Gravity Models. Elena Nikolaeva, Egon Elbre, Roland Pihlakas. MTAT Graph Mining
|
|
- Rosamond Henry
- 5 years ago
- Views:
Transcription
1 Gravity Models Elena Nikolaeva, Egon Elbre, Roland Pihlakas
2 G=(V,C) network graph Introduction Origin Destination Flow as traffic FLOW
3 Traffic flow
4 Characteristics Of The Network Flows
5 Characteristics Of The Network Flows How does the traffic move throughout the network?
6 Characteristics Of The Network Flows How does the traffic move throughout the network? Routing Matrix
7 Routing Matrix Captures the manner in which traffic moves throughout the network. B - binary values - fraction of flow in case multiple routes are possible A 1 B 2 C 3 D B e;ij = AC AD BD BC CD Figures are from Lauri Eskor s slides
8 Characteristics Of The Network Flows How much traffic flows from point A to point B?
9 Characteristics Of The Network Flows How much traffic flows from point A to point B? Traffic Matrix
10 Constructing Traffic Matrix A B A B C D E Ti A C 30 B C D D E E Tj Copyright , Dr. Jean-Paul Rodrigue, Dept. of Global Studies & Geography, Hofstra University.
11 Origin-Destination Matrix (Traffic Matrix) Where Z ij is the total volume of traffic flowing from origin vertex i to a destination vertex j in a given period of time. Net out-flow corresponding to vertices i Net in-flow corresponding to vertices j
12 Link Totals,where X e the total flow over a given link e E,where Z-traffic matrix written as a vector A 1 B 2 Xe = C i, j X 1 AC AD BD BC CD X 2 = X D Be;ij Zij X X B Z AC Z AD Z BD Z BC Z CD Z
13 Characteristics Of The Network Flows How much will it cost us?
14 Characteristics Of The Network Flows How much will it cost us? Cost
15 The Four Ts in International Trade Transaction costs Tariff and non-tariff costs Transport costs Time costs Copyright , Dr. Jean-Paul Rodrigue, Dept. of Global Studies & Geography, Hofstra University.
16 Total Logistics Costs Tradeoff Total Logistics Costs Costs Warehousing Costs Transport Costs Shipment Size or Number of Warehouses Copyright , Dr. Jean-Paul Rodrigue, Dept. of Global Studies & Geography, Hofstra University.
17 Additional Measurements Of Traffic Volume C cost associated with paths or links. i.e. generalized cost (in transport economics)-is the sum of the monetary and non-monetary costs of a journey Costs associated with QoS - quality of service (in computer and telecommunication networks ) is the ability to provide different priority to different applications, users, or data flows, or to guarantee a certain level of performance to a data flow
18 Characteristics Of The Network Flows How will traffic change over time?
19 Characteristics Of The Network Flows How will traffic change over time? Time
20 Time-Varying Perspective Flows have dynamic nature Z (t) - time dependent traffic matrix B - fixed (changes in routing occur in longer time than those associated with the scale )
21 Characteristics Summary Origin FLOW Destination B Routing Matrix Z - Traffic Matrix C - Cost T - Time
22 Flow analysis classification Measurements Goal Method OD flow volumes Z ij Link volumes X e OD costs c ij Model observed flow volumes Z ij Predict unobserved OD flow volumes Z ij Predict unobserved OD and link costs Gravity Models Traffic matrix estimation(static, dynamic) Estimation of network flow costs
23 Gravity Models Metaphor of physical gravity Tij = G Mi Mj Dij 2 M i, M j -population size (mass) D ij - measure of separation (distance, cost) Applications: Social science (interaction between people of different populations), geography, economics, analysis of computer network traffic etc.
24 Application of an Elementary Spatial Interaction Equation 2,000,000 X 800 km 2,000,000 Y Elementary Formulation T ij = k P i P j D ij W X Y Z Ti 400 km W 100, ,000 W Z X 100,000 50,000 25, ,000 2,000,000 k = (people per week) 1,000,000 Y 50,000 50,000 Z 25,000 25,000 Centroid (i) Weight (P) Distance (D) Constant (k) Interaction (T) Tj 100, ,000 50,000 25, ,000 Copyright , Dr. Jean-Paul Rodrigue, Dept. of Global Studies & Geography, Hofstra University.
