Related papers: The extended Bregman divergence and parametric est…

We discuss unbiased estimation equations in a class of objective function using a monotonically increasing function $f$ and Bregman divergence. The choice of the function $f$ gives desirable properties such as robustness against outliers.…

The estimation of an f-divergence between two probability distributions based on samples is a fundamental problem in statistics and machine learning. Most works study this problem under very weak assumptions, in which case it is provably…

Density power divergence (DPD) is designed to robustly estimate the underlying distribution of observations, in the presence of outliers. However, DPD involves an integral of the power of the parametric density models to be estimated; the…

We first introduce the class of strictly quasiconvex and strictly quasiconcave Jensen divergences which are oriented (asymmetric) distances, and study some of their properties. We then define the strictly quasiconvex Bregman divergences as…

Zhang (2019) presented a general estimation approach based on the Gaussian distribution for general parametric models where the likelihood of the data is difficult to obtain or unknown, but the mean and variance-covariance matrix are known.…

We study the variational inference problem of minimizing a regularized R\'enyi divergence over an exponential family. We propose to solve this problem with a Bregman proximal gradient algorithm. We propose a sampling-based algorithm to…

While efficient distribution learning is no doubt behind the groundbreaking success of diffusion modeling, its theoretical guarantees are quite limited. In this paper, we provide the first rigorous analysis on approximation and…

As the complexity of learning tasks surges, modern machine learning encounters a new constrained learning paradigm characterized by more intricate and data-driven function constraints. Prominent applications include Neyman-Pearson…

Lack-of-fit testing of a regression model with Berkson measurement error has not been discussed in the literature to date. To fill this void, we propose a class of tests based on minimized integrated square distances between a nonparametric…

Gromov-Wasserstein (GW) distance is a powerful tool for comparing and aligning probability distributions supported on different metric spaces. Recently, GW has become the main modeling technique for aligning heterogeneous data for a wide…

Bregman proximal point algorithm (BPPA) has witnessed emerging machine learning applications, yet its theoretical understanding has been largely unexplored. We study the computational properties of BPPA through learning linear classifiers…

The Bregman-Wasserstein divergence is the optimal transport cost when the underlying cost function is given by a Bregman divergence, and arises naturally in fields such as statistics and machine learning. We establish fundamental properties…

Existing algorithms for subgroup discovery with numerical targets do not optimize the error or target variable dispersion of the groups they find. This often leads to unreliable or inconsistent statements about the data, rendering practical…

Reliably estimating the uncertainty of a prediction throughout the model lifecycle is crucial in many safety-critical applications. The most common way to measure this uncertainty is via the predicted confidence. While this tends to work…

This paper focuses on the Bregman divergence defined by the reciprocal function, called the inverse divergence. For the loss function defined by the monotonically increasing function $f$ and inverse divergence, the conditions for the…

A robust estimation framework for binary regression models is studied, aiming to extend traditional approaches like logistic regression models. While previous studies largely focused on logistic models, we explore a broader class of models…

Binary density ratio estimation (DRE), the problem of estimating the ratio $p_1/p_2$ given their empirical samples, provides the foundation for many state-of-the-art machine learning algorithms such as contrastive representation learning…

Many metric learning tasks, such as triplet learning, nearest neighbor retrieval, and visualization, are treated primarily as embedding tasks where the ultimate metric is some variant of the Euclidean distance (e.g., cosine or Mahalanobis),…

Although Bayesian inference is an immensely popular paradigm among a large segment of scientists including statisticians, most applications consider objective priors and need critical investigations (Efron, 2013, Science). While it has…

Morden deep ensembles technique achieves strong uncertainty estimation performance by going through multiple forward passes with different models. This is at the price of a high storage space and a slow speed in the inference (test) time.…