New measures quantify mutual dependence between multiple random vectors.
problem Measuring mutual dependence between multiple random vectors.
method Proposes three measures based on generalized distance covariance.
result Empirical and simplified empirical measures effectively test mutual independence.
In data science, it is often required to estimate dependencies between different data sources. These dependencies are typically calculated using Pearson's correlation, distance correlation, and/or mutual information. However, none of these measures satisfy all the Granger's axioms for an "ideal measure". One such ideal…
Improves ICA via novel mutual dependence measures.
problem Improving Independent Component Analysis (ICA) for better component independence.
method Combines distance-based and kernel-based mutual dependence measures, introduces Latin hypercube sampling and Bayesian optimization for initialization.
result MDMICA outperforms other methods in terms of mutual independence of estimated components, especially when the ICA model is misspecified.
TCMI assesses mutual dependence of continuous variables without parametric assumptions.
problem Estimating mutual information from continuous distributions.
method TCMI extends mutual information to continuous variables using cumulative distributions.
result TCMI facilitates feature selection and ranking of variable sets.
The paper argues that normalized mutual information is biased in clustering and community detection.
problem Bias in normalized mutual information for clustering and community detection.
method Introducing a modified version of mutual information to correct for information content and spurious dependence.
result The modified mutual information leads to different conclusions about which algorithms are best for community detection.
Empirical study on dependency in auto-encoding networks using HSIC.
problem Inaccurate measurement of mutual information in DNNs.
method Proposed using Hilbert-Schmidt Independence Criterion (HSIC) to measure dependency between layers in auto-encoding architectures.
result HSIC can measure dependence without density estimation, improving generalization evaluation.
Wasserstein dependency measure improves unsupervised representation learning.
problem Incomplete representations from mutual information maximization.
method Wasserstein dependency measure using Wasserstein distance instead of KL divergence.
result Improved results on tasks with high mutual information.
Neural estimator improves mutual information estimation in high dimensions.
problem Estimating mutual information in high dimensions is challenging.
method Parametrizing conditional densities with normalizing flows and using block autoregressive structure.
result Improved mutual information estimation on benchmark tasks.
Reshef et al. recently proposed a new statistical measure, the "maximal information coefficient" (MIC), for quantifying arbitrary dependencies between pairs of stochastic quantities. MIC is based on mutual information, a fundamental quantity in information theory that is widely understood to serve this need. MIC, howev…
Introduces a new geometric method for optimal experimental design.
problem Restrictive invariance properties of traditional OED approaches based on probability densities.
method Mutual transport dependence (MTD) using optimal transport theory.
result Demonstrates high-quality designs and flexibility compared to standard methods.
Generalizes underlap coefficient for multivariate group separation.
problem Quantifying distributional separation across groups in statistical learning.
method Generalizes underlap coefficient (UNL) to multivariate settings, studies its relationship with Bayes risk and mutual information, proposes an efficient importance sampling estimator.
result UNL as a measure of dependence between group labels and variables of interest, interpretable measure of partition-covariate dependence in clustering.
A novel kernel models latent variable couplings across multiple processes.
problem Modeling latent variable couplings across multiple processes.
method Mutually-dependent Hadamard kernel and latent correlation Gaussian process (LCGP) model.
result The LCGP model recovers latent signal correlations and achieves state-of-the-art performance.
New bounds derived for machine learning algorithms using convex functions.
problem Bounding generalization error in machine learning.
method Using strongly convex functions and subgaussian loss tails, derived new generalization bounds.
result Generalization bounds can be derived using any strongly convex function of the joint input-output distribution.
The use of mutual information as a similarity measure in agglomerative hierarchical clustering (AHC) raises an important issue: some correction needs to be applied for the dimensionality of variables. In this work, we formulate the decision of merging dependent multivariate normal variables in an AHC procedure as a Bay…
Improved method for encoding contingency tables reduces mutual information bias.
problem Mutual information bias in measuring label similarity.
method Improved method for encoding contingency tables to reduce information cost.
result Better bound on reduced mutual information in typical use cases.
Improved bounds for SGLD via data-dependent estimates.
problem Improving generalization bounds for noisy iterative learning algorithms.
method Variational characterization of mutual information and data-dependent priors.
result Significantly improved mutual information bounds for SGLD.
