Pyif: a Fast and Light Weight Implementation to Estimate Bivariate Transfer Entropy for Big Data

Total Page:16

File Type:pdf, Size:1020Kb

Pyif: a Fast and Light Weight Implementation to Estimate Bivariate Transfer Entropy for Big Data PyIF: A Fast and Light Weight Implementation to Estimate Bivariate Transfer Entropy for Big Data Kelechi M. Ikegwu Jacob Trauger Jeff McMullin IIlinois Informatics Institute Department of Computer Science Department of Accounting University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign Indiana University Urbana, IL USA Urbana, IL, USA Bloomington, IN, USA [email protected] [email protected] [email protected] Robert J. Brunner Department of Accountancy University of Illinois at Urbana-Champaign Urbana, IL, USA [email protected] Abstract—Transfer entropy is an information measure that perform index-to-index analysis with the Dow Jones Share quantifies information flow between processes evolving in time. Market (DJIA) and the Frankfurt Stock index (DAX) [4] and Transfer entropy has a plethora of potential applications in finan- document the extent to which one index drives the behavior of cial markets, canonical systems, neuroscience, and social media. We offer a fast open source Python implementation called PyIF the other. Following Marschinski and Kantz, other researchers that estimates Transfer Entropy with Kraskov’s method. PyIF apply TE to examine related research questions about financial utilizes KD-Trees, multiple processes by parallelizing queries on markets. These include measuring TE from market indexes, said KD-Trees, and can be used with CUDA compatible GPUs to such as S&P 500 or the DJIA, to individual equities as well significantly reduce the wall time for estimating transfer entropy. as between individual equities [5]. We find from our analyses that PyIF’s GPU implementation is up to 1072 times faster (and it’s CPU implementation is up 181 times Network Inference is another application area of TE. An faster) than existing implementations to estimate transfer entropy objective of network inference is to infer a network by inden- on large data and scales better than existing implementations. tifying relationships between individual processes in the data. Index Terms—Transfer Entropy, Parallel Processing Computational neuroscience, financial market analysis, gene regulatory networks, social media, and multi-agent systems I. INTRODUCTION are areas where TE has been used to model networks. Early Information theory provides a framework for studying the approaches that used TE for network inference either measure quantification, storage, and communication of information [1]. pairwise TE between all pairs of variables in a network or This theory defines entropy as the amount of uncertainty or threshold the TE values to select connections between nodes disorder in a random process. Mutual Information is another in a network [12], [13], and [14]. Recent approaches have measure in this theory which quantifies the amount of informa- used statistical significance tests of pairwise TE to determine tion shared across random variables. While similar to mutual whether links exist [15] and [16]. [5] offers more examples of information, transfer entropy (TE) also considers the dynamics TE applications. of information and how these dynamics evolves in time [2]. Put simply, TE quantifies the reduction in uncertainty in one B. Outline random process from knowing past realizations of another In the next section we formally define TE. The following random process. This is a particularly useful property of TE section discusses TE estimation methods. We then discuss our as many real-world phenomena, from stock market prices to proposed implementation called PyIF to estimate bivariate TE. neural signals, are dynamic processes evolving in time. TE is Next, we describe a comparative analysis between PyIF and also an asymmetric measure of information transfer. Ergo, TE existing implementations that estimate bivariate TE. Lastly, we computed from process A to process B may yield a different conclude the paper with a discussion and future work. result than TE computed from B to A. The information theoretic framework and these measures have led to a variety II. DEFINITION OF TRANSFER ENTROPY of applications in different research areas [1], [5]. In 2000, Schreiber [2] discovered TE and coined the name A. Applications of Transfer Entropy “transfer entropy,” although Milian Palus [3] also indepen- dently discovered the concept as well. Let the function I TE is particularly useful for detecting information transfer represent mutual information between two probability distri- in financial markets [5]. Marschinski and Kantz used TE to butions. Lagged mutual information I(Xt : Yt−k) can be used 978-1-7281-6861-6/20/$31.00 ©2020 IEEE as a time-asymmetric measure of information