MuTE: a MATLAB toolbox to compare established and novel estimators of the multivariate transfer entropy
|
|
|
- Arnold Lucas
- 5 years ago
- Views:
Transcription
1 FACULTY OF PSYCHOLOGY AND EDUCATIONAL SCIENCES MuTE: a MATLAB toolbox to compare established and novel estimators of the multivariate transfer entropy Alessandro Montalto Department of Data Analysis Prof. dr. Daniele Marinazzo (promoter)
2 To understand complex systems we need to infer how their components are dynamically connected Undirected measures Correlations Mutual information Phase synchronization Generalized synchronization Coherence Directed measures Granger causality Transfer entropy Alessandro Montalto 2 / 21
3 We do not know the model underlying the data so we need a model free approach Transfer Entropy Different entropy estimators implemented in a modular toolbox Alessandro Montalto 3 / 21
4 Starting from Granger Causality: Predict the future of a time series Using only values from its past Alessandro Montalto 4 / 21
5 Starting from Granger Causality: Predict the future of a time series Using only values from its past Using also values from another time series Alessandro Montalto 4 / 21
6 Definition (Wiener 1956, Granger, 1969) Two time series X and Y x, the future values of X Alessandro Montalto 5 / 21
7 Definition (Wiener 1956, Granger, 1969) Two time series X and Y x, the future values of X Definition Y is Granger cause of X if the knowledge of Y allows to make more precise predictions about x. Alessandro Montalto 5 / 21
8 Which predictive models? (linear) Autoregressive Model Dynamical Causal Model - biologically inspired Alessandro Montalto 6 / 21
9 Model Based Approaches Advantages faster significance assessed by robust statistical methods Disadvantages Not suitable for all data: we usually do not know anything about the dynamics that could explain the data so we need a model free approach Alessandro Montalto 7 / 21
10 What about no model at all? Generalized Markov property P(x X ) = p(x X, Y ) Transfer Entropy Transfer Entropy (Schreiber 2000) quantifies the violation of the generalized Markov property T (Y X ) = p(x X, Y ) log p(x X, Y ) dx dx dy p(x X ) T measures the information transfer from one series to the other. Alessandro Montalto 8 / 21
11 Model Free Approaches Advantages applicable to every kind of data they can give more informations about the system dynamics (es. choice of the past terms involved in causality) can solve problems due to mixing and instantaneous effects (es. scalp EEG volume conduction) Disadvantages slow a construction of a null distribution from data is necessary Alessandro Montalto 9 / 21
12 Link between Granger Causality and Transfer Entropy GC and TE are equivalent for jointly Gaussian variables and other quasi-gaussian distributions (Barnett et al 2009, Hlavackova-Schindler 2011, Barnett and Bossomaier 2012) In this case they both measure information transfer. Alessandro Montalto 10 / 21
13 Link between Granger Causality and Transfer Entropy GC and TE are equivalent for jointly Gaussian variables and other quasi-gaussian distributions (Barnett et al 2009, Hlavackova-Schindler 2011, Barnett and Bossomaier 2012) In this case they both measure information transfer. Unified approach (model based and model free) Mathematically more treatable Alessandro Montalto 10 / 21
14 What did we implement? Alessandro Montalto 11 / 21
15 Which past states do we choose? We are looking for the right candidates from the past of the series that can better explain the future of X Figure : Uniform embedding: fixed amount of past states Figure : Non uniform embedding: procedure to choose only the past states that can explain the future of X Alessandro Montalto 12 / 21
16 Linear Transfer Entropy estimator Statistical significance UE: Ftest/surrogates technique NUE: surrogates technique Alessandro Montalto 13 / 21
17 Binning Transfer Entropy estimator Figure : Estimation of the entropy approximating probabilities with the frequency of visitation of the quantized states Statistical significance UE and NUE: surrogates technique Alessandro Montalto 14 / 21
18 Nearest Neighbour Transfer Entropy estimator Statistical significance UE and NUE: surrogates technique Alessandro Montalto 15 / 21
