Faculty of Informatics, Masaryk University,
Classification by Support Vector Machines
Classification by Support Vector Machines Florian Markowetz Max-Planck-Institute for Molecular Genetics Computational Molecular Biology Berlin Practical DNA Microarray Analysis 2003 1 Overview I II III
12 Classification using Support Vector Machines
160 Bioinformatics I, WS 14/15, D. Huson, January 28, 2015 12 Classification using Support Vector Machines This lecture is based on the following sources, which are all recommended reading: F. Markowetz.
All lecture slides will be available at CSC2515_Winter15.html
CSC2515 Fall 2015 Introduc3on to Machine Learning Lecture 9: Support Vector Machines All lecture slides will be available at http://www.cs.toronto.edu/~urtasun/courses/csc2515/ CSC2515_Winter15.html Many
Large-Scale Machine Learning
Chapter 12 Large-Scale Machine Learning Many algorithms are today classified as machine learning. These algorithms share the goal of extracting information from data with the other algorithms studied in
Support Vector Machines.
Support Vector Machines srihari@buffalo.edu SVM Discussion Overview 1. Overview of SVMs 2. Margin Geometry 3. SVM Optimization 4. Overlapping Distributions 5. Relationship to Logistic Regression 6. Dealing
Lecture Linear Support Vector Machines
Lecture 8 In this lecture we return to the task of classification. As seen earlier, examples include spam filters, letter recognition, or text classification. In this lecture we introduce a popular method
CS 8520: Artificial Intelligence
CS 8520: Artificial Intelligence Machine Learning 2 Paula Matuszek Spring, 2013 1 Regression Classifiers We said earlier that the task of a supervised learning system can be viewed as learning a function
Cluster Analysis, Multidimensional Scaling and Graph Theory. Cluster Analysis, Multidimensional Scaling and Graph Theory
Cluster Analysis, Multidimensional Scaling and Graph Theory Dpto. de Estadística, E.E. y O.E.I. Universidad de Alcalá luisf.rivera@uah.es 1 Outline The problem of statistical classification Cluster analysis
More Learning. Ensembles Bayes Rule Neural Nets K-means Clustering EM Clustering WEKA
More Learning Ensembles Bayes Rule Neural Nets K-means Clustering EM Clustering WEKA 1 Ensembles An ensemble is a set of classifiers whose combined results give the final decision. test feature vector
CS273 Midterm Exam Introduction to Machine Learning: Winter 2015 Tuesday February 10th, 2014
CS273 Midterm Eam Introduction to Machine Learning: Winter 2015 Tuesday February 10th, 2014 Your name: Your UCINetID (e.g., myname@uci.edu): Your seat (row and number): Total time is 80 minutes. READ THE
CSE 417T: Introduction to Machine Learning. Lecture 22: The Kernel Trick. Henry Chai 11/15/18
CSE 417T: Introduction to Machine Learning Lecture 22: The Kernel Trick Henry Chai 11/15/18 Linearly Inseparable Data What can we do if the data is not linearly separable? Accept some non-zero in-sample
Geometry Sixth Grade
Standard 6-4: The student will demonstrate through the mathematical processes an understanding of shape, location, and movement within a coordinate system; similarity, complementary, and supplementary
6.034 Quiz 2, Spring 2005
6.034 Quiz 2, Spring 2005 Open Book, Open Notes Name: Problem 1 (13 pts) 2 (8 pts) 3 (7 pts) 4 (9 pts) 5 (8 pts) 6 (16 pts) 7 (15 pts) 8 (12 pts) 9 (12 pts) Total (100 pts) Score 1 1 Decision Trees (13
Machine Learning. Classification
10-701 Machine Learning Classification Inputs Inputs Inputs Where we are Density Estimator Probability Classifier Predict category Today Regressor Predict real no. Later Classification Assume we want to
SUPPORT VECTOR MACHINES
SUPPORT VECTOR MACHINES Today Reading AIMA 18.9 Goals (Naïve Bayes classifiers) Support vector machines 1 Support Vector Machines (SVMs) SVMs are probably the most popular off-the-shelf classifier! Software
Applied Statistics for Neuroscientists Part IIa: Machine Learning
