Related papers: Edgeworth Expansion for Semi-hard Triplet Loss

It has become standard for empirical studies to conduct inference robust to cluster dependence and heterogeneity. With a small number of clusters, the normal approximation for the $t$-statistics of regression coefficients may be poor. This…

We study the problem of $(\epsilon,\delta)$-differentially private learning of linear predictors with convex losses. We provide results for two subclasses of loss functions. The first case is when the loss is smooth and non-negative but not…

Given a weakly dependent stationary process, we describe the transition between a Berry-Esseen bound and a second order Edgeworth expansion in terms of the Berry-Esseen characteristic. This characteristic is sharp: We show that Edgeworth…

We use series expansions to study dynamics of equilibrium and non-equilibrium systems on networks. This analytical method enables us to include detailed non-universal effects of the network structure. We show that even low order…

Despite the undeniable progress in visual recognition tasks fueled by deep neural networks, there exists recent evidence showing that these models are poorly calibrated, resulting in over-confident predictions. The standard practices of…

The m-out-of-n bootstrap, originally proposed by Bickel, Gotze, and Zwet (1992), approximates the distribution of a statistic by repeatedly drawing m subsamples (with m much smaller than n) without replacement from an original sample of…

The focal-loss has become a widely used alternative to cross-entropy in class-imbalanced classification problems, particularly in computer vision. Despite its empirical success, a systematic information-theoretic study of the focal-loss…

Concentration of measure has been argued to be the fundamental cause of adversarial vulnerability. Mahloujifar et al. presented an empirical way to measure the concentration of a data distribution using samples, and employed it to find…

For a singular and symmetric discrete memoryless channel with positive dispersion, the third-order term in the normal approximation is shown to be upper bounded by a constant. This finding completes the characterization of the third-order…

Many recent loss functions in deep metric learning are expressed with logarithmic and exponential forms, and they involve margin and scale as essential hyper-parameters. Since each data class has an intrinsic characteristic, several…

Minimizing loss functions is central to machine-learning training. Although first-order methods dominate practical applications, higher-order techniques such as Newton's method can deliver greater accuracy and faster convergence, yet are…

We study asymptotic behaviour of stochastic approximation procedures with three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function.…

We introduce a novel loss function for training deep learning architectures to perform classification. It consists in minimizing the smoothness of label signals on similarity graphs built at the output of the architecture. Equivalently, it…

This paper is the third part of our study started with Cattiaux, Le\'{o}n and Prieur [Stochastic Process. Appl. 124 (2014) 1236-1260; ALEA Lat. Am. J. Probab. Math. Stat. 11 (2014) 359-384]. For some ergodic Hamiltonian systems, we obtained…

I propose a method to fit the probability distribution function (hereafter PDF) of the large scale density field rho, motivated by a Lagrangian version of the continuity equation. It consists in applying the Edgeworth expansion to the…

In this paper, we derive an asymptotic error expansion for the eigenvalue approximations by the lowest order Raviart-Thomas mixed finite element method for the general second order elliptic eigenvalue problems. Extrapolation based on such…

In this work, we study the learning theory of reward modeling with pairwise comparison data using deep neural networks. We establish a novel non-asymptotic regret bound for deep reward estimators in a non-parametric setting, which depends…

In this article, we derive the asymptotic expansion, up to an arbitrary order in theory, for the solution of a two-dimensional elliptic equation with strongly anisotropic diffusion coefficients along different directions, subject to the…

Tight bounds for several symmetric divergence measures are derived in terms of the total variation distance. It is shown that each of these bounds is attained by a pair of 2 or 3-element probability distributions. An application of these…

Most of the non-asymptotic theoretical work in regression is carried out for the square loss, where estimators can be obtained through closed-form expressions. In this paper, we use and extend tools from the convex optimization literature,…