W-BASED VS LATENT VARIABLES SPATIAL AUTOREGRESSIVE MODELS: EVIDENCE FROM MONTE CARLO SIMULATIONS
|
|
- Evan McKinney
- 5 years ago
- Views:
Transcription
1 W-BASED VS LATENT VARIABLES SPATIAL AUTOREGRESSIVE MODELS: EVIDENCE FROM MONTE CARLO SIMULATIONS. Introduction When it coes to applying econoetric odels to analyze georeferenced data, researchers are well aware that ignoring spatial dependencies would lead to inefficient and biased estiates. A lot of theoretical and siulation studies have been undertaken seeking efficient and consistent estiators for spatial data analysis and one ajor issue concerns the kind of decisions to ake regarding the specification of the structure of spatial dependence including the type of spatial weights to be incorporated into the odel. Therefore, our study focuses on the evaluation of two approaches that explicitly odel spatial autocorrelation: classical W-based regression and the recently proposed latent variables spatial autoregressive odel. In the spatial econoetrics literature the W-based spatial regressions have been predoinant and ost coonly used. The approach is based on one or ore spatial structural atrices, usually denoted W, that accounts for spatial dependence and spill-over effects. The selection of spatial weight atrices is a crucial feature of spatial odels because they ipose a priori a structure of spatial dependence on the odels and affect estiates (Bhattacharjee and Jensen-Butler, 6; Anselin, and Fingleton, 3) and substantive interpretation of the research findings (Hepple, 995). Autoregressive odels can include several types of spatial weight atrices. Most coon are the contiguity-based atrices. Two regions are said to be first-order contiguous if they share a coon border. Higher-order contiguity is defined in a siilar way. The contiguity atrix is based on different fors (whether the units of observation share coon boundaries or vertices) or orders of contiguity. The other type of weight atrix is Another approach to dealing with spatial autocorrelation is spatial filtering. It coes down to the reoval of spatial dependence in a spatially autocorrelated variable by partioning it into a filtered nonspatial variable and a residual spatial variable such that conventional regression techniques can be applied to the filtered data (see aongst others Getis and Griffith () and Tiefelsdorf and Griffith (7). Spatial filtering is not considered in this paper
2 distance based and calculated using either an algorith with distance, such as inverse distance or inverse distance squared, or a fixed distance band. Much progress has been ade with respect to the coparison of spatial weights atrices (Hepple, 995), the construction of spatial weights atrices (Getis and Aldstadt, 3; Aldstadt and Getis (6) and estiating spatial weights atrices that are consistent with an observed pattern of spatial dependence rather than assuing a priori the nature of spatial interaction. In spite of all these developents the ost coon procedure is still to assue a priori first order contiguity, as expressed by a atrix W with diagonal eleents equal to zero and off-diagonal eleents equal to one if two regions are first-order contiguous and zero elsewhere. The alternative, a latent variables based approach was introduced by Foler and Oud (8). It proceeds on the basis of a structural equation odel (SEM). SEM allows siultaneous handling of observed and latent variables within one odel fraework. Latent variables refer to those phenoena that are supposed to exist but cannot be observed directly. One exaple is socio-econoic status. It carries the concept of an individual s standing in the society which cannot be observed or easured directly. However, it can be easured via observable indicators like educational attainent, incoe, occupational status, etc. The structure of a SEM includes two parts: (i) the structural odel presenting the causal relationships between latent variables and (ii) the easureent odel showing the relationships between the latent variables and their observable indicators (Oud and Foler, 8). The latent variables approach replaces the spatially lagged variables in the structural odel (which is the analogue of the spatial dependence odel in the W-based approach) by latent variables and odels the relationship between latent spatially lagged variables and its observed indicators in the easureent odel. Since one latent variable can be easured by several indicators, this approach allows for the straightforward inclusion of spatial dependence in the odel. It is also capable of testing distance decay in a straightforward fashion so as to identify the spatial units that evoke a distance effect and those that do not. Moreover, it is possible to include various different types of contiguity as it allows easureent of spatial dependence by several sets of indicators. In that case ore than one
3 latent spatial dependence variable enters the structural odel with corresponding indicators in the easureent odel. Foler and Oud (8) shows that the latent variables approach can produce the sae estiates as obtained by the W-based approach but also that it is ore general than the W-based approach. However, further coparison is needed to draw up the pros and cons of each approach. To gain ore insight into the quality of the estiators of the regression coefficients including the spatial autocorrelation coefficient in both approaches, we carry out a nuber of Monte Carlo siulations. The coparison of the two approaches is done by considering Anselin s (988) Colubus, Ohio, crie dataset. The perforance of the approaches will be analyzed in ters of bias and ean squared error for various values of spatial autocorrelation. The rest of the paper is organized as follows: Section explains the W-based spatial regression approach and the latent variables approach and specifies their odel structures. A detailed description of the experiental design is given in section 3. In section 4 we report the siulation results and section 5 concludes the paper.. Model Specifications. The W-based Autoregressive Model We only consider the spatial lag odel which assues that the dependent variable is a function of exogenous variables and the dependent variable at other locations. We just refer to this odel as the W-based spatial autoregressive odel. The specification for the odel reads: y = ρ Wy + X + ε () ε ~ N(, σ ) () I n where y is an n vector of observations on the dependent variable, X is an n k data atrix of explanatory variables with the associated coefficient vector, ε is an 3
