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Explicit formulas for the mean and variance of linear stochastic differential equations are derived in terms of an exponential matrix. This result improved a previous one by means of which the mean and variance are expressed in terms of a…
We introduce a new discrepancy score between two distributions that gives an indication on their similarity. While much research has been done to determine if two samples come from exactly the same distribution, much less research…
We present difference schemes for stochastic transport equations with low-regularity velocity fields. We establish $L^2$ stability and convergence of the difference approximations under conditions that are less strict than those required…
We study the problