One of the problems with calculating mutual information from empirical data lies in the fact that the underlying pdf is unknown. This is a consequence of the selfequitability of mutual information. Multivariate mutual information is a general enough term that contributions from williams and beer, griffith and koch, and more, should be included here. Estimating mi is nontrivial and requires notable computation power for high estimation quality. Grassberger 1988, submitted presents a number of improved estimators for, and, in each case, provides an explicit analytic formula for the bias. We propose to use precise estimators of mutual information mi to find least dependent components in a linearly mixed signal. The simplest method estimates p j by the fraction of sample points falling in the jth box, which yields a negatively biased estimator.
There are accurate methods for estimating mi that avoid problems with binning when both data sets are discrete or when both data sets are continuous. We present here a new estimator of mi that uses the concept of a statistical copula to provide the advantages of gaussian parametric estimation section 2. This technique, which gives an exact value for the proportion of linear dependence, is then compared with another common test for linearity, the brock, dechert and. Calculator for mutual information between a discrete and a. Detecting novel associations in large data sets science.
The mutual information therefore provides a tight upper bound on how well any test of dependence can perform on data drawn from. On estimating mutual information for feature selection. The main concern with estimations of mutual information mi is their robustness under the class of transformations for which it remains invariant. Whitening as a tool for estimating mutual information in. This prints the mutual information between column 5 and 9, conditioned on columns 15 and 17. A selfcontained, crossplatform, package for computing mutual information, jointconditional probability, entropy, and more. Comparative studies 19, 30, 20, 22 have shown that the kraskov estima. By clicking the points or using the slider, you can observe that the kernel size is small in densely populated regions of the space, but increases in sparsely. For example, at a sample size of 250, the kraskov et al. We present two classes of improved estimators for mutual information mx,y, from samples of random points distributed according to some joint probability. Least dependent component analysis based on mutual information. A statistical framework for neuroimaging data analysis.
Alexander kraskov, harald stogbauer, and peter grassberger. An accurate method for calculating mi between two realvalued data sets was previously developed kraskov et al. Pdf mutual information mi is a powerful concept from information theory used in many application fields. Mutual information mi is a powerful concept from information theory used in many application fields. We develop a jackknife approach that does not incur predetermined tuning parameters. Unlike r2, the mutual information values i of the underlying relationships in fig.
Ty cpaper ti efficient estimation of mutual information for strongly dependent variables au shuyang gao au greg ver steeg au aram galstyan bt proceedings of the eighteenth international conference on artificial intelligence and statistics py 20150221 da 20150221 ed guy lebanon ed s. This means that they are data efficient with k1 we resolve structures down to the smallest. We call this estimator gaussian copula mutual information gcmi. Mi is easy to calculate when both data sets are discrete, but not when one or both data sets are realvalued. To investigate directed interactions in neural networks we often use norbert wieners famous definition of observational causality. The mutual information estimator is from kraskov et. Identification of protein interaction network is a very important step for understanding the molecular mechanisms in cancer. Mutual information computation file exchange matlab.
In this paper comparison studies on mutual information estimation is considered. Vishwanathan id pmlrv38gao15 pb pmlr sp 277 dp pmlr ep 286 l1. Both should be mentioned, along with references to usage. February 2, 2008 we present two classes of improved estimators for mutual information mx,y, from samples.
Pdf on estimating mutual information for feature selection. Several methods have been developed to integrate proteinprotein interaction ppi data with gene expression data for network identification. Mutual information mi is in many ways an ideal statistic for detecting relationships between two data sets. The concept of mutual information originates in information theory, and, intuitively speaking, measures the amount of information that two variables share, i. Determining the strength of nonlinear, statistical dependencies between two variables is a crucial matter in many research fields. Accurately estimating mutual information from finite continuous data, however, is nontrivial. In this paper we focus on the estimation of mutual information from finite samples x.
A computationally efficient estimator for mutual information. We present two classes of improved estimators for mutual information mx,y, from samples of random points distributed according to some joint probability density mux,y. Wieners definition states that an improvement of the prediction of the future of a time series x from its own past by the incorporation of information from the past of a second time series y is seen as an indication of a causal interaction from y to x. Mutual information between discrete and continuous data. Estimating mutual information from observed samples is a basic primitive, useful in several machine learning tasks including correlation mining, information bottleneck clustering, learning a chow. The established measure for quantifying such relations is the mutual information. Mutual information mi is an established measure for linear and nonlinear dependencies between two variables.
