Proposes a new bound on generalization error using conditional mutual information.
problem Improving the generalization error bound in machine learning.
method Combines error decomposition and conditional mutual information techniques.
result New bound is order-wise better than previous ones in a simple Gaussian setting.
Improved bounds on learning algorithms' performance using conditional mutual information.
problem Bounding the generalization error of learning algorithms.
method Introducing conditional mutual information and disintegrated mutual information to tighten bounds.
result New bounds are tighter than previous ones, especially for noisy, iterative algorithms.
Revisits information metric as pseudo metric on observables, with applications to conditional independence.
problem Clarifying the nature of information metric on manifolds of observables.
method Characterizes geodesics and applies Pythagorean theorem to conditional independence.
result Illustrates computation of information metric on Diabetes dataset.
Dynamic acquisition of features improves predictions with limited data.
problem Limited or uncertain data requires additional relevant information for accurate assessments.
method Proposes models that dynamically acquire new features using conditional mutual information and arbitrary conditional flow.
result Demonstrates superior performance over baselines in multiple settings.
Estimates conditional mutual information using a minmax formulation.
problem Estimating conditional mutual information in high dimensions.
method Uses a minmax optimization problem to train a neural network.
result Improves estimation accuracy compared to existing methods.
New bounds derived using conditional f-information for machine learning models.
problem Improving generalization bounds in machine learning.
method Introducing novel information-theoretic generalization bounds via conditional f-information. result Derives generalization bounds applicable to both bounded and unbounded loss functions.
We formulate and prove an axiomatic characterization of conditional information geometry, for both the normalized and the nonnormalized cases. This characterization extends the axiomatic derivation of the Fisher geometry by Cencov and Campbell to the cone of positive conditional models, and as a special case to the man…
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…
The article examines entropy-information inequalities for continuous-time Markov chains under curvature-dimension conditions.
problem Proving Li-Yau inequalities and modified logarithmic Sobolev inequalities for reversible Markov chains.
method Introducing the CDΥ(κ,F) condition and deriving entropy-information inequalities. result Derives functional inequalities relating entropy to Fisher information.
The condition number predicts efficient information encoding in neural units, aiding model fine-tuning.
problem Efficient information encoding in neural units for various tasks and input modalities.
method Linking the condition number to the log-volume scaling factor and entropy of the output distribution.
result High condition number indicates efficient encoding, reducing overall information transfer.
DIET tests conditional independence using marginal dependence measures of residual information.
problem Computational intractability of conditional randomization tests (CRTs).
method DIET avoids fitting large models by leveraging marginal independence statistics of information residuals.
result DIET achieves higher power than other tractable CRTs on synthetic and real benchmarks.
Integrates side information for robust portfolio optimization.
problem Portfolio optimization under uncertainty and side information.
method Distributionally robust optimization with optimal transport ambiguity set.
result The problem can be reformulated as a finite-dimensional optimization problem.
This paper focuses on the stability of the non-arbitrage condition in discrete time market models when some unknown information τ is partially/fully incorporated into the market. Our main conclusions are twofold. On the one hand, for a fixed market S, we prove that the non-arbitrage condition is preserved under a m…
New bounds on neural network test loss derived from conditional information measures.
problem Estimating test loss of neural networks trained on limited data.
method Framework based on conditional information density between hypothesis and training set.
result Tail bounds on test loss decay as 1/n, improving over previous 1/sqrt{n} bounds.
Proposes a new GAN architecture for generating data conditioned on partial information.
problem Generating data conditioned on partial ancillary information.
method Introduces a new Adversarial Network architecture and training strategy.
result The proposed method outperforms standard Conditional GANs in generating data under partial conditioning.
Within the well-known framework of financial portfolio optimization, we analyze the existing relationships between the condition of arbitrage and the utility maximization in presence of \emph{insider information}. We assume that, since the initial time, the information flow is altered by adding the knowledge of an addi…
Meta-learning bound uses conditional mutual information.
problem Bounding generalization performance in meta-learning.
method Extends CMI framework to meta-learning with a meta-supersample.
result Explicit bound involving two CMI terms.
