Results 1 - 10
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16
Whitening as a tool for estimating mutual information in spatiotemporal data sets
- Journal of Statistical Physics
"... We address the issue of inferring the connectivity structure of spatially extended dynamical systems by estimation of mutual information between pairs of sites. The well-known problems resulting from correlations within and between the time series are addressed by explicit temporal and spatial model ..."
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We address the issue of inferring the connectivity structure of spatially extended dynamical systems by estimation of mutual information between pairs of sites. The well-known problems resulting from correlations within and between the time series are addressed by explicit temporal and spatial modelling steps which aim at approximately removing all spatial and temporal correlations, i.e. at whitening the data, such that it is replaced by spatiotemporal innovations; this approach provides a link to the maximum-likelihood method and, for appropriately chosen models, removes the problem of estimating probability distributions of unknown, possibly complicated shape. A parsimonious multivariate autoregressive model based on nearest-neighbour interactions is employed. Mutual information can be reinterpreted in the framework of dynamical model comparison (i.e. likelihood ratio testing), since it is shown to be equivalent to the difference of the log-likelihoods of coupled and uncoupled models for a pair of sites, and a parametric estimator of mutual information can be derived. We also discuss, within the framework of model comparison, the relationship between the coefficient of linear correlation and mutual information. The practical application of this methodology is demonstrated for
Mutual information in the frequency domain
- JOURNAL OF STATISTICAL PLANNING AND INFERENCE
, 2006
"... Coefficients of mutual information (MI) can provide powerful extensions of classical coefficients of correlation. In particular, they have the property of vanishing if and only if the components involved are statistically independent of each other. This characteristic can prove useful in preparato ..."
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Coefficients of mutual information (MI) can provide powerful extensions of classical coefficients of correlation. In particular, they have the property of vanishing if and only if the components involved are statistically independent of each other. This characteristic can prove useful in preparatory work to model building. In this article a frequency domain variant of MI is developed and studied for bivariate stationary time series. As a scientific example an ambient seismic noise data set is studied and a lack of independence of the components inferred. The character of the dependence of the MI on frequency may be used to suggest the nature of the statistical dependence.
Information Capacity of Full-Body Movements
"... We present a novel metric for information capacity of fullbody movements. It accommodates HCI scenarios involving continuous movement of multiple limbs. Throughput is calculated as mutual information in repeated motor sequences. It is affected by the complexity of movements and the precision with wh ..."
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We present a novel metric for information capacity of fullbody movements. It accommodates HCI scenarios involving continuous movement of multiple limbs. Throughput is calculated as mutual information in repeated motor sequences. It is affected by the complexity of movements and the precision with which an actor reproduces them. Computation requires decorrelating co-dependencies of movement features (e.g., wrist and elbow) and temporal alignment of sequences. HCI researchers can use the metric as an analysis tool when designing and studying user interfaces. Author Keywords Information capacity; full-body movement; measurement; throughput; gesture-based interfaces; information theory ACM Classification Keywords H.5.m. Information interfaces and presentation (e.g., HCI):
MODELLING SOME NORWEGIAN SOCCER DATA
"... Results of Norwegian Elite Division soccer games are studied for the year 2003. Previous writers have modelled the number of goals a given team scores in a game and then moved on to evaluating the probabilities of a win, a tie and a loss. However in this work the probabilities of win, tie and loss a ..."
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Results of Norwegian Elite Division soccer games are studied for the year 2003. Previous writers have modelled the number of goals a given team scores in a game and then moved on to evaluating the probabilities of a win, a tie and a loss. However in this work the probabilities of win, tie and loss are modelled directly. There are attempts to improve the fit by including various explanatories.
Realtime market microstructure analysis: online Transaction Cost Analysis
, 2013
"... Motivated by the practical challenge in monitoring the performance of a large num-ber of algorithmic trading orders, this paper provides a methodology that leads to automatic discovery of causes that lie behind poor trading performance. It also gives theoretical foundations to a generic framework fo ..."
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Motivated by the practical challenge in monitoring the performance of a large num-ber of algorithmic trading orders, this paper provides a methodology that leads to automatic discovery of causes that lie behind poor trading performance. It also gives theoretical foundations to a generic framework for real-time trading analysis. The com-mon acronym for investigating the causes of bad and good performance of trading is TCA (Transaction Cost Analysis [Rosenthal, 2009]). Automated algorithms take care of most of the traded flows on electronic markets (more than 70 % in the US, 45 % in Europe and 35 % in Japan in 2012). Academic literature provides different ways to formalize these algorithms and show how optimal they can be from a mean-variance [Almgren and Chriss, 2000], a stochastic control [Guéant et al., 2012], an impulse con-trol [Bouchard et al., 2011] or a statistical learning [Laruelle et al., 2011] viewpoint. This paper is agnostic about the way the algorithm has been built and provides a theoretical formalism to identify in real-time the market conditions that influenced its efficiency or inefficiency. For a given set of characteristics describing the mar-
WILDLAND FIRE PROBABILITIES ESTIMATED FROM WEATHER MODEL-DEDUCED MONTHLY MEAN FIRE DANGER INDICES
, 2007
"... parametric logistic regression, spline functions ..."
MODELLING DYADIC INTERACTION WITH HAWKES PROCESS
, 2012
"... We apply Hawkes process to the analysis of dyadic interaction. Hawkes process is applicable to excitatory interactions, wherein the actions of each individual increase the probability of further actions in the near future. We consider the representation of Hawkes process both as a conditional intens ..."
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We apply Hawkes process to the analysis of dyadic interaction. Hawkes process is applicable to excitatory interactions, wherein the actions of each individual increase the probability of further actions in the near future. We consider the representation of Hawkes process both as a conditional intensity function and as a cluster Poisson process. The former treats the probability of an action in continuous time via non-stationary distributions with arbitrarily long historical dependency, while the latter is conducive to maximum likelihood estimation using the EM algorithm. We first outline the interpretation of Hawkes process in the dyadic context, and then illustrate its application with an example concerning email transactions in the work place.
Nonlinear Dependence and Extremes in Hydrology and Climate
, 2007
"... Nonlinear dependence and extremes in hydrology and climate ..."
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Estimating Mutual Information in Under-Reported Variables Konstantinos Sechidis Matthew Sperrin Emily Petherick
"... Abstract Under-reporting occurs in survey data when there is a reason to systematically misreport the response to a question. For example, in studies dealing with low birth weight infants, the smoking habits of the mother are very likely to be misreported. This creates problems for calculating effe ..."
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Abstract Under-reporting occurs in survey data when there is a reason to systematically misreport the response to a question. For example, in studies dealing with low birth weight infants, the smoking habits of the mother are very likely to be misreported. This creates problems for calculating effect sizes, such as bias, but these problems are commonly ignored due to lack of generally accepted solutions. We reinterpret this as a problem of learning from missing data, and particularly learning from positive and unlabelled data. By this formalisation we provide a simple method to incorporate prior knowledge of the misreporting and we present how we can use this knowledge to derive corrected point and interval estimates of the mutual information. Then we show how our corrected estimators outperform more complex approaches and we present applications of our theoretical results in real world problems and machine learning tasks.
Computing and Information A COMPARATIVE STUDY OF COHERENCE, MUTUAL INFORMATION AND CROSS-INTENSITY MODELS
"... Abstract. Coherence is a measure of the time invariant linear dependence of two processes at certain frequencies, and provides a measure of the degree of linear predictability of one process from another process. The coherence is inadequate as a measure of general association for it may be identical ..."
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Abstract. Coherence is a measure of the time invariant linear dependence of two processes at certain frequencies, and provides a measure of the degree of linear predictability of one process from another process. The coherence is inadequate as a measure of general association for it may be identically 0 when two series are in fact related. However, such behavior does not occur for the coefficient of mutual information, which is a measure of the amount of information that one random variable contains about another random variable. The Lin-Lin model, which describes the influence of an input on a point process output, can identify linear causal relationships between one sequence of events and another. This paper presents a comparative study of the three approaches using a case study of the relationship between groundwater level data from Tangshan Well and global earthquakes with minimum magnitude 5.8.
