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.
New bounds show limitations of sample-wise information-theoretic generalization.
problem Limitations of sample-wise information-theoretic generalization bounds.
method Analysis of existing bounds and derivation of new bounds.
result No sample-wise information-theoretic bounds exist for expected squared generalization gap.
Information-theoretic Bayesian regret bounds of Russo and Van Roy capture the dependence of regret on prior uncertainty. However, this dependence is through entropy, which can become arbitrarily large as the number of actions increases. We establish new bounds that depend instead on a notion of rate-distortion. Among o…
New tighter bounds for learning algorithms from Steinke & Zakynthinou's supersample setting.
problem Improving generalization bounds for machine learning algorithms.
method Information-theoretic approach using projected loss and Rademacher sequence.
result The new bounds are tighter than previous information-theoretic bounds.
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 bounds estimate learning algorithm performance using prediction information.
problem Estimating the performance of black-box learning algorithms.
method Information-theoretic bounds based on prediction information.
result Improved bounds applicable to deterministic algorithms and easier to estimate.
Study reveals mutual information is crucial for understanding algorithm performance in stochastic convex optimization.
problem Uncertainty in capturing the exceptional performance of learning algorithms using existing information-theoretic generalization bounds.
method Examined the relationship between mutual information and generalization in stochastic convex optimization.
result Mutual information is necessary for true risk minimization in stochastic convex optimization, indicating existing bounds fall short.
We integrate information-theoretic concepts into the design and analysis of optimistic algorithms and Thompson sampling. By making a connection between information-theoretic quantities and confidence bounds, we obtain results that relate the per-period performance of the agent with its information gain about the enviro…
Unified framework for information-theoretic bounds on learning algorithms.
problem Deriving generalization bounds for learning algorithms.
method Probabilistic decorrelation lemma, symmetrization, couplings, chaining, Young's inequality.
result New upper bounds on generalization error in expectation and high probability.
Optimizes SGLD noise structure for better generalization bounds.
problem Improving generalization bounds for large models trained with SGLD.
method Manipulates the noise structure in SGLD to optimize information-theoretical bounds.
result Optimal noise covariance is the square root of the expected gradient covariance under certain constraints.
Novel bounds for SGLD show generalization error decreases with more samples.
problem Understanding the generalization error of SGLD in non-convex optimization.
method Information-theoretic approach focusing on Kullback-Leibler divergence and sub-exponential loss function.
result Time-independent generalization bounds for SGLD, independent of step size and number of iterations.
Paper analyzes ECE bias and provides bounds for its estimation.
problem Understanding the estimation bias in ECE for machine learning models.
method Information-theoretic approach to analyze bias in uniform mass and uniform width binning strategies.
result Established upper bounds on ECE estimation bias and optimal number of bins.
The paper sets information-theoretic lower bounds for neural networks' parameter recovery and excess risk.
problem Establishing sample complexity lower bounds for neural network parameters and excess risk.
method Using information-theoretic tools, the paper proves lower bounds by constructing a generative network.
result Proves information-theoretic lower bounds for exact parameter recovery and positive excess risk.
New analysis improves generalization bounds for meta-learning.
problem Improving generalization in meta-learning algorithms.
method Information-theoretic analysis of MAML and its stochastic variant.
result Data-dependent generalization bound is tighter and non-vacuous.
This work improves generalisation bounds using chaining and information theory.
problem Improving generalisation bounds for supervised learning algorithms.
method Developed a theoretical framework linking generalisation bounds to their chained counterparts, derived new bounds using Wasserstein distance.
result Chained generalisation bounds can be tighter than standard bounds, especially for concentrated hypothesis distributions.
In this paper, we derive generic bounds on the maximum deviations in prediction errors for sequential prediction via an information-theoretic approach. The fundamental bounds are shown to depend only on the conditional entropy of the data point to be predicted given the previous data points. In the asymptotic case, the…
Unified framework improves meta-learning generalization bounds.
problem Limited sharpness of existing meta-generalization bounds.
method Unified information-theoretic derivation for single-step bounds.
result Unified bounds exhibit tighter scaling and computational advantages.
New framework controls generalization for heavy-tailed data in RLHF and SGLD.
problem Heavy-tailed data in modern learning pipelines.
method Tail-dependent information-theoretic framework for sub-Weibull data.
result Sharp generalization bounds for heavy-tailed data.
Study on maximizing submodular functions with limited updates, achieving tight bounds and poly-time algorithms.
problem Online submodular maximization with constant recourse.
method Information-theoretic bounds and poly-time randomized algorithms.
result Achieved tight bounds of 2/3 and 3/4 for general and coverage functions, respectively, with a 0.51 approximation.
The information-theoretic analysis by Russo and Van Roy (2014) in combination with minimax duality has proved a powerful tool for the analysis of online learning algorithms in full and partial information settings. In most applications there is a tantalising similarity to the classical analysis based on mirror descent.…
New information-theoretic bounds improve machine learning generalization.
problem Improving machine learning generalization beyond traditional complexity-based methods.
method Introducing bounds using Wasserstein distance and structured methods to incorporate geometry and individual data dependence.
result Established connections between different bounds and introduced new tighter bounds for various loss functions.
New bound matches exact generalization error for quadratic Gaussian problem.
problem Understanding generalization error in quadratic Gaussian problems.
method Information-theoretic approach with new ingredients.
result Exact tight bound for generalization error.
This paper tightens information-theoretic bounds on generalization errors.
problem Understanding the discrepancy between training and testing data losses.
method Investigates the tightness of information-theoretic bounds on generalization error.
result The individual sample mutual information bound can be asymptotically tight under specific assumptions.
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.