A general multivariate matching method for achieving balance in observational studies. Informationbased centralization of locomotion in animals. Mutual information can be reinterpreted in the framework of dynamical model comparison i. Note that it corresponds to the estimator they call i1 in eq. More specifically, it quantifies the amount of information in units such as shannons, commonly called bits obtained about one random variable through observing the other random variable. E cient estimation of mutual information for strongly. Iterative estimation of mutual information with error bounds.
In probability theory and information theory, the mutual information mi of two random variables is a measure of the mutual dependence between the two variables. The difficulty lies in estimating the joint distribution from a finite sample of n data points. In order to quantify the differences, we calculated the mutual information using a nonparametric kraskov estimator kraskov et al. Moreover, the estimates were robust to noise by use of surrogate. Jackknife approach to the estimation of mutual information. The conditional mutual information estimator comes from palus et. The present method provides a competitive estimate of mi that is much less computationally intensive. We present an accurate, nonbinning mi estimator for the case of one discrete data set and one continuous data set. Estimating mutual information by local gaussian approximation. While some estimation techniques allow trading result quality for lower runtimes, this tradeo is xed per task and cannot be adjusted. Pdf a common problem found in statistics, signal processing, data analysis and image processing. As a fundamental concept in information theory, mutual information has been commonly applied to quantify the dependence between variables. However, existing estimations have unstable statistical performance since they involve a set of tuning parameters. Here, we present parmigene parallel mutual information calculation for gene network reconstruction a novel fast and parallel r package that i performs network inference implementing a minimally biased mi estimator, following kraskov s algorithm hereafter knnmi kraskov et al.
However, estimating mutual information from limited samples is a challenging task. Amongst the traditional mutual information estimators, kraskov estimation has emerged as a leading approach 22, 19, 30, 20. Mutual information based matching for causal inference. Meister, 1997, without regard to how that information is encoded. Mutual information is copula entropy sciencedirect. Estimating entropy and mutual information with scikitlearn. When im trying to estimate the joint mutual information of two features with y, so ix1, x2. This strategy bears a striking resemblance to regularization methods employed in abstract statistical inference grenander, 1981, generally known. Quantifying the effects of social influence scientific. There are, essentially, three different methods for estimating mutual information.
February 2, 2008 we present two classes of improved estimators for. However, they often fail to model the dependency between genes in the network, which makes many important genes, especially. Section 4 introduces local likelihood density estimation. In contrast to conventional estimators based on binnings, they are based on entropy estimates from k nearest neighbor distances. We used a nearestneighbour based kraskov entropy estimator, suitable to the nongaussian distributions of the up and fhr signals. Estimating mutual information on data streams ipd bohm kit. Estimating the mutual information between two discrete. Pdf estimating mutual information peter grassberger. Alexander kraskov, harald stoegbauer, peter grassberger download pdf.
As an application, we show how to use such a result to optimally estimate the density function and graph of a distribution which is markov to a forest graph. Estimation of entropy and mutual information 1195 ducing anything particularly novel, but merely formalizing what statisticians have been doing naturally since well before shannon wrote his papers. In section 5 we use this density estimator to propose a novel entropy and mutual information estimator. Estimating mutual information for feature selection in the. A mutual information approach to calculating nonlinearity. This package has also been used for general machine learning and data mining purposes such as feature selection.
Estimating mi between two continuous variables with a gaussian copula. Estimating mutual information alexander kraskov, harald st. Modelbased centralization schemes, though able to quantify locomotion control in animals and bioinspired robots, are limited to specific systems. Mutual information between discrete and continuous data sets. Bias reduction in the estimation of mutual information. Kraskov ksg estimator of mutual information wolfram. A new method to measure nonlinear dependence between two variables is described using mutual information to analyse the separate linear and nonlinear components of dependence. Since the mutual information is the difference of two entropies, the existing bayesian estimators of.
Im new to editing, but will try to collect some examples e. Kernel density estimation or the kraskovs nearest neighbor metho d. Again, these results are not surprisingthey correctly reflect. We examined the use of bivariate mutual information mi and its conditional variant transfer entropy te to address synchronization of perinatal uterine pressure up and fetal heart rate fhr. The continuous entropy estimator is based on kozachenko and leonenko 5, but, as a nonrussian speaker, i implemented it based on the kraskov paper. Estimating mutual information for discretecontinuous. Mutual information mi is a powerful method for detecting relationships between data sets.
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