We propose a novel, projection based way to incorporate the conditional information into the discriminator of GANs that respects the role of the conditional information in the underlining probabilistic model. This approach is in contrast with most frameworks of conditional GANs used in application today, which use the …
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.
The paper derives a new theorem for predicting batches of data.
problem Finding lower bounds on minimal batch regret.
method Derives a conditional version of the regret-capacity theorem.
result Reveals a connection between conditional Rényi divergence and conditional Sibson's mutual information.
New bounds improve generalization in learning scenarios.
problem Limitations of existing information-theoretic bounds in SCO problems.
method Sample-conditioned hypothesis stability and neighboring-hypothesis matrix.
result Sharper generalization guarantees in various learning scenarios.
The information-based asset-pricing framework of Brody, Hughston and Macrina (BHM) is extended to include a wider class of models for market information. In the BHM framework, each asset is associated with a collection of random cash flows. The price of the asset is the sum of the discounted conditional expectations of…
New bounds on learning algorithm generalization error derived using information density.
problem Bounding the generalization error of learning algorithms.
method Exponential inequalities and information density/conditional information density.
result Novel bounds on average and tail probability of generalization error.
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.
New bound on machine learning model performance using Jensen-Shannon information.
problem Understanding the performance of machine learning models.
method Proposes a new information-theoretic bound on generalization error.
result Shows that the new bound can be tighter than mutual information-based bounds under certain conditions.
We study 'meta-dependence' in conditional independence tests across different empirical distributions.
problem Understanding the breakdown of conditional independence properties in finite data.
method Geometric intuition and information projections to measure meta-dependence between conditional independences.
result We provide a measure of meta-dependence that consolidates findings across synthetic and real-world data.
Technical proofs for Radon-Nikodym derivative identities.
problem Formalizing and proving theorems on Radon-Nikodym derivatives.
method Careful consideration of conditional and marginal probability measures.
result New interpretation of mutual and lattum information sums.
This paper offers a characterization of fundamental limits on the classification and reconstruction of high-dimensional signals from low-dimensional features, in the presence of side information. We consider a scenario where a decoder has access both to linear features of the signal of interest and to linear features o…
PINN-FEM combines PINNs and FEM for accurate Dirichlet boundary condition enforcement.
problem Challenges in enforcing Dirichlet boundary conditions in PINNs.
method Hybrid approach combining PINNs and FEM for strong boundary condition enforcement.
result PINN-FEM outperforms standard PINN models in accuracy and robustness.
Due to the advantage of achieving a better performance under weak regularization, elastic net has attracted wide attention in statistics, machine learning, bioinformatics, and other fields. In particular, a variation of the elastic net, adaptive elastic net (AEN), integrates the adaptive grouping effect. In this paper,…
In recent years, unsupervised/weakly-supervised conditional generative adversarial networks (GANs) have achieved many successes on the task of modeling and generating data. However, one of their weaknesses lies in their poor ability to separate, or disentangle, the different factors that characterize the representation…
Often in machine learning, data are collected as a combination of multiple conditions, e.g., the voice recordings of multiple persons, each labeled with an ID. How could we build a model that captures the latent information related to these conditions and generalize to a new one with few data? We present a new model ca…
Physics-informed GCRL tackles sparse feedback learning with hybrid dynamics.
problem Sparse feedback learning with high-dimensional, hybrid, or contact-dependent dynamics.
method Introduces physics-informed inductive biases into goal-conditioned value learning.
result Contact-rich manipulation tasks degrade existing Pi-GCRL methods.
The paper establishes bounds for transductive learning using information theory.
problem Transductive learning generalization gap control.
method Information theory, PAC-Bayes, mutual information, conditional mutual information, different information measures.
result Established transductive information-theoretic and PAC-Bayesian bounds.