4 n vector of error ters. W is the row-standardized n n spatial weight (contiguity) atrix, ρ is the spatial lag paraeter. Anselin (988) presents a axiu likelihood ethod for estiating the paraeters of this odel that he labels a ixed regressive spatial autoregressive odel as it cobines the standard regression odel with a spatially lagged dependent variable (analogue to the lagged dependent variable odel in tie-series analysis). Maxiu likelihood estiation of this odel is based on a concentrated likelihood function in the sense that the axiization can be reduced to an expression in one paraeter, conditional upon the values of the other paraeters. The corresponding log-likelihood fuction is of the for: N N L = lnπ lnσ + ln A ( Ay X ) ( Ay X ) σ (3) with A = I ρw. (4) A few regressions are carried out along with a univariate paraeter optiization of the siplified likelihood function over values of the autoregressive paraeter ρ. The steps are described in Anselin (988):. Perfor OLS of X on y : y = X O + ε O. Perfor OLS of X on Wy : Wy = X L + ε L 3. Copute residuals: eo = y Xˆ O, el = Wy Xˆ L 4. Given e O and e L, find ρ that axiizes the concentrated likelihood function: L C N = C ln O L O L N ln ( e ρe ) ( e ρe ) + I ρw, which is a result of the substitution of estiated and σ into the log-likelihood, with C as the constant 5. Given ρˆ that axiizes L C, copute: ˆ = ˆ O ρ ˆ L, ˆ σ = ( eo ρel ) ( eo ρel ). N 4
5 The likelihood function discussed above contains a Jacobian ter ln A. Since the atrix A is of diension equal to the nuber of observations, its presence in the function to be optiized akes the nuerical analysis considerably coplex. The deterinant and its derivative need to be evaluated at each iteration for a new value of the spatial paraeter ρ. Ord (977) has derived a siplification of deterinants such as A in ters of its eigenvalues, ore specifically: ln I ρw = ln Π ( ρw ) = Σ ln( ρw ) (5) i i i i where the w i are the eigenvalues of W.. The Latent Variables Autoregressive Model A SEM in general for consists of three basic equations: = y Λ η + ε y with ( ) ε Λ ξ +δ = x x with ( ) δ η η + Γξ + ζ cov ε = Θ, (6) cov δ = Θ, (7) = B with cov ( ξ ) = Φ, ( ζ ) = Ψ cov. (8) In the easureent odels () and (), the vectors y and x are observed endogenous and exogenous variables; the vectors η and ξ contain latent endogenous and exogenous variables; the atrices Λ y and Λ x specify the loadings of the observed variables (indicators) on the vectors of latent variables y and x, and Θ ε and Θ δ are the easureent error covariance atrices. Directly observed variables can be conveniently handled in the structural odel by specifying an identity relationship between a given observed variable and the corresponding latent variable in the easureent odel. In the structural odel (3) B specifies the structural relationships aong the latent endogenous variables utually and Γ contains the ipacts of the exogenous latent variables on the endogenous. Φ is the covariance atrix of latent exogenous variables and Ψ the covariance atrices of the errors in the structural odel. The easureent 5
6 errors in ε and δ are assued to be uncorrelated with the latent variables in η and ξ as well as with the structural errors inζ. In a SEM odelling fraework paraeter estiation is done by iniizing the distance between the theoretical covariance atrix (based on hypotheses relating to the odel structure as specified in the paraeter atrices Λ x, Λ y, Θε, Θδ, B, Γ, Φ and Ψ ) and the observed covariance atrix. Several estiators for SEM have been developed including instruental variables (IV), two-stage least squares (TSLS), unweighted least squares (ULS), generalized least squares (GLS), fully weighted (WLS) and diagonally weighted least squares (DWLS), and axiu likelihood (ML). ML ethod is the ost coonly used ethod in estiating SEM odels and the default in the statistical packages Mx and LISREL. Below we apply the ML estiation. It axiizes the log-likelihood function: l N N ( θ Y ) = ln Σ tr( SΣ ) ln π pn where Σ is the theoretical variance covariance atrix in ters of the free and constrained eleents in the 8 paraeter atrices: (9) Λ Σ = y ( I B)( ΓΦΓ + Ψ)( I B) Λ Λ ΦΓ ( I B) Λ x y y + Θ ε Λ y ( I B) ΓΦΛ x Λ ΦΛ + Θ x x δ () S is the observed variance covariance atrix for given data Y. The ML-estiator ˆ arg axl ( θ Y ) axiizes l ( θ Y ) θ = chooses that value of θ which. Miniizing the fit function: F ML = ln Σ + tr ( SΣ ) ln S p () gives the sae results as axiizing the above likelihood function (Oud and Foler, 8). The LISREL software package also contains a variety of test and odel evaluation statistics and gives hints about identification probles (see Joreskog and Sorbo, 996 for details). On the basis of SEM, we propose a odel structure to represent the spatial lag odel. We specify the lag odel as a SEM and estiate it using the software package Mx. 6
7 The odel is referred to as latent variables spatial autoregressive odel in this paper. We apply the concept of a latent variable to the spatially lagged dependent variable such that in the structural odel Wy is replaced by a latent variable while in the easureent odel the latent spatially lagged dependent variable is related to its indicators. It replaces the spatially lagged variable Wy in the W-based spatial autoregressive odel by a latent variableη : y = ρη + γ ' x + ζ () and is copleted by a easureent equation: with y = Λη + ε (3) y y y =, M y λ λ Λ =, M λ σ ε Θ = σ ε O σ ε (4) (Observe that without an appropriate constraint, the loadings λi will not be identified. For that reason, one often chooses λ =.) We assue that the spatially lagged observed variables are chosen on the basis of theoretical or ad hoc considerations. Moreover, as pointed out in the introduction ore than one spatial feature can be taken into account. For instance, both the relationships to neighbouring regions as relationships to the core regions could be included in the case of the crie odel. We first turn to the easureent odel. This odel is constructed by eans of selection functions or selection atrices S i which select relevant observations fro the vector of observations as follows. In order to distinguish between the standard definition of a SEM in ters of variables and a SEM defined in units of observations, as in standard spatial econoetrics, we denote the latter by tilde (~). 7
8 ~ y ~ y ~ y = S ~ y, = S ~ y, = M S ~ y. (5) That is, S selects the values for the first indicator ~ y, S for the second indicator ~ y, etc. For exaple, S ay be defined as the selector of the observations on, say crie, in the nearest contiguous neighbour, S as the selector of the observations on crie in the next nearest contiguous neighbour, S 3 as the spillover of crie fro the core, easured, for exaple, as crie in the core divided by a region s distance fro the core, etc. Thus, for the easureent odel we obtain: ~ y ~ y ~ y = S ~ ~ ~ y = λη + ε, = S ~ y = λ ~ η + ~ ε, = S M ~ y = λ ~ η + ~ ε. (6) Fro the above one observes that spatial dependence is captured by two kinds of paraeters, ρ and λ i, whereas in the standard lag odel only the average effect ρy w shows up. This eans that a uch richer representation and testing of the spatial structure can be obtained than by way of standard spatial econoetric approaches. For instance, it allows for deterining those units that evoke a distance effect and those that do not, as suggested by Getis and Aldstadt (4) by testing the significance of the λ i coefficients. The standard SEM log-likelihood function needs correction so as to account for the presence of the spatially lagged dependent variable aong the explanatory variables. Fro Foler and Oud (8), for ρ ρ ρ A = I S S L λ λ λ S (7) we need to add ln A to the log-likelihood function. 8