transfer from Y to X where X and Y are both random processes, k is a B. Kraskov Estimator lag period, and t is the current time period. However, lagged Transfer Entropy can be estimated using k-nearest neighbors mutual information is unsatisfactory as it does not account for [8]. Note that entropy can be estimated with: a shared history between the processes X and Y [6]. n TE considers the shared history between two processes via 1 X H^ (X) = − lnp^(x ) (5) conditional mutual information. Specifically, TE conditions on n i i=1 the past of Xt to remove any redundant or shared information between Xt and its past. This also removes any information Kraskov et al. expanded this definition to estimate entropy to: in the process Y about X at time t that is in the past of X [7]. n Transfer entropy T (where the transfer of information occurs 1 X 1 H^ (X) = − (n (i)) − + (n) + ln(c ) + from Y to X) can be defined as: n x k dx i=1 n TY !X (t) ≡ I(Xt : Yt−kjXt−k) (1) dx X ln((i)) (6) n Kraskov [8] shows that transfer entropy can be expressed as i=1 the difference between two conditional mutual information computations: where n are the number of data points, k are the nearest neighbors, dx is the dimension of x, and cdx is the volume of TY !X (t) = I(XtjXt−k;Yt−k) − I(XtjXt−k) (2) the dx-dimensional unit ball. For two random variables X and (i) th Y, let 2 be the distance between (xi; yi) and it’s k neighbor . x(i) y (i) be denoted by (kxi; kyi). Let and be defined as The intuition of this definition is that TE measures the 2 2 jjxi − kxijj and jjyi − yijj respectively. nx(i) is the number of amount of information in Yt−k about Xt after considering the points xj such that jjxi −xjjj ≤ x(i)=2, (x) is the digamma information in Xt−k about Xt. Put differently, TE quantifies function where the reduction in uncertainty about Xt from knowing Yt−k after considering the reduction in uncertainty about Xt from (x) = Γ(x)−1dΓ(x)=dx (7) knowing Xt−k. and Γ(x) is the ordinary gamma function. Lastly (1) = −C III. ESTIMATING TRANSFER ENTROPY where C = 0:5772156649 and is the Euler-Mascheroni con- There are many techniques for estimating mutual informa- stant. To estimate the entropy for the random variable Y, Y ^ tion. Khan et al. explored the utility of different methods for can be substituted into H(X). mutual information estimation [10] and many of the methods Joint entropy between X and Y can then be estimated as: they considered are applicable to estimate TE. 1 H^ (X; Y ) = − (k) − + (n) + ln(c c ) + k dx dy A. Kernel Density Estimator n dx + dy X ln((i) (8) Kernel Density Estimators can be used to estimate TE [11]. n i For a bivariate dataset of size n with variables X and Y, Mutual Information can be estimated as: where dy is the dimension of y, and cdy is the column of the ^ ^ ^ n dy-dimensional unit ball. Using H(X); H(Y ); and H(X; Y ) 1 X p^XY (xi; yj) I^(X; Y ) = ln (3) mutual information can be estimated as: n p^ (x )^p (y ) i=1 X i Y i n 1 1 X where p^X (xi) and p^Y (yi) are the estimated marginal prob- I^(X; Y ) = (k) − − [ (n (i)) + (n (i))] + (n) k n x y ability density functions and p^XY (xi; yj) is the joint esti- i=1 mated probability density function. For a multivariate dataset (9) containing: x1; x2; :::; xn where each x is in a d-dimensional where ny(i) is the number of points yj such that jjyi − y (i) space, the multivariate kernel density estimator with kernel K yjjj ≤ 2 . This method has been referred to as the Kraskov is defined by: estimator in literature. 1 X x − xi C. Additional Estimators p^(x) = = 1nK( ) (4) nhd h Khan et al. also explored the utility of Edgeworth approxi- i mation of differential entropy to calculate Mutual Information where h is the smoothing parameter, and in this case, K is and adaptive partitioning of the XY plane to estimate the joint a standard multivariate normal kernel defined by K(x) = T probability density, which can be used to estimate mutual −d=2 x x (2π) e 2 . Moon et al. outlined a procedure to estimate information. Ultimately Khan et al. found that a KDE esti- Mutual Information using marginal and joint probabilities with mator and Kraskov estimator outperform other methods with Kernel Density Estimators [11]. respect to their ability to capture the dependence structure of random processes. Currently our software supports estimating data. We make the assumption that there is relatively little bivariate TE using the Kraskov estimator with plans to add to no information transfer between the random processes. We other estimators in the future. run each of the implementations (excluding Transfer Entropy Toolbox) on nano, a cluster of eight SuperMicro servers with IV. PYIF Intel Haswell/Broadwell CPUs and NVIDIA Tesla P100/V100 Our proposed software implementation PyIF 1 is an open GPUs hosted by the National Center of Super Computing Ap- source implementation.