The paper measures semantic information production in generative models using information theory.
problem Measuring when semantic decisions are made during generative model training.
method Using an online formula for the optimal Bayesian classifier, the paper estimates conditional entropy and determines time intervals for highest information transfer.
result Semantic information transfer is highest in intermediate stages of diffusion, with different classes making decisions at different times.
The GANs are generative models whose random samples realistically reflect natural images. It also can generate samples with specific attributes by concatenating a condition vector into the input, yet research on this field is not well studied. We propose novel methods of conditioning generative adversarial networks (GA…
New research shows existing information-theoretic methods can't establish minimax rates for gradient descent in stochastic convex optimization.
problem Establishing minimax rates for gradient descent in stochastic convex optimization using information-theoretic methods.
method Examined several information-theoretic frameworks including input-output mutual information bounds, conditional mutual information bounds, PAC-Bayes bounds, and their variants.
result Proved that none of the examined information-theoretic frameworks can establish minimax rates for gradient descent in stochastic convex optimization.
New measures for causal entropy and information gain studied.
problem Quantifying causal relationships in machine learning.
method Formal study of causal entropy and information gain.
result Established fundamental properties and relationships.
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.
New method improves DMs for solving inverse problems by maximizing conditional mutual information.
problem Efficiently solving noisy linear inverse problems without additional task-specific training.
method Maximizing conditional mutual information between reconstructed signal and measurement.
result Significantly improves the quality of generated images in inverse problems.
Enhances reinforcement learning with partial state information.
problem Improving learning under partial observability with limited privileged signals.
method Introduced informed asymmetric actor-critic framework that uses arbitrary state-dependent privileged signals.
result Unbiased policy gradient estimates with arbitrary privileged signals.
Markov blanket feature selection, while theoretically optimal, is generally challenging to implement. This is due to the shortcomings of existing approaches to conditional independence (CI) testing, which tend to struggle either with the curse of dimensionality or computational complexity. We propose a novel two-step a…
IndiSeek learns disentangled representations by balancing independence and completeness.
problem Learning disentangled representations with mutual information in multi-modal data.
method Combines independence-enforcing objective with a reconstruction loss that bounds conditional mutual information.
result Demonstrates effectiveness on synthetic data, CITE-seq, and real-world multi-modal benchmarks.
The paper decomposes probabilistic scores into reliability, uncertainty, and information loss.
problem Understanding the reliability and uncertainty of probabilistic predictions.
method Developed decomposition identities for proper losses, quantifying reliability, residual uncertainty, and information gain.
result A three-term identity for classification scores, revealing miscalibration, grouping term, and feature-level uncertainty.
Deep NURBS improves PINNs for solving PDEs on arbitrary geometries.
problem Solving partial differential equations on complex geometries with physics constraints.
method Combines admissible NURBS parametrizations and PINN solver for arbitrary geometries.
result High convergence rate and accuracy for most PDEs using Deep NURBS.
The paper proposes methods to extract and analyze individual variable information from complex dependencies.
problem Analyzing and understanding complex dependencies between multiple variables.
method Reversible normalization and iterative dependency reduction to extract individual information, and use it for direct mutual information and multi-feature Granger causality analysis.
result Decoupling of variables to analyze their individual information and direct mutual information transfers.
A semi-supervised framework using stochastic interpolation and latent representations.
problem Challenges in conditional generative modeling with scarce labeled data.
method Combines conditional stochastic interpolation with low-dimensional latent representations.
result Significantly improves sample complexity and achieves faster convergence rate.
PI-SAC agents learn predictive information to improve RL efficiency.
problem Improving sample efficiency in reinforcement learning.
method PI-SAC agents use a contrastive version of Conditional Entropy Bottleneck to learn predictive information from past and future states.
result PI-SAC agents significantly improve sample efficiency on challenging continuous control tasks.