9 3. Experiental Design To investigate the perforances of the two odelling approaches specified in section, we conduct a nuber of Monte Carlo siulations. Both approaches are applied to Anselin s (988) Colubus, Ohio, crie dataset. The first step is the design of a data-generating procedure. We first explain the data generating procedure for the W-based spatial lag odel. For this purpose we rewrite equation () according to the nuber of variables and observations involved in Anselin s crie odel: y ρ Wy + + x + + ε (8) = x Thus the expression of y is: y = I ρ W ) ( + x + x + ε ) (9) ( The steps for generating saples are:. Fix values for the vector (,, ) as: = 45, =., =. 3, and vary ρ over the interval [, ).. Generate saples of error ter ε by randoly drawing fro a unifor (, ) distribution. 3. Copute y according to (9). Next the spatial lag odel is estiated for each saple which gives: ρ,,, and σ, on the basis of which we copute bias and ean squared error (MSE). The procedure is siilar for the latent variables approach. Specifically, the Wy in standard spatial lag odel is replaced by a latent variable while in the easureent odel the latent spatially lagged dependent variable is related to its indicators. Here we take the observables for the three contiguous nearest neighbouring regions. Next we estiate the latent spatial lag odel for each of the sae saples generated fro steps ~3 in the siulation procedure of the standard spatial lag odel, which gives ρ (aongst others),,, and σ. Then the bias and MSE of the estiators are calculated. The nuber of replications is set to and the ain diensions over which the 9
10 variation in power of the approaches and the distribution of the pre-test estiators are investigated are the changing values of the spatial lag paraeter ρ. We exaine the paraeter space fro [.,.9] using increents of.. The experient consists of coparisons in ters of odel estiators and their bias and MSE of the two approaches. The results are displayed in tables and graphs in the next section. 4. Siulation Results
11 Table. Mean of estiation results on the Colubus, Ohio, crie dataset by W-based and latent variables spatial autoregressive odels ρ σ Paraeter ρ W-based Latent W-based Latent W-based Latent W-based Latent W-based Latent (.69) (.43) (.63) (.45) (.55) (.3) (.46) (.54) (.35) (.4) (.) (.6) (.8) (.4) (.93) (.3) (.78) (.6) (.6) (.69) (.35) (.44) (.38) (.38) (.3) (.38) (.33) (.394) (.36) (.345) (.39) (.34) (.3) (.3) (.36) (.33) (.334) (.369) (.353) (.433) (.93) (.3) (.93) (.) (.94) (.6) (.94) (.3) (.94) (.) (.94) (.94) (.94) (.94) (.94) (.94) (.94) (.93) (.94) (.) (6.8) (88.589) (6.334) (37.36) (6.67) (.58) (6.98) (.44) (7.44) (.59) (7.633) (.) (8.6) (9.65) (8.874) (9.5) (.39) (4.363) (4.83) (58.67) (9.345) (8.78) (9.376) (.86) (9.43) (9.8) (9.5) (.453) (9.6) (.635) (9.737) (.895) (9.886) (5.45) (.43) (6.83) (.34) (3.348) (.65) (3.55)
12 Table. Bias of the estiators for ρ, and, with different values for the spatial lag paraeter ρ Paraeter ρ W-based Latent W-based Latent W-based Latent
13 Table 3. Mean squared error ( ) of the estiators for ρ, and, with different values for the spatial lag paraeter ρ Paraeter ρ W-based Latent W-based Latent W-based Latent
14 5. Conclusions 4
15 Reference Aldstadt, J. and Getis, A. (6). Using AMOEBA to create a spatial weights atrix and identify spatial clusters. Geographical Analysis, 38, Aldstadt, J. and Getis, A. (4). Constructing the spatial weights atrix using a local statistic. Geographical Analysis, 36,, 9-4. Anselin, L. (). Under the hood: Issues in the specification and interpretation of spatial regression odels. Agricultural Econoics 7, 3, Anselin, L. (988). Spatial Econoetrics: Methods and Models. Dordrecht: Kluwer Acadeic Publishers. Bhattacharjee, A. and Jensen-Butler, C. (6). Estiation of the spatial weights atrix in the spatial error odel, with an application to diffusion in housing deand. Available: Fingleton, B. (3). Externalities, econoic geography and spatial econoetrics: conceptual and odeling developents, International Regional Science Review, 6,, Foler, H. and Oud, J. (8). How to get rid of W? A latent variables approach to odeling spatially lagged variables. Environent and Planning A, 4, Hepple, L.W. (995). Bayesian techniques in spatial and network econoetrics:. Model coparison and posterior odds. Environent and Planning A, 7, Hepple, L.W. (995). Bayesian techniques in spatial and network econoetrics:. Coputational ethods and algoriths. Environent and planning A, 7, LeSage, J.P. (999). The Theory and Practice of Spatial Econoetrics, 999. Available: Neale M.C., Boker S.M., Xie G., Maes H.H. (3). Mx: Statistical Modeling. VCU Box 96, Richond, VA 398: Departent of Psychiatry. 6th Edition. 5
W-BASED VS LATENT VARIABLES SPATIAL AUTOREGRESSIVE MODELS: EVIDENCE FROM MONTE CARLO SIMULATIONS
1 W-BASED VS LATENT VARIABLES SPATIAL AUTOREGRESSIVE MODELS: EVIDENCE FROM MONTE CARLO SIMULATIONS An Liu University of Groningen Henk Folmer University of Groningen Wageningen University Han Oud Radboud
More informationModel Fitting. CURM Background Material, Fall 2014 Dr. Doreen De Leon
Model Fitting CURM Background Material, Fall 014 Dr. Doreen De Leon 1 Introduction Given a set of data points, we often want to fit a selected odel or type to the data (e.g., we suspect an exponential
More informationExperimental Design For Model Discrimination And Precise Parameter Estimation In WDS Analysis
City University of New York (CUNY) CUNY Acadeic Works International Conference on Hydroinforatics 8-1-2014 Experiental Design For Model Discriination And Precise Paraeter Estiation In WDS Analysis Giovanna
More informationMachine Learning Basics: Estimators, Bias and Variance
Machine Learning Basics: Estiators, Bias and Variance Sargur N. srihari@cedar.buffalo.edu This is part of lecture slides on Deep Learning: http://www.cedar.buffalo.edu/~srihari/cse676 1 Topics in Basics
More informationFeature Extraction Techniques
Feature Extraction Techniques Unsupervised Learning II Feature Extraction Unsupervised ethods can also be used to find features which can be useful for categorization. There are unsupervised ethods that
More informationBayes Decision Rule and Naïve Bayes Classifier
Bayes Decision Rule and Naïve Bayes Classifier Le Song Machine Learning I CSE 6740, Fall 2013 Gaussian Mixture odel A density odel p(x) ay be ulti-odal: odel it as a ixture of uni-odal distributions (e.g.
More informationProc. of the IEEE/OES Seventh Working Conference on Current Measurement Technology UNCERTAINTIES IN SEASONDE CURRENT VELOCITIES
Proc. of the IEEE/OES Seventh Working Conference on Current Measureent Technology UNCERTAINTIES IN SEASONDE CURRENT VELOCITIES Belinda Lipa Codar Ocean Sensors 15 La Sandra Way, Portola Valley, CA 98 blipa@pogo.co
More informationCOS 424: Interacting with Data. Written Exercises
COS 424: Interacting with Data Hoework #4 Spring 2007 Regression Due: Wednesday, April 18 Written Exercises See the course website for iportant inforation about collaboration and late policies, as well
More informationBlock designs and statistics
Bloc designs and statistics Notes for Math 447 May 3, 2011 The ain paraeters of a bloc design are nuber of varieties v, bloc size, nuber of blocs b. A design is built on a set of v eleents. Each eleent
More informationA Simple Regression Problem
A Siple Regression Proble R. M. Castro March 23, 2 In this brief note a siple regression proble will be introduced, illustrating clearly the bias-variance tradeoff. Let Y i f(x i ) + W i, i,..., n, where
More informationIntelligent Systems: Reasoning and Recognition. Perceptrons and Support Vector Machines
Intelligent Systes: Reasoning and Recognition Jaes L. Crowley osig 1 Winter Seester 2018 Lesson 6 27 February 2018 Outline Perceptrons and Support Vector achines Notation...2 Linear odels...3 Lines, Planes
More informationTracking using CONDENSATION: Conditional Density Propagation
Tracking using CONDENSATION: Conditional Density Propagation Goal Model-based visual tracking in dense clutter at near video frae rates M. Isard and A. Blake, CONDENSATION Conditional density propagation
More informationTopic 5a Introduction to Curve Fitting & Linear Regression
/7/08 Course Instructor Dr. Rayond C. Rup Oice: A 337 Phone: (95) 747 6958 E ail: rcrup@utep.edu opic 5a Introduction to Curve Fitting & Linear Regression EE 4386/530 Coputational ethods in EE Outline
More informationOnline Supplement. and. Pradeep K. Chintagunta Graduate School of Business University of Chicago
Online Suppleent easuring Cross-Category Price Effects with Aggregate Store Data Inseong Song ksong@usthk Departent of arketing, HKUST Hong Kong University of Science and Technology and Pradeep K Chintagunta
More informationCh 12: Variations on Backpropagation
Ch 2: Variations on Backpropagation The basic backpropagation algorith is too slow for ost practical applications. It ay take days or weeks of coputer tie. We deonstrate why the backpropagation algorith
More informationNon-Parametric Non-Line-of-Sight Identification 1
Non-Paraetric Non-Line-of-Sight Identification Sinan Gezici, Hisashi Kobayashi and H. Vincent Poor Departent of Electrical Engineering School of Engineering and Applied Science Princeton University, Princeton,
More informationInspection; structural health monitoring; reliability; Bayesian analysis; updating; decision analysis; value of information
Cite as: Straub D. (2014). Value of inforation analysis with structural reliability ethods. Structural Safety, 49: 75-86. Value of Inforation Analysis with Structural Reliability Methods Daniel Straub
More informationExtension of CSRSM for the Parametric Study of the Face Stability of Pressurized Tunnels
Extension of CSRSM for the Paraetric Study of the Face Stability of Pressurized Tunnels Guilhe Mollon 1, Daniel Dias 2, and Abdul-Haid Soubra 3, M.ASCE 1 LGCIE, INSA Lyon, Université de Lyon, Doaine scientifique
More informationKernel Methods and Support Vector Machines
Intelligent Systes: Reasoning and Recognition Jaes L. Crowley ENSIAG 2 / osig 1 Second Seester 2012/2013 Lesson 20 2 ay 2013 Kernel ethods and Support Vector achines Contents Kernel Functions...2 Quadratic
More informationKeywords: Estimator, Bias, Mean-squared error, normality, generalized Pareto distribution
Testing approxiate norality of an estiator using the estiated MSE and bias with an application to the shape paraeter of the generalized Pareto distribution J. Martin van Zyl Abstract In this work the norality
More informationBoosting with log-loss
Boosting with log-loss Marco Cusuano-Towner Septeber 2, 202 The proble Suppose we have data exaples {x i, y i ) i =... } for a two-class proble with y i {, }. Let F x) be the predictor function with the
More informationAn Improved Particle Filter with Applications in Ballistic Target Tracking
Sensors & ransducers Vol. 72 Issue 6 June 204 pp. 96-20 Sensors & ransducers 204 by IFSA Publishing S. L. http://www.sensorsportal.co An Iproved Particle Filter with Applications in Ballistic arget racing
More informationare equal to zero, where, q = p 1. For each gene j, the pairwise null and alternative hypotheses are,
Page of 8 Suppleentary Materials: A ultiple testing procedure for ulti-diensional pairwise coparisons with application to gene expression studies Anjana Grandhi, Wenge Guo, Shyaal D. Peddada S Notations
More informationŞtefan ŞTEFĂNESCU * is the minimum global value for the function h (x)
7Applying Nelder Mead s Optiization Algorith APPLYING NELDER MEAD S OPTIMIZATION ALGORITHM FOR MULTIPLE GLOBAL MINIMA Abstract Ştefan ŞTEFĂNESCU * The iterative deterinistic optiization ethod could not
More informationSupport Vector Machine Classification of Uncertain and Imbalanced data using Robust Optimization
Recent Researches in Coputer Science Support Vector Machine Classification of Uncertain and Ibalanced data using Robust Optiization RAGHAV PAT, THEODORE B. TRAFALIS, KASH BARKER School of Industrial Engineering
More information13.2 Fully Polynomial Randomized Approximation Scheme for Permanent of Random 0-1 Matrices
CS71 Randoness & Coputation Spring 018 Instructor: Alistair Sinclair Lecture 13: February 7 Disclaier: These notes have not been subjected to the usual scrutiny accorded to foral publications. They ay
More informationThis model assumes that the probability of a gap has size i is proportional to 1/i. i.e., i log m e. j=1. E[gap size] = i P r(i) = N f t.
