Ksg mutual information estimator, which is based on the distances of each sample to its kth nearest neighbor, is widely used to estimate mutual information between two continuous random variables. The primary motivation for this work originates in work with physiologic time series extracted from electronic health records ehr 4. The choice of sample size in estimating mutual information. Estimating mutual information using bspline functions an. Variational approaches based on neural networks are showing promise for estimating mutual information mi between high dimensional variables. We demonstrate empirically that for strong relationships, the proposed estimator needs signi. It can be viewed as a statistical test against a null hypothesis that two variables are statistically independent, but in addition its effect size measured in bits has a number of useful properties and interpretations kinney and atwal, 2014. However, estimating the quantities involved such as entropy and mutual. To this end, we propose the mutual information gradient. February 2, 2008 we present two classes of improved estimators for mutual information mx,y, from samples.
Estimating mutual information under measurement error biorxiv. You could always employ the straightforward approach of estimating the joint pdf. I am afraid there is no simple and accurate algorithm for this task. Most of these estimators operate using the 3h principle, i. This strategy bears a striking resemblance to regularization methods employed in abstract statistical inference grenander, 1981, generally known. Since the mutual information is the difference of two entropies, the existing bayesian estimators of. In this work, we propose a method for the numerical estimation of mutual information from continuous data. Estimating the tdmi requires estimating probability densities pdf, and pdf estimates fundamentally have two components, the pdf estimate and the bias or noise floor associated with the estimation of the pdf. Estimating mutual information for discretecontinuous mixtures. Estimating mutual information under measurement error. It can be used to quantify conditional dependence among variables in many datadriven inference problems such as graphical models, causal learning, feature selection and timeseries analysis. We address the practical problems of estimating the information relations that characterize large networks.
The demixing transformation is then a convolution of the ob. Mutual information between discrete variables with many. Sep 25, 2019 we argue that directly estimating the gradients of mi is more appealing for representation learning than estimating mi in itself. The mutual information is useful measure of a random vector component dependence. Kraskov and others published estimating mutual information phys find, read and cite all the research you need on researchgate. For example, how strongly smoking is correlated with low birth weight. However, estimating the quantities involved such as entropy and mutual information from finite samples is notoriously hard and any direct estimate is known to be heavily biased. Estimating mutual information using gaussian mixture model for feature ranking and selection tian lan, deniz erdogmus, umut ozertem, yonghong huang f. You could always employ the straightforward approach of estimating the joint pdf of the two variables based on the histograms and computing the mutual information by numerical integration. Copulas offer a natural approach for estimating mutual information, since the joint probability. Limitations to estimating mutual information in large. Therefore, estimating mutual information can be achieved by an estimation of entropy. We compare our algorithms in detail with existing algorithms.
The choice of sample size in estimating mutual information m. Estimating mutual information using gaussian mixture model. Dominik endres estimating mutual information by bayesian binning cns 2006 workshop methods of information theory in computational neuroscience 32 bayesian bin distribution inference runtime. Building on methods developed for analysis of the neural code, we show that reliable. Mutual information, redundancy, adaptive histogram. For practical tasks it is often necessary to estimate the mutual information from. While mutual information is a quantity welldefined for general probability spaces, estimators have been developed only in the special case of discrete or continuous pairs of random variables. Estimating mutual information on data streams pavel efros fabian keller, emmanuel muller, klemens bohm kit university of the state of badenwuerttemberg and national laboratory of the helmholtz association.
The dimension does not enter into the estimators, only. Since mutual information is defined in terms of discrete variables, its application to. Determining the strength of nonlinear, statistical dependencies between two variables is a crucial matter in many research fields. However, the estimation of mutual information is difficult since the estimation of the joint probability density function pdf. Stream estimation allows a user to issue mutual informa tion queries in arbitrary time windows. Estimating mutual information and multiinformation in. Estimating mutual information in underreported variables. This happens for example in the convolutive mixture case. Estimating information flow in deep neural networks ziv goldfeld mit 56th allerton conference on communication, control, and computing monticello, illinois, us october 4th, 2018 collaborators. Estimating mutual information alexander kraskov, harald st. On simulated data, our corrected estimator leads to a more accurate estimation for mutual information when the sample size is not the limiting factor for estimating pmf or pdf accurately.
Pdf a common problem found in statistics, signal processing, data analysis and image processing research is the estimation of mutual information. 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. This means that they are data efficient with k1 we resolve structures down to the smallest. Conditional mutual information cmi is a measure of conditional dependence between random variables x and y, given another random variable z. Dominik endres estimating mutual information by bayesian binning cns 2006 workshop methods of information theory in computational neuroscience 32 bayesian bin distribution inference runtime ok2 instead of okm for exact bayesian inference, if instances of x are totally ordered. We argue that directly estimating the gradients of mi is more appealing for representation learning than estimating mi in itself. In other contexts quantization is just a convenience e. Mutual information mi measures the statistical dependence between two random variables cover and thomas, 1991. Estimating mutual information using bspline functions. Since mi is a special case of kldivergence, their neural. We investigate the characteristic properties arising from the application of our algorithm and show that our approach outperforms commonly used algorithms.
Section 4 introduces local likelihood density estimation. An important problem in any of these applications is to estimate mutual information effectively from samples. The dependence between random variables may be measured by mutual information. We compare the uncorrected and corrected estimator on the gene expression data of tcga breast cancer samples and show a difference in both the value and the. Request pdf estimating mutual information we present two classes of improved estimators for mutual information mx,y, from samples of random points distributed according to some joint. While the qualitative features like the diverging mutual information at lag 0, 50 and 100, but the magnitude is far off and the overall shape is not right. Pdf estimating mutual information peter grassberger. In the context of the clustering of genes with similar patterns of expression it has been suggested as a general quantity of similarity to extend commonly used linear measures. We demonstrate empirically that for strong relationships, the proposed estimator needs. Estimating information flow in deep neural networks. The dimension does not enter into the estimators, only nearest neighbors in the joint and marginal subspaces. Estimating mutual information for feature selection in the.
