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.
Paper describes profiles of multivariate normal distributions and novel estimators for mutual information.
problem Estimating mutual information for complex distributions.
method Analytical description of profiles, introduction of Bend and Mix Models, Monte Carlo estimation.
result Bend and Mix Models accurately estimate mutual information profiles and provide Bayesian estimates.
MIM learns joint distributions with mutual information and low divergence.
problem Learning joint distributions over observations and latent variables.
method Probabilistic auto-encoder with three design principles: low divergence, high mutual information, and low marginal entropy.
result MIM learns representations with high mutual information, consistent encoding and decoding distributions, effective latent clustering, and comparable data log likelihood to VAE.
New estimator improves mutual information estimation.
problem Estimating mutual information in data science and machine learning.
method Proposes a new estimator that uses a preliminary estimate of the data distribution.
result A preliminary estimate helps in estimating mutual information more accurately.
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.
MIM learns useful representations with high mutual information.
problem Learning useful representations for downstream tasks.
method Symmetric Jensen-Shannon divergence and mutual information regularizer in an encoder/decoder framework.
result MIM learns high mutual information representations without posterior collapse.
Many machine learning problems can be characterized by mutual contamination models. In these problems, one observes several random samples from different convex combinations of a set of unknown base distributions. It is of interest to decontaminate mutual contamination models, i.e., to recover the base distributions ei…
Bayesian method finds patterns of mutual independence in data.
problem Investigating mutual independence in statistics.
method Bayesian model comparison using Markov chain Monte Carlo (MCMC).
result Automated search for patterns of mutual independence.
New method estimates mutual information using normalizing flows.
problem Mutual information estimation in high-dimensional data.
method Normalizing flows to map data to target distributions with known MI.
result Theoretical guarantees and practical advantages demonstrated.
Measuring mutual information from finite data is difficult. Recent work has considered variational methods maximizing a lower bound. In this paper, we prove that serious statistical limitations are inherent to any method of measuring mutual information. More specifically, we show that any distribution-free high-confide…
Study curvature invariants in sub-Riemannian manifolds.
problem Understand curvature invariants in sub-Riemannian geometry.
method Prove geometrical inequalities for submanifolds with orthogonal distributions.
result Inequalities for submanifolds with orthogonal distributions are derived.
Paper formulates mutual information optimal control for discrete-time systems.
problem Optimal control of discrete-time linear systems with mutual information.
method Formulates MIOCP as an extension of MEOCP, derives optimal policy and prior, proposes alternating minimization algorithm.
result Proposes an alternating minimization algorithm for MIOCP.
The mutual fund industry manages about a quarter of the assets in the U.S. stock market and thus plays an important role in the U.S. economy. The question of how much control is concentrated in the hands of the largest players is best quantitatively discussed in terms of the tail behavior of the mutual fund size distri…
The conditional mutual information I(X;Y|Z) measures the average information that X and Y contain about each other given Z. This is an important primitive in many learning problems including conditional independence testing, graphical model inference, causal strength estimation and time-series problems. In several appl…
A method to improve image synthesis diversity using mutual information.
problem Mode collapse in conditional GANs for multimodal image synthesis.
method Explicitly estimate and maximize mutual information between latent code and output image.
result Prevents mode collapse and encourages synthesis of diverse images.
A new method estimates mutual information using neural classifiers.
problem Estimating mutual information for high-dimensional data is challenging.
method Trains a classifier to estimate joint distribution probability.
result Demonstrates high accuracy and reduces variance compared to variational methods.
The paper tackles adversarial robustness by maximizing worst-case mutual information.
problem Training robust machine learning models against adversarial inputs is challenging.
method Develops a notion of representation vulnerability and an unsupervised learning method to maximize worst-case mutual information.
result Proves a lower bound on minimum adversarial risk and supports robustness of representations.
Proposes Mutual Regression Distance for better distribution comparison.
problem Lack of effective distance measures for manifold data.
method Constrained mutual regression problem to exploit manifold properties.
result Mutual Regression Distance (MRD) is a pseudometric effective for manifold data.
Hybrid method improves mutual information estimation from samples.
problem Estimating mutual information from joint distributions is challenging.
method Proposes a hybrid method combining discriminative and generative approaches.
result Hybrid methods yield tighter variational bounds on mutual information.
We propose three measures of mutual dependence between multiple random vectors. All the measures are zero if and only if the random vectors are mutually independent. The first measure generalizes distance covariance from pairwise dependence to mutual dependence, while the other two measures are sums of squared distance…
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. Efficiently learns Gaussian tree models with near-optimal sample complexity.
problem Learning tree-structured Gaussian distributions efficiently.
method Conditional mutual information tester for Gaussian variables, near-optimal sample complexity.
result Near-optimal sample complexity for structure learning of Gaussian tree models.
MSRL learns a representation maximizing mutual info with response variables.
problem Learning sufficient representations for complex, multi-dimensional data.
method Variational mutual information, deep neural networks, generalized Dudley's inequality.
result MSRL achieves consistent and accurate representation learning.
Study curvature of orthogonal distributions on manifolds.
problem Understanding curvature of orthogonal distributions on manifolds.
method Derived Euler-Lagrange equations for a functional of Riemannian metrics.
result Examples of critical metrics for specific distributions.
In this paper, we propose novel strategies for neutral vector variable decorrelation. Two fundamental invertible transformations, namely serial nonlinear transformation and parallel nonlinear transformation, are proposed to carry out the decorrelation. For a neutral vector variable, which is not multivariate Gaussian d…
The paper proposes a method to learn structured representations from unlabeled data using mutual information maximization.
problem Learning structured representations from unlabeled data.
method Adversarial maximization of mutual information between a structured latent variable and a target variable.
result The proposed method outperforms current baselines in document hashing and yields highly compressed interpretable representations.