CS 493: Algoriths for Massive Data Sets Feb 2, 2002 Local Models, Bloo Filter Scribe: Qin Lv Local Models In global odels, every inverted file entry is copressed with the sae odel. This work wells when
More informationEffective joint probabilistic data association using maximum a posteriori estimates of target states
Effective joint probabilistic data association using axiu a posteriori estiates of target states 1 Viji Paul Panakkal, 2 Rajbabu Velurugan 1 Central Research Laboratory, Bharat Electronics Ltd., Bangalore,
More informationProbability Distributions
Probability Distributions In Chapter, we ephasized the central role played by probability theory in the solution of pattern recognition probles. We turn now to an exploration of soe particular exaples
More informationC na (1) a=l. c = CO + Clm + CZ TWO-STAGE SAMPLE DESIGN WITH SMALL CLUSTERS. 1. Introduction
TWO-STGE SMPLE DESIGN WITH SMLL CLUSTERS Robert G. Clark and David G. Steel School of Matheatics and pplied Statistics, University of Wollongong, NSW 5 ustralia. (robert.clark@abs.gov.au) Key Words: saple
More informationUsing EM To Estimate A Probablity Density With A Mixture Of Gaussians
Using EM To Estiate A Probablity Density With A Mixture Of Gaussians Aaron A. D Souza adsouza@usc.edu Introduction The proble we are trying to address in this note is siple. Given a set of data points
More informationA Self-Organizing Model for Logical Regression Jerry Farlow 1 University of Maine. (1900 words)
1 A Self-Organizing Model for Logical Regression Jerry Farlow 1 University of Maine (1900 words) Contact: Jerry Farlow Dept of Matheatics Univeristy of Maine Orono, ME 04469 Tel (07) 866-3540 Eail: farlow@ath.uaine.edu
More informationPattern Recognition and Machine Learning. Artificial Neural networks
Pattern Recognition and Machine Learning Jaes L. Crowley ENSIMAG 3 - MMIS Fall Seester 2016 Lessons 7 14 Dec 2016 Outline Artificial Neural networks Notation...2 1. Introduction...3... 3 The Artificial
More informationEnsemble Based on Data Envelopment Analysis
Enseble Based on Data Envelopent Analysis So Young Sohn & Hong Choi Departent of Coputer Science & Industrial Systes Engineering, Yonsei University, Seoul, Korea Tel) 82-2-223-404, Fax) 82-2- 364-7807
More informationEstimation of the Mean of the Exponential Distribution Using Maximum Ranked Set Sampling with Unequal Samples
Open Journal of Statistics, 4, 4, 64-649 Published Online Septeber 4 in SciRes http//wwwscirporg/ournal/os http//ddoiorg/436/os4486 Estiation of the Mean of the Eponential Distribution Using Maiu Ranked
More informationCS Lecture 13. More Maximum Likelihood
CS 6347 Lecture 13 More Maxiu Likelihood Recap Last tie: Introduction to axiu likelihood estiation MLE for Bayesian networks Optial CPTs correspond to epirical counts Today: MLE for CRFs 2 Maxiu Likelihood
More informationTesting the lag length of vector autoregressive models: A power comparison between portmanteau and Lagrange multiplier tests
Working Papers 2017-03 Testing the lag length of vector autoregressive odels: A power coparison between portanteau and Lagrange ultiplier tests Raja Ben Hajria National Engineering School, University of
More informationDetection and Estimation Theory
ESE 54 Detection and Estiation Theory Joseph A. O Sullivan Sauel C. Sachs Professor Electronic Systes and Signals Research Laboratory Electrical and Systes Engineering Washington University 11 Urbauer
More informationA general forulation of the cross-nested logit odel Michel Bierlaire, Dpt of Matheatics, EPFL, Lausanne Phone: Fax:
A general forulation of the cross-nested logit odel Michel Bierlaire, EPFL Conference paper STRC 2001 Session: Choices A general forulation of the cross-nested logit odel Michel Bierlaire, Dpt of Matheatics,
More informationIntroduction to Machine Learning. Recitation 11
Introduction to Machine Learning Lecturer: Regev Schweiger Recitation Fall Seester Scribe: Regev Schweiger. Kernel Ridge Regression We now take on the task of kernel-izing ridge regression. Let x,...,
More informationE0 370 Statistical Learning Theory Lecture 6 (Aug 30, 2011) Margin Analysis
E0 370 tatistical Learning Theory Lecture 6 (Aug 30, 20) Margin Analysis Lecturer: hivani Agarwal cribe: Narasihan R Introduction In the last few lectures we have seen how to obtain high confidence bounds
More informationNonmonotonic Networks. a. IRST, I Povo (Trento) Italy, b. Univ. of Trento, Physics Dept., I Povo (Trento) Italy
Storage Capacity and Dynaics of Nononotonic Networks Bruno Crespi a and Ignazio Lazzizzera b a. IRST, I-38050 Povo (Trento) Italy, b. Univ. of Trento, Physics Dept., I-38050 Povo (Trento) Italy INFN Gruppo
More informationProbabilistic Machine Learning
Probabilistic Machine Learning by Prof. Seungchul Lee isystes Design Lab http://isystes.unist.ac.kr/ UNIST Table of Contents I.. Probabilistic Linear Regression I... Maxiu Likelihood Solution II... Maxiu-a-Posteriori
More informationChapter 6 1-D Continuous Groups
Chapter 6 1-D Continuous Groups Continuous groups consist of group eleents labelled by one or ore continuous variables, say a 1, a 2,, a r, where each variable has a well- defined range. This chapter explores:
More informationA method to determine relative stroke detection efficiencies from multiplicity distributions
A ethod to deterine relative stroke detection eiciencies ro ultiplicity distributions Schulz W. and Cuins K. 2. Austrian Lightning Detection and Inoration Syste (ALDIS), Kahlenberger Str.2A, 90 Vienna,
More informationThe Distribution of the Covariance Matrix for a Subset of Elliptical Distributions with Extension to Two Kurtosis Parameters
journal of ultivariate analysis 58, 96106 (1996) article no. 0041 The Distribution of the Covariance Matrix for a Subset of Elliptical Distributions with Extension to Two Kurtosis Paraeters H. S. Steyn
More informationThe Transactional Nature of Quantum Information
The Transactional Nature of Quantu Inforation Subhash Kak Departent of Coputer Science Oklahoa State University Stillwater, OK 7478 ABSTRACT Inforation, in its counications sense, is a transactional property.