25 Relationship between Distance and Interactions T(B-A) A B T(C-A) A C Interaction T(D-A) A D A B C D Copyright , Dr. Jean-Paul Rodrigue, Dept. of Global Studies & Geography, Hofstra University. Distance
26 General Gravity Model Specifies that the traffic flows Z ij to be in the form of counts, with independent Poisson distributions and the mean function of the form of: T ij = k P i P j D ij 2,000,000 P i D ij =800 km 2,000,000 P j,where T ij =E(Z ij )- expected value of interaction h O (i)=p i - origin function h D (j)=p j - destination function h S (c ij )=D ij - separation function c ij - vector of K separation attributes
27 Extension of the Gravity Model. 2,000,000 X λ = 0.95 α = km 2,000,000 Y Simple Formulation T ij = k P α β i P j θ D ij W 2,000, km λ = 1.03 α = 0.96 k = (people per week) Z 1,000,000 λ = 1.00 α = 0.90 λ = 1.2 α = 0.7 W X Y Z Ti W 71,378 71,378 X 6,059 2, ,298 Y 19,420 19,420 Z 153, ,893 Centroid (i) Weight (P) Distance (D) Constant (k) Interaction (T) Exponent Tj 6, ,692 2, ,990 Copyright , Dr. Jean-Paul Rodrigue, Dept. of Global Studies & Geography, Hofstra University.
28 Extension of the Gravity Model. Power functions,where origin function h O (i) = (Pi) α = (π O,i) α destination function h D ( j) = (Pj) β = (π D j) β flow ~1/x a separation function h S (cij) = (Dij) θ = (cij) θ C ij -scalar, 0 ~exp() OR cost
29 Gravity Models. Example Austrian Call Data Need to understand the spatial structure of telecommunication interactions among populations between different geographical regions
30 Gravity Models. Example Austrian Call Data Need to understand the spatial structure of telecommunication interactions among populations between different geographical regions WHY?
31 Gravity Models. Example Austrian Call Data Need to understand the spatial structure of telecommunication interactions among populations between different geographical regions Regulation of the telecommunication sector Anticipating the influence of telecommunication technologies on regional development
32 Number of districts - 32 Time -1 year Measurements - intensity z ij, i j=1,,32 Austrian Call Data π O, i is the GRP of origin i, π D, j is the GRP of destination j, c i j is the distance from origin i to destination j
33 Austrian Call Data Scatter plots: Call flow volume versus each of Origin GRP Destination GRP Distance nonparametric smoother linear regression
34 Alternative Representation. Interaction Probabilities represent the expected relative frequency at which interactions are specifically ij-interactions,where Under the general gravity model specification they can be expressed as:
35 Alternative Representation. Destination Gravity Models related to the counts of Z ij from given origin i to all destinations j Conditional destination probabilities: P(A B) = P(A B) P(B) In terms of components in general probabilities:
36 Inference For The Gravity Models Z ij independent Poisson random variables with means: General model specification:,where
37 Poisson Distribution is a discrete probability distribution that expresses the probability of a number of events occurring in a fixed period of time if these events occur with a known average rate and independently of the time since the last event. (The Poisson distribution can also be used for the number of events in other specified intervals such as distance, area or volume.) The horizontal axis is the index k, the number of occurrences. The function is only defined at integer values of k.
38 Ma Given a sample of n measured values ki we wish to estimate the value of the parameter of the Poisson population from which the sample was drawn. To calculate the maximum likelihood value, we form the log-likelihood function Take the derivative of L with respect to and equate it to zero: Solving for yields a stationary point, which if the second derivative is negative is the maximum-likelihood estimate of : Checking the second derivative, it is found that it is negative for all and ki greater than zero, therefore this stationary point is indeed a maximum of the initial likelihood function:
39 Inference For The Gravity Models. Maximum Likelihood Z = z be an (IJ) 1 vector of observations of the flows Zij, ordered by origin i, and by destination j within origin i Poisson log-likelihood for : maximum likelihood for estimates: for i j satisfys the equations:,where
40 Example. Analysis Of The Austrian Call Data consider two models Fitted using generic iteratively weighted least- squares method for generalized linear models Model arguments are considered significant at the 0,05 level
41 Fitted Values versus Flow Volume Shows the fitted values ˆ i j versus observed flow volumes z ij The relationship between the two quantities is found to be fairly linear for both models, and the variation around their linear trend, fairly uniform The standard model tends to over-estimate in somewhat greater frequency than the general model, particularly for medium- and low-volume flows
42 Relative Error versus Flow Volume Shows the relative errors (z ij ˆij )/z ij versus the flow volumes z ij light and dark points indicate under- and over- estimation, respectively For both models the relative error varies widely in magnitude. The relative error decreases with volume. For low volumes both models are inclined to over-estimate, while for higher volumes, they are increasingly inclined to under-estimate.