KSG mutual information estimator, which is based on the distances of each sample to its k-th nearest neighbor, is widely used to estimate mutual information between two continuous random variables. Existing work has analyzed the convergence rate of this estimator for random variables whose densities are bounded away fr…
The paper explores how machine learning models generalize when the true distribution differs from the training distribution.
problem Understanding generalization beyond the training distribution in machine learning.
method Study through information measures, focusing on mutual information between input samples and representations.
result Bounding the testing gap with high probability using mutual information between input samples and representations.
Extracts the finest pattern of mutual independence from data.
problem Inferring the finest mutual independence pattern from data.
method Estimate the set of valid patterns of dichotomic independence and use their intersection to infer the finest pattern.
result The method can estimate the finest mutual independence pattern from i.i.d. realizations of a multivariate normal distribution.
Proposes CLUB for reliable MI minimization in high dimensions.
problem Estimating and minimizing mutual information in high-dimensional spaces.
method Contrastive Log-ratio Upper Bound (CLUB) for MI minimization.
result CLUB provides reliable estimation of mutual information.
A new multi-label CPC method improves mutual information estimation and representation learning.
problem Underestimation of mutual information in contrastive predictive coding.
method Introducing a multi-label classification problem to overcome the logm bound in mutual information estimation. result The new method exceeds the logm bound and leads to better mutual information estimation and improved unsupervised representation learning. Study higher arity self-distributive operations and their cohomology.
problem Understanding cohomology groups of higher arity operations.
method Introduced mutually distributive n-ary operations and defined a cohomology theory.
result Geometric interpretation of cohomology in terms of framed links.
Optimal adversarial attacks minimize mutual information, revealing classifier vulnerabilities.
problem Designing optimal attacks to degrade machine learning performance.
method Information-theoretic approach to finding optimal perturbations.
result Optimal attacks minimize mutual information between degraded and original signals.
Feature selection is one of the most fundamental problems in machine learning. An extensive body of work on information-theoretic feature selection exists which is based on maximizing mutual information between subsets of features and class labels. Practical methods are forced to rely on approximations due to the diffi…
Lumbermark clusters data robustly, slicing limbs of mutual reachability trees.
problem Detecting clusters of varying sizes, densities, and shapes in datasets.
method Iteratively chops limbs of a mutual reachability minimum spanning tree.
result Lumbermark produces partitions with user-specified sizes.
Paper proposes a novel method to reduce mutual information for missing data imputation.
problem Missing data imputation in datasets with missingness patterns.
method Iterative minimization of KL divergence between imputed data and missingness mask, using rectified flow training objective.
result The proposed method achieves superior imputation performance on synthetic and real-world datasets.
We propose Bayesian extensions of two nonparametric regression methods which are kernel and mutual k-nearest neighbor regression methods. Derived based on Gaussian process models for regression, the extensions provide distributions for target value estimates and the framework to select the hyperparameters. It is show…
Many machine learning problems can be characterized by mutual contamination models. In these problems, one observes several random samples from different convex combinations of a set of unknown base distributions and the goal is to infer these base distributions. This paper considers the general setting where the base …
Develops LSH schemes for f-divergences and mutual information loss.
problem Approximating nearest neighbors in high-dimensional probability distributions.
method General framework and specific LSH schemes for f-divergences and mutual information loss.
result Generalized Jensen-Shannon divergence can be approximated by Hellinger distance.
Paper proposes mutual information learning for deep learning classifiers.
problem Overfitting in deep learning models.
method Mutual information learning framework to train classifiers.
result MILCs achieve better generalization than conditional entropy classifiers.
Proposes a new method to measure epistemic uncertainty in Bayesian neural networks.
problem Measuring epistemic uncertainty in Bayesian neural networks for out-of-distribution detection.
method Proposes measuring disagreement between logits and their pre-softmax counterparts as an epistemic uncertainty measure.
result Proposed epistemic uncertainty scores outperform mutual information and equal predictive entropy performance.
Cycles in causal learning cause feedback loops under intervention.
problem Cyclic causal structures lead to feedback loops in causal inference.
method Theoretical observations about self-referential distributions and their factorizations.
result Cyclic causal dependence can exist even when observational data suggest independence.
Estimates copula density for complex data distributions.
problem Estimating copula density from observed data.
method Neural network-based copula density neural estimation (CODINE).
result Novel approach capable of modeling complex distributions.
A new mutual information lower bound for multimodal regression active learning.
problem Lack of effective acquisition functions for multimodal regression active learning.
method Introduces a Two-Index framework for separating epistemic and aleatoric sources of uncertainty, deriving MI-LB as a closed-form approximation.
result MI-LB consistently outperforms baselines on multimodal regression tasks.
A neural network approach for feature selection using mutual information.
problem Feature ranking and selection leading to sub-optimal solutions for class separability.
method Stochastic mutual information gradient estimation for dimensionality reduction.
result The network projects features onto an output space maximizing mutual information with class labels.
Mutual information minimum spanning trees are used to explore nonlinear dependencies on Brazilian equity network in the periods from June/01/2015 to January/26/2016, in which Brazil was under the government of President Dilma Rousseff, and from January/27/2016 to September/08/2016 which includes the government transiti…
AMI framework improves text generation by optimizing mutual information between source and target.
problem Previous MI approaches ignored the backward network, leading to loose variational bounds.
method AMI is a saddle point optimization framework that iteratively promotes and demotes generated instances.
result AMI significantly outperforms baselines on various text generation tasks.
MIND estimates mutual information from ordinal data without full distributional knowledge.
problem Estimating mutual information from ordinal data with limited data.
method Copula-based maximum-entropy estimation of copula entropies.
result MIND estimator is consistent, data-efficient, and unbounded for any sample size.