More informationAnalyzing Simulation Results
Analyzing Siulation Results Dr. John Mellor-Cruey Departent of Coputer Science Rice University johnc@cs.rice.edu COMP 528 Lecture 20 31 March 2005 Topics for Today Model verification Model validation Transient
More informationTEST OF HOMOGENEITY OF PARALLEL SAMPLES FROM LOGNORMAL POPULATIONS WITH UNEQUAL VARIANCES
TEST OF HOMOGENEITY OF PARALLEL SAMPLES FROM LOGNORMAL POPULATIONS WITH UNEQUAL VARIANCES S. E. Ahed, R. J. Tokins and A. I. Volodin Departent of Matheatics and Statistics University of Regina Regina,
More informationQualitative Modelling of Time Series Using Self-Organizing Maps: Application to Animal Science
Proceedings of the 6th WSEAS International Conference on Applied Coputer Science, Tenerife, Canary Islands, Spain, Deceber 16-18, 2006 183 Qualitative Modelling of Tie Series Using Self-Organizing Maps:
More informationREDUCTION OF FINITE ELEMENT MODELS BY PARAMETER IDENTIFICATION
ISSN 139 14X INFORMATION TECHNOLOGY AND CONTROL, 008, Vol.37, No.3 REDUCTION OF FINITE ELEMENT MODELS BY PARAMETER IDENTIFICATION Riantas Barauskas, Vidantas Riavičius Departent of Syste Analysis, Kaunas
More informationOPTIMIZATION in multi-agent networks has attracted
Distributed constrained optiization and consensus in uncertain networks via proxial iniization Kostas Margellos, Alessandro Falsone, Sione Garatti and Maria Prandini arxiv:603.039v3 [ath.oc] 3 May 07 Abstract
More informationINNER CONSTRAINTS FOR A 3-D SURVEY NETWORK
eospatial Science INNER CONSRAINS FOR A 3-D SURVEY NEWORK hese notes follow closely the developent of inner constraint equations by Dr Willie an, Departent of Building, School of Design and Environent,
More informatione-companion ONLY AVAILABLE IN ELECTRONIC FORM
OPERATIONS RESEARCH doi 10.1287/opre.1070.0427ec pp. ec1 ec5 e-copanion ONLY AVAILABLE IN ELECTRONIC FORM infors 07 INFORMS Electronic Copanion A Learning Approach for Interactive Marketing to a Custoer
More informationPattern Recognition and Machine Learning. Learning and Evaluation for Pattern Recognition
Pattern Recognition and Machine Learning Jaes L. Crowley ENSIMAG 3 - MMIS Fall Seester 2017 Lesson 1 4 October 2017 Outline Learning and Evaluation for Pattern Recognition Notation...2 1. The Pattern Recognition
More informationESTIMATING AND FORMING CONFIDENCE INTERVALS FOR EXTREMA OF RANDOM POLYNOMIALS. A Thesis. Presented to. The Faculty of the Department of Mathematics
ESTIMATING AND FORMING CONFIDENCE INTERVALS FOR EXTREMA OF RANDOM POLYNOMIALS A Thesis Presented to The Faculty of the Departent of Matheatics San Jose State University In Partial Fulfillent of the Requireents
More informationMULTISTEP YULE-WALKER ESTIMATION OF AUTOREGRESSIVE MODELS YOU TINGYAN
MULTISTEP YULE-WALKER ESTIMATION OF AUTOREGRESSIVE MODELS YOU TINGYAN NATIONAL UNIVERSITY OF SINGAPORE 2010 MULTISTEP YULE-WALKER ESTIMATION OF AUTOREGRESSIVE MODELS YOU TINGYAN (B.Sc. Nanjing Noral University)
More informationStatistical Logic Cell Delay Analysis Using a Current-based Model
Statistical Logic Cell Delay Analysis Using a Current-based Model Hanif Fatei Shahin Nazarian Massoud Pedra Dept. of EE-Systes, University of Southern California, Los Angeles, CA 90089 {fatei, shahin,
More informationPredicting FTSE 100 Close Price Using Hybrid Model
SAI Intelligent Systes Conference 2015 Noveber 10-11, 2015 London, UK Predicting FTSE 100 Close Price Using Hybrid Model Bashar Al-hnaity, Departent of Electronic and Coputer Engineering, Brunel University
More informationBiostatistics Department Technical Report
Biostatistics Departent Technical Report BST006-00 Estiation of Prevalence by Pool Screening With Equal Sized Pools and a egative Binoial Sapling Model Charles R. Katholi, Ph.D. Eeritus Professor Departent
More informationSpine Fin Efficiency A Three Sided Pyramidal Fin of Equilateral Triangular Cross-Sectional Area
Proceedings of the 006 WSEAS/IASME International Conference on Heat and Mass Transfer, Miai, Florida, USA, January 18-0, 006 (pp13-18) Spine Fin Efficiency A Three Sided Pyraidal Fin of Equilateral Triangular
More informationEstimating Parameters for a Gaussian pdf
Pattern Recognition and achine Learning Jaes L. Crowley ENSIAG 3 IS First Seester 00/0 Lesson 5 7 Noveber 00 Contents Estiating Paraeters for a Gaussian pdf Notation... The Pattern Recognition Proble...3
More informationSPECTRUM sensing is a core concept of cognitive radio
World Acadey of Science, Engineering and Technology International Journal of Electronics and Counication Engineering Vol:6, o:2, 202 Efficient Detection Using Sequential Probability Ratio Test in Mobile
More informationIdentical Maximum Likelihood State Estimation Based on Incremental Finite Mixture Model in PHD Filter
Identical Maxiu Lielihood State Estiation Based on Increental Finite Mixture Model in PHD Filter Gang Wu Eail: xjtuwugang@gail.co Jing Liu Eail: elelj20080730@ail.xjtu.edu.cn Chongzhao Han Eail: czhan@ail.xjtu.edu.cn
More informationThe proofs of Theorem 1-3 are along the lines of Wied and Galeano (2013).
