CS 4700: Artificial Intelligence
|
|
- Stanley Shelton
- 5 years ago
- Views:
Transcription
1 CS 4700: Foundations of Artificial Intelligence Fall 2017 Instructor: Prof. Haym Hirsh Lecture 18
2 Prelim Grade Distribution
3 Homework 3: Out Today
4 Extra Credit Opportunity: 4:15pm Today, Gates G01 Relaxing Bottlenecks for Fast Machine Learning Christopher De Sa, Stanford University As machine learning applications become larger and more widely used, there is an increasing need for efficient systems solutions. The performance of essentially all machine learning applications is limited by bottlenecks with effects that cut across traditional layers in the software stack. Because of this, addressing these bottlenecks effectively requires a broad combination of work in theory, algorithms, systems, and hardware. To do this in a principled way, I propose a general approach called mindful relaxation. The approach starts by finding a way to eliminate a bottleneck by changing the algorithm's semantics. It proceeds by identifying structural conditions that let us prove guarantees that the altered algorithm will still work. Finally, it applies this structural knowledge to implement improvements to the performance and accuracy of entire systems. In this talk, I will describe the mindful relaxation approach, and demonstrate how it can be applied to a specific bottleneck (parallel overheads), problem (inference), and algorithm (asynchronous Gibbs sampling). I will demonstrate the effectiveness of this approach on a range of problems including CNNs, and finish with a discussion of my future work on methods for fast machine learning.
5 Today First-Order Logic (R&N Ch 8-9) Machine Learning (R&N Ch 18) Tuesday, April 5 Machine Learning (R&N Ch 18)
6 Resolution Conversion to CNF maintains satisfiability All steps guarantee equivalence except for Skolemization, which only maintains satisfiability Resolution is sound: If α Ͱ β then α β Resolution is refutation complete: If α β then α β Ͱ {} Godel s completeness theorem (No generalization that encompasses arithmetic is complete: Godel s incompleteness theorem)
7 Machine Learning
8 Learning
9 Learn: (dictionary.com) Learning 1. to acquire knowledge of or skill in by study, instruction, or experience 2. to become informed of or acquainted with; ascertain: to learn the truth. 3. to memorize: He learned the poem so he could recite it at the dinner. 4. to gain (a habit, mannerism, etc.) by experience, exposure to example, or the like; acquire: She learned patience from her father. 5. (of a device or machine, especially a computer) to perform an analogue of human learning with artificial intelligence. 6. Nonstandard. to instruct in; teach.
10 Machine Learning An agent is learning if it improves its performance on future tasks after making observations about the world.
11 Supervised Learning Given a training set of N example input-output pairs (x 1,y 1 ), (x 2,y 2 ),, (x n,y n ) where each y i was generated by an unknown function y = f(x), discover a function h that approximates the true function f.
12 Supervised Learning Given a training set of N example input-output pairs (x 1,y 1 ), (x 2,y 2 ),, (x n,y n ) where each y i was generated by an unknown function y = f(x), discover a function h that approximates the true function f. Example: Regression Domain of f is real numbers
13 Supervised Learning Given a training set of m example input-output pairs (x 1,y 1 ), (x 2,y 2 ),, (x m,y m ) where each y i was generated by an unknown function y = f(x), discover a function h that approximates the true function f. Classification learning: Domain of f is finite set of values
14 Supervised Learning Given a training set of m example input-output pairs (x 1,y 1 ), (x 2,y 2 ),, (x m,y m ) where each y i was generated by an unknown function y = f(x), discover a function h that approximates the true function f. Classification learning: Domain of f is finite set of values
