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Maryland - ENEE - 303
File: f:/coursesS12/303/303S12hmwk1.doc RWN01/29/12 corrected 02/02/12303 Spring 2012 Homework 1 Due 02/06/12 in classFor the following it will be helpful if you change the Probe background from black towhite so that the curves can be well distinguish
Maryland - ENEE - 303
File: f:/coursesS12/303/303S12hmwk2.doc RWN02/10/12b303 Spring 2012 Homework 2 Due M 02/13/12 in classIn the following all the transistors are 4007s.1. (50 points, CMOS biasing)a) For the following circuit run curves to show the possible Q points for
Maryland - ENEE - 303
File: f:/coursesS12/303/303S12hmwk3.doc RWN02/12/12303 Spring 2012 Homework 3 Due M 02/20/12 in class1. (40 points, BJT curves)a) For the following circuit run curves for IC versus VCC with 0 IB 40 uA in10uA steps.b) If the Q points are at VCEnpn=3=
Maryland - ENEE - 303
File: f:/coursesS12/303/303S12hmwk4.doc RWN02/19/12b303 Spring 2012 Homework 4 Due M 02/27/12 in class1. (50points, BJT OTA)Using the 2N3904s for the differential pair, design an OTA to givevi out = I tanh( d )2VTChoose I = 5mA and use 2N3904 & 2
Maryland - ENEE - 303
File: f:/coursesS12/303/303S12hmwk5.doc RWN02/23/12303 Spring 2012 Homework 5 Due M 03/05/12 in class1. (50 points, BJT npn and pnp amplifiers)Design an npn amplifier (using a 2N3904) for |IC|=5.2mA, RL=RC=1Kohm andRE=100Ohm. Repeat for a pnp one (us
SUNY Buffalo - CSE - 574
Machine LearningSrihariBayesian Model ComparisonSargur Sriharisrihari@cedar.buffalo.edu1Machine LearningSrihariMotivation In frequentist setting Over-fitting is a problem Cross-validation used for Setting values for regularization parameters
SUNY Buffalo - CSE - 574
Machine LearningSrihariBayesian Linear RegressionSargur Sriharisrihari@cedar.buffalo.edu1Machine LearningSrihariMotivation In maximum likelihood model complexity (number of basis functions)needs to be controlled according to the size ofthe dat
SUNY Buffalo - CSE - 574
Machine LearningSrihariBias-Variance Decomposition Choosing in maximum likelihood/least squares estimation Five part discussion:1. On-line regression demo 2. Point estimateChinese Emperors Height3. Formulation for regression 4. Example 5. Choice of
SUNY Buffalo - CSE - 574
Linear Models for Classification:IntroductionSargur N. SrihariUniversity at Buffalo, State University of New YorkUSAMachine LearningSrihariTopics Regression vs Classification Linear Classification Models Converting probabilistic regression outpu
SUNY Buffalo - CSE - 574
Linear Models for ClassificationDiscriminant FunctionsSargur N. SrihariUniversity at Buffalo, State University of New YorkUSA1Machine LearningSrihariTopics Linear Discriminant Functions Definition (2-class), Geometry Generalization to K > 2 cla
SUNY Buffalo - CSE - 574
Machine LearningSrihariLinear Classification:Probabilistic Generative ModelsSargur N. SrihariUniversity at Buffalo, State University of New YorkUSA1Machine LearningSrihariLinear Classification usingProbabilistic Generative Models Topics1. Ove
SUNY Buffalo - CSE - 574
Logistic RegressionSargur N. SrihariUniversity at Buffalo, State University of New YorkUSAMachine LearningSrihariTopics in Linear Classification usingProbabilistic Discriminative Models1. Generative vs Discriminative2. Nonlinear basis funcs in li
SUNY Buffalo - CSE - 574
Bayesian Logistic RegressionSargur N. SrihariUniversity at Buffalo, State University of New YorkUSAMachine LearningSrihariTopicsRecap of Logistic RegressionRoadmap of Bayesian Logistic RegressionLaplace ApproximationEvaluation of posterior distr
SUNY Buffalo - CSE - 574
Machine Learning Neural NetworksIntroductionSargur SrihariSrihariMachine Learning SrihariTopics1.Introduction1.2.3.2.Network Training1.2.3.4.3.4.5.6.7.Extending linear modelsFeed-forward Network FunctionsWeight-space symmetriesP
SUNY Buffalo - CSE - 574
Machine Learning Neural Network TrainingSargur SrihariSrihariMachine Learning SrihariTopics Neural network parameters Probabilistic problem formulation Determining the error function Regression Binary classication Multi-class classicationPa