A Appendix: Proofs The proofs of Theore 1-3 are along the lines of Wied and Galeano (2013) Proof of Theore 1 Let D[d 1, d 2 ] be the space of càdlàg functions on the interval [d 1, d 2 ] equipped with
More informationA Note on Scheduling Tall/Small Multiprocessor Tasks with Unit Processing Time to Minimize Maximum Tardiness
A Note on Scheduling Tall/Sall Multiprocessor Tasks with Unit Processing Tie to Miniize Maxiu Tardiness Philippe Baptiste and Baruch Schieber IBM T.J. Watson Research Center P.O. Box 218, Yorktown Heights,
More informationDetermining OWA Operator Weights by Mean Absolute Deviation Minimization
Deterining OWA Operator Weights by Mean Absolute Deviation Miniization Micha l Majdan 1,2 and W lodziierz Ogryczak 1 1 Institute of Control and Coputation Engineering, Warsaw University of Technology,
More informationOcean 420 Physical Processes in the Ocean Project 1: Hydrostatic Balance, Advection and Diffusion Answers
Ocean 40 Physical Processes in the Ocean Project 1: Hydrostatic Balance, Advection and Diffusion Answers 1. Hydrostatic Balance a) Set all of the levels on one of the coluns to the lowest possible density.
More informationSymbolic Analysis as Universal Tool for Deriving Properties of Non-linear Algorithms Case study of EM Algorithm
Acta Polytechnica Hungarica Vol., No., 04 Sybolic Analysis as Universal Tool for Deriving Properties of Non-linear Algoriths Case study of EM Algorith Vladiir Mladenović, Miroslav Lutovac, Dana Porrat
More information1 Proof of learning bounds
COS 511: Theoretical Machine Learning Lecturer: Rob Schapire Lecture #4 Scribe: Akshay Mittal February 13, 2013 1 Proof of learning bounds For intuition of the following theore, suppose there exists a
More informationAn Inverse Interpolation Method Utilizing In-Flight Strain Measurements for Determining Loads and Structural Response of Aerospace Vehicles
An Inverse Interpolation Method Utilizing In-Flight Strain Measureents for Deterining Loads and Structural Response of Aerospace Vehicles S. Shkarayev and R. Krashantisa University of Arizona, Tucson,
More informationA NEW ROBUST AND EFFICIENT ESTIMATOR FOR ILL-CONDITIONED LINEAR INVERSE PROBLEMS WITH OUTLIERS
A NEW ROBUST AND EFFICIENT ESTIMATOR FOR ILL-CONDITIONED LINEAR INVERSE PROBLEMS WITH OUTLIERS Marta Martinez-Caara 1, Michael Mua 2, Abdelhak M. Zoubir 2, Martin Vetterli 1 1 School of Coputer and Counication
More informationA note on the multiplication of sparse matrices
Cent. Eur. J. Cop. Sci. 41) 2014 1-11 DOI: 10.2478/s13537-014-0201-x Central European Journal of Coputer Science A note on the ultiplication of sparse atrices Research Article Keivan Borna 12, Sohrab Aboozarkhani
More informationReduction of Uncertainty in Post-Event Seismic Loss Estimates Using Observation Data and Bayesian Updating
Reduction of Uncertainty in Post-Event Seisic Loss Estiates Using Observation Data and Bayesian Updating Maura Torres Subitted in partial fulfillent of the requireents for the degree of Doctor of Philosophy
More informationData-Driven Imaging in Anisotropic Media
18 th World Conference on Non destructive Testing, 16- April 1, Durban, South Africa Data-Driven Iaging in Anisotropic Media Arno VOLKER 1 and Alan HUNTER 1 TNO Stieltjesweg 1, 6 AD, Delft, The Netherlands
More informationAlgorithms for parallel processor scheduling with distinct due windows and unit-time jobs
BULLETIN OF THE POLISH ACADEMY OF SCIENCES TECHNICAL SCIENCES Vol. 57, No. 3, 2009 Algoriths for parallel processor scheduling with distinct due windows and unit-tie obs A. JANIAK 1, W.A. JANIAK 2, and
More informationCSE525: Randomized Algorithms and Probabilistic Analysis May 16, Lecture 13
CSE55: Randoied Algoriths and obabilistic Analysis May 6, Lecture Lecturer: Anna Karlin Scribe: Noah Siegel, Jonathan Shi Rando walks and Markov chains This lecture discusses Markov chains, which capture
More informationDetermining the Robot-to-Robot Relative Pose Using Range-only Measurements
Deterining the Robot-to-Robot Relative Pose Using Range-only Measureents Xun S Zhou and Stergios I Roueliotis Abstract In this paper we address the proble of deterining the relative pose of pairs robots
More informationComputational and Statistical Learning Theory
Coputational and Statistical Learning Theory Proble sets 5 and 6 Due: Noveber th Please send your solutions to learning-subissions@ttic.edu Notations/Definitions Recall the definition of saple based Radeacher
More informationPAC-Bayes Analysis Of Maximum Entropy Learning
PAC-Bayes Analysis Of Maxiu Entropy Learning John Shawe-Taylor and David R. Hardoon Centre for Coputational Statistics and Machine Learning Departent of Coputer Science University College London, UK, WC1E
More information2nd Workshop on Joints Modelling Dartington April 2009 Identification of Nonlinear Bolted Lap Joint Parameters using Force State Mapping
Identification of Nonlinear Bolted Lap Joint Paraeters using Force State Mapping International Journal of Solids and Structures, 44 (007) 8087 808 Hassan Jalali, Haed Ahadian and John E Mottershead _ Γ
More informationAbout the definition of parameters and regimes of active two-port networks with variable loads on the basis of projective geometry
About the definition of paraeters and regies of active two-port networks with variable loads on the basis of projective geoetry PENN ALEXANDR nstitute of Electronic Engineering and Nanotechnologies "D