43 Thank you for your attention!
Trip Distribution Modeling Milos N. Mladenovic Assistant Professor Department of Built Environment
Trip Distribution Modeling Milos N. Mladenovic Assistant Professor Department of Built Environment 25.04.2017 Course Outline Forecasting overview and data management Trip generation modeling Trip distribution
More informationTransportation Theory and Applications
Fall 2017 - MTAT.08.043 Transportation Theory and Applications Lecture IV: Trip distribution A. Hadachi outline Our objective Introducing two main methods for trip generation objective Trip generation
More informationCIV3703 Transport Engineering. Module 2 Transport Modelling
CIV3703 Transport Engineering Module Transport Modelling Objectives Upon successful completion of this module you should be able to: carry out trip generation calculations using linear regression and category
More informationRandomized Algorithms
Randomized Algorithms Prof. Tapio Elomaa tapio.elomaa@tut.fi Course Basics A new 4 credit unit course Part of Theoretical Computer Science courses at the Department of Mathematics There will be 4 hours
More informationGeographically weighted regression approach for origin-destination flows
Geographically weighted regression approach for origin-destination flows Kazuki Tamesue 1 and Morito Tsutsumi 2 1 Graduate School of Information and Engineering, University of Tsukuba 1-1-1 Tennodai, Tsukuba,
More information( ).666 Information Extraction from Speech and Text
(520 600).666 Information Extraction from Speech and Text HMM Parameters Estimation for Gaussian Output Densities April 27, 205. Generalization of the Results of Section 9.4. It is suggested in Section
More informationAn Overview of Traffic Matrix Estimation Methods
An Overview of Traffic Matrix Estimation Methods Nina Taft Berkeley www.intel.com/research Problem Statement 1 st generation solutions 2 nd generation solutions 3 rd generation solutions Summary Outline
More informationEXAMINATIONS OF THE ROYAL STATISTICAL SOCIETY
EXAMINATIONS OF THE ROYAL STATISTICAL SOCIETY GRADUATE DIPLOMA, 00 MODULE : Statistical Inference Time Allowed: Three Hours Candidates should answer FIVE questions. All questions carry equal marks. The
More informationIntroduction to Signal Detection and Classification. Phani Chavali
Introduction to Signal Detection and Classification Phani Chavali Outline Detection Problem Performance Measures Receiver Operating Characteristics (ROC) F-Test - Test Linear Discriminant Analysis (LDA)
More informationEE/ACM Applications of Convex Optimization in Signal Processing and Communications Lecture 18
EE/ACM 150 - Applications of Convex Optimization in Signal Processing and Communications Lecture 18 Andre Tkacenko Signal Processing Research Group Jet Propulsion Laboratory May 31, 2012 Andre Tkacenko
More informationProbabilistic Graphical Models
Probabilistic Graphical Models David Sontag New York University Lecture 4, February 16, 2012 David Sontag (NYU) Graphical Models Lecture 4, February 16, 2012 1 / 27 Undirected graphical models Reminder
More informationCorrelation and Regression
Elementary Statistics A Step by Step Approach Sixth Edition by Allan G. Bluman http://www.mhhe.com/math/stat/blumanbrief SLIDES PREPARED BY LLOYD R. JAISINGH MOREHEAD STATE UNIVERSITY MOREHEAD KY Updated
More informationHigh-Throughput Sequencing Course
High-Throughput Sequencing Course DESeq Model for RNA-Seq Biostatistics and Bioinformatics Summer 2017 Outline Review: Standard linear regression model (e.g., to model gene expression as function of an
More informationStatistics 572 Semester Review
Statistics 572 Semester Review Final Exam Information: The final exam is Friday, May 16, 10:05-12:05, in Social Science 6104. The format will be 8 True/False and explains questions (3 pts. each/ 24 pts.
More informationLecture 14: Introduction to Poisson Regression
Lecture 14: Introduction to Poisson Regression Ani Manichaikul amanicha@jhsph.edu 8 May 2007 1 / 52 Overview Modelling counts Contingency tables Poisson regression models 2 / 52 Modelling counts I Why
More informationModelling counts. Lecture 14: Introduction to Poisson Regression. Overview