SUNY Buffalo - CSE - 574
Machine Learning SrihariError BackpropagationSargur Srihari1Machine Learning SrihariTopicsNeural Network Learning ProblemNeed for computing derivatives of Error functionForward propagation of activationsBackward propagation of errorsStatement
SUNY Buffalo - CSE - 574
Machine Learning SrihariThe Hessian Matrix Sargur Srihari 1Machine Learning SrihariHessian of Neural Network Error Function Backpropagation can be used to obtain rst derivatives of error function wrt weights in network It can also be used to deri
SUNY Buffalo - CSE - 574
Machine Learning SrihariRegularization in Neural NetworksSargur Srihari1Machine Learning SrihariTopics in Neural Network Regularization What is regularization? Methods1. Determining optimal number of hidden units2. Use of regularizer in error f
SUNY Buffalo - CSE - 574
Machine Learning SrihariMixture Density NetworksSargur Srihari 1Machine Learning SrihariMixture Density Networks In some problems distribution can be multimodal Particularly in inverse problems Gaussian assumption can lead to poor results In r
SUNY Buffalo - CSE - 574
Machine Learning SrihariBayesian Neural NetworksSargur Sriharisrihari@cedar.buffalo.edu1Machine Learning SrihariTopics discussed here1. Why Bayesian?2. Difculty of exact Bayesian treatment and need forapproximation3. Two approximate approaches
SUNY Buffalo - CSE - 574
Machine Learning SrihariKernel Methods Sargur Srihari 1Machine Learning SrihariTopics in Kernel Methods 1. 2. 3. 4. 5. 6. 7.Kernel Methods vs Linear Models/Neural Networks Stored Sample Methods Kernel Functions Dual Representations Constructing K
SUNY Buffalo - CSE - 574
Machine Learning SrihariRadial Basis Function Networks Sargur Srihari 1Machine Learning SrihariTopics Basis Functions Radial Basis Functions Gaussian Basis Functions Nadaraya Watson Kernel Regression Model2Machine Learning SrihariBasis Functi
SUNY Buffalo - CSE - 574
Machine Learning SrihariRadial Basis Function Networks Sargur Srihari 1Machine Learning SrihariTopics Basis Functions Radial Basis Functions Gaussian Basis Functions Nadaraya Watson Kernel Regression Model2Machine Learning SrihariBasis Functi
SUNY Buffalo - CSE - 574
Machine Learning SrihariGaussian ProcessesSargur Srihari1Machine Learning SrihariTopics in Gaussian Processes1.2.3.4.5.6.Examples of use of GPDuality: From Basis Functions to Kernel FunctionsGP Denition and IntuitionLinear regression revi
SUNY Buffalo - CSE - 574
Machine LearningSrihariDecision TheorySargur Sriharisrihari@cedar.buffalo.edu1Machine LearningSrihariDecision Theory Using probability theory to make optimal decisions Input vector x, target vector t Regression: t is continuous Classification:
SUNY Buffalo - CSE - 574
Machine LearningSrihariEvidence Approximation:Determining hyper-parametersSargur Sriharisrihari@cedar.buffalo.edu1Machine LearningSrihariTopics Linear Regression with Basis Functions Fully Bayesian Treatment Hyper-parameters for noise and weig
SUNY Buffalo - CSE - 574
Machine LearningSrihariInformation TheorySargur N. Srihari1Machine LearningSrihariTopics1. Entropy as an Information Measure1. Discrete variable definitionRelationship to Code Length2. Continuous VariableDifferential Entropy2.3.4.5.Maximu
SUNY Buffalo - CSE - 574
Machine Learning OverviewSargur N. SrihariUniversity at Buffalo, State University of New YorkUSA1Outline1. What is Machine Learning (ML)?2. Types of Information ProcessingProblems Solved1.2.3.4.RegressionClassificationClusteringProbabilist
SUNY Buffalo - CSE - 574
Machine Learning!!!!!SrihariProbability TheorySargur N. Sriharisrihari@cedar.buffalo.edu1Machine Learning!!!!!SrihariProbability Theory with Several Variables Key concept is dealingwith uncertainty2 apples3 oranges3 apples1 orange D
SUNY Buffalo - CSE - 574