More informationpaper prepared for the 1996 PTRC Conference, September 2-6, Brunel University, UK ON THE CALIBRATION OF THE GRAVITY MODEL
paper prepared for the 1996 PTRC Conference, Septeber 2-6, Brunel University, UK ON THE CALIBRATION OF THE GRAVITY MODEL Nanne J. van der Zijpp 1 Transportation and Traffic Engineering Section Delft University
More informationASSUME a source over an alphabet size m, from which a sequence of n independent samples are drawn. The classical
IEEE TRANSACTIONS ON INFORMATION THEORY Large Alphabet Source Coding using Independent Coponent Analysis Aichai Painsky, Meber, IEEE, Saharon Rosset and Meir Feder, Fellow, IEEE arxiv:67.7v [cs.it] Jul
More informationA LOSS FUNCTION APPROACH TO GROUP PREFERENCE AGGREGATION IN THE AHP
ISAHP 003, Bali, Indonesia, August 7-9, 003 A OSS FUNCTION APPROACH TO GROUP PREFERENCE AGGREGATION IN THE AHP Keun-Tae Cho and Yong-Gon Cho School of Systes Engineering Manageent, Sungkyunkwan University
More informationWeb Appendix for Joint Variable Selection for Fixed and Random Effects in Linear Mixed-Effects Models
Web Appendix for Joint Variable Selection for Fixed and Rando Effects in Linear Mixed-Effects Models Howard D. Bondell, Arun Krishna, and Sujit K. Ghosh APPENDIX A A. Regularity Conditions Assue that the
More informationA remark on a success rate model for DPA and CPA
A reark on a success rate odel for DPA and CPA A. Wieers, BSI Version 0.5 andreas.wieers@bsi.bund.de Septeber 5, 2018 Abstract The success rate is the ost coon evaluation etric for easuring the perforance
More informationRandomized Recovery for Boolean Compressed Sensing
Randoized Recovery for Boolean Copressed Sensing Mitra Fatei and Martin Vetterli Laboratory of Audiovisual Counication École Polytechnique Fédéral de Lausanne (EPFL) Eail: {itra.fatei, artin.vetterli}@epfl.ch
More informationForecasting Financial Indices: The Baltic Dry Indices
International Journal of Maritie, Trade & Econoic Issues pp. 109-130 Volue I, Issue (1), 2013 Forecasting Financial Indices: The Baltic Dry Indices Eleftherios I. Thalassinos 1, Mike P. Hanias 2, Panayiotis
More informationGeneral structural model Part 1: Covariance structure and identification. Psychology 588: Covariance structure and factor models
General structural model Part 1: Covariance structure and identification Psychology 588: Covariance structure and factor models Latent variables 2 Interchangeably used: constructs --- substantively defined
More informationQuantum algorithms (CO 781, Winter 2008) Prof. Andrew Childs, University of Waterloo LECTURE 15: Unstructured search and spatial search
Quantu algoriths (CO 781, Winter 2008) Prof Andrew Childs, University of Waterloo LECTURE 15: Unstructured search and spatial search ow we begin to discuss applications of quantu walks to search algoriths
More informationarxiv: v1 [stat.ot] 7 Jul 2010
Hotelling s test for highly correlated data P. Bubeliny e-ail: bubeliny@karlin.ff.cuni.cz Charles University, Faculty of Matheatics and Physics, KPMS, Sokolovska 83, Prague, Czech Republic, 8675. arxiv:007.094v
More informationBest Linear Unbiased and Invariant Reconstructors for the Past Records
BULLETIN of the MALAYSIAN MATHEMATICAL SCIENCES SOCIETY http:/athusy/bulletin Bull Malays Math Sci Soc (2) 37(4) (2014), 1017 1028 Best Linear Unbiased and Invariant Reconstructors for the Past Records
More informationOptimal nonlinear Bayesian experimental design: an application to amplitude versus offset experiments
Geophys. J. Int. (23) 155, 411 421 Optial nonlinear Bayesian experiental design: an application to aplitude versus offset experients Jojanneke van den Berg, 1, Andrew Curtis 2,3 and Jeannot Trapert 1 1
More informationOptimal Jamming Over Additive Noise: Vector Source-Channel Case
Fifty-first Annual Allerton Conference Allerton House, UIUC, Illinois, USA October 2-3, 2013 Optial Jaing Over Additive Noise: Vector Source-Channel Case Erah Akyol and Kenneth Rose Abstract This paper
More informationTesting equality of variances for multiple univariate normal populations
University of Wollongong Research Online Centre for Statistical & Survey Methodology Working Paper Series Faculty of Engineering and Inforation Sciences 0 esting equality of variances for ultiple univariate
More informationWarning System of Dangerous Chemical Gas in Factory Based on Wireless Sensor Network
565 A publication of CHEMICAL ENGINEERING TRANSACTIONS VOL. 59, 07 Guest Editors: Zhuo Yang, Junie Ba, Jing Pan Copyright 07, AIDIC Servizi S.r.l. ISBN 978-88-95608-49-5; ISSN 83-96 The Italian Association
More informationRecovering Data from Underdetermined Quadratic Measurements (CS 229a Project: Final Writeup)
Recovering Data fro Underdeterined Quadratic Measureents (CS 229a Project: Final Writeup) Mahdi Soltanolkotabi Deceber 16, 2011 1 Introduction Data that arises fro engineering applications often contains
More informationCourse Notes for EE227C (Spring 2018): Convex Optimization and Approximation
Course Notes for EE7C (Spring 018: Convex Optiization and Approxiation Instructor: Moritz Hardt Eail: hardt+ee7c@berkeley.edu Graduate Instructor: Max Sichowitz Eail: sichow+ee7c@berkeley.edu October 15,
More informationIntelligent Systems: Reasoning and Recognition. Artificial Neural Networks
Intelligent Systes: Reasoning and Recognition Jaes L. Crowley MOSIG M1 Winter Seester 2018 Lesson 7 1 March 2018 Outline Artificial Neural Networks Notation...2 Introduction...3 Key Equations... 3 Artificial
More information