Modelling counts I Lecture 14: Introduction to Poisson Regression Ani Manichaikul amanicha@jhsph.edu Why count data? Number of traffic accidents per day Mortality counts in a given neighborhood, per week
More informationCIE4801 Transportation and spatial modelling Modal split
CIE4801 Transportation and spatial modelling Modal split Rob van Nes, Transport & Planning 31-08-18 Delft University of Technology Challenge the future Content Nested logit part 2 Modelling component 3:
More informationA NOTE ON A SINGLE VEHICLE AND ONE DESTINATION ROUTING PROBLEM AND ITS GAME-THEORETIC MODELS
ALS Advanced Logistic Systems A NOTE ON A SINGLE VEHICLE AND ONE DESTINATION ROUTING PROBLEM AND ITS GAME-THEORETIC MODELS Andrzej Grzybowski Czestochowa University of Technology, Poland Abstract: In the
More informationMohammed. Research in Pharmacoepidemiology National School of Pharmacy, University of Otago
Mohammed Research in Pharmacoepidemiology (RIPE) @ National School of Pharmacy, University of Otago What is zero inflation? Suppose you want to study hippos and the effect of habitat variables on their
More informationb k b m 1 b m 2 b 1 b 0 b k
International Mathematical Forum, Vol. 6, 2011, no. 62, 3087-3092 Estimating Changes in Traffic Intensity for M/M/1/m Queueing Systems Sarat Kumar Acharya Departament of Statistics, Sambalpur University
More informationSPACE Workshop NSF NCGIA CSISS UCGIS SDSU. Aldstadt, Getis, Jankowski, Rey, Weeks SDSU F. Goodchild, M. Goodchild, Janelle, Rebich UCSB
SPACE Workshop NSF NCGIA CSISS UCGIS SDSU Aldstadt, Getis, Jankowski, Rey, Weeks SDSU F. Goodchild, M. Goodchild, Janelle, Rebich UCSB August 2-8, 2004 San Diego State University Some Examples of Spatial
More informationEven Simpler Standard Errors for Two-Stage Optimization Estimators: Mata Implementation via the DERIV Command
Even Simpler Standard Errors for Two-Stage Optimization Estimators: Mata Implementation via the DERIV Command by Joseph V. Terza Department of Economics Indiana University Purdue University Indianapolis
More informationProblem #1 #2 #3 #4 #5 #6 Total Points /6 /8 /14 /10 /8 /10 /56
STAT 391 - Spring Quarter 2017 - Midterm 1 - April 27, 2017 Name: Student ID Number: Problem #1 #2 #3 #4 #5 #6 Total Points /6 /8 /14 /10 /8 /10 /56 Directions. Read directions carefully and show all your
More informationThe Model Research of Urban Land Planning and Traffic Integration. Lang Wang
International Conference on Materials, Environmental and Biological Engineering (MEBE 2015) The Model Research of Urban Land Planning and Traffic Integration Lang Wang Zhejiang Gongshang University, Hangzhou
More informationGenerative Learning. INFO-4604, Applied Machine Learning University of Colorado Boulder. November 29, 2018 Prof. Michael Paul
Generative Learning INFO-4604, Applied Machine Learning University of Colorado Boulder November 29, 2018 Prof. Michael Paul Generative vs Discriminative The classification algorithms we have seen so far
More informationModels for Count and Binary Data. Poisson and Logistic GWR Models. 24/07/2008 GWR Workshop 1
Models for Count and Binary Data Poisson and Logistic GWR Models 24/07/2008 GWR Workshop 1 Outline I: Modelling counts Poisson regression II: Modelling binary events Logistic Regression III: Poisson Regression
More informationCalculus first semester exam information and practice problems
Calculus first semester exam information and practice problems As I ve been promising for the past year, the first semester exam in this course encompasses all three semesters of Math SL thus far. It is
More informationNotes on Markov Networks
Notes on Markov Networks Lili Mou moull12@sei.pku.edu.cn December, 2014 This note covers basic topics in Markov networks. We mainly talk about the formal definition, Gibbs sampling for inference, and maximum
More informationFuzzy Geographically Weighted Clustering
Fuzzy Geographically Weighted Clustering G. A. Mason 1, R. D. Jacobson 2 1 University of Calgary, Dept. of Geography 2500 University Drive NW Calgary, AB, T2N 1N4 Telephone: +1 403 210 9723 Fax: +1 403
More informationCSC321 Lecture 6: Backpropagation
CSC321 Lecture 6: Backpropagation Roger Grosse Roger Grosse CSC321 Lecture 6: Backpropagation 1 / 21 Overview We ve seen that multilayer neural networks are powerful. But how can we actually learn them?
More informationHidden Markov Models
Hidden Markov Models Slides revised and adapted to Bioinformática 55 Engª Biomédica/IST 2005 Ana Teresa Freitas Forward Algorithm For Markov chains we calculate the probability of a sequence, P(x) How
More informationGraph Detection and Estimation Theory
Introduction Detection Estimation Graph Detection and Estimation Theory (and algorithms, and applications) Patrick J. Wolfe Statistics and Information Sciences Laboratory (SISL) School of Engineering and
More informationLecture 1: Introduction to Sublinear Algorithms
CSE 522: Sublinear (and Streaming) Algorithms Spring 2014 Lecture 1: Introduction to Sublinear Algorithms March 31, 2014 Lecturer: Paul Beame Scribe: Paul Beame Too much data, too little time, space for
More informationNumber, Number Sense, and Operations Data Analysis and Probability
Algebra 1 Unit 1 Numbers 3 weeks Number, Number Sense, and Operations Data Analysis and Probability NC Apply properties of operations and the real number system, and justify when they hold for a set of
More informationBayesian non-parametric model to longitudinally predict churn
Bayesian non-parametric model to longitudinally predict churn Bruno Scarpa Università di Padova Conference of European Statistics Stakeholders Methodologists, Producers and Users of European Statistics
More informationGeneralized Linear Models
York SPIDA John Fox Notes Generalized Linear Models Copyright 2010 by John Fox Generalized Linear Models 1 1. Topics I The structure of generalized linear models I Poisson and other generalized linear
More informationBiostat 2065 Analysis of Incomplete Data
Biostat 2065 Analysis of Incomplete Data Gong Tang Dept of Biostatistics University of Pittsburgh October 20, 2005 1. Large-sample inference based on ML Let θ is the MLE, then the large-sample theory implies
More informationCommunications in Statistics - Simulation and Computation. Comparison of EM and SEM Algorithms in Poisson Regression Models: a simulation study
Comparison of EM and SEM Algorithms in Poisson Regression Models: a simulation study Journal: Manuscript ID: LSSP-00-0.R Manuscript Type: Original Paper Date Submitted by the Author: -May-0 Complete List
More informationExploring spatial decay effect in mass media and social media: a case study of China
Exploring spatial decay effect in mass media and social media: a case study of China 1. Introduction Yihong Yuan Department of Geography, Texas State University, San Marcos, TX, USA, 78666. Tel: +1(512)-245-3208
More informationSTA216: Generalized Linear Models. Lecture 1. Review and Introduction
STA216: Generalized Linear Models Lecture 1. Review and Introduction Let y 1,..., y n denote n independent observations on a response Treat y i as a realization of a random variable Y i In the general
More informationFrom transport to accessibility: the new lease of life of an old concept
Paris 07 /01/ 2015 From transport to accessibility: the new lease of life of an old concept Pr. Yves Crozet Laboratory of Transport Economics (LET) University of Lyon (IEP) - France yves.crozet@let.ish-lyon.cnrs.fr
More informationUsing Markov Chains To Model Human Migration in a Network Equilibrium Framework
Using Markov Chains To Model Human Migration in a Network Equilibrium Framework Jie Pan Department of Mathematics and Computer Science Saint Joseph s University Philadelphia, PA 19131 Anna Nagurney School
More informationGenerative Clustering, Topic Modeling, & Bayesian Inference
Generative Clustering, Topic Modeling, & Bayesian Inference INFO-4604, Applied Machine Learning University of Colorado Boulder December 12-14, 2017 Prof. Michael Paul Unsupervised Naïve Bayes Last week
More informationDynamic Factor Models and Factor Augmented Vector Autoregressions. Lawrence J. Christiano
Dynamic Factor Models and Factor Augmented Vector Autoregressions Lawrence J Christiano Dynamic Factor Models and Factor Augmented Vector Autoregressions Problem: the time series dimension of data is relatively
More informationAssessing Model Adequacy
Assessing Model Adequacy A number of assumptions were made about the model, and these need to be verified in order to use the model for inferences. In cases where some assumptions are violated, there are
More informationMultilevel Modeling Day 2 Intermediate and Advanced Issues: Multilevel Models as Mixed Models. Jian Wang September 18, 2012
Multilevel Modeling Day 2 Intermediate and Advanced Issues: Multilevel Models as Mixed Models Jian Wang September 18, 2012 What are mixed models The simplest multilevel models are in fact mixed models:
More informationRepresent processes and observations that span multiple levels (aka multi level models) R 2
Hierarchical models Hierarchical models Represent processes and observations that span multiple levels (aka multi level models) R 1 R 2 R 3 N 1 N 2 N 3 N 4 N 5 N 6 N 7 N 8 N 9 N i = true abundance on a
More informationStatistics 203: Introduction to Regression and Analysis of Variance Course review
Statistics 203: Introduction to Regression and Analysis of Variance Course review Jonathan Taylor - p. 1/?? Today Review / overview of what we learned. - p. 2/?? General themes in regression models Specifying