19 Toolbox Three Transfer Entropy Estimators ; Two Embedding frameworks Linear method for GC in the UE and NUE framework Binning estimator for TE in the UE and NUE framework Nearest Neighbour estimator for TE in the UE and NUE framework Kind of analysis Conditioned analysis: it is possible to choose the target series, the driver series for each target and the conditioning variables for each target Analysis that takes into account the instantaneous effects Possibility to easily integrate a new method Alessandro Montalto 16 / 21
20 Toolbox: preliminary settings How to set the input parameters: an example Name Parameter datadir resdir numprocessors datatype datafilename channels samplingrate endpoint autopairwisetardriv Description folder containing data to be analysed choose a name for this folder in which all the results will be stored. This folder will be created automatically number of processors used for the parallel session filename extension data filename vector containing the series id, among the available series, chosen for the analysis variable used to resample data value to cut the series length if necessary vector containing a 1 or a 0 for each chosen method, reflecting whether TE has to be computed among all the pairs or not. In this latter case, the desired drivers and targets will be specified by idtargets and iddrivers Alessandro Montalto 17 / 21
21 Toolbox: method settings Alessandro Montalto 18 / 21
22 Toolbox: summary Possible settings Choose the drivers for each of the targets you want to study; Possibility to perform multivariate or bivariate analysis choosing for each series different number of paste states d (and step between the past states τ); Take into account the instantaneous effects for some of the drivers and the conditioning variables; Run in parallel mode all the methods you need; Possibility to integrate your own methods Alessandro Montalto 19 / 21
23 Applications Figure : AR System Figure : Henon Maps Alessandro Montalto 20 / 21
24 Appendix A: Transfer Entropy TE X Y Z = H(y pre y pas, z pas ) H(y pre x pas, y pas, z pas ) H(y pre y pas, z pas ) = H(y pre, y pas, z pas ) H(y pas, z pas ) H(y pre x pas, y pas, z pas ) = H(y pre, y pas, x pas, z pas ) H(y pas, x pas, z pas ) H(a) = p(a) ln p(a) Alessandro Montalto 21 / 21
ISSN Article. Simulation Study of Direct Causality Measures in Multivariate Time Series
Entropy 2013, 15, 2635-2661; doi:10.3390/e15072635 OPEN ACCESS entropy ISSN 1099-4300 www.mdpi.com/journal/entropy Article Simulation Study of Direct Causality Measures in Multivariate Time Series Angeliki
Causal information approach to partial conditioning in multivariate data sets
Causal information approach to partial conditioning in multivariate data sets D. Marinazzo, M. Pellicoro 2,3,4, S. Stramaglia 2,3,4 Department of Data Analysis, Faculty of Psychology and Pedagogical Sciences,
Comparison of Resampling Techniques for the Non-Causality Hypothesis
Chapter 1 Comparison of Resampling Techniques for the Non-Causality Hypothesis Angeliki Papana, Catherine Kyrtsou, Dimitris Kugiumtzis and Cees G.H. Diks Abstract Different resampling schemes for the null
arxiv: v1 [stat.me] 26 Mar 2013
![arxiv: v1 [stat.me] 26 Mar 2013](/thumbs/90/104152213.jpg "arxiv: v1 [stat.me] 26 Mar 2013")
EPJ manuscript No. (will be inserted by the editor) Partial Transfer Entropy on Rank Vectors Dimitris Kugiumtzis a Department of Mathematical, Physical and Computational Sciences, Faculty of Engineering,
Chapter 2 Review of Classical Information Theory
Chapter 2 Review of Classical Information Theory Abstract This chapter presents a review of the classical information theory which plays a crucial role in this thesis. We introduce the various types of
CAUSALITY MEASURES IN NEUROSCIENCE: WIENER-GRANGER CAUSALITY AND TRANSFER ENTROPY APPLIED TO INTRACRANIAL EEG DATA
CAUSALITY MEASURES IN NEUROSCIENCE: WIENER-GRANGER CAUSALITY AND TRANSFER ENTROPY APPLIED TO INTRACRANIAL EEG DATA A 30 credit project submitted to the University of Manchester for the degree of Master
Information Flow/Transfer Review of Theory and Applications