15
16 + -
17 1 0
18 1-1
19
20 x 2 = 1.7x 1 4.9
21 x 2 = 1.7x x 2 1.7x 1 = 4.9
22 x 2 = 1.7x x 2 1.7x 1 = 4.9 2x 2 3.4x 1 = x 2 17x 1 = 49
23 Points above the line: x 2 1.7x x 2 1.7x x 2 3.4x x 2 17x 1 49
24 f(x 1,x 2 ) = 1 if x 2 1.7x otherwise 1 0
25 Formula for a line w 1 x 1 + w 2 x 2 = b
26 Formula for a line w 1 x 1 + w 2 x 2 = b Points above the line w 1 x 1 + w 2 x 2 b
27 f(x 1,x 2 ) = 1 if w 1 x 1 + w 2 x 2 b 0 otherwise 1 0
28 Generalizing to n dimensions: Formula for a line ( hyperplane ): w 1 x 1 + w 2 x w n x n = b σ i=1 w i x i = b n
29 Generalizing to n dimensions: Formula for a line ( hyperplane ): w 1 x 1 + w 2 x w n x n = b σ i=1 w i x i = b w x = b
30 Generalizing to n dimensions: Formula for a line ( hyperplane ): w 1 x 1 + w 2 x w n x n = b σ i=1 w i x i = b w x = b Points above the line w 1 x 1 + w 2 x w n x n b σn i=1 w i x i b w x b
31 Linear discriminant function: f(x 1,x 2,,x n ) = n 1 if σ i=1 w i x i b 0 otherwise
32 Linear discriminant function: f(x 1,x 2,,x n ) = n 1 if σ i=1 w i x i b 0 otherwise Goal of classification learning: Given: ((x 1,1,x 1,2,,x 1,n ),y 1 ), ((x 2,1,x 2,2,,x 2,n ),y 2 ),, ((x m,1,x m,2,,x m,n ),y m ) x 1 x 2 x m Find: (w 1,, w n ) and b
33 Notational trick : Equivalent to: w 1 x 1 + w 2 x w n x n b w 1 x 1 + w 2 x w n x n b 0
34 Notational trick : Equivalent to: w 1 x 1 + w 2 x w n x n b w 1 x 1 + w 2 x w n x n b 0 b + w 1 x 1 + w 2 x w n x n 0
35 Notational trick : w 1 x 1 + w 2 x w n x n b Equivalent to: w 1 x 1 + w 2 x w n x n b 0 b + w 1 x 1 + w 2 x w n x n 0 If x 0 = 1 bx 0 + w 1 x 1 + w 2 x w n x n 0
36 Notational trick : w 1 x 1 + w 2 x w n x n b Equivalent to: w 1 x 1 + w 2 x w n x n b 0 b + w 1 x 1 + w 2 x w n x n 0 If x 0 = 1 bx 0 + w 1 x 1 + w 2 x w n x n 0 w 0 x 0 + w 1 x 1 + w 2 x w n x n 0
37 Notational trick : w 1 x 1 + w 2 x w n x n b Equivalent to: w 1 x 1 + w 2 x w n x n b 0 b + w 1 x 1 + w 2 x w n x n 0 If x 0 = 1 bx 0 + w 1 x 1 + w 2 x w n x n 0 w 0 x 0 + w 1 x 1 + w 2 x w n x n 0 σn i=0 w i x i 0
38 Linear discriminant function: f(x 0,x 1,x 2,,x n ) = 1 if σ n i=0 w i x i 0 0 otherwise Goal of classification learning: Given: ((1,x 1,1,x 1,2,,x 1,n ),y 1 ), ((1,x 2,1,x 2,2,,x 2,n ),y 2 ),, ((1,x m,1,x m,2,,x m,n ),y m ) x 1 x 2 x m Find: (w 0,, w n )
39 Linear discriminant function: f(x 0,x 1,x 2,,x n ) = 1 if σ n i=0 w i x i 0 0 otherwise Goal of classification learning: Given: ((1,x 1,1,x 1,2,,x 1,n ),y 1 ), ((1,x 2,1,x 2,2,,x 2,n ),y 2 ),, ((1,x m,1,x m,2,,x m,n ),y m ) x 1 x 2 x m Find: (w 0,, w n )
40 Linear discriminant function: f(x 0,x 1,x 2,,x n ) = f w (x) 1 if σ n i=0 w i x i 0 h w (x) 0 otherwise Goal of classification learning: Given: ((1,x 1,1,x 1,2,,x 1,n ),y 1 ), ((1,x 2,1,x 2,2,,x 2,n ),y 2 ),, ((1,x m,1,x m,2,,x m,n ),y m ) x 1 x 2 x m Find: (w 0,, w n )
41
42 Perceptrons
43 Neuron
44 Perceptrons
45 Perceptron Learning Rule Current hypothesis: h w (x) w 0 = w 1 = w 2 = = w n = 0 [alternatively: set to random values] Repeat For i = 1 to m [for each example] For j = 1 to n [for each feature] w j w j + αx i,j (y i h w (x i )) Until h w (x) gets all data correct [reorder data after each iteration]
46 Perceptron Learning Rule w j w j + αx j (y i h w (x i )) If h w (x) is correct, all w j are unchanged y i = h w (x i ), so (y i h w (x i )) = 0 If h w (x) is too big, w j decreases If h w (x) is too small, w j increases α is the learning rate (sometimes called η)
47 Perceptron Learning Rule: Example w j w j + αx j (y i h w (x i ))
48 Perceptron Learning Rule: Example w j w j + αx j (y i h w (x i )) x 1 x 2 f(x 1,x 2 )
49 Perceptron Learning Rule: Example w j w j + αx j (y i h w (x i )) And gate x 1 x 2 f(x 1,x 2 )