Recommended publications
  • JIDT: an Information-Theoretic Toolkit for Studying the Dynamics of Complex Systems
    JIDT: An information-theoretic toolkit for studying the dynamics of complex systems Joseph T. Lizier1, 2, ∗ 1Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, 04103 Leipzig, Germany 2CSIRO Digital Productivity Flagship, Marsfield, NSW 2122, Australia (Dated: December 4, 2014) Complex systems are increasingly being viewed as distributed information processing systems, particularly in the domains of computational neuroscience, bioinformatics and Artificial Life. This trend has resulted in a strong uptake in the use of (Shannon) information-theoretic measures to analyse the dynamics of complex systems in these fields. We introduce the Java Information Dy- namics Toolkit (JIDT): a Google code project which provides a standalone, (GNU GPL v3 licensed) open-source code implementation for empirical estimation of information-theoretic measures from time-series data. While the toolkit provides classic information-theoretic measures (e.g. entropy, mutual information, conditional mutual information), it ultimately focusses on implementing higher- level measures for information dynamics. That is, JIDT focusses on quantifying information storage, transfer and modification, and the dynamics of these operations in space and time. For this purpose, it includes implementations of the transfer entropy and active information storage, their multivariate extensions and local or pointwise variants. JIDT provides implementations for both discrete and continuous-valued data for each measure, including various types of estimator for continuous data (e.g. Gaussian, box-kernel and Kraskov-St¨ogbauer-Grassberger) which can be swapped at run-time due to Java's object-oriented polymorphism. Furthermore, while written in Java, the toolkit can be used directly in MATLAB, GNU Octave, Python and other environments. We present the principles behind the code design, and provide several examples to guide users.
    [Show full text]
  • Exploratory Causal Analysis in Bivariate Time Series Data
    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 and data analysis techniques are required for identifying causal information and relationships directly from observational data. This need has lead to the development of many different time series causality approaches and tools including transfer entropy, convergent cross-mapping (CCM), and Granger causality statistics. A practicing analyst can explore the literature to find many proposals for identifying drivers and causal connections in times series data sets, but little research exists of how these tools compare to each other in practice. This work introduces and defines exploratory causal analysis (ECA) to address this issue. The motivation is to provide a framework for exploring potential causal structures in time series data sets. J. M. McCracken Defense talk for PhD in Physics, Department of Physics and Astronomy 10:00 AM November 20, 2015; Exploratory Hall, 3301 Advisor: Dr. Robert Weigel; Committee: Dr. Paul So, Dr. Tim Sauer J. M. McCracken (GMU) ECA w/ time series causality November 20, 2015 1 / 50 Exploratory Causal Analysis in Bivariate Time Series Data J. M. McCracken Department of Physics and Astronomy George Mason University, Fairfax, VA November 20, 2015 J. M. McCracken (GMU) ECA w/ time series causality November 20, 2015 2 / 50 Outline 1. Motivation 2. Causality studies 3. Data causality 4. Exploratory causal analysis 5. Making an ECA summary Transfer entropy difference Granger causality statistic Pairwise asymmetric inference Weighed mean observed leaning Lagged cross-correlation difference 6.