More informationEXPLORATORY SPATIAL DATA ANALYSIS OF BUILDING ENERGY IN URBAN ENVIRONMENTS. Food Machinery and Equipment, Tianjin , China
EXPLORATORY SPATIAL DATA ANALYSIS OF BUILDING ENERGY IN URBAN ENVIRONMENTS Wei Tian 1,2, Lai Wei 1,2, Pieter de Wilde 3, Song Yang 1,2, QingXin Meng 1 1 College of Mechanical Engineering, Tianjin University
More informationFacility Location and Distribution System Planning. Thomas L. Magnanti
Facility Location and Distribution System Planning Thomas L. Magnanti Today s Agenda Why study facility location? Issues to be modeled Basic models Fixed charge problems Core uncapacitated and capacitated
More informationMaximum Likelihood Estimation of the Flow Size Distribution Tail Index from Sampled Packet Data
Maximum Likelihood Estimation of the Flow Size Distribution Tail Index from Sampled Packet Data Patrick Loiseau 1, Paulo Gonçalves 1, Stéphane Girard 2, Florence Forbes 2, Pascale Vicat-Blanc Primet 1
More informationMachine Learning I Continuous Reinforcement Learning
Machine Learning I Continuous Reinforcement Learning Thomas Rückstieß Technische Universität München January 7/8, 2010 RL Problem Statement (reminder) state s t+1 ENVIRONMENT reward r t+1 new step r t
More informationLogistic Regression. Advanced Methods for Data Analysis (36-402/36-608) Spring 2014
Logistic Regression Advanced Methods for Data Analysis (36-402/36-608 Spring 204 Classification. Introduction to classification Classification, like regression, is a predictive task, but one in which the
More informationICS141: Discrete Mathematics for Computer Science I
ICS141: Discrete Mathematics for Computer Science I Dept. Information & Computer Sci., Jan Stelovsky based on slides by Dr. Baek and Dr. Still Originals by Dr. M. P. Frank and Dr. J.L. Gross Provided by
More information+ τ t R t 1B t 1 + M t 1. = R t 1B t 1 + M t 1. = λ t (1 + γ f t + γ f t v t )
Eco504, Part II Spring 2006 C. Sims FTPL WITH MONEY 1. FTPL WITH MONEY This model is that of Sims (1994). Agent: [ ] max E β t log C t {C t,m t,b t } t=0 s.t. C t (1 + γ f (v t )) + M t + B t + τ t R t
More informationBased on slides by Richard Zemel
CSC 412/2506 Winter 2018 Probabilistic Learning and Reasoning Lecture 3: Directed Graphical Models and Latent Variables Based on slides by Richard Zemel Learning outcomes What aspects of a model can we
More informationLearning Bayesian Networks (part 1) Goals for the lecture
Learning Bayesian Networks (part 1) Mark Craven and David Page Computer Scices 760 Spring 2018 www.biostat.wisc.edu/~craven/cs760/ Some ohe slides in these lectures have been adapted/borrowed from materials
More informationp(d θ ) l(θ ) 1.2 x x x
p(d θ ).2 x 0-7 0.8 x 0-7 0.4 x 0-7 l(θ ) -20-40 -60-80 -00 2 3 4 5 6 7 θ ˆ 2 3 4 5 6 7 θ ˆ 2 3 4 5 6 7 θ θ x FIGURE 3.. The top graph shows several training points in one dimension, known or assumed to
More informationCreated by T. Madas 2D VECTORS. Created by T. Madas
2D VECTORS Question 1 (**) Relative to a fixed origin O, the point A has coordinates ( 2, 3). The point B is such so that AB = 3i 7j, where i and j are mutually perpendicular unit vectors lying on the
More informationOutline. 15. Descriptive Summary, Design, and Inference. Descriptive summaries. Data mining. The centroid
Outline 15. Descriptive Summary, Design, and Inference Geographic Information Systems and Science SECOND EDITION Paul A. Longley, Michael F. Goodchild, David J. Maguire, David W. Rhind 2005 John Wiley
More informationApplied Probability. School of Mathematics and Statistics, University of Sheffield. (University of Sheffield) Applied Probability / 8
Applied Probability School of Mathematics and Statistics, University of Sheffield 2018 19 (University of Sheffield) Applied Probability 2018 19 1 / 8 Introduction You will have seen probability models.
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 informationMachine Learning 2017
Machine Learning 2017 Volker Roth Department of Mathematics & Computer Science University of Basel 21st March 2017 Volker Roth (University of Basel) Machine Learning 2017 21st March 2017 1 / 41 Section
More informationTHE METHOD OF CONDITIONAL PROBABILITIES: DERANDOMIZING THE PROBABILISTIC METHOD
THE METHOD OF CONDITIONAL PROBABILITIES: DERANDOMIZING THE PROBABILISTIC METHOD JAMES ZHOU Abstract. We describe the probabilistic method as a nonconstructive way of proving the existence of combinatorial
More informationBayesian Analysis of Risk for Data Mining Based on Empirical Likelihood
1 / 29 Bayesian Analysis of Risk for Data Mining Based on Empirical Likelihood Yuan Liao Wenxin Jiang Northwestern University Presented at: Department of Statistics and Biostatistics Rutgers University
More informationECEN 689 Special Topics in Data Science for Communications Networks
ECEN 689 Special Topics in Data Science for Communications Networks Nick Duffield Department of Electrical & Computer Engineering Texas A&M University Lecture 13 Measuring and Inferring Traffic Matrices
More informationURBAN TRANSPORTATION SYSTEM (ASSIGNMENT)
BRANCH : CIVIL ENGINEERING SEMESTER : 6th Assignment-1 CHAPTER-1 URBANIZATION 1. What is Urbanization? Explain by drawing Urbanization cycle. 2. What is urban agglomeration? 3. Explain Urban Class Groups.
