arXiv research

Study on $L_p$ affine surface areas and their inequalities for convex bodies.

Unified technique for sequential estimation of convex divergences.

The paper develops sum-of-squares relaxations for computing $f$-divergences.

Study compares chi-squared divergence and KL-divergence posteriors for PAC-Bayesian bounds.

New proof finds three divergence-free vector fields for any 3D manifold.

Paper relaxes optimal transport using convex functions for data science.

Paper tackles non-convex constrained DRO with a stochastic algorithm for large-scale applications.

New sampler improves uniform sampling over convex bodies with fewer queries.

Optimal payoff choice constrained by Bregman-Wasserstein divergence.

New algorithm solves saddle point problems in Banach spaces.

Unified framework improves robust causal inference, overcoming Gaussian barriers and optimization issues.

Optimal transport with $f$-divergence regularization using generalized Sinkhorn algorithm.

In Riemannian geometry geodesics are integral curves of the Riemannian distance gradient. We extend this classical result to the framework of Information Geometry. In particular, we prove that the rays of level-sets defined by a pseudo-distance are generated by the sum of two tangent vectors. By relying on these vector…

Proposes a new neural head for asymmetric representation learning.

Generative adversarial network (GAN) is a minimax game between a generator mimicking the true model and a discriminator distinguishing the samples produced by the generator from the real training samples. Given an unconstrained discriminator able to approximate any function, this game reduces to finding the generative …

New algorithm uniformly samples high-dimensional convex bodies efficiently.

LMC algorithm converges to target in Chi-squared and Renyi divergence.

Geodesic flows on specific manifolds are structurally stable.

New bounds found for optimizing non-convex functions with noisy data.

This manuscript develops the theory of agglomerative clustering with Bregman divergences. Geometric smoothing techniques are developed to deal with degenerate clusters. To allow for cluster models based on exponential families with overcomplete representations, Bregman divergences are developed for nondifferentiable co…

Dual-ISL improves implicit generative model training with convex optimization and explicit density approximation.

Rényi divergence is related to Rényi entropy much like Kullback-Leibler divergence is related to Shannon's entropy, and comes up in many settings. It was introduced by Rényi as a measure of information that satisfies almost the same axioms as Kullback-Leibler divergence, and depends on a parameter that is called its or…

New algorithms sample convex bodies using Markov chains and restricted Gaussian oracles.

Bounds on chemical reaction network relaxation rates using convex analysis.

Decentralized Bayesian learning reduces KL-divergence exponentially.

Although many convex relaxations of clustering have been proposed in the past decade, current formulations remain restricted to spherical Gaussian or discriminative models and are susceptible to imbalanced clusters. To address these shortcomings, we propose a new class of convex relaxations that can be flexibly applied…

Optimized AIS scheme reduces bias and MSE for general proposals.

The Bregman divergence (Bregman distance, Bregman measure of distance) is a certain useful substitute for a distance, obtained from a well-chosen function (the "Bregman function"). Bregman functions and divergences have been extensively investigated during the last decades and have found applications in optimization, o…

EGMU optimizes portfolios using KL divergence, ensuring positive solutions.

New separation concepts for Anosov representations help bound Thurston asymmetric metric.

The paper introduces a new risk assessment framework using φ-divergence.

Variational inference with α-divergences has been widely used in modern probabilistic machine learning. Compared to Kullback-Leibler (KL) divergence, a major advantage of using α-divergences (with positive α values) is their mass-covering property. However, estimating and optimizing α-divergences require to use importa…

Accelerates convergence in global non-convex optimization with reversible diffusion.

Bregman divergences generalize measures such as the squared Euclidean distance and the KL divergence, and arise throughout many areas of machine learning. In this paper, we focus on the problem of approximating an arbitrary Bregman divergence from supervision, and we provide a well-principled approach to analyzing such…

In the field of statistics, many kind of divergence functions have been studied as an amount which measures the discrepancy between two probability distributions. In the differential geometrical approach in statistics (information geometry), dually flat spaces play a key role. In a dually flat space, there exist dual a…

Paper introduces a new method for learning Bregman divergence from data.

Mixability of a loss is known to characterise when constant regret bounds are achievable in games of prediction with expert advice through the use of Vovk's aggregating algorithm. We provide a new interpretation of mixability via convex analysis that highlights the role of the Kullback-Leibler divergence in its definit…

On the predual of a von Neumann algebra, we define a differentiable manifold structure and affine connections by embeddings into non-commutative L_p-spaces. Using the geometry of uniformly convex Banach spaces and duality of the L_p and L_q spaces for 1/p+1/q=1, we show that we can introduce the α-divergence, for αin (…

Optimal convex loss function improves regression coefficient estimation.

Paper improves differential privacy analysis for machine learning.

The paper develops inequalities for log-concave functions and related surface areas.

Exponential dispersion model is a useful framework in machine learning and statistics. Primarily, thanks to the additive structure of the model, it can be achieved without difficulty to estimate parameters including mean. However, tight conditions on cumulant function, such as analyticity, strict convexity, and steepne…

Geometric analysis improves convergence of variational inference.

Develops a contraction framework for MCMC mixing rates.

Faster algorithms solve convex function learning problems.

To ensure stability of learning, state-of-the-art generalized policy iteration algorithms augment the policy improvement step with a trust region constraint bounding the information loss. The size of the trust region is commonly determined by the Kullback-Leibler (KL) divergence, which not only captures the notion of d…

New loss functions based on f-divergences improve language model performance.

Langevin diffusion is a commonly used tool for sampling from a given distribution. In this work, we establish that when the target density $p^*$ is such that $\log p^*$ is $L$ smooth and $m$ strongly convex, discrete Langevin diffusion produces a distribution $p$ with $KL(p||p^*)\leq ε$ in $\tilde{O}(\frac{d}ε)$ steps,…