50 Perceptron Learning Rule: Example w j w j + αx j (y i h w (x i )) α = 0.3, w 0 = w 1 = w 2 = 0 Training Data x 1 x 2 f(x 1,x 2 )
51 Perceptron Learning Rule: Example w j w j + αx j (y i h w (x i )) α = 0.3, w 0 = w 1 = w 2 = 0 Training Data x 1 x 2 f(x 1,x 2 )
CS 4700: Artificial Intelligence
CS 4700: Foundations of Artificial Intelligence Fall 2017 Instructor: Prof. Haym Hirsh Lecture 12 Prelim Tuesday, March 21 8:40-9:55am Statler Auditorium Homework 2 To be posted on Piazza 4701 Projects:
More informationMachine Learning Linear Models
Machine Learning Linear Models Outline II - Linear Models 1. Linear Regression (a) Linear regression: History (b) Linear regression with Least Squares (c) Matrix representation and Normal Equation Method
More informationMachine Learning (CS 567) Lecture 3
Machine Learning (CS 567) Lecture 3 Time: T-Th 5:00pm - 6:20pm Location: GFS 118 Instructor: Sofus A. Macskassy (macskass@usc.edu) Office: SAL 216 Office hours: by appointment Teaching assistant: Cheol
More informationMachine Learning Basics Lecture 3: Perceptron. Princeton University COS 495 Instructor: Yingyu Liang
Machine Learning Basics Lecture 3: Perceptron Princeton University COS 495 Instructor: Yingyu Liang Perceptron Overview Previous lectures: (Principle for loss function) MLE to derive loss Example: linear
More informationML in Practice: CMSC 422 Slides adapted from Prof. CARPUAT and Prof. Roth
ML in Practice: CMSC 422 Slides adapted from Prof. CARPUAT and Prof. Roth N-fold cross validation Instead of a single test-training split: train test Split data into N equal-sized parts Train and test
More informationArtificial Neural Network
Artificial Neural Network Contents 2 What is ANN? Biological Neuron Structure of Neuron Types of Neuron Models of Neuron Analogy with human NN Perceptron OCR Multilayer Neural Network Back propagation
More informationMachine Learning (CS 567) Lecture 5
Machine Learning (CS 567) Lecture 5 Time: T-Th 5:00pm - 6:20pm Location: GFS 118 Instructor: Sofus A. Macskassy (macskass@usc.edu) Office: SAL 216 Office hours: by appointment Teaching assistant: Cheol
More informationCS 4700: Foundations of Artificial Intelligence Ungraded Homework Solutions
CS 4700: Foundations of Artificial Intelligence Ungraded Homework Solutions 1. Neural Networks: a. There are 2 2n distinct Boolean functions over n inputs. Thus there are 16 distinct Boolean functions
More informationLecture 7 Artificial neural networks: Supervised learning
Lecture 7 Artificial neural networks: Supervised learning Introduction, or how the brain works The neuron as a simple computing element The perceptron Multilayer neural networks Accelerated learning in
More informationCS 4700: Artificial Intelligence
CS 4700: Foundations of Artificial Intelligence Fall 2017 Instructor: Prof. Haym Hirsh Lecture 14 Today Knowledge Representation and Reasoning (R&N Ch 7-9) Prelim, Statler Auditorium Tuesday, March 21
More informationLinear Classifiers. Michael Collins. January 18, 2012
Linear Classifiers Michael Collins January 18, 2012 Today s Lecture Binary classification problems Linear classifiers The perceptron algorithm Classification Problems: An Example Goal: build a system that
More informationCSC Neural Networks. Perceptron Learning Rule
CSC 302 1.5 Neural Networks Perceptron Learning Rule 1 Objectives Determining the weight matrix and bias for perceptron networks with many inputs. Explaining what a learning rule is. Developing the perceptron
More informationCSC242: Intro to AI. Lecture 21
CSC242: Intro to AI Lecture 21 Administrivia Project 4 (homeworks 18 & 19) due Mon Apr 16 11:59PM Posters Apr 24 and 26 You need an idea! You need to present it nicely on 2-wide by 4-high landscape pages
More informationCE213 Artificial Intelligence Lecture 14