Machine Learning!!!!!SrihariLinear Models for RegressionSargur Sriharisrihari@cedar.buffalo.edu1Machine Learning!!!!!SrihariOverview Plan: Discuss supervised learning starting withregression Goal: predict value of one or more target var
SUNY Buffalo - CSE - 574
Machine Learning!!!!!SrihariGraphical ModelsSargur Sriharisrihari@cedar.buffalo.edu1Machine Learning!!!!!SrihariWhat are Graphical Models? They are diagrammatic representations ofprobability distributions marriage between probability
SUNY Buffalo - CSE - 574
Machine LearningSrihariQuerying ProbabilisticGraphical ModelsSargur Sriharisrihari@cedar.buffalo.edu1Machine LearningSrihariProbabilistic Graphical Models Represent joint probabilitydistributions over multiplevariables in terms of conditional
SUNY Buffalo - CSE - 574
Machine Learning!!!!!SrihariGenetic Inheritance andBayesian NetworksSargur Sriharisrihari@cedar.buffalo.edu1Machine Learning!!!!!SrihariGenetics Pedigree Example One of the earliest uses of BayesianNetworks Before general framework w
SUNY Buffalo - CSE - 574
Machine Learning!!!!!SrihariGraphs and DistributionsSargur Sriharisrihari@cedar.buffalo.edu1Machine Learning!!!!!SrihariTopics I-Maps I-Map to Factorization Factorization to I-Map Perfect Map Knowledge Engineering Picking Variables
SUNY Buffalo - CSE - 574
Machine Learning!!!!!SrihariReasoning Patterns and DSeparationSargur Sriharisrihari@cedar.buffalo.edu1Machine Learning!!!!!SrihariTopics Reasoning Patterns Causal and Evidential Reasoning D-separation Direct Connection Indirect Conn
SUNY Buffalo - CSE - 574
Machine Learning!!!!!SrihariReasoning Patterns and DSeparationSargur Sriharisrihari@cedar.buffalo.edu1Machine Learning!!!!!SrihariTopics Reasoning Patterns Causal and Evidential Reasoning D-separation Direct Connection Indirect Conn
SUNY Buffalo - CSE - 574
Machine LearningSrihariFrom Distributions to GraphsSargur Sriharisrihari@cedar.buffalo.edu1Machine LearningSrihariTopics Bayesian Network Semantics of Bayesian Networks Minimal I-Maps Perfect Maps Finding Perfect Maps Identifying the undirec
SUNY Buffalo - CSE - 574
Machine Learning!!!!!SrihariLearning Graphical Models:OverviewSargur Sriharisrihari@cedar.buffalo.edu1Machine Learning!!!Topics!! Motivation Goals of LearningSrihariBN1. Density Estimation2. Specific Prediction Tasks3. Knowledge D
SUNY Buffalo - CSE - 574
Machine Learning!!!!!SrihariLearning as OptimizationSargur Sriharisrihari@cedar.buffalo.edu1Machine Learning!!!!!SrihariTopics in Learning as Optimization Evaluation of Learned Model Empirical Risk and Overfitting Bias vs. Variance Tr
SUNY Buffalo - CSE - 574
Machine Learning!!!!!SrihariUndirected Graphical ModelsSargur Sriharisrihari@cedar.buffalo.edu1Machine Learning!!!!!SrihariTopicsDirected versus Undirected graphical modelsComponents of a Markov NetworkIndependence PropertiesParamete
SUNY Buffalo - CSE - 574
Machine Learning!!!!!SrihariSemantics of Markov NetworksSargur Sriharisrihari@cedar.buffalo.edu1Machine Learning!!!Topics!!Srihari Independencies in Markov Networks Global and Local Independencies From Distributions to Graphs Paramet
SUNY Buffalo - CSE - 574
Machine LearningSrihariMarkov Networks in Computer VisionSargur Sriharisrihari@cedar.buffalo.edu1Machine LearningSrihariTopics1. Computer Vision Applications2. Image Segmentation3. Denoising2Machine LearningSrihariMarkov Networks for Comput
SUNY Buffalo - CSE - 574
Machine Learning!!!!!SrihariPartially Directed Models andConditional Random FieldsSargur Sriharisrihari@cedar.buffalo.edu1Machine Learning!!!!!SrihariTopics Unifying directed and undirected graphs Conditional Random Fields CRF Semant
SUNY Buffalo - CSE - 574
Machine LearningSrihariParameter Estimation forBayesian NetworksSargur Sriharisrihari@cedar.buffalo.edu1Machine LearningSrihariTopics Problem Statement Maximum Likelihood Approach Thumb-tack (Bernoulli), Multinomial, Gaussian Application to B
SUNY Buffalo - CSE - 574
Machine LearningSrihariBayesian Parameter Estimationin Bayesian NetworksSargur Sriharisrihari@cedar.buffalo.edu1Machine LearningSrihariTopics1. Bayesian network where parameters are included as variable nodes2. Global parameter independence L