Information Flow/Transfer Review of Theory and Applications Richard Kleeman Courant Institute of Mathematical Sciences With help from X. San Liang, Andy Majda and John Harlim and support from the NSF CMG
Directionality of coupling from bivariate time series: How to avoid false causalities and missed connections
Directionality of coupling from bivariate time series: How to avoid false causalities and missed connections Milan Paluš and Martin Vejmelka Institute of Computer Science, Academy of Sciences of the Czech
A Recipe for the Estimation of Information Flow in a Dynamical System
Entropy 2015, 17, 438-470; doi:10.3390/e17010438 Article OPEN ACCESS entropy ISSN 1099-4300 www.mdpi.com/journal/entropy A Recipe for the Estimation of Information Flow in a Dynamical System Deniz Gencaga
Exploratory Causal Analysis in Bivariate Time Series Data Abstract
Exploratory Causal Analysis in Bivariate Time Series Data Abstract Many scientific disciplines rely on observational data of systems for which it is difficult (or impossible) to implement controlled experiments
Spectral Interdependency Methods
Spectral Interdependency Methods Mukesh Dhamala* Department of Physics and Astronomy, Neuroscience Institute, Georgia State University, Atlanta, Georgia, USA Synonyms Coherence and Granger causality spectral
Minimum Sample Size for Reliable Causal Inference Using Transfer Entropy
entropy Article Minimum Sample Size for Reliable Causal Inference Using Transfer Entropy Antônio M. T. Ramos * and Elbert E. N. Macau National Institute for Space Research, São José dos Campos 12227-1,
Time, Frequency & Time-Varying Causality Measures in Neuroscience
arxiv:1704.03177v1 [stat.ap] 11 Apr 2017 Time, Frequency & Time-Varying Causality Measures in Neuroscience Sezen Cekic Methodology and Data Analysis, Department of Psychology, University of Geneva, Didier
Transfer entropy a model-free measure of effective connectivity for the neurosciences
J Comput Neurosci (2) 3:45 67 DOI.7/s827--262-3 Transfer entropy a model-free measure of effective connectivity for the neurosciences Raul Vicente Michael Wibral Michael Lindner Gordon Pipa Received: 5
Pattern Recognition and Machine Learning. Bishop Chapter 11: Sampling Methods
Pattern Recognition and Machine Learning Chapter 11: Sampling Methods Elise Arnaud Jakob Verbeek May 22, 2008 Outline of the chapter 11.1 Basic Sampling Algorithms 11.2 Markov Chain Monte Carlo 11.3 Gibbs
Causal modeling of fmri: temporal precedence and spatial exploration
Causal modeling of fmri: temporal precedence and spatial exploration Alard Roebroeck Maastricht Brain Imaging Center (MBIC) Faculty of Psychology & Neuroscience Maastricht University Intro: What is Brain
PERFORMANCE STUDY OF CAUSALITY MEASURES
PERFORMANCE STUDY OF CAUSALITY MEASURES T. Bořil, P. Sovka Department of Circuit Theory, Faculty of Electrical Engineering, Czech Technical University in Prague Abstract Analysis of dynamic relations in
Causality, dynamical systems and the arrow of time a)
Causality, dynamical systems and the arrow of time a) Milan Paluš, 1, b) Anna Krakovská, 2 Jozef Jakubík, 2 and Martina Chvosteková 2 1) Institute of Computer Science, Czech Academy of Sciences, Pod Vodárenskou
Curve Fitting Re-visited, Bishop1.2.5
Curve Fitting Re-visited, Bishop1.2.5 Maximum Likelihood Bishop 1.2.5 Model Likelihood differentiation p(t x, w, β) = Maximum Likelihood N N ( t n y(x n, w), β 1). (1.61) n=1 As we did in the case of the
arxiv: v1 [stat.me] 29 Apr 2015
![arxiv: v1 [stat.me] 29 Apr 2015](/thumbs/80/81037927.jpg "arxiv: v1 [stat.me] 29 Apr 2015")
Estimation of connectivity measures in gappy time series G. Papadopoulos a, D. Kugiumtzis b ariv:155.3v1 [stat.me] 29 Apr 215 a Economics Department, Democritus University of Thrace, Komotini, Greece b
Lecture 17: Differential Entropy
Lecture 17: Differential Entropy Differential entropy AEP for differential entropy Quantization Maximum differential entropy Estimation counterpart of Fano s inequality Dr. Yao Xie, ECE587, Information
Anna Zaremba and Tomaso Aste Measures of causality in complex datasets with application to financial data
Anna Zaremba and Tomaso Aste Measures of causality in complex datasets with application to financial data Article (Published version) (Refereed) Original citation: Zaremba, Anna and Aste, Tomaso (24) Measures
c 2010 Christopher John Quinn
c 2010 Christopher John Quinn ESTIMATING DIRECTED INFORMATION TO INFER CAUSAL RELATIONSHIPS BETWEEN NEURAL SPIKE TRAINS AND APPROXIMATING DISCRETE PROBABILITY DISTRIBUTIONS WITH CAUSAL DEPENDENCE TREES
Time Series Analysis. James D. Hamilton PRINCETON UNIVERSITY PRESS PRINCETON, NEW JERSEY
Time Series Analysis James D. Hamilton PRINCETON UNIVERSITY PRESS PRINCETON, NEW JERSEY PREFACE xiii 1 Difference Equations 1.1. First-Order Difference Equations 1 1.2. pth-order Difference Equations 7
NCoVaR Granger Causality
NCoVaR Granger Causality Cees Diks 1 Marcin Wolski 2 1 Universiteit van Amsterdam 2 European Investment Bank Bank of Italy Rome, 26 January 2018 The opinions expressed herein are those of the authors and
Compensated Transfer Entropy as a Tool for Reliably Estimating Information Transfer in Physiological Time Series
Entropy 2013, 15, 198-219; doi:10.3390/e15010198 Article OPEN ACCESS entropy ISSN 1099-4300 www.mdpi.com/journal/entropy Compensated Transfer Entropy as a Tool for Reliably Estimating Information Transfer
Lecture 11: Continuous-valued signals and differential entropy
Lecture 11: Continuous-valued signals and differential entropy Biology 429 Carl Bergstrom September 20, 2008 Sources: Parts of today s lecture follow Chapter 8 from Cover and Thomas (2007). Some components
Information Theory. Coding and Information Theory. Information Theory Textbooks. Entropy
Coding and Information Theory Chris Williams, School of Informatics, University of Edinburgh Overview What is information theory? Entropy Coding Information Theory Shannon (1948): Information theory is
Symbolic Causation Entropy
Symbolic Causation Entropy Carlo Cafaro 1, Dane Taylor 2, Jie Sun 1, and Erik Bollt 1 Clarkson University 1, Potsdam NY, USA University of North Carolina 2, Chapel Hill NC, USA cidnet14, Max-Planck Institute,
Time Series Analysis. James D. Hamilton PRINCETON UNIVERSITY PRESS PRINCETON, NEW JERSEY
Time Series Analysis James D. Hamilton PRINCETON UNIVERSITY PRESS PRINCETON, NEW JERSEY & Contents PREFACE xiii 1 1.1. 1.2. Difference Equations First-Order Difference Equations 1 /?th-order Difference
9 Graphical modelling of dynamic relationships in multivariate time series
9 Graphical modelling of dynamic relationships in multivariate time series Michael Eichler Institut für Angewandte Mathematik Universität Heidelberg Germany SUMMARY The identification and analysis of interactions
A Multivariate Time-Frequency Based Phase Synchrony Measure for Quantifying Functional Connectivity in the Brain
A Multivariate Time-Frequency Based Phase Synchrony Measure for Quantifying Functional Connectivity in the Brain Dr. Ali Yener Mutlu Department of Electrical and Electronics Engineering, Izmir Katip Celebi
Information Dynamics Foundations and Applications
Gustavo Deco Bernd Schürmann Information Dynamics Foundations and Applications With 89 Illustrations Springer PREFACE vii CHAPTER 1 Introduction 1 CHAPTER 2 Dynamical Systems: An Overview 7 2.1 Deterministic
NONLINEAR TIME SERIES ANALYSIS, WITH APPLICATIONS TO MEDICINE
NONLINEAR TIME SERIES ANALYSIS, WITH APPLICATIONS TO MEDICINE José María Amigó Centro de Investigación Operativa, Universidad Miguel Hernández, Elche (Spain) J.M. Amigó (CIO) Nonlinear time series analysis
Introduction to Probability and Statistics (Continued)
Introduction to Probability and Statistics (Continued) Prof. icholas Zabaras Center for Informatics and Computational Science https://cics.nd.edu/ University of otre Dame otre Dame, Indiana, USA Email:
Simultaneous Equation Models Learning Objectives Introduction Introduction (2) Introduction (3) Solving the Model structural equations
Simultaneous Equation Models. Introduction: basic definitions 2. Consequences of ignoring simultaneity 3. The identification problem 4. Estimation of simultaneous equation models 5. Example: IS LM model
Professor Wiston Adrián RISSO, PhD Institute of Economics (IECON), University of the Republic (Uruguay)
Professor Wiston Adrián RISSO, PhD E-mail: arisso@iecon.ccee.edu.uy Institute of Economics (IECON), University of the Republic (Uruguay) A FIRST APPROACH ON TESTING NON-CAUSALITY WITH SYMBOLIC TIME SERIES
If we want to analyze experimental or simulated data we might encounter the following tasks:
Chapter 1 Introduction If we want to analyze experimental or simulated data we might encounter the following tasks: Characterization of the source of the signal and diagnosis Studying dependencies Prediction
Testing for Chaos in Type-I ELM Dynamics on JET with the ILW. Fabio Pisano
Testing for Chaos in Type-I ELM Dynamics on JET with the ILW Fabio Pisano ACKNOWLEDGMENTS B. Cannas 1, A. Fanni 1, A. Murari 2, F. Pisano 1 and JET Contributors* EUROfusion Consortium, JET, Culham Science
Detection of Nonlinearity and Stochastic Nature in Time Series by Delay Vector Variance Method
International Journal of Engineering & Technology IJET-IJENS Vol:10 No:02 11 Detection of Nonlinearity and Stochastic Nature in Time Series by Delay Vector Variance Method Imtiaz Ahmed Abstract-- This
Fundamentals to Biostatistics. Prof. Chandan Chakraborty Associate Professor School of Medical Science & Technology IIT Kharagpur
Fundamentals to Biostatistics Prof. Chandan Chakraborty Associate Professor School of Medical Science & Technology IIT Kharagpur Statistics collection, analysis, interpretation of data development of new
On the spectral formulation of Granger causality
Noname manuscript No. (will be inserted b the editor) On the spectral formulation of Granger causalit the date of receipt and acceptance should be inserted later Abstract Spectral measures of causalit
Potentials and pitfalls of connectivity analyses in EEG data
Potentials and pitfalls of connectivity analyses in EEG data Prof. Dr. T. Koenig Translational Research Center University Hospital of Psychiatry and Psychotherapy University of Bern, Switzerland thomas.koenig@puk.unibe.ch
Statistical Analysis of fmrl Data
Statistical Analysis of fmrl Data F. Gregory Ashby The MIT Press Cambridge, Massachusetts London, England Preface xi Acronyms xv 1 Introduction 1 What Is fmri? 2 The Scanning Session 4 Experimental Design
Kyle Reing University of Southern California April 18, 2018
Renormalization Group and Information Theory Kyle Reing University of Southern California April 18, 2018 Overview Renormalization Group Overview Information Theoretic Preliminaries Real Space Mutual Information
Statistical modelling in climate science
Statistical modelling in climate science Nikola Jajcay supervisor Milan Paluš Seminář strojového učení a modelovaní MFF UK seminář 2016 1 Introduction modelling in climate science dynamical model initial
Probabilistic Graphical Models
Probabilistic Graphical Models Brown University CSCI 295-P, Spring 213 Prof. Erik Sudderth Lecture 11: Inference & Learning Overview, Gaussian Graphical Models Some figures courtesy Michael Jordan s draft
Exercises with solutions (Set D)
Exercises with solutions Set D. A fair die is rolled at the same time as a fair coin is tossed. Let A be the number on the upper surface of the die and let B describe the outcome of the coin toss, where
A variational radial basis function approximation for diffusion processes
A variational radial basis function approximation for diffusion processes Michail D. Vrettas, Dan Cornford and Yuan Shen Aston University - Neural Computing Research Group Aston Triangle, Birmingham B4
x log x, which is strictly convex, and use Jensen s Inequality:
2. Information measures: mutual information 2.1 Divergence: main inequality Theorem 2.1 (Information Inequality). D(P Q) 0 ; D(P Q) = 0 iff P = Q Proof. Let ϕ(x) x log x, which is strictly convex, and
Multidimensional scaling (MDS)
Multidimensional scaling (MDS) Just like SOM and principal curves or surfaces, MDS aims to map data points in R p to a lower-dimensional coordinate system. However, MSD approaches the problem somewhat
Conditional Likelihood Maximization: A Unifying Framework for Information Theoretic Feature Selection
Conditional Likelihood Maximization: A Unifying Framework for Information Theoretic Feature Selection Gavin Brown, Adam Pocock, Mingjie Zhao and Mikel Lujan School of Computer Science University of Manchester
ELEC546 Review of Information Theory
ELEC546 Review of Information Theory Vincent Lau 1/1/004 1 Review of Information Theory Entropy: Measure of uncertainty of a random variable X. The entropy of X, H(X), is given by: If X is a discrete random
ECE 4400:693 - Information Theory
ECE 4400:693 - Information Theory Dr. Nghi Tran Lecture 8: Differential Entropy Dr. Nghi Tran (ECE-University of Akron) ECE 4400:693 Lecture 1 / 43 Outline 1 Review: Entropy of discrete RVs 2 Differential
Lecture 5: Unit Roots, Cointegration and Error Correction Models The Spurious Regression Problem
Lecture 5: Unit Roots, Cointegration and Error Correction Models The Spurious Regression Problem Prof. Massimo Guidolin 20192 Financial Econometrics Winter/Spring 2018 Overview Defining cointegration Vector
Econ 423 Lecture Notes: Additional Topics in Time Series 1
Econ 423 Lecture Notes: Additional Topics in Time Series 1 John C. Chao April 25, 2017 1 These notes are based in large part on Chapter 16 of Stock and Watson (2011). They are for instructional purposes
Directional and Causal Information Flow in EEG for Assessing Perceived Audio Quality
1 Directional and Causal Information Flow in EEG for Assessing Perceived Audio Quality Ketan Mehta and Jörg Kliewer, Senior Member, IEEE Klipsch School of Electrical and Computer Engineering, New Mexico
Adaptive Rejection Sampling with fixed number of nodes
Adaptive Rejection Sampling with fixed number of nodes L. Martino, F. Louzada Institute of Mathematical Sciences and Computing, Universidade de São Paulo, Brazil. Abstract The adaptive rejection sampling
Probabilistic Graphical Models Lecture 17: Markov chain Monte Carlo
Probabilistic Graphical Models Lecture 17: Markov chain Monte Carlo Andrew Gordon Wilson www.cs.cmu.edu/~andrewgw Carnegie Mellon University March 18, 2015 1 / 45 Resources and Attribution Image credits,
Observed Brain Dynamics
Observed Brain Dynamics Partha P. Mitra Hemant Bokil OXTORD UNIVERSITY PRESS 2008 \ PART I Conceptual Background 1 1 Why Study Brain Dynamics? 3 1.1 Why Dynamics? An Active Perspective 3 Vi Qimnü^iQ^Dv.aamics'v
Fisher Information in Gaussian Graphical Models
Fisher Information in Gaussian Graphical Models Jason K. Johnson September 21, 2006 Abstract This note summarizes various derivations, formulas and computational algorithms relevant to the Fisher information
Conditional Least Squares and Copulae in Claims Reserving for a Single Line of Business
Conditional Least Squares and Copulae in Claims Reserving for a Single Line of Business Michal Pešta Charles University in Prague Faculty of Mathematics and Physics Ostap Okhrin Dresden University of Technology
Independent Component Analysis
Independent Component Analysis Seungjin Choi Department of Computer Science Pohang University of Science and Technology, Korea seungjin@postech.ac.kr March 4, 2009 1 / 78 Outline Theory and Preliminaries
directed information theory: a review
The relation between Granger causality and 1 directed information theory: a review Pierre-Olivier Amblard 1,2 and Olivier J.J. Michel 1 1 GIPSAlab/CNRS UMR 5216/ BP46, arxiv:1211.3169v1 [cs.it] 14 Nov
Causality detection based on information-theoretic approaches in time series analysis
Physics Reports 441 (2007) 1 46 www.elsevier.com/locate/physrep Causality detection based on information-theoretic approaches in time series analysis Katerina Hlaváčková-Schindler a,, Milan Paluš b, Martin
Heavy Tailed Time Series with Extremal Independence
Heavy Tailed Time Series with Extremal Independence Rafa l Kulik and Philippe Soulier Conference in honour of Prof. Herold Dehling Bochum January 16, 2015 Rafa l Kulik and Philippe Soulier Regular variation
Recognition Performance from SAR Imagery Subject to System Resource Constraints
Recognition Performance from SAR Imagery Subject to System Resource Constraints Michael D. DeVore Advisor: Joseph A. O SullivanO Washington University in St. Louis Electronic Systems and Signals Research
Multiaccess Channels with State Known to One Encoder: A Case of Degraded Message Sets
Multiaccess Channels with State Known to One Encoder: A Case of Degraded Message Sets Shivaprasad Kotagiri and J. Nicholas Laneman Department of Electrical Engineering University of Notre Dame Notre Dame,
Information Theory and Neuroscience II
John Z. Sun and Da Wang Massachusetts Institute of Technology October 14, 2009 Outline System Model & Problem Formulation Information Rate Analysis Recap 2 / 23 Neurons Neuron (denoted by j) I/O: via synapses
On similarity measures for spike trains
On similarity measures for spike trains Justin Dauwels, François Vialatte, Theophane Weber, and Andrzej Cichocki RIKEN Brain Science Institute, Saitama, Japan Massachusetts Institute of Technology, Cambridge,
Information Thermodynamics on Causal Networks
1/39 Information Thermodynamics on Causal Networks FSPIP 2013, July 12 2013. Sosuke Ito Dept. of Phys., the Univ. of Tokyo (In collaboration with T. Sagawa) ariv:1306.2756 The second law of thermodynamics
Distinguishing between Cause and Effect: Estimation of Causal Graphs with two Variables
Distinguishing between Cause and Effect: Estimation of Causal Graphs with two Variables Jonas Peters ETH Zürich Tutorial NIPS 2013 Workshop on Causality 9th December 2013 F. H. Messerli: Chocolate Consumption,
Probabilistic Graphical Models
2016 Robert Nowak Probabilistic Graphical Models 1 Introduction We have focused mainly on linear models for signals, in particular the subspace model x = Uθ, where U is a n k matrix and θ R k is a vector
Markov properties for graphical time series models
Markov properties for graphical time series models Michael Eichler Universität Heidelberg Abstract This paper deals with the Markov properties of a new class of graphical time series models which focus
Radial Basis Function Networks. Ravi Kaushik Project 1 CSC Neural Networks and Pattern Recognition
Radial Basis Function Networks Ravi Kaushik Project 1 CSC 84010 Neural Networks and Pattern Recognition History Radial Basis Function (RBF) emerged in late 1980 s as a variant of artificial neural network.
DAMOCO: MATLAB toolbox for multivariate data analysis, based on coupled oscillators approach Version 1.0
DAMOCO: MATLAB toolbox for multivariate data analysis, based on coupled oscillators approach Version 1.0 Björn Kralemann 1, Michael Rosenblum 2, Arkady Pikovsky 2 1 Institut für Pädagogik, Christian-Albrechts-Universität
= first derivative evaluated at that point: ( )
Calculus 130, section 5.1-5. Functions: Increasing, Decreasing, Extrema notes by Tim Pilachowski Reminder: You will not be able to use a graphing calculator on tests! First, a quick scan of what we know
Probability Models in Electrical and Computer Engineering Mathematical models as tools in analysis and design Deterministic models Probability models
Probability Models in Electrical and Computer Engineering Mathematical models as tools in analysis and design Deterministic models Probability models Statistical regularity Properties of relative frequency
Phase-Space Reconstruction. Gerrit Ansmann
Phase-Space Reconstruction Gerrit Ansmann Reprise: The Need for Non-Linear Methods. Lorenz oscillator x = 1(y x), y = x(28 z) y, z = xy 8z 3 Autoregressive process measured with non-linearity: y t =.8y
Adaptive Rejection Sampling with fixed number of nodes
Adaptive Rejection Sampling with fixed number of nodes L. Martino, F. Louzada Institute of Mathematical Sciences and Computing, Universidade de São Paulo, São Carlos (São Paulo). Abstract The adaptive
Probabilistic Graphical Models
Probabilistic Graphical Models Brown University CSCI 2950-P, Spring 2013 Prof. Erik Sudderth Lecture 12: Gaussian Belief Propagation, State Space Models and Kalman Filters Guest Kalman Filter Lecture by
Lecture 4 October 18th
Directed and undirected graphical models Fall 2017 Lecture 4 October 18th Lecturer: Guillaume Obozinski Scribe: In this lecture, we will assume that all random variables are discrete, to keep notations
On the Causal Structure of the Universe
On the Causal Structure of the Universe Blazej Kot * Abstract I suggest we treat causality, not matter, as the fundamental constituent of reality. I introduce a unit of causality named toma and outline
Information in Biology
Lecture 3: Information in Biology Tsvi Tlusty, tsvi@unist.ac.kr Living information is carried by molecular channels Living systems I. Self-replicating information processors Environment II. III. Evolve
UQ, Semester 1, 2017, Companion to STAT2201/CIVL2530 Exam Formulae and Tables
UQ, Semester 1, 2017, Companion to STAT2201/CIVL2530 Exam Formulae and Tables To be provided to students with STAT2201 or CIVIL-2530 (Probability and Statistics) Exam Main exam date: Tuesday, 20 June 1
Calibrating Environmental Engineering Models and Uncertainty Analysis
Models and Cornell University Oct 14, 2008 Project Team Christine Shoemaker, co-pi, Professor of Civil and works in applied optimization, co-pi Nikolai Blizniouk, PhD student in Operations Research now
Introduction to Graphical Models
Introduction to Graphical Models The 15 th Winter School of Statistical Physics POSCO International Center & POSTECH, Pohang 2018. 1. 9 (Tue.) Yung-Kyun Noh GENERALIZATION FOR PREDICTION 2 Probabilistic
A Unified Estimation Framework for State- Related Changes in Effective Brain Connectivity
Universiti Teknologi Malaysia From the SelectedWorks of Chee-Ming Ting PhD 6 A Unified Estimation Framework for State- Related Changes in Effective Brain Connectivity Chee-Ming Ting, PhD S. Balqis Samdin
2 Two Random Variables
Two Random Variables 19 2 Two Random Variables A number of features of the two-variable problem follow by direct analogy with the one-variable case: the joint probability density, the joint probability
Blind Source Separation via Generalized Eigenvalue Decomposition
Journal of Machine Learning Research 4 (2003) 1261-1269 Submitted 10/02; Published 12/03 Blind Source Separation via Generalized Eigenvalue Decomposition Lucas Parra Department of Biomedical Engineering
Channel capacity. Outline : 1. Source entropy 2. Discrete memoryless channel 3. Mutual information 4. Channel capacity 5.
Channel capacity Outline : 1. Source entropy 2. Discrete memoryless channel 3. Mutual information 4. Channel capacity 5. Exercices Exercise session 11 : Channel capacity 1 1. Source entropy Given X a memoryless
Analyzing Anatomical and Functional Brain Connectivity. - M/EEG Functional and Resting-State Connectivity Maren Grigutsch
Analyzing Anatomical and Functional Brain Connectivity - M/EEG Functional and Resting-State Connectivity Maren Grigutsch Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig Functional
AP Calculus BC Multiple-Choice Answer Key!
Multiple-Choice Answer Key!!!!! "#$$%&'! "#$$%&'!!,#-! ()*+%$,#-! ()*+%$!!!!!! "!!!!! "!! 5!! 6! 7!! 8! 7! 9!!! 5:!!!!! 5! (!!!! 5! "! 5!!! 5!! 8! (!! 56! "! :!!! 59!!!!! 5! 7!!!! 5!!!!! 55! "! 6! "!!
Information in Biology
Information in Biology CRI - Centre de Recherches Interdisciplinaires, Paris May 2012 Information processing is an essential part of Life. Thinking about it in quantitative terms may is useful. 1 Living
Review of probabilities
CS 1675 Introduction to Machine Learning Lecture 5 Density estimation Milos Hauskrecht milos@pitt.edu 5329 Sennott Square Review of probabilities 1 robability theory Studies and describes random processes
6. Brownian Motion. Q(A) = P [ ω : x(, ω) A )
6. Brownian Motion. stochastic process can be thought of in one of many equivalent ways. We can begin with an underlying probability space (Ω, Σ, P) and a real valued stochastic process can be defined
Capacity of the Discrete Memoryless Energy Harvesting Channel with Side Information
204 IEEE International Symposium on Information Theory Capacity of the Discrete Memoryless Energy Harvesting Channel with Side Information Omur Ozel, Kaya Tutuncuoglu 2, Sennur Ulukus, and Aylin Yener
Switching Regime Estimation
Switching Regime Estimation Series de Tiempo BIrkbeck March 2013 Martin Sola (FE) Markov Switching models 01/13 1 / 52 The economy (the time series) often behaves very different in periods such as booms
Bayesian Learning in Undirected Graphical Models
Bayesian Learning in Undirected Graphical Models Zoubin Ghahramani Gatsby Computational Neuroscience Unit University College London, UK http://www.gatsby.ucl.ac.uk/ Work with: Iain Murray and Hyun-Chul
Coding for Discrete Source
EGR 544 Communication Theory 3. Coding for Discrete Sources Z. Aliyazicioglu Electrical and Computer Engineering Department Cal Poly Pomona Coding for Discrete Source Coding Represent source data effectively