CE213 Artificial Intelligence Lecture 14 Neural Networks: Part 2 Learning Rules -Hebb Rule - Perceptron Rule -Delta Rule Neural Networks Using Linear Units [ Difficulty warning: equations! ] 1 Learning
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 informationPropositional Reasoning
Propositional Reasoning CS 440 / ECE 448 Introduction to Artificial Intelligence Instructor: Eyal Amir Grad TAs: Wen Pu, Yonatan Bisk Undergrad TAs: Sam Johnson, Nikhil Johri Spring 2010 Intro to AI (CS
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 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 informationThe Perceptron. Volker Tresp Summer 2014
The Perceptron Volker Tresp Summer 2014 1 Introduction One of the first serious learning machines Most important elements in learning tasks Collection and preprocessing of training data Definition of a
More informationMachine Learning Support Vector Machines. Prof. Matteo Matteucci
Machine Learning Support Vector Machines Prof. Matteo Matteucci Discriminative vs. Generative Approaches 2 o Generative approach: we derived the classifier from some generative hypothesis about the way
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 Introduction to Machine Learning. Matt Gormley Lecture 8 Feb. 12, 2018
10-601 Introduction to Machine Learning Machine Learning Department School of Computer Science Carnegie Mellon University Logistic Regression Matt Gormley Lecture 8 Feb. 12, 2018 1 10-601 Introduction
More informationCS 188: Artificial Intelligence Spring Announcements
CS 188: Artificial Intelligence Spring 2010 Lecture 24: Perceptrons and More! 4/22/2010 Pieter Abbeel UC Berkeley Slides adapted from Dan Klein Announcements W7 due tonight [this is your last written for
More informationNeural Networks Introduction CIS 32
Neural Networks Introduction CIS 32 Functionalia Office Hours (Last Change!) - Location Moved to 0317 N (Bridges Room) Today: Alpha-Beta Example Neural Networks Learning with T-R Agent (from before) direction
More informationComputational Intelligence Winter Term 2017/18
Computational Intelligence Winter Term 207/8 Prof. Dr. Günter Rudolph Lehrstuhl für Algorithm Engineering (LS ) Fakultät für Informatik TU Dortmund Plan for Today Single-Layer Perceptron Accelerated Learning
More informationLinear Regression. S. Sumitra
Linear Regression S Sumitra Notations: x i : ith data point; x T : transpose of x; x ij : ith data point s jth attribute Let {(x 1, y 1 ), (x, y )(x N, y N )} be the given data, x i D and y i Y Here D
More informationThe Perceptron. Volker Tresp Summer 2018
The Perceptron Volker Tresp Summer 2018 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 informationLecture Notes in Machine Learning Chapter 4: Version space learning
Lecture Notes in Machine Learning Chapter 4: Version space learning Zdravko Markov February 17, 2004 Let us consider an example. We shall use an attribute-value language for both the examples and the hypotheses
More informationLogistic Regression Introduction to Machine Learning. Matt Gormley Lecture 9 Sep. 26, 2018
10-601 Introduction to Machine Learning Machine Learning Department School of Computer Science Carnegie Mellon University Logistic Regression Matt Gormley Lecture 9 Sep. 26, 2018 1 Reminders Homework 3:
More informationSupport Vector Machines (SVM) in bioinformatics. Day 1: Introduction to SVM
1 Support Vector Machines (SVM) in bioinformatics Day 1: Introduction to SVM Jean-Philippe Vert Bioinformatics Center, Kyoto University, Japan Jean-Philippe.Vert@mines.org Human Genome Center, University
More informationThe exam is closed book, closed calculator, and closed notes except your one-page crib sheet.
CS 188 Fall 2015 Introduction to Artificial Intelligence Final You have approximately 2 hours and 50 minutes. The exam is closed book, closed calculator, and closed notes except your one-page crib sheet.
More informationPerceptron. (c) Marcin Sydow. Summary. Perceptron
Topics covered by this lecture: Neuron and its properties Mathematical model of neuron: as a classier ' Learning Rule (Delta Rule) Neuron Human neural system has been a natural source of inspiration for
More informationIntelligent Systems (AI-2)
Intelligent Systems (AI-2) Computer Science cpsc422, Lecture 19 Oct, 23, 2015 Slide Sources Raymond J. Mooney University of Texas at Austin D. Koller, Stanford CS - Probabilistic Graphical Models D. Page,
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 informationComputational Intelligence
Plan for Today Single-Layer Perceptron Computational Intelligence Winter Term 00/ Prof. Dr. Günter Rudolph Lehrstuhl für Algorithm Engineering (LS ) Fakultät für Informatik TU Dortmund Accelerated Learning
More informationCS 540: Machine Learning Lecture 1: Introduction
CS 540: Machine Learning Lecture 1: Introduction AD January 2008 AD () January 2008 1 / 41 Acknowledgments Thanks to Nando de Freitas Kevin Murphy AD () January 2008 2 / 41 Administrivia & Announcement
More informationRegression and Classification" with Linear Models" CMPSCI 383 Nov 15, 2011!
Regression and Classification" with Linear Models" CMPSCI 383 Nov 15, 2011! 1 Todayʼs topics" Learning from Examples: brief review! Univariate Linear Regression! Batch gradient descent! Stochastic gradient
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 informationAI Programming CS S-09 Knowledge Representation
AI Programming CS662-2013S-09 Knowledge Representation David Galles Department of Computer Science University of San Francisco 09-0: Overview So far, we ve talked about search, which is a means of considering
More informationVote. Vote on timing for night section: Option 1 (what we have now) Option 2. Lecture, 6:10-7:50 25 minute dinner break Tutorial, 8:15-9
Vote Vote on timing for night section: Option 1 (what we have now) Lecture, 6:10-7:50 25 minute dinner break Tutorial, 8:15-9 Option 2 Lecture, 6:10-7 10 minute break Lecture, 7:10-8 10 minute break Tutorial,
More informationLinear Classifiers: Expressiveness
Linear Classifiers: Expressiveness Machine Learning Spring 2018 The slides are mainly from Vivek Srikumar 1 Lecture outline Linear classifiers: Introduction What functions do linear classifiers express?
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 informationDeductive Systems. Lecture - 3
Deductive Systems Lecture - 3 Axiomatic System Axiomatic System (AS) for PL AS is based on the set of only three axioms and one rule of deduction. It is minimal in structure but as powerful as the truth
More information6.825 Techniques in Artificial Intelligence. Logic Miscellanea. Completeness and Incompleteness Equality Paramodulation
6.825 Techniques in Artificial Intelligence Logic Miscellanea Completeness and Incompleteness Equality Paramodulation Lecture 9 1 Logic is a huge subject. It includes esoteric mathematical and philosophical
More informationValue Function Methods. CS : Deep Reinforcement Learning Sergey Levine
Value Function Methods CS 294-112: Deep Reinforcement Learning Sergey Levine Class Notes 1. Homework 2 is due in one week 2. Remember to start forming final project groups and writing your proposal! Proposal
More informationLinear smoother. ŷ = S y. where s ij = s ij (x) e.g. s ij = diag(l i (x))
Linear smoother ŷ = S y where s ij = s ij (x) e.g. s ij = diag(l i (x)) 2 Online Learning: LMS and Perceptrons Partially adapted from slides by Ryan Gabbard and Mitch Marcus (and lots original slides by
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 informationUNSUPERVISED LEARNING
UNSUPERVISED LEARNING Topics Layer-wise (unsupervised) pre-training Restricted Boltzmann Machines Auto-encoders LAYER-WISE (UNSUPERVISED) PRE-TRAINING Breakthrough in 2006 Layer-wise (unsupervised) pre-training
More informationA summary of Deep Learning without Poor Local Minima
A summary of Deep Learning without Poor Local Minima by Kenji Kawaguchi MIT oral presentation at NIPS 2016 Learning Supervised (or Predictive) learning Learn a mapping from inputs x to outputs y, given
More informationApril 9, Depto. de Ing. de Sistemas e Industrial Universidad Nacional de Colombia, Bogotá. Linear Classification Models. Fabio A. González Ph.D.
Depto. de Ing. de Sistemas e Industrial Universidad Nacional de Colombia, Bogotá April 9, 2018 Content 1 2 3 4 Outline 1 2 3 4 problems { C 1, y(x) threshold predict(x) = C 2, y(x) < threshold, with threshold
More informationSelf-assessment due: Monday 3/18/2019 at 11:59pm (submit via Gradescope)
CS 188 Spring 2019 Introduction to Artificial Intelligence Written HW 6 Sol. Self-assessment due: Monday 3/18/2019 at 11:59pm (submit via Gradescope) Instructions for self-assessment: Take your original
More informationAdministration. Registration Hw3 is out. Lecture Captioning (Extra-Credit) Scribing lectures. Questions. Due on Thursday 10/6
Administration Registration Hw3 is out Due on Thursday 10/6 Questions Lecture Captioning (Extra-Credit) Look at Piazza for details Scribing lectures With pay; come talk to me/send email. 1 Projects Projects
More informationCS325 Artificial Intelligence Chs. 18 & 4 Supervised Machine Learning (cont)
CS325 Artificial Intelligence Cengiz Spring 2013 Model Complexity in Learning f(x) x Model Complexity in Learning f(x) x Let s start with the linear case... Linear Regression Linear Regression price =
More informationLogic and machine learning review. CS 540 Yingyu Liang
Logic and machine learning review CS 540 Yingyu Liang Propositional logic Logic If the rules of the world are presented formally, then a decision maker can use logical reasoning to make rational decisions.
More informationKnowledge based Agents
Knowledge based Agents Shobhanjana Kalita Dept. of Computer Science & Engineering Tezpur University Slides prepared from Artificial Intelligence A Modern approach by Russell & Norvig Knowledge Based Agents
More informationInference in first-order logic
CS 57 Introduction to AI Lecture 5 Inference in first-order logic Milos Hauskrecht milos@cs.pitt.edu 5329 Sennott Square Logical inference in FOL Logical inference problem: Given a knowledge base KB (a
More informationMachine Learning Basics Lecture 4: SVM I. Princeton University COS 495 Instructor: Yingyu Liang
Machine Learning Basics Lecture 4: SVM I Princeton University COS 495 Instructor: Yingyu Liang Review: machine learning basics Math formulation Given training data x i, y i : 1 i n i.i.d. from distribution
More informationCOGS Q250 Fall Homework 7: Learning in Neural Networks Due: 9:00am, Friday 2nd November.
COGS Q250 Fall 2012 Homework 7: Learning in Neural Networks Due: 9:00am, Friday 2nd November. For the first two questions of the homework you will need to understand the learning algorithm using the delta
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 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 informationCS 4700: Foundations of Artificial Intelligence
CS 4700: Foundations of Artificial Intelligence Prof. Bart Selman selman@cs.cornell.edu Machine Learning: Neural Networks R&N 18.7 Intro & perceptron learning 1 2 Neuron: How the brain works # neurons
More informationCOMP 551 Applied Machine Learning Lecture 2: Linear regression
COMP 551 Applied Machine Learning Lecture 2: Linear regression Instructor: (jpineau@cs.mcgill.ca) Class web page: www.cs.mcgill.ca/~jpineau/comp551 Unless otherwise noted, all material posted for this
More informationJakub Hajic Artificial Intelligence Seminar I
Jakub Hajic Artificial Intelligence Seminar I. 11. 11. 2014 Outline Key concepts Deep Belief Networks Convolutional Neural Networks A couple of questions Convolution Perceptron Feedforward Neural Network
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 informationPerceptron (Theory) + Linear Regression
10601 Introduction to Machine Learning Machine Learning Department School of Computer Science Carnegie Mellon University Perceptron (Theory) Linear Regression Matt Gormley Lecture 6 Feb. 5, 2018 1 Q&A
More informationMachine Learning (CS 567) Lecture 2
Machine Learning (CS 567) Lecture 2 Time: T-Th 5:00pm - 6:20pm Location: GFS118 Instructor: Sofus A. Macskassy (macskass@usc.edu) Office: SAL 216 Office hours: by appointment Teaching assistant: Cheol
More information@SoyGema GEMA PARREÑO PIQUERAS