    [Show full text]
  • Empirical Analysis Using Symbolic Transfer Entropy
    University of South Florida Scholar Commons Graduate Theses and Dissertations Graduate School June 2019 Measuring Influence Across Social Media Platforms: Empirical Analysis Using Symbolic Transfer Entropy Abhishek Bhattacharjee University of South Florida, [email protected] Follow this and additional works at: https://scholarcommons.usf.edu/etd Part of the Computer Sciences Commons Scholar Commons Citation Bhattacharjee, Abhishek, "Measuring Influence Across Social Media Platforms: Empirical Analysis Using Symbolic Transfer Entropy" (2019). Graduate Theses and Dissertations. https://scholarcommons.usf.edu/etd/7745 This Thesis is brought to you for free and open access by the Graduate School at Scholar Commons. It has been accepted for inclusion in Graduate Theses and Dissertations by an authorized administrator of Scholar Commons. For more information, please contact [email protected]. Measuring Influence Across Social Media Platforms: Empirical Analysis Using Symbolic Transfer Entropy by Abhishek Bhattacharjee A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science Department of Computer Science and Engineering College of Engineering University of South Florida Major Professor: Adriana Iamnitchi, Ph.D. John Skvoretz, Ph.D. Giovanni Luca Ciampaglia, Ph.D. Date of Approval: April 29, 2019 Keywords: Social Networks, Cross-platform influence Copyright © 2019, Abhishek Bhattacharjee DEDICATION Dedicated to my parents, brother, girlfriend and those five humans. ACKNOWLEDGMENTS I would like to pay my thanks to my advisor Dr Adriana Iamnitchi for her constant support and feedback throughout this project. The work wouldn’t have been possible without Leidos who provided us the data, and DARPA for funding this research work. I would also like to acknowledge the contributions made by Dr.
    [Show full text]
  • Entropic Measures of Connectivity with an Application to Intracerebral Epileptic Signals Jie Zhu
    Entropic measures of connectivity with an application to intracerebral epileptic signals Jie Zhu To cite this version: Jie Zhu. Entropic measures of connectivity with an application to intracerebral epileptic signals. Signal and Image processing. Université Rennes 1, 2016. English. NNT : 2016REN1S006. tel-01359072 HAL Id: tel-01359072 https://tel.archives-ouvertes.fr/tel-01359072 Submitted on 1 Sep 2016 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. ANNÉE 2016 THÈSE / UNIVERSITÉ DE RENNES 1 sous le sceau de l’Université Bretagne Loire pour le grade de DOCTEUR DE L’UNIVERSITÉ DE RENNES 1 Mention : Traitement du Signal et Télécommunications Ecole doctorale MATISSE Ecole Doctorale Mathématiques, Télécommunications, Informatique, Signal, Systèmes, Electronique Jie ZHU Préparée à l’unité de recherche LTSI - INSERM UMR 1099 Laboratoire Traitement du Signal et de l’Image ISTIC UFR Informatique et Électronique Thèse soutenue à Rennes Entropic Measures of le 22 juin 2016 Connectivity with an devant le jury composé de : MICHEL Olivier Application to Professeur
    [Show full text]
  • Fast and Effective Pseudo Transfer Entropy for Bivariate Data-Driven
    www.nature.com/scientificreports OPEN Fast and efective pseudo transfer entropy for bivariate data‑driven causal inference Riccardo Silini* & Cristina Masoller Identifying, from time series analysis, reliable indicators of causal relationships is essential for many disciplines. Main challenges are distinguishing correlation from causality and discriminating between direct and indirect interactions. Over the years many methods for data‑driven causal inference have been proposed; however, their success largely depends on the characteristics of the system under investigation. Often, their data requirements, computational cost or number of parameters limit their applicability. Here we propose a computationally efcient measure for causality testing, which we refer to as pseudo transfer entropy (pTE), that we derive from the standard defnition of transfer entropy (TE) by using a Gaussian approximation. We demonstrate the power of the pTE measure on simulated and on real‑world data. In all cases we fnd that pTE returns results that are very similar to those returned by Granger causality (GC). Importantly, for short time series, pTE combined with time‑shifted (T‑S) surrogates for signifcance testing strongly reduces the computational cost with respect to the widely used iterative amplitude adjusted Fourier transform (IAAFT) surrogate testing. For example, for time series of 100 data points, pTE and T‑S reduce the computational time by 82% with respect to GC and IAAFT. We also show that pTE is robust against observational noise. Therefore, we argue that the causal inference approach proposed here will be extremely valuable when causality networks need to be inferred from the analysis of a large number of short time series.
    [Show full text]
  • TRENTOOL 3.3.1 Beta – User Documentation
    TRENTOOL 3.3.1 beta – User Documentation Patricia Wollstadt∗ Michael Lindner Raul Vicente Michael Wibral Nicu Pampu Mario Martinez-Zarzuela Version 0.93 http://www.trentool.de/ Contents 1 Introduction 4 2 Installation and configuration6 3 Background 7 3.1 Transfer entropy....................................7 3.2 Notation and preliminaries..............................7 3.3 Practical TE estimation in TRENTOOL.......................8 3.4 Additional functionalities implemented in TRENTOOL.............. 11 3.4.1 Reconstruction of interaction delays..................... 11 3.4.2 Estimating TE from an ensemble of time series............... 11 3.4.3 Group analysis................................. 12 3.4.4 Graph correction for multivariate effects................... 12 4 Using TRENTOOL 14 4.1 Overview........................................ 14 4.2 TRENTOOL core functions.............................. 16 4.2.1 TEprepare.m .................................. 18 4.2.2 TEsurrogatestats.m ............................. 18 4.3 Reconstruction of interaction delays......................... 19 4.3.1 InteractionDelayReconstruction_calculate.m ............. 21 4.3.2 InteractionDelayReconstruction_plotting.m .............. 22 4.4 Estimating time-resolved transfer entropy from an ensemble of time series.... 22 4.4.1 TEsurrogatestats_ensemble.m ....................... 24 4.4.2 Combining time-resolved transfer entropy estimation with interaction delay reconstruction................................. 25 4.5 Binomial Test for Single Subject Results......................
    [Show full text]
  • Direction of Information Flow in Large-Scale Resting-State
    Direction of information flow in large-scale resting- state networks is frequency-dependent Arjan Hillebranda,1, Prejaas Tewariea, Edwin van Dellena,b, Meichen Yua, Ellen W. S. Carboc, Linda Douwc,d, Alida A. Gouwa,e, Elisabeth C. W. van Straatena,f, and Cornelis J. Stama aDepartment of Clinical Neurophysiology and Magnetoencephalography Center, VU University Medical Center, 1081 HV Amsterdam, The Netherlands; bDepartment of Psychiatry, Brain Center Rudolf Magnus, University Medical Center Utrecht, 3508 GA Utrecht, The Netherlands; cDepartment of Anatomy and Neurosciences, VU University Medical Center, 1081 HV Amsterdam, The Netherlands; dDepartment of Radiology, Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Charlestown, MA 02129; eAlzheimer Center and Department of Neurology, VU University Medical Center, 1081 HV Amsterdam, The Netherlands; and fNutricia Advanced Medical Nutrition, Nutricia Research, 3584 CT Utrecht, The Netherlands Edited by Marcus E. Raichle, Washington University in St. Louis, St. Louis, MO, and approved February 24, 2016 (received for review August 8, 2015) Normal brain function requires interactions between spatially sepa- front pattern has also been observed in EEG (26–28). An important rated, and functionally specialized, macroscopic regions, yet the advantage of MEG over EEG in this context is that it is reference- directionality of these interactions in large-scale functional networks free. Moreover, the large number of sensors (several hundreds) in is unknown. Magnetoencephalography was used to determine the modern whole-head MEG systems allow for sophisticated spatial directionality of these interactions, where directionality was inferred filtering approaches to accurately reconstruct time series of neuronal from time series of beamformer-reconstructed estimates of neuronal activation across the cortex (29, 30).
    [Show full text]
  • Causal Coupling Inference from Multivariate Time Seriesbasedonordinalpartitiontransitionnetworks
    CAUSAL COUPLING INFERENCE FROM MULTIVARIATE TIME SERIES BASED ON ORDINAL PARTITION TRANSITION NETWORKS Narayan Puthanmadam Subramaniyam Faculty of Medicine and Health Technology Tampere University [email protected] Reik V. Donner Magdeburg–Stendal University of Applied Sciences and Potsdam Institute for Climate Impact Research (PIK) – Member of the Leibniz Association Davide Caron Gabriella Pannucio Enhanced Regenerative Medicine Enhanced Regenerative Medicine Istituto Italiano di Tecnologia Istituto Italiano di Tecnologia Jari Hyttinen Faculty of Medicine and Health Technology Tampere University June 3, 2021 ABSTRACT Identifying causal relationships is a challenging yet crucial problem in many fields of science like epidemiology, climatology, ecology, genomics, economics and neuroscience, to mention only a few. Recent studies have demonstrated that ordinal partition transition networks (OPTNs) allow inferring the coupling direction between two dynamical systems. In this work, we generalize this concept to the study of the interactions among multiple dynamical systems and we propose a new method to de- tect causality in multivariate observational data. By applying this method to numerical simulations of coupled linear stochastic processes as well as two examples of interacting nonlinear dynamical systems (coupled Lorenz systems and a network of neural mass models), we demonstrate that our approach can reliably identify the direction of interactions and the associated coupling delays. Fi- arXiv:2010.00948v4 [stat.ME] 1 Jun 2021 nally, we study real-world observational microelectrode array electrophysiology data from rodent brain slices to identify the causal coupling structures underlying epileptiform activity. Our results, both from simulations and real-world data, suggest that OPTNs can provide a complementary and robust approach to infer causal effect networks from multivariate observational data.