Applied Statistics for Neuroscientists Part IIa: Machine Learning Dr. Seyed-Ahmad Ahmadi 04.04.2017 16.11.2017 Outline Machine Learning Difference between statistics and machine learning Modeling the problem
CS 6140: Machine Learning Spring Final Exams. What we learned Final Exams 2/26/16
Logis@cs CS 6140: Machine Learning Spring 2016 Instructor: Lu Wang College of Computer and Informa@on Science Northeastern University Webpage: www.ccs.neu.edu/home/luwang Email: luwang@ccs.neu.edu Assignment
CSCI 111 First Midterm Exam Fall Solutions 09.00am 09.50am, Wednesday, October 18, 2017
QUEENS COLLEGE Department of Computer Science CSCI 111 First Midterm Exam Fall 2017 10.18.17 Solutions 09.00am 09.50am, Wednesday, October 18, 2017 Problem 1 (10 points) The following C++ program has errors
CS 6140: Machine Learning Spring 2016
CS 6140: Machine Learning Spring 2016 Instructor: Lu Wang College of Computer and Informa?on Science Northeastern University Webpage: www.ccs.neu.edu/home/luwang Email: luwang@ccs.neu.edu Logis?cs Assignment
Introduction to Supervised Learning
Introduction to Supervised Learning Erik G. Learned-Miller Department of Computer Science University of Massachusetts, Amherst Amherst, MA 01003 February 17, 2014 Abstract This document introduces the
!!! Warning!!! Learning jargon is always painful even if the concepts behind the jargon are not hard. So, let s get used to it. In mathematics you don't understand things. You just get used to them. von
An Introduction to Machine Learning
TRIPODS Summer Boorcamp: Topology and Machine Learning August 6, 2018 General Set-up Introduction Set-up and Goal Suppose we have X 1,X 2,...,X n data samples. Can we predict properites about any given
CS 8520: Artificial Intelligence. Machine Learning 2. Paula Matuszek Fall, CSC 8520 Fall Paula Matuszek
CS 8520: Artificial Intelligence Machine Learning 2 Paula Matuszek Fall, 2015!1 Regression Classifiers We said earlier that the task of a supervised learning system can be viewed as learning a function
Notes on Support Vector Machines
Western Kentucky University From the SelectedWorks of Matt Bogard Summer May, 2012 Notes on Support Vector Machines Matt Bogard, Western Kentucky University Available at: https://works.bepress.com/matt_bogard/20/
Stat 602X Exam 2 Spring 2011
Stat 60X Exam Spring 0 I have neither given nor received unauthorized assistance on this exam. Name Signed Date Name Printed . Below is a small p classification training set (for classes) displayed in
Data Analysis 3. Support Vector Machines. Jan Platoš October 30, 2017
Data Analysis 3 Support Vector Machines Jan Platoš October 30, 2017 Department of Computer Science Faculty of Electrical Engineering and Computer Science VŠB - Technical University of Ostrava Table of
Instance-based Learning
Instance-based Learning Machine Learning 10701/15781 Carlos Guestrin Carnegie Mellon University February 19 th, 2007 2005-2007 Carlos Guestrin 1 Why not just use Linear Regression? 2005-2007 Carlos Guestrin
Machine Learning: Algorithms and Applications Mockup Examination
Machine Learning: Algorithms and Applications Mockup Examination 14 May 2012 FIRST NAME STUDENT NUMBER LAST NAME SIGNATURE Instructions for students Write First Name, Last Name, Student Number and Signature
AREA Judo Math Inc.
AREA 2013 Judo Math Inc. 6 th grade Problem Solving Discipline: Black Belt Training Order of Mastery: Area 1. Area of triangles by composition 2. Area of quadrilaterals by decomposing 3. Draw polygons
Data Preprocessing. Supervised Learning
Supervised Learning Regression Given the value of an input X, the output Y belongs to the set of real values R. The goal is to predict output accurately for a new input. The predictions or outputs y are
COMPUTER SIMULATION OF COMPLEX SYSTEMS USING AUTOMATA NETWORKS K. Ming Leung
POLYTECHNIC UNIVERSITY Department of Computer and Information Science COMPUTER SIMULATION OF COMPLEX SYSTEMS USING AUTOMATA NETWORKS K. Ming Leung Abstract: Computer simulation of the dynamics of complex
Supervised Learning with Neural Networks. We now look at how an agent might learn to solve a general problem by seeing examples.
Supervised Learning with Neural Networks We now look at how an agent might learn to solve a general problem by seeing examples. Aims: to present an outline of supervised learning as part of AI; to introduce
LOGISTIC REGRESSION FOR MULTIPLE CLASSES
Peter Orbanz Applied Data Mining Not examinable. 111 LOGISTIC REGRESSION FOR MULTIPLE CLASSES Bernoulli and multinomial distributions The mulitnomial distribution of N draws from K categories with parameter
Lecture 20: Neural Networks for NLP. Zubin Pahuja
Lecture 20: Neural Networks for NLP Zubin Pahuja zpahuja2@illinois.edu courses.engr.illinois.edu/cs447 CS447: Natural Language Processing 1 Today s Lecture Feed-forward neural networks as classifiers simple
Neural Networks. By Laurence Squires
Neural Networks By Laurence Squires Machine learning What is it? Type of A.I. (possibly the ultimate A.I.?!?!?!) Algorithms that learn how to classify data The algorithms slowly change their own variables
1 Case study of SVM (Rob)
DRAFT a final version will be posted shortly COS 424: Interacting with Data Lecturer: Rob Schapire and David Blei Lecture # 8 Scribe: Indraneel Mukherjee March 1, 2007 In the previous lecture we saw how
Data Mining and Analytics
Data Mining and Analytics Aik Choon Tan, Ph.D. Associate Professor of Bioinformatics Division of Medical Oncology Department of Medicine aikchoon.tan@ucdenver.edu 9/22/2017 http://tanlab.ucdenver.edu/labhomepage/teaching/bsbt6111/
Learning and Generalization in Single Layer Perceptrons
Learning and Generalization in Single Layer Perceptrons Neural Computation : Lecture 4 John A. Bullinaria, 2015 1. What Can Perceptrons do? 2. Decision Boundaries The Two Dimensional Case 3. Decision Boundaries
Basis Functions. Volker Tresp Summer 2017
Basis Functions Volker Tresp Summer 2017 1 Nonlinear Mappings and Nonlinear Classifiers Regression: Linearity is often a good assumption when many inputs influence the output Some natural laws are (approximately)
Kuratowski Notes , Fall 2005, Prof. Peter Shor Revised Fall 2007
Kuratowski Notes 8.30, Fall 005, Prof. Peter Shor Revised Fall 007 Unfortunately, the OCW notes on Kuratowski s theorem seem to have several things substantially wrong with the proof, and the notes from
Machine Learning - Lecture 15 Support Vector Machines
Machine Learning - Lecture 5 Support Vector Machines Chris Thornton November 22, 2 Introduction to max-margin classifiers If there is a line (hyperplane) separating two sets of datapoints, we can use error-correction
Lecture 9: Support Vector Machines
Lecture 9: Support Vector Machines William Webber (william@williamwebber.com) COMP90042, 2014, Semester 1, Lecture 8 What we ll learn in this lecture Support Vector Machines (SVMs) a highly robust and
Ensembles. An ensemble is a set of classifiers whose combined results give the final decision. test feature vector
Ensembles An ensemble is a set of classifiers whose combined results give the final decision. test feature vector classifier 1 classifier 2 classifier 3 super classifier result 1 * *A model is the learned
CS229 Final Project: Predicting Expected Response Times
CS229 Final Project: Predicting Expected Email Response Times Laura Cruz-Albrecht (lcruzalb), Kevin Khieu (kkhieu) December 15, 2017 1 Introduction Each day, countless emails are sent out, yet the time
Text Classification and Clustering Using Kernels for Structured Data
Text Mining SVM Conclusion Text Classification and Clustering Using, pgeibel@uos.de DGFS Institut für Kognitionswissenschaft Universität Osnabrück February 2005 Outline Text Mining SVM Conclusion 1 Text
Support Vector Machines + Classification for IR
Support Vector Machines + Classification for IR Pierre Lison University of Oslo, Dep. of Informatics INF3800: Søketeknologi April 30, 2014 Outline of the lecture Recap of last week Support Vector Machines
CS112 Lecture: Defining Instantiable Classes
CS112 Lecture: Defining Instantiable Classes Last revised 2/3/05 Objectives: 1. To describe the process of defining an instantiable class 2. To discuss public and private visibility modifiers. Materials:
Practical example - classifier margin
Support Vector Machines (SVMs) SVMs are very powerful binary classifiers, based on the Statistical Learning Theory (SLT) framework. SVMs can be used to solve hard classification problems, where they look
Essay Fundamentals 8-Converting Outlines to Essays
Essay Fundamentals 8-Converting Outlines to Essays Every barebones outline begins with a thesis sentence, which governs or controls the essay. Most commonly, our thesis sentence becomes the last sentence
Image Classification pipeline. Lecture 2-1
Lecture 2: Image Classification pipeline Lecture 2-1 Administrative: Piazza For questions about midterm, poster session, projects, etc, use Piazza! SCPD students: Use your @stanford.edu address to register
Notes for Comp 454 Week 2
Notes for Comp 454 Week 2 This week we look at the material in chapters 3 and 4. Homework on Chapters 2, 3 and 4 is assigned (see end of notes). Answers to the homework problems are due by September 10th.
Lecture 10: Support Vector Machines and their Applications
Lecture 10: Support Vector Machines and their Applications Cognitive Systems - Machine Learning Part II: Special Aspects of Concept Learning SVM, kernel trick, linear separability, text mining, active
Lecture 1 Notes. Outline. Machine Learning. What is it? Instructors: Parth Shah, Riju Pahwa
Instructors: Parth Shah, Riju Pahwa Lecture 1 Notes Outline 1. Machine Learning What is it? Classification vs. Regression Error Training Error vs. Test Error 2. Linear Classifiers Goals and Motivations
Instance-based Learning
Instance-based Learning Machine Learning 10701/15781 Carlos Guestrin Carnegie Mellon University October 15 th, 2007 2005-2007 Carlos Guestrin 1 1-Nearest Neighbor Four things make a memory based learner: