arXiv research

Estimating IPM is as hard as estimating under IPM, both requiring similar optimal rates.

Unified view of KL-divergence and IPMs via DRE, with new DRM metrics.

Study minimax rates for density estimation under Huber contamination and Besov IPM losses.

A new IPM uses ReLU networks to measure probability discrepancies.

We study the problem of estimating a nonparametric probability density under a large family of losses called Besov IPMs, which include, for example, $\mathcal{L}^p$ distances, total variation distance, and generalizations of both Wasserstein and Kolmogorov-Smirnov distances. For a wide variety of settings, we provide b…

Novel algorithm speeds up computation of Sobolev IPM for graph-based probability measures.

We propose a new Integral Probability Metric (IPM) between distributions: the Sobolev IPM. The Sobolev IPM compares the mean discrepancy of two distributions for functions (critic) restricted to a Sobolev ball defined with respect to a dominant measure $μ$. We show that the Sobolev IPM compares two distributions in hig…

New framework improves experimental design using integral probability metrics.

We introduce new families of Integral Probability Metrics (IPM) for training Generative Adversarial Networks (GAN). Our IPMs are based on matching statistics of distributions embedded in a finite dimensional feature space. Mean and covariance feature matching IPMs allow for stable training of GANs, which we will call M…

TMLE improves IPM estimation for ecological population dynamics.

The paper explores fair predictors in supervised learning using IPMs and Kolmogorov distance.

Generalizes Sobolev IPM for graph-based measures using Orlicz geometric structure.

The paper proposes a new method for covariate balancing using IPM to improve causal inference.

New divergences improve estimation and GAN training performance.

Develops a new divergence framework that combines $f$-divergences and IPMs.

Toda flow explained as a porous medium equation.

Proposes tests for comparing high-dimensional manifold samples.

New bounds use IPMs to improve generalization in machine learning.

IPMs struggle with hyperbolic spaces due to polynomially growing barrier parameters.

The paper bounds the expectation of empirical processes indexed by Hölder classes.

Study extends DRO with IPMs, linking robustness to regularization and GANs.

Improved image generation quality using closed-form discriminator guidance in diffusion models.

New error bounds for GANs with nonlinear objective functions derived.

A nonparametric two-sample test using a parametric integral probability metric

Paper explores robust estimators for kernel exponential families using smoothed total variation distances.

This paper is concerned with sequential filtering based stochastic optimization (FSO) approaches that leverage a probabilistic perspective to implement the incremental proximity method (IPM). The present FSO methods are derived based on the Kalman filter (KF) and the extended KF (EKF). In contrast with typical methods …

Generative Adversarial Networks (GANs) are powerful models for learning complex distributions. Stable training of GANs has been addressed in many recent works which explore different metrics between distributions. In this paper we introduce Fisher GAN which fits within the Integral Probability Metrics (IPM) framework f…

Paper proposes a new framework to improve policy optimization by aligning real and simulated data distributions.

The recent empirical success of unsupervised cross-domain mapping algorithms, between two domains that share common characteristics, is not well-supported by theoretical justifications. This lacuna is especially troubling, given the clear ambiguity in such mappings. We work with adversarial training methods based on IP…

We present an extension of the Kolmogorov-Smirnov (KS) two-sample test, which can be more sensitive to differences in the tails. Our test statistic is an integral probability metric (IPM) defined over a higher-order total variation ball, recovering the original KS test as its simplest case. We give an exact representer…

An important class of distance metrics proposed for training generative adversarial networks (GANs) is the integral probability metric (IPM), in which the neural net distance captures the practical GAN training via two neural networks. This paper investigates the minimax estimation problem of the neural net distance ba…

We present a quantum interior-point method (IPM) for second-order cone programming (SOCP) that runs in time $\widetilde{O} \left( n\sqrt{r} \frac{ζκ}{δ^2} \log \left(1/ε\right) \right)$ where $r$ is the rank and $n$ the dimension of the SOCP, $δ$ bounds the distance of intermediate solutions from the cone boundary, $ζ$…

In standard generative adversarial network (SGAN), the discriminator estimates the probability that the input data is real. The generator is trained to increase the probability that fake data is real. We argue that it should also simultaneously decrease the probability that real data is real because 1) this would accou…

Paper proposes a new method to quantify uncertainty in machine learning models.

New findings show fixed-kernel discriminators are weaker than feature-learning ones.

Unified score and distance-based GoF tests for model adequacy.

Expands learning paradigm to stochastic orders using Choquet-Toland distance and Variational Dominance Criterion.

A new meta-learning framework that assigns weights to source tasks based on target samples.

SIC measures dependency between variables, promoting feature selection.

New method solves optimization problems with stochastic objectives and constraints.

While Generative Adversarial Networks (GANs) have empirically produced impressive results on learning complex real-world distributions, recent works have shown that they suffer from lack of diversity or mode collapse. The theoretical work of Arora et al. suggests a dilemma about GANs' statistical properties: powerful d…

A new GAN model uses characteristic functions to improve image generation.

Measuring conditional dependencies among the variables of a network is of great interest to many disciplines. This paper studies some shortcomings of the existing dependency measures in detecting direct causal influences or their lack of ability for group selection to capture strong dependencies and accordingly introdu…

A new algorithm STE for model-based RL improves learning rates.

Unified framework for convergence of discrete diffusion models without state space size dependence.

New test uses neural networks to compare distributions, outperforming traditional methods.

This paper explores the possibility of near-optimally solving multi-agent, multi-task NP-hard planning problems with time-dependent rewards using a learning-based algorithm. In particular, we consider a class of robot/machine scheduling problems called the multi-robot reward collection problem (MRRC). Such MRRC problem…

As an effective way of metric learning, triplet loss has been widely used in many deep learning tasks, including face recognition and person-ReID, leading to many states of the arts. The main innovation of triplet loss is using feature map to replace softmax in the classification task. Inspired by this concept, we prop…