    [Show full text]
  • Disentangling Causal Webs in the Brain Using Functional Magnetic Resonance Imaging: a Review of Current Approaches
    REVIEW Disentangling causal webs in the brain using functional magnetic resonance imaging: A review of current approaches Natalia Z. Bielczyk 1,2, Sebo Uithol 1,3, Tim van Mourik 1,2,PaulAnderson 1,4, Jeffrey C. Glennon1,2, and Jan K. Buitelaar 1,2 1Donders Institute for Brain, Cognition and Behavior, Nijmegen, the Netherlands 2Department of Cognitive Neuroscience, Radboud University Nijmegen Medical Centre, Nijmegen, the Netherlands 3Bernstein Centre for Computational Neuroscience, Charité Universitätsmedizin, Berlin, Germany 4Faculty of Science, Radboud University Nijmegen, Nijmegen, the Netherlands an open access journal Keywords: Causal inference, Effective connectivity, Functional Magnetic Resonance Imaging, Dynamic Causal Modeling, Granger Causality, Structural Equation Modeling, Bayesian Nets, Directed Acyclic Graphs, Pairwise inference, Large-scale brain networks ABSTRACT In the past two decades, functional Magnetic Resonance Imaging (fMRI) has been used to relate neuronal network activity to cognitive processing and behavior. Recently this approach has been augmented by algorithms that allow us to infer causal links between component populations of neuronal networks. Multiple inference procedures have been proposed to approach this research question but so far, each method has limitations when it comes to establishing whole-brain connectivity patterns. In this paper, we discuss eight ways to infer causality in fMRI research: Bayesian Nets, Dynamical Causal Modelling, Granger Citation: Bielczyk, N. Z., Uithol, S., Causality, Likelihood Ratios, Linear Non-Gaussian Acyclic Models, Patel’s Tau, Structural van Mourik, T., Anderson, P., Glennon, J. C., & Buitelaar, J. K. (2019). Equation Modelling, and Transfer Entropy. We finish with formulating some recommendations Disentangling causal webs in the brain using functional magnetic resonance for the future directions in this area.
    [Show full text]
  • Exploratory Causal Analysis with Time Series Data Synthesis Lectures on Data Mining and Knowledge Discovery
    Exploratory Causal Analysis with Time Series Data Synthesis Lectures on Data Mining and Knowledge Discovery Editors Jiawei Han, University of Illinois at Urbana-Champaign Lise Getoor, University of Maryland Wei Wang, University of North Carolina, Chapel Hill Johannes Gehrke, Cornell University Robert Grossman, University of Chicago Synthesis Lectures on Data Mining and Knowledge Discovery is edited by Jiawei Han, Lise Getoor, Wei Wang, Johannes Gehrke, and Robert Grossman. e series publishes 50- to 150-page publications on topics pertaining to data mining, web mining, text mining, and knowledge discovery, including tutorials and case studies. Potential topics include: data mining algorithms, innovative data mining applications, data mining systems, mining text, web and semi-structured data, high performance and parallel/distributed data mining, data mining standards, data mining and knowledge discovery framework and process, data mining foundations, mining data streams and sensor data, mining multi-media data, mining social networks and graph data, mining spatial and temporal data, pre-processing and post-processing in data mining, robust and scalable statistical methods, security, privacy, and adversarial data mining, visual data mining, visual analytics, and data visualization. Exploratory Causal Analysis with Time Series Data James M. McCracken 2016 Mining Human Mobility in Location-Based Social Networks Huiji Gao and Huan Liu 2015 Mining Latent Entity Structures Chi Wang and Jiawei Han 2015 Probabilistic Approaches to Recommendations Nicola Barbieri, Giuseppe Manco, and Ettore Ritacco 2014 iii Outlier Detection for Temporal Data Manish Gupta, Jing Gao, Charu Aggarwal, and Jiawei Han 2014 Provenance Data in Social Media Geoffrey Barbier, Zhuo Feng, Pritam Gundecha, and Huan Liu 2013 Graph Mining: Laws, Tools, and Case Studies D.