Measures dependence between two systems using Bayesian model comparison.
problem Quantifying dependence between two systems in a dataset.
method Bayesian model comparison of independence and dependence models.
result Dependence measure quantifies evidence for dependence in data.
New methods estimate point-wise dependency from neural MI models.
problem Estimating point-wise dependency between different events.
method Developed two methods: Probabilistic Classifier and Density-Ratio Fitting.
result Demonstrated effectiveness in MI estimation, self-supervised representation learning, and cross-modal retrieval.
We discuss the connection between information and copula theories by showing that a copula can be employed to decompose the information content of a multivariate distribution into marginal and dependence components, with the latter quantified by the mutual information. We define the information excess as a measure of d…
Paper benchmarks mutual info estimators on diverse distributions.
problem Evaluating mutual information estimators on complex, real-world distributions.
method Constructs a diverse family of known-ground truth distributions, proposes a benchmark platform.
result Highlights differences in classical and neural estimators' performance across various conditions.
InfoAtlas speeds up MI estimation for real-time data analysis.
problem Efficiently measuring statistical dependency between high-dimensional datasets.
method Directly infers mutual information in a single forward pass using a pretrained model.
result Matches state-of-the-art accuracy with 100x speedup.
The paper proves mutual information measurement is statistically limited.
problem Measuring mutual information from finite data is difficult.
method Proves statistical limitations on any method of measuring mutual information.
result Any distribution-free high-confidence lower bound on mutual information estimated from N samples cannot be larger than O(ln N ).
We simplify information measure computation using learned features.
problem Computing information measures from raw data is computationally expensive.
method Developed a separable design for computing information measures from learned feature representations.
result A variety of information measures can be computed efficiently through learned feature representations.
We discuss the behavior of two magnitudes, physical complexity and mutual information function of the outcome of a model of heterogeneous, inductive rational agents inspired in the El Farol Bar problem and the Minority Game. The first is a measure rooted in Kolmogorov-Chaitin theory and the second one a measure related…
Investigates mutual information for fitting deep models without hidden layer knowledge.
problem Deep nonlinear models' parameters are hard to fit due to hidden layer and non-affine relation.
method Used mutual information and KL divergence as objective functions for fitting models without hidden layer knowledge.
result Mutual information and KL divergence are successful objective functions for fitting deep models.
The paper presents a new copula based method for measuring dependence between random variables. Our approach extends the Maximum Mean Discrepancy to the copula of the joint distribution. We prove that this approach has several advantageous properties. Similarly to Shannon mutual information, the proposed dependence mea…
The paper studies how quickly samples from Langevin dynamics become independent.
problem Understanding the dependence between samples along Langevin dynamics and related algorithms.
method Measures dependence via Φ-mutual information and proves strong data processing inequalities. result The Φ-mutual information between samples decreases exponentially to zero. New bounds explain modern machine learning algorithms' generalization.
problem Explaining generalization behavior of modern machine learning algorithms.
method Proposes a new complexity measure based on empirical Rademacher complexity of an algorithm- and data-dependent hypothesis class.
result Obtains novel bounds with finite fractal dimension, simplifies proofs, and recovers known results.
In this survey, we present and compare different approaches to estimate Mutual Information (MI) from data to analyse general dependencies between variables of interest in a system. We demonstrate the performance difference of MI versus correlation analysis, which is only optimal in case of linear dependencies. First, w…
New bounds improve neural network generalization through slicing.
problem Difficulty in evaluating mutual information in high dimensions for neural networks.
method Slicing the parameter space and using disintegrated mutual information and k-sliced mutual information.
result Slicing improves generalization and offers significant computational and statistical advantages.
This study quantifies the scalability of k-Sliced Mutual Information (k-SMI) with dimension.
problem Understanding how SMI and its estimation rates depend on the ambient dimension.
method Developed k-SMI framework and derived bounds on MC estimates, established optimal convergence rates, and provided asymptotic results.
result Sharp bounds and optimal convergence rates for k-SMI estimation, revealing interplay with dimension and sample size.
A new regularizer boosts long-range dependency in sequence data.
problem Improving long-range dependency in sequence data models.
method Developed a mutual information regularizer to enhance sequence learning.
result The approach increases mutual information and likelihood on holdout data.
