Related papers: UMVUE-Type Estimators under Bregman Losses

We revisit resampling procedures for error estimation in binary classification in terms of U-statistics. In particular, we exploit the fact that the error rate estimator involving all learning-testing splits is a U-statistic. Thus, it has…

Ensembles are a straightforward, remarkably effective method for improving the accuracy,calibration, and robustness of models on classification tasks; yet, the reasons that underlie their success remain an active area of research. We build…

Bayesian models provide a framework for probabilistic modelling of complex datasets. However, many of such models are computationally demanding especially in the presence of large datasets. On the other hand, in sensor network applications,…

In knowledge graph embedding, the theoretical relationship between the softmax cross-entropy and negative sampling loss functions has not been investigated. This makes it difficult to fairly compare the results of the two different loss…

We derive an unbiased estimator for expectations over discrete random variables based on sampling without replacement, which reduces variance as it avoids duplicate samples. We show that our estimator can be derived as the…

We address the problem of aggregating an ensemble of predictors with known loss bounds in a semi-supervised binary classification setting, to minimize prediction loss incurred on the unlabeled data. We find the minimax optimal predictions…

Bregman divergences are a class of distance-like comparison functions which play fundamental roles in optimization, statistics, and information theory. One important property of Bregman divergences is that they cause two useful formulations…

Supervised learning requires the specification of a loss function to minimise. While the theory of admissible losses from both a computational and statistical perspective is well-developed, these offer a panoply of different choices. In…

Let $\bx_j = \btheta +\bep_j, j=1,...,n$, be observations of an unknown parameter $\btheta$ in a Euclidean or separable Hilbert space $\scrH$, where $\bep_j$ are noises as random elements in $\scrH$ from a general distribution. We study the…

This paper considers reparameterization invariant Bayesian point estimates and credible regions of model parameters for scientific inference and communication. The effect of intrinsic loss function choice in Bayesian intrinsic estimates and…

We study adaptive estimation and inference in ill-posed linear inverse problems defined by conditional moment restrictions. Existing regularized estimators such as Regularized DeepIV (RDIV) require prior knowledge of the smoothness of the…

We develop a novel and general framework for reduced-bias $M$-estimation from asymptotically unbiased estimating functions. The framework relies on an empirical approximation of the bias by a function of derivatives of estimating function…

Training energy-based models (EBMs) on discrete spaces is challenging because sampling over such spaces can be difficult. We propose to train discrete EBMs with energy discrepancy (ED), a novel type of contrastive loss functional which only…

Estimating causal effects of continuous treatments is a common problem in practice, for example, in studying average dose-response functions. Classical analyses typically assume that all confounders are fully observed, whereas in real-world…

In various applications of regression analysis, in addition to errors in the dependent observations also errors in the predictor variables play a substantial role and need to be incorporated in the statistical modeling process. In this…

The Bregman proximal mapping and Bregman-Moreau envelope are traditionally studied for functions defined on the entire space $\mathbb{R}^n$, even though these constructions depend only on the values of the function within (the interior of)…

In this paper, we prove a Brezis-Merle type inequality for $k$-convex functions vanishing on the boundary. As an application, we establish an Alexandrov-Bakelman-Pucci type estimate for the intermediate Hessian equation. Furthermore, we…

We develop the first general-purpose estimator for infinite-horizon dynamic discrete choice models whose estimation problem, after pre-computation, is unencumbered by large systems of linear equations -- either imposed as constraints, or…

Density-power-based divergences are known to provide robust inference procedures against outliers, and their extensions have been widely studied. A characteristic of successful divergences is that the estimation problem can be reduced to…

We construct a density estimator and an estimator of the distribution function in the uniform deconvolution model. The estimators are based on inversion formulas and kernel estimators of the density of the observations and its derivative.…