Related papers: The Bregman-Tweedie Classification Model

List-wise learning to rank methods are considered to be the state-of-the-art. One of the major problems with these methods is that the ambiguous nature of relevance labels in learning to rank data is ignored. Ambiguity of relevance labels…

We develop a unifying framework for Bayesian nonparametric regression to study the rates of contraction with respect to the integrated $L_2$-distance without assuming the regression function space to be uniformly bounded. The framework is…

Loss functions are widely used to compare several competing forecasts. However, forecast comparisons are often based on mismeasured proxy variables for the true target. We introduce the concept of exact robustness to measurement error for…

Valiant's (2007) model of evolvability models the evolutionary process of acquiring useful functionality as a restricted form of learning from random examples. Linear threshold functions and their various subclasses, such as conjunctions…

Due to its linear complexity, naive Bayes classification remains an attractive supervised learning method, especially in very large-scale settings. We propose a sparse version of naive Bayes, which can be used for feature selection. This…

Exponential families are statistical models which are the workhorses in statistics, information theory, and machine learning among others. An exponential family can either be normalized subtractively by its cumulant or free energy function…

We describe the underlying probabilistic interpretation of alpha and beta divergences. We first show that beta divergences are inherently tied to Tweedie distributions, a particular type of exponential family, known as exponential…

In the applications of signal processing and data analytics, there is a wide class of non-convex problems whose objective function is freed from the common global Lipschitz continuous gradient assumption (e.g., the nonnegative matrix…

Leveraging a transferability estimation metric facilitates the non-trivial challenge of selecting the optimal model for the downstream task from a pool of pre-trained models. Most existing metrics primarily focus on identifying the…

While deep neural networks are highly performant and successful in a wide range of real-world problems, estimating their predictive uncertainty remains a challenging task. To address this challenge, we propose and implement a loss function…

The linearized Bregman iterations (LBreI) and its variants have received considerable attention in signal/image processing and compressed sensing. Recently, LBreI has been extended to a larger class of nonconvex functions, along with…

We propose EBLIME to explain black-box machine learning models and obtain the distribution of feature importance using Bayesian ridge regression models. We provide mathematical expressions of the Bayesian framework and theoretical outcomes…

We propose a model-based lifelong reinforcement-learning approach that estimates a hierarchical Bayesian posterior distilling the common structure shared across different tasks. The learned posterior combined with a sample-based Bayesian…

When function approximation is used, solving the Bellman optimality equation with stability guarantees has remained a major open problem in reinforcement learning for decades. The fundamental difficulty is that the Bellman operator may…

The convex conjugate (i.e., the Legendre transform) of Type II error probability (volume) as a function of Type I error probability (volume) is determined for the hypothesis testing problem with randomized detectors. The derivation relies…

Most high-dimensional estimation and prediction methods propose to minimize a cost function (empirical risk) that is written as a sum of losses associated to each data point. In this paper we focus on the case of non-convex losses, which is…

We introduce a new Bayesian multi-class support vector machine by formulating a pseudo-likelihood for a multi-class hinge loss in the form of a location-scale mixture of Gaussians. We derive a variational-inference-based training objective…

Bregman divergences $D_\phi$ are a class of divergences parametrized by a convex function $\phi$ and include well known distance functions like $\ell_2^2$ and the Kullback-Leibler divergence. There has been extensive research on algorithms…

Classic subdifferentials in variational analysis may fail to fully represent the Bregman proximal operator in the absence of convexity. In this paper, we fill this gap by introducing the left and right \emph{Bregman level proximal…

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…