LMI approximates mutual information in high dimensions using learned low-dimensional representations.
problem Estimating mutual information between high-dimensional variables is challenging due to sample size limitations.
method Developed a method called latent MI (LMI) approximation that applies a nonparametric MI estimator to low-dimensional representations learned by a simple model architecture.
result LMI can approximate MI well for variables with >10^3 dimensions if their dependence structure has low intrinsic dimensionality.
The paper introduces submodular information measures for machine learning applications.
problem Generalizing information-theoretic measures to non-random variables.
method Developing combinatorial information measures based on submodular functions.
result Submodular mutual information is submodular in one argument for certain submodular functions.
Investigates stock correlations during market crises, finds nonlinear dependencies increase, and optimizes portfolios.
problem Investigating stock correlations during market crises.
method Pearson correlation and mutual information based complex networks, surrogate data for nonlinear dependencies, Markowitz mean variance portfolio optimization.
result Nonlinear dependencies increase during financial market crises, not reducing to linear correlations.
Adversarial nets learn independent features from joint distributions.
problem Learning independent features from complex joint distributions.
method Adversarial objectives to optimize mutual information implicitly.
result Adversarial nets can solve both linear and non-linear ICA problems.
The paper applies information theory to financial markets, improving risk management and asset allocation.
problem Improving risk management and asset allocation in financial markets.
method Information-theoretic measures (entropy, mutual information, etc.) applied to financial time series.
result Normalized mutual information (NMI) is a powerful measure of temporal dependence in financial markets.
New mutual information measure improves classification and community detection accuracy.
problem Standard mutual information measure can be inaccurate under real-world conditions.
method Corrected mutual information measure that accounts for all cases.
result Improved mutual information measure reduces errors in classification and community detection.
Mutual info trees show higher risk in Brazilian equity network during transition.
problem Identifying nonlinear dependencies in Brazilian equity network.
method Used mutual information minimum spanning trees to compare with linear correlation.
result Mutual info trees indicate higher risk and power law tail in volatility transmission.
The goal of temporal alignment is to establish time correspondence between two sequences, which has many applications in a variety of areas such as speech processing, bioinformatics, computer vision, and computer graphics. In this paper, we propose a novel temporal alignment method called least-squares dynamic time war…
A new MI estimator reduces complexity to linear time, achieving optimal MSE rates.
problem High computational complexity of MI estimators.
method Ensemble Dependency Graph Estimator (EDGE) combining LSH, dependency graphs, and ensemble bias-reduction.
result EDGE achieves optimal computational complexity O(N) and parametric MSE rate O(1/N). We demonstrate that the gain/loss asymmetry observed for stock indices vanishes if the temporal dependence structure is destroyed by scrambling the time series. We also show that an artificial index constructed by a simple average of a number of individual stocks display gain/loss asymmetry - this allows us to explicit…
Combines chaining and mutual information methods for tighter generalization bounds.
problem Bounding generalization error of learning algorithms, especially in deep learning.
method Integrates chaining and mutual information methods to create a new generalization bound.
result Example shows significant improvement over existing bounds.
Improves data efficiency for estimating mutual information.
problem Estimating mutual information from limited data.
method Developed a Data-Efficient MINE Estimator (DEMINE) and Meta-DEMINE.
result Significantly improved data efficiency in estimating mutual information.
Using an inverse system of metric graphs as in: J. Cheeger and B. Kleiner, "Inverse limit spaces satisfying a Poincaré inequality", we provide a simple example of a metric space X that admits Poincaré inequalities for a continuum of mutually singular measures.
While it is an important problem to identify the existence of causal associations between two components of a multivariate time series, a topic addressed in Runge et al. (2012), it is even more important to assess the strength of their association in a meaningful way. In the present article we focus on the problem of d…
Generalizes underlap coefficient for multivariate group separation.
problem Quantifying distributional separation across groups in statistical learning.
method Generalizes underlap coefficient (UNL) to multivariate variables, establishes key properties, interprets as dependence measure, proposes efficient estimator.
result Highlights the UNL's utility in clustering for evaluating group structure dependence on covariates.
We consider fundamental questions of arbitrage pricing arising when the uncertainty model is given by a set of possible mutually singular probability measures. With a single probability model, essential equivalence between the absence of arbitrage and the existence of an equivalent martingale measure is a folk theorem,…