SUNY Buffalo - CSE - 574
Machine Learning!!!!!SrihariInference in Graphical ModelsSargur Sriharisrihari@cedar.buffalo.edu1Machine Learning!!!Topics!!Srihari1. Objective of Inference Algorithms2. Cases1. Bayes Theorem Inference2. Inference on a Chain3. Trees
SUNY Buffalo - CSE - 574
Machine Learning!!!!!SrihariFactor Graphs and InferenceSargur Sriharisrihari@cedar.buffalo.edu1Machine Learning!!!Topics!!Srihari1. Factor Graphs1. Factors in probability distributions2. Deriving them from graphical models2. Exact In
SUNY Buffalo - CSE - 574
Machine Learning!!!!!SrihariMax-Sum Inference AlgorithmSargur Sriharisrihari@cedar.buffalo.edu1Machine Learning!!!!!SrihariThe max-sum algorithmSum-product algorithmTakes joint distribution expressed as a factor graphEfficiently finds
SUNY Buffalo - CSE - 574
Machine Learning!!!!!SrihariMax-Sum Inference AlgorithmSargur Sriharisrihari@cedar.buffalo.edu1Machine Learning!!!!!SrihariThe max-sum algorithmSum-product algorithmTakes joint distribution expressed as a factor graphEfficiently finds
SUNY Buffalo - CSE - 574
Machine Learning!!!!!SrihariInference: Loopy BeliefPropagationSargur Sriharisrihari@cedar.buffalo.edu1Machine Learning!!!!!SrihariLoopy belief propagationIn practice exact inference may not be possibleApproaches in such cases:1.2.V
SUNY Buffalo - CSE - 574
Machine Learning!!!!!SrihariLatent Variable View of EMSargur Sriharisrihari@cedar.buffalo.edu1Machine Learning!!!!!SrihariMain Idea of EM Goal of EM is: find maximum likelihood solutions for models having latentvariables In case of m
SUNY Buffalo - CSE - 574
Machine LearningSrihariBasic Sampling MethodsSargur Sriharisrihari@cedar.buffalo.edu1Machine LearningSrihariTopics1.2.3.4.5.6.MotivationAncestral SamplingBasic Sampling AlgorithmsRejection SamplingImportance SamplingSampling-Importance
SUNY Buffalo - CSE - 574
Machine LearningSrihari Monte Carlo Sampling MethodsSargur Sriharisrihari@cedar.buffalo.edu1Machine LearningSrihari Topics1.2.3.4.5.6.Markov Chain Monte CarloBasic Metropolis AlgorithmMarkov ChainsMetropolis-Hastings AlgorithmGibbs Samp
Aurora - MATHEMATIC - 101
Horizontal Asymptotes Occurs when the function approaches a specic y value as x approachespositive or negative innity End Behavior Models Occurs when x approaches +/- innity, and the function is a rationalfunction (p(x)/q(x) where p is of higher or
Aurora - MATHEMATIC - 101
Continuity Def: a function is continuous at point c if the limit as xapproaches c of the function is equal to the function ofc (Figure 2.3) Behavior = Location Types of Discontinuities Removable- it is xableContinuous FunctionHole in Graphremova
Aurora - MATHEMATIC - 101
Average Rate of Change vs. Instantaneous Rate of Change Average Rate of Change Instantaneous Rate of Change Tangent Line cfw_ y=m(x-x1) + y1 Normal line (perpendicular to the tangent line) cfw_ y= (-1/m)(x-x1) + y1
Aurora - MATHEMATIC - 101
The derivative of a function f(x) is the slope formula given by: (Figure 1)Figure 1Example 2Example 1Notations for derivatives: How to create derivatives from tablesAge vs. Weight Gain
Aurora - MATHEMATIC - 101
Differentiability In order for f(x) to be differentiable at x=c F(x) must be continuous at c The limit as x approaches c of f '(c) exists LHD [f(c)] = RHD [f(x)]Example 1 The Four Types of Non-Differentiability Corner Point Example: the absolute
Aurora - MATHEMATIC - 101
Rules of DerivativesConstantProduct RulePower RuleQuotient RuleConstant MultipleSum/Difference Rule Constant Rule Power Rule Constant Multiple Rule Sum/Difference Rule Product Rule Quotient Rule Power RulePower Rule Proof Product RuleExam
Aurora - MATHEMATIC - 101
Position S(t) Displacement- change in position Average Rate of Change = Average Velocity Velocity Derivative if the Position function withrespect to time ds/dt = v(t) Speed = |v(t)| Acceleration Change in velocity/change in time dv/dt JerkPo