More informationLocation Theory and Decision Analysis
Location Theory and Decision Analysis Analytics of Spatial Information Second Edition Yupo Chan Professor & Founding Chair Department of Systems Engineering Donaghey College of Engineering and Information
More informationAd Placement Strategies
Case Study 1: Estimating Click Probabilities Tackling an Unknown Number of Features with Sketching Machine Learning for Big Data CSE547/STAT548, University of Washington Emily Fox 2014 Emily Fox January
More informationMULTIPLE CHOICE QUESTIONS DECISION SCIENCE
MULTIPLE CHOICE QUESTIONS DECISION SCIENCE 1. Decision Science approach is a. Multi-disciplinary b. Scientific c. Intuitive 2. For analyzing a problem, decision-makers should study a. Its qualitative aspects
More informationSpatial Economics and Potential Games
Outline Spatial Economics and Potential Games Daisuke Oyama Graduate School of Economics, Hitotsubashi University Hitotsubashi Game Theory Workshop 2007 Session Potential Games March 4, 2007 Potential
More information11 : Gaussian Graphic Models and Ising Models
10-708: Probabilistic Graphical Models 10-708, Spring 2017 11 : Gaussian Graphic Models and Ising Models Lecturer: Bryon Aragam Scribes: Chao-Ming Yen 1 Introduction Different from previous maximum likelihood
More informationTied survival times; estimation of survival probabilities
Tied survival times; estimation of survival probabilities Patrick Breheny November 5 Patrick Breheny Survival Data Analysis (BIOS 7210) 1/22 Introduction Tied survival times Introduction Breslow approximation
More informationST MARY S DSG, KLOOF GRADE: SEPTEMBER 2017 MATHEMATICS PAPER 2
ST MARY S DSG, KLOOF GRADE: 12 12 SEPTEMBER 2017 MATHEMATICS PAPER 2 TIME: 3 HOURS ASSESSOR: S Drew TOTAL: 150 MARKS MODERATORS: J van Rooyen E Robertson EXAMINATION NUMBER: TEACHER: INSTRUCTIONS: 1. This
More informationbound on the likelihood through the use of a simpler variational approximating distribution. A lower bound is particularly useful since maximization o
Category: Algorithms and Architectures. Address correspondence to rst author. Preferred Presentation: oral. Variational Belief Networks for Approximate Inference Wim Wiegerinck David Barber Stichting Neurale
More informationGeospatial Analysis of Job-Housing Mismatch Using ArcGIS and Python
Geospatial Analysis of Job-Housing Mismatch Using ArcGIS and Python 2016 ESRI User Conference June 29, 2016 San Diego, CA Jung Seo, Frank Wen, Simon Choi and Tom Vo, Research & Analysis Southern California
More informationarxiv: v1 [cs.it] 21 Feb 2013
q-ary Compressive Sensing arxiv:30.568v [cs.it] Feb 03 Youssef Mroueh,, Lorenzo Rosasco, CBCL, CSAIL, Massachusetts Institute of Technology LCSL, Istituto Italiano di Tecnologia and IIT@MIT lab, Istituto
More informationThe spatial autocorrelation problem in spatial interaction modelling: a comparison of two common solutions
MPRA Munich Personal RePEc Archive The spatial autocorrelation problem in spatial interaction modelling: a comparison of two common solutions Daniel A. Griffith and Manfred M. Fischer and James P. LeSage
More informationFinal. Introduction to Artificial Intelligence. CS 188 Spring You have approximately 2 hours and 50 minutes.
CS 188 Spring 2014 Introduction to Artificial Intelligence Final You have approximately 2 hours and 50 minutes. The exam is closed book, closed notes except your two-page crib sheet. Mark your answers
More informationCS 2750: Machine Learning. Bayesian Networks. Prof. Adriana Kovashka University of Pittsburgh March 14, 2016
CS 2750: Machine Learning Bayesian Networks Prof. Adriana Kovashka University of Pittsburgh March 14, 2016 Plan for today and next week Today and next time: Bayesian networks (Bishop Sec. 8.1) Conditional
More informationModeling Longitudinal Count Data with Excess Zeros and Time-Dependent Covariates: Application to Drug Use
Modeling Longitudinal Count Data with Excess Zeros and : Application to Drug Use University of Northern Colorado November 17, 2014 Presentation Outline I and Data Issues II Correlated Count Regression
More informationCommuting in Northern Ireland: Exploring Spatial Variations through Spatial Interaction Modelling
Commuting in Northern Ireland: Exploring Spatial Variations through Spatial Interaction Modelling 1. Introduction C. D. Lloyd, I. G. Shuttleworth, G. Catney School of Geography, Archaeology and Palaeoecology,
More informationText Mining for Economics and Finance Latent Dirichlet Allocation
Text Mining for Economics and Finance Latent Dirichlet Allocation Stephen Hansen Text Mining Lecture 5 1 / 45 Introduction Recall we are interested in mixed-membership modeling, but that the plsi model
More informationComputational statistics