@SoyGema GEMA PARREÑO PIQUERAS WHAT IS AN ARTIFICIAL NEURON? WHAT IS AN ARTIFICIAL NEURON? Image Recognition Classification using Softmax Regressions and Convolutional Neural Networks Languaje Understanding
More informationLecture 16: Perceptron and Exponential Weights Algorithm
EECS 598-005: Theoretical Foundations of Machine Learning Fall 2015 Lecture 16: Perceptron and Exponential Weights Algorithm Lecturer: Jacob Abernethy Scribes: Yue Wang, Editors: Weiqing Yu and Andrew
More informationIntelligent Systems Discriminative Learning, Neural Networks
Intelligent Systems Discriminative Learning, Neural Networks Carsten Rother, Dmitrij Schlesinger WS2014/2015, Outline 1. Discriminative learning 2. Neurons and linear classifiers: 1) Perceptron-Algorithm
More informationLogic. Introduction to Artificial Intelligence CS/ECE 348 Lecture 11 September 27, 2001
Logic Introduction to Artificial Intelligence CS/ECE 348 Lecture 11 September 27, 2001 Last Lecture Games Cont. α-β pruning Outline Games with chance, e.g. Backgammon Logical Agents and thewumpus World
More informationNeural Networks. Mark van Rossum. January 15, School of Informatics, University of Edinburgh 1 / 28
1 / 28 Neural Networks Mark van Rossum School of Informatics, University of Edinburgh January 15, 2018 2 / 28 Goals: Understand how (recurrent) networks behave Find a way to teach networks to do a certain
More informationThe Perceptron algorithm
The Perceptron algorithm Tirgul 3 November 2016 Agnostic PAC Learnability A hypothesis class H is agnostic PAC learnable if there exists a function m H : 0,1 2 N and a learning algorithm with the following
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 informationLast updated: Oct 22, 2012 LINEAR CLASSIFIERS. J. Elder CSE 4404/5327 Introduction to Machine Learning and Pattern Recognition
Last updated: Oct 22, 2012 LINEAR CLASSIFIERS Problems 2 Please do Problem 8.3 in the textbook. We will discuss this in class. Classification: Problem Statement 3 In regression, we are modeling the relationship
More informationMore about the Perceptron
More about the Perceptron CMSC 422 MARINE CARPUAT marine@cs.umd.edu Credit: figures by Piyush Rai and Hal Daume III Recap: Perceptron for binary classification Classifier = hyperplane that separates positive
More informationNONSTANDARD MODELS AND KRIPKE S PROOF OF THE GÖDEL THEOREM
Notre Dame Journal of Formal Logic Volume 41, Number 1, 2000 NONSTANDARD MODELS AND KRIPKE S PROOF OF THE GÖDEL THEOREM HILARY PUTNAM Abstract This lecture, given at Beijing University in 1984, presents
More informationOptimization and Gradient Descent
Optimization and Gradient Descent INFO-4604, Applied Machine Learning University of Colorado Boulder September 12, 2017 Prof. Michael Paul Prediction Functions Remember: a prediction function is the function
More informationDiscrete Mathematics
Discrete Mathematics Discrete mathematics is devoted to the study of discrete or distinct unconnected objects. Classical mathematics deals with functions on real numbers. Real numbers form a continuous
More informationWe choose parameter values that will minimize the difference between the model outputs & the true function values.
CSE 4502/5717 Big Data Analytics Lecture #16, 4/2/2018 with Dr Sanguthevar Rajasekaran Notes from Yenhsiang Lai Machine learning is the task of inferring a function, eg, f : R " R This inference has to
More informationDeep Learning Autoencoder Models
Deep Learning Autoencoder Models Davide Bacciu Dipartimento di Informatica Università di Pisa Intelligent Systems for Pattern Recognition (ISPR) Generative Models Wrap-up Deep Learning Module Lecture Generative
More informationWarm up: risk prediction with logistic regression
Warm up: risk prediction with logistic regression Boss gives you a bunch of data on loans defaulting or not: {(x i,y i )} n i= x i 2 R d, y i 2 {, } You model the data as: P (Y = y x, w) = + exp( yw T
More informationLinear models: the perceptron and closest centroid algorithms. D = {(x i,y i )} n i=1. x i 2 R d 9/3/13. Preliminaries. Chapter 1, 7.
Preliminaries Linear models: the perceptron and closest centroid algorithms Chapter 1, 7 Definition: The Euclidean dot product beteen to vectors is the expression d T x = i x i The dot product is also
More informationCOMS 4771 Introduction to Machine Learning. Nakul Verma
COMS 4771 Introduction to Machine Learning Nakul Verma Announcements HW1 due next lecture Project details are available decide on the group and topic by Thursday Last time Generative vs. Discriminative
More informationHOMEWORK 4: SVMS AND KERNELS
HOMEWORK 4: SVMS AND KERNELS CMU 060: MACHINE LEARNING (FALL 206) OUT: Sep. 26, 206 DUE: 5:30 pm, Oct. 05, 206 TAs: Simon Shaolei Du, Tianshu Ren, Hsiao-Yu Fish Tung Instructions Homework Submission: Submit
More informationLinear Algebra. Introduction. Marek Petrik 3/23/2017. Many slides adapted from Linear Algebra Lectures by Martin Scharlemann
Linear Algebra Introduction Marek Petrik 3/23/2017 Many slides adapted from Linear Algebra Lectures by Martin Scharlemann Midterm Results Highest score on the non-r part: 67 / 77 Score scaling: Additive
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 informationHopfield Neural Network
Lecture 4 Hopfield Neural Network Hopfield Neural Network A Hopfield net is a form of recurrent artificial neural network invented by John Hopfield. Hopfield nets serve as content-addressable memory systems
More informationMonday May 12, :00 to 1:30 AM
ASTRONOMY 108: Descriptive Astronomy Spring 2008 Instructor: Hugh Gallagher Office: Physical Science Building 130 Phone, Email: 436-3177, gallagha@oneonta.edu Office Hours: M 2:00-3:00 PM, Th 10:00-11:00
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 informationMLPR: Logistic Regression and Neural Networks
MLPR: Logistic Regression and Neural Networks Machine Learning and Pattern Recognition Amos Storkey Amos Storkey MLPR: Logistic Regression and Neural Networks 1/28 Outline 1 Logistic Regression 2 Multi-layer
More informationDeep Learning: a gentle introduction
Deep Learning: a gentle introduction Jamal Atif jamal.atif@dauphine.fr PSL, Université Paris-Dauphine, LAMSADE February 8, 206 Jamal Atif (Université Paris-Dauphine) Deep Learning February 8, 206 / Why
More informationCOMP 551 Applied Machine Learning Lecture 2: Linear Regression
COMP 551 Applied Machine Learning Lecture 2: Linear Regression Instructor: Herke van Hoof (herke.vanhoof@mail.mcgill.ca) Slides mostly by: Class web page: www.cs.mcgill.ca/~hvanho2/comp551 Unless otherwise
More informationCS 188: Artificial Intelligence. Outline
CS 188: Artificial Intelligence Lecture 21: Perceptrons Pieter Abbeel UC Berkeley Many slides adapted from Dan Klein. Outline Generative vs. Discriminative Binary Linear Classifiers Perceptron Multi-class
More informationIntelligent Systems (AI-2)
Intelligent Systems (AI-2) Computer Science cpsc422, Lecture 19 Oct, 24, 2016 Slide Sources Raymond J. Mooney University of Texas at Austin D. Koller, Stanford CS - Probabilistic Graphical Models D. Page,
More informationLesson Plan Bond Prediction Tenth Grade Chemistry By Rich Wilczewski
Lesson Plan Bond Prediction Tenth Grade Chemistry By Rich Wilczewski LEARNING OUTCOMES: Students will use their textbook outlines to define the following: Chemical Bond, Covalent Bond, Ionic Bond and Polar
More informationOutline. MLPR: Logistic Regression and Neural Networks Machine Learning and Pattern Recognition. Which is the correct model? Recap.
Outline MLPR: and Neural Networks Machine Learning and Pattern Recognition 2 Amos Storkey Amos Storkey MLPR: and Neural Networks /28 Recap Amos Storkey MLPR: and Neural Networks 2/28 Which is the correct
More informationINTRODUCTION TO ARTIFICIAL INTELLIGENCE
v=1 v= 1 v= 1 v= 1 v= 1 v=1 optima 2) 3) 5) 6) 7) 8) 9) 12) 11) 13) INTRDUCTIN T ARTIFICIAL INTELLIGENCE DATA15001 EPISDE 8: NEURAL NETWRKS TDAY S MENU 1. NEURAL CMPUTATIN 2. FEEDFRWARD NETWRKS (PERCEPTRN)
More information- - - - - - - - - - - - - - - - - - DISCLAIMER - - - - - - - - - - - - - - - - - - General Information: This is a midterm from a previous semester. This means: This midterm contains problems that are of
More informationAnnouncements - Homework
Announcements - Homework Homework 1 is graded, please collect at end of lecture Homework 2 due today Homework 3 out soon (watch email) Ques 1 midterm review HW1 score distribution 40 HW1 total score 35
More informationECE 6504: Advanced Topics in Machine Learning Probabilistic Graphical Models and Large-Scale Learning
ECE 6504: Advanced Topics in Machine Learning Probabilistic Graphical Models and Large-Scale Learning Topics Summary of Class Advanced Topics Dhruv Batra Virginia Tech HW1 Grades Mean: 28.5/38 ~= 74.9%
More information