Estimating mutual information request pdf researchgate. We present here a new estimator of mi that uses the concept of a statistical copula to provide the advantages of. Estimating mutual information by alexander kraskov, harald stoegbauer and peter grassberger get pdf 629 kb. Understanding the limitations of variational mutual.
Request pdf estimating mutual information we present two classes of improved estimators for mutual information mx,y, from samples of random points. Estimating mi between two continuous variables with a gaussian copula. May 28, 2003 we compare our algorithms in detail with existing algorithms. Estimating mutual information on data streams ipd bohm kit. In section 5 we use this density estimator to propose a novel entropy and mutual information estimator. In the context of the clustering of genes with similar. Finally, we demonstrate the usefulness of our estimators for assessing the actual independence of components obtained from independent component analysis ica, for improving ica, and for estimating the reliability of blind source separation. Estimation of entropy and mutual information uc berkeley statistics.
Aug 31, 2004 the information theoretic concept of mutual information provides a general framework to evaluate dependencies between variables. Alexander kraskov, harald stogbauer, and peter grassberger. The kozachenkoleonenkoestimator 21 is a famous nonparametric approach to estimate entropy based on nearest neighbor information. Limitations to estimating mutual information in large neural. Nov 23, 2019 on simulated data, our corrected estimator leads to a more accurate estimation for mutual information when the sample size is not the limiting factor for estimating pmf or pdf accurately. Copulas offer a natural approach for estimating mutual information, since the joint probability density function of random variables can be expressed as the product. Information theory provides a powerful framework to analyse the representation of sensory stimuli in neural population activity. The information theoretic concept of mutual information provides a general framework to evaluate dependencies between variables. A statistical framework for neuroimaging data analysis. On simulated data, our corrected estimator leads to a more accurate estimation for mutual information when the sample size is not the limiting factor for estimating pmf or pdf. Since the mutual information is the difference of two entropies, the existing bayesian estimators of entropy may be used to estimate information. However, estimating mutual information from limited samples is a challenging task.
To this end, we propose the mutual information gradient estimator mige for representation learning based on the score estimation of implicit distributions. The estimation methods are often based on the well known relation between the mutual information and the appropriate entropies. Estimation of entropy, mutual information and related. We investigate this nice property of mutual information estimators 10. 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. A test for conditional independence can be based on mutual information since the latter is zero for independent variables. Entropy free fulltext estimating the mutual information. E cient estimation of mutual information for strongly. Mutual information estimation as can be understood from equation 3, the mi cannot be directly computed for realworld problems, as the probability density function pdf of x is not known in. Jun 01, 2012 estimating the tdmi requires estimating probability densities pdf, and pdf estimates fundamentally have two components, the pdf estimate and the bias or noise floor associated with the estimation of the pdf. However, the estimation of mutual information is difficult since the estimation of the joint probability density function pdf of nongaussian distributed data is a hard problem.
Alexander kraskov, harald stoegbauer, peter grassberger download pdf. This papers proposes a fast algorithm for estimating the mutual information, difference score function, conditional score and conditional entropy, in possibly high. Fast algorithm for estimating mutual information, entropies and. This method exhibits several advantages, such as it is computationally efficient and flexible, and it is also suitable for high dimensional data. Finally, we demonstrate the usefulness of our estimators for assessing the actual independence of components obtained from. We investigate the characteristic properties arising from the application of our.
Estimating mutual information and multiinformation in large. In contrast to conventional estimators based on binnings, they are based on entropy estimates from k nearest neighbor distances. Jackknife approach to the estimation of mutual information pnas. However, there are cases when one would minimize the mutual information directly. It also offers an r interface to the nsb estimator. Just giving a yesno answer through a hypothesis test may not be of much interest. Algorithm for calculating the mutual information between. Furthermore, it provides functions for estimating kullbackleibler divergence, chisquared, mutual information, and chisquared statistic of. Computationalstatisticsanddataanalysis712014832848 anefficientalternativeoftenencounteredintheliteratureistousegreedyprocedures.
Mutual information gradient estimation for representation. Estimating mutual information by local gaussian approximation. Estimation of mutual information using copula density function abstract. Mutual information estimation as can be understood from equation 3, the mi cannot be directly computed for realworld problems, as the probability density function pdf of x is not known in practice. Estimation of timedelayed mutual information and bias for. The established measure for quantifying such relations is the mutual information. Estimation of mutual information using copula density. However, the resulting estimate will be biased, and typically unreliable.
A statistical framework for neuroimaging data analysis based. Just giving a yesno answer through a hypothesis test may not be of much interest, and estimating the size of the effect gives more useful information. Mutual information, a general measure of the relatedness between two random variables, has been actively used in the analysis of biomedical data. The established measure for quantifying such relations is the mutual. However, unfortunately, reliably estimating mutual information from finite continuous data remains a. The significance, as a measure of the power of distinction from random correlation, is significantly increased. Elogdetg0x and estimating elogdetg0x is easy because it is an expectation. On estimating mutual information for feature selection. Pdf estimating mutual information by bayesian binning. My 1st suspicion is the fact that i used different window widths for joint pdf and marginal pdf. Estimating the mutual information between two discrete. Mutual information mi is a powerful concept from information theory used in many application fields.
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