Computational statistics Lecture 3: Neural networks Thierry Denœux 5 March, 2016 Neural networks A class of learning methods that was developed separately in different fields statistics and artificial
More informationMeasuring the impact of freeway infrastructure on the accessibility of the city of Fez
Measuring the impact of freeway infrastructure on the accessibility of the city of Fez Imane MOUFAD Laboratory of Energy & Sustainable Development (LPE2D) Sidi Mohamed Ben Abdellah University - EST, Road
More informationChanges in the Spatial Distribution of Mobile Source Emissions due to the Interactions between Land-use and Regional Transportation Systems
Changes in the Spatial Distribution of Mobile Source Emissions due to the Interactions between Land-use and Regional Transportation Systems A Framework for Analysis Urban Transportation Center University
More informationPoverty and Inclusion in the West Bank and Gaza. Tara Vishwanath and Roy Van der Weide
Poverty and Inclusion in the West Bank and Gaza Tara Vishwanath and Roy Van der Weide Oslo accord created a fragmented territory, with no Palestinian control over Area C Overlaid by a regime of internal
More informationNonparametric Location Tests: k-sample
Nonparametric Location Tests: k-sample Nathaniel E. Helwig Assistant Professor of Psychology and Statistics University of Minnesota (Twin Cities) Updated 04-Jan-2017 Nathaniel E. Helwig (U of Minnesota)
More informationEfficiency and Braess Paradox under Pricing
Efficiency and Braess Paradox under Pricing Asuman Ozdaglar Joint work with Xin Huang, [EECS, MIT], Daron Acemoglu [Economics, MIT] October, 2004 Electrical Engineering and Computer Science Dept. Massachusetts
More informationAn online data and consulting resource of THE UNIVERSITY OF TOLEDO THE JACK FORD URBAN AFFAIRS CENTER
An online data and consulting resource of THE JACK FORD URBAN AFFAIRS CENTER THE CENTER FOR GEOGRAPHIC INFORMATION SCIENCE AND APPLIED GEOGRAPHICS DEPARTMENT OF GEOGRAPHY AND PLANNING THE UNIVERSITY OF
More information13.7 ANOTHER TEST FOR TREND: KENDALL S TAU
13.7 ANOTHER TEST FOR TREND: KENDALL S TAU In 1969 the U.S. government instituted a draft lottery for choosing young men to be drafted into the military. Numbers from 1 to 366 were randomly assigned to
More informationCSE 546 Final Exam, Autumn 2013
CSE 546 Final Exam, Autumn 0. Personal info: Name: Student ID: E-mail address:. There should be 5 numbered pages in this exam (including this cover sheet).. You can use any material you brought: any book,
More informationYEAR 12 - Mathematics Pure (C1) Term 1 plan
Week YEAR 12 - Mathematics Pure (C1) Term 1 plan 2016-2017 1-2 Algebra Laws of indices for all rational exponents. Use and manipulation of surds. Quadratic functions and their graphs. The discriminant
More informationBayesian nonparametric models for bipartite graphs
Bayesian nonparametric models for bipartite graphs François Caron Department of Statistics, Oxford Statistics Colloquium, Harvard University November 11, 2013 F. Caron 1 / 27 Bipartite networks Readers/Customers
More informationCSCI-567: Machine Learning (Spring 2019)
CSCI-567: Machine Learning (Spring 2019) Prof. Victor Adamchik U of Southern California Mar. 19, 2019 March 19, 2019 1 / 43 Administration March 19, 2019 2 / 43 Administration TA3 is due this week March
More informationSTA 216: GENERALIZED LINEAR MODELS. Lecture 1. Review and Introduction. Much of statistics is based on the assumption that random
STA 216: GENERALIZED LINEAR MODELS Lecture 1. Review and Introduction Much of statistics is based on the assumption that random variables are continuous & normally distributed. Normal linear regression
More informationAPPENDIX Should the Private Sector Provide Public Capital?
APPENIX Should the Private Sector Provide Public Capital? Santanu Chatterjee epartment of Economics Terry College of Business University of eorgia Appendix A The appendix describes the optimization problem
More informationModeling Network Optimization Problems
Modeling Network Optimization Problems John E. Mitchell http://www.rpi.edu/~mitchj Mathematical Models of Operations Research MATP4700 / ISYE4770 October 19, 01 Mitchell (MATP4700) Network Optimization
More informationLarge-Scale Behavioral Targeting
Large-Scale Behavioral Targeting Ye Chen, Dmitry Pavlov, John Canny ebay, Yandex, UC Berkeley (This work was conducted at Yahoo! Labs.) June 30, 2009 Chen et al. (KDD 09) Large-Scale Behavioral Targeting
More informationChapter 7 Network Flow Problems, I
Chapter 7 Network Flow Problems, I Network flow problems are the most frequently solved linear programming problems. They include as special cases, the assignment, transportation, maximum flow, and shortest
More information