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Found 20 papers, 6 papers with code
Gradient Flows and Riemannian Structure in the Gromov-Wasserstein Geometry
Motivated by scenarios where the global structure of the data needs to be preserved, this work initiates the study of gradient flows and Riemannian structure in the Gromov-Wasserstein (GW) geometry, which is particularly suited for such purposes.
Robust Distribution Learning with Local and Global Adversarial Corruptions
We characterize the optimal population-limit risk for this task and then develop an efficient finite-sample algorithm with error bounded by $\sqrt{\varepsilon k} + \rho + \tilde{O}(d\sqrt{k}n^{-1/(k \lor 2)})$ when $P$ has bounded covariance.
Information-Theoretic Generalization Bounds for Deep Neural Networks
This enables refining our generalization bounds to capture the contraction as a function of the network architecture parameters.
Quantum Neural Estimation of Entropies
Entropy measures quantify the amount of information and correlation present in a quantum system.
Quantum Pufferfish Privacy: A Flexible Privacy Framework for Quantum Systems
We propose a versatile privacy framework for quantum systems, termed quantum pufferfish privacy (QPP).
Robust Estimation under the Wasserstein Distance
We study the problem of robust distribution estimation under the Wasserstein metric, a popular discrepancy measure between probability distributions rooted in optimal transport (OT) theory.
Data-Driven Optimization of Directed Information over Discrete Alphabets
Directed information (DI) is a fundamental measure for the study and analysis of sequential stochastic models.
Statistical, Robustness, and Computational Guarantees for Sliced Wasserstein Distances
The goal of this work is to quantify this scalability from three key aspects: (i) empirical convergence rates; (ii) robustness to data contamination; and (iii) efficient computational methods.
k-Sliced Mutual Information: A Quantitative Study of Scalability with Dimension
However, a quantitative characterization of how SMI itself and estimation rates thereof depend on the ambient dimension, which is crucial to the understanding of scalability, remain obscure.
Cycle Consistent Probability Divergences Across Different Spaces
Discrepancy measures between probability distributions are at the core of statistical inference and machine learning.
Outlier-Robust Optimal Transport: Duality, Structure, and Statistical Analysis
The Wasserstein distance, rooted in optimal transport (OT) theory, is a popular discrepancy measure between probability distributions with various applications to statistics and machine learning.
Neural Estimation of Statistical Divergences
Statistical divergences (SDs), which quantify the dissimilarity between probability distributions, are a basic constituent of statistical inference and machine learning.
Limit Distribution Theory for the Smooth 1-Wasserstein Distance with Applications
This result is then used to derive new empirical convergence rates for classic $W_1$ in terms of the intrinsic dimension.
Non-Asymptotic Performance Guarantees for Neural Estimation of $\mathsf{f}$-Divergences
Statistical distances (SDs), which quantify the dissimilarity between probability distributions, are central to machine learning and statistics.
Smooth $p$-Wasserstein Distance: Structure, Empirical Approximation, and Statistical Applications
Discrepancy measures between probability distributions, often termed statistical distances, are ubiquitous in probability theory, statistics and machine learning.
The Information Bottleneck Problem and Its Applications in Machine Learning
The information bottleneck (IB) theory recently emerged as a bold information-theoretic paradigm for analyzing DL systems.
Capacity of Continuous Channels with Memory via Directed Information Neural Estimator
When no analytic solution is present or the channel model is unknown, there is no unified framework for calculating or even approximating capacity.
Estimating Information Flow in DNNs
We then develop a rigorous estimator for I(X;T) in noisy DNNs and observe compression in various models.
Estimating Information Flow in Deep Neural Networks
We then develop a rigorous estimator for $I(X;T)$ in noisy DNNs and observe compression in various models.
Information Storage in the Stochastic Ising Model
We first show that at zero temperature, order of $\sqrt{n}$ bits can be stored in the system indefinitely by coding over stable, striped configurations.
Information Theory Statistical Mechanics Information Theory