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…
Lower bounds show many sampling algorithms need many gradient queries.
problem Sampling from strongly log-concave densities in high dimensions.
method Information theory and stochastic gradient methods.
result Lower bound on number of gradient queries needed.
Unified framework for active learning problems using information theory.
problem Combining level set estimation and Bayesian optimization.
method Information-theoretic criterion and acquisition function.
result Unified framework achieves state-of-the-art performance.
The paper develops a theory for identifying the best arm in non-parametric multi-armed bandits with a fixed budget.
problem Identifying the best arm in non-parametric multi-armed bandits with a limited number of trials.
method The paper proposes upper and lower bounds on the average log-probability of misidentification using information-theoretic quantities and a refined analysis of the successive-rejects strategy.
result The paper provides new upper and lower bounds on the average log-probability of misidentification, which generalize existing bounds.
We study the information-theoretic lower bound of the sample complexity of the correct recovery of diffusion network structures. We introduce a discrete-time diffusion model based on the Independent Cascade model for which we obtain a lower bound of order Ω(klogp), for directed graphs of p nodes, and at most k…
This paper improves DNN generalization by accurately estimating mutual information.
problem Intractability of estimating mutual information in DNNs.
method Introduces a probabilistic representation of DNNs to accurately estimate mutual information.
result Derives a tighter generalization bound than previous relaxations.
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.
We derive upper bounds on the generalization error of a learning algorithm in terms of the mutual information between its input and output. The bounds provide an information-theoretic understanding of generalization in learning problems, and give theoretical guidelines for striking the right balance between data fit an…
Framework sharpens causal effect estimates without external assumptions.
problem Estimating causal effects under unmeasured confounding.
method Information-theoretic divergence bounds, Neyman orthogonality, machine learning.
result Sharp partial identification of conditional causal effects from observational data.
A new method clusters intersecting lines using hypergraphs.
problem Clustering intersecting lines in subspace clustering.
method Constructing a geometric hypergraph and using spectral algorithm.
result Achieves information-theoretic bounds for line clustering.
SGD generalization bounds derived from information theory.
problem Understanding generalization of SGD for non-convex functions.
method Combining information-theoretic bounds with perturbation analysis.
result Upper bounds on SGD's generalization error based on gradient variance and function smoothness.
Framework for understanding overfitting and underfitting using information theory.
problem Understanding and preventing overfitting and underfitting in machine learning.
method Information-theoretic framework measuring algorithm capacity and dataset information transfer.
result Upper-bounding algorithm capacity and establishing its relationship to machine learning quantities.
Information-theoretic bounded rationality describes utility-optimizing decision-makers whose limited information-processing capabilities are formalized by information constraints. One of the consequences of bounded rationality is that resource-limited decision-makers can join together to solve decision-making problems …
Unified treatment of PAC-Bayesian and information-theoretic generalization bounds.
problem Generalization capabilities of machine learning algorithms.
method PAC-Bayesian and information-theoretic perspectives.
result Unified treatment and modular structure of proofs.
In this work, we improve upon the stepwise analysis of noisy iterative learning algorithms initiated by Pensia, Jog, and Loh (2018) and recently extended by Bu, Zou, and Veeravalli (2019). Our main contributions are significantly improved mutual information bounds for Stochastic Gradient Langevin Dynamics via data-depe…
Novel kernelized Renyi's entropy improves deep learning generalization bounds.
problem Improving generalization bounds for deep learning algorithms.
method Kernelized Renyi's entropy, a new information theoretical measure.
result Theoretical bounds are tighter than current SOTA results.
Improved robust regression with clean covariates achieves better rates than Huber's model.
problem Robust regression under adaptive contamination of responses with clean covariates.
method Exploiting clean covariates to construct an estimator achieving better rates than Huber's model.
result Improved estimation rate even with constant contamination, achieving consistency.
Improved regret bounds for bandits with fixed expert advice using information theory.
problem Optimizing regret in bandit problems with fixed expert distributions.
method Information-theoretic analysis and KL-divergence measures.
result First regret bounds for EXP4 that can get arbitrarily close to zero under certain conditions.
Despite great popularity of applying softmax to map the non-normalised outputs of a neural network to a probability distribution over predicting classes, this normalised exponential transformation still seems to be artificial. A theoretic framework that incorporates softmax as an intrinsic component is still lacking. I…
We analyze the necessary number of samples for sparse vector recovery in a noisy linear prediction setup. This model includes problems such as linear regression and classification. We focus on structured graph models. In particular, we prove that sufficient number of samples for the weighted graph model proposed by Heg…
Proposes a new information-theoretic framework for analyzing deep neural networks.
problem Difficulty in analyzing deep neural networks using existing theoretical frameworks.
method Introduces an information-theoretic framework with new notions of regret and sample complexity.
result Establishes sample complexity bounds for deep neural networks that are width-independent and linear in depth.
New framework connects online learning to statistical learning for better generalization bounds.
problem Deriving generalization bounds for statistical learning algorithms.
method Constructing an online learning game and showing a connection to statistical learning.
result Established a connection between online and statistical learning, leading to new generalization bounds.
The paper explores the information-theoretic nature of excess risk in machine learning.
problem Understanding the excess risk in machine learning models.
method Formulates the minimax excess risk as a zero-sum game and modifies it to allow swapping of the order of play.
result Proves that under certain conditions, the duality gap is zero, allowing for the application of Bayesian results to provide bounds on minimax excess risk.
Study OOD generalization in meta-reinforcement learning using information theory.
problem Understanding how meta-reinforcement learning handles distribution shifts.
method Information-theoretic analysis of Markov Decision Processes and gradient-based algorithms.
result Established fine-grained generalization bounds for meta-reinforcement learning.