    [Show full text]
  • On the Use of Transfer Entropy to Investigate the Time Horizon of Causal Influences Between Signals
    entropy Article On the Use of Transfer Entropy to Investigate the Time Horizon of Causal Influences between Signals Andrea Murari 1, Michele Lungaroni 2 ID , Emmanuele Peluso 2,*, Pasquale Gaudio 2 ID , Ernesto Lerche 3,4, Luca Garzotti 3, Michela Gelfusa 2 ID and JET Contributors † 1 Consorzio RFX (CNR, ENEA, INFN, Universita’ di Padova, Acciaierie Venete SpA), I-35127 Padova, Italy; [email protected] 2 Associazione EUROfusion—University of Rome “Tor Vergata”, Via Orazio Raimondo, 18, 00173 Roma, Italy; [email protected] (M.L.); [email protected] (P.G.); [email protected] (M.G.) 3 EUROfusion Programme Management Unit, JET, Culham Science Centre, Abingdon OX14 3DB, UK; [email protected] (E.L.); [email protected] (L.G.) 4 LPP-ERM/KMS, Association EUROFUSION-Belgian State, TEC partner, Brussels 1000, Belgium * Correspondence: [email protected]; Tel.: +39-06-7259-7196 † See the author list of “X. Litaudon et al., 2017 Nucl. Fusion 57 102001. Received: 28 June 2018; Accepted: 15 August 2018; Published: 22 August 2018 Abstract: Understanding the details of the correlation between time series is an essential step on the route to assessing the causal relation between systems. Traditional statistical indicators, such as the Pearson correlation coefficient and the mutual information, have some significant limitations. More recently, transfer entropy has been proposed as a powerful tool to understand the flow of information between signals. In this paper, the comparative advantages of transfer entropy, for determining the time horizon of causal influence, are illustrated with the help of synthetic data. The technique has been specifically revised for the analysis of synchronization experiments.
    [Show full text]
  • Arxiv:1706.01954V2 [Stat.ME] 5 Oct 2017 Models and Predictions by Themselves
    SPARSE CAUSALITY NETWORK RETRIEVAL FROM SHORT TIME SERIES TOMASO ASTE1;2;3 AND T. DI MATTEO1;2;3;4 1 Department of Computer Science, UCL, London, UK 2 UCL Centre for Blockchain Technologies, UCL, London, UK 3 Systemic Risk Centre, London School of Economics and Political Sciences, London, UK 4 Department of Mathematics King's College London, London, UK Abstract. We investigate how efficiently a known underlying sparse causality structure of a sim- ulated multivariate linear process can be retrieved from the analysis of time-series of short lengths. Causality is quantified from conditional transfer entropy and the network is constructed by retaining only the statistically validated contributions. We compare results from three methodologies: two commonly used regularization methods, Glasso and ridge, and a newly introduced technique, LoGo, based on the combination of information filtering network and graphical modelling. For these three methodologies we explore the regions of time series lengths and model-parameters where a signifi- cant fraction of true causality links is retrieved. We conclude that, when time-series are short, with their lengths shorter than the number of variables, sparse models are better suited to uncover true causality links with LoGo retrieving the true causality network more accurately than Glasso and ridge. Keywords: LoGo, Sparse Modelling, Information Filtering Networks, Graphical Modeling, Machine Learning. 1. Introduction Establishing causal relations between variables from observation of their behaviour in time is central to scientific investigation and it is at the core of data-science where these causal relations are the basis for the construction of useful models and tools capable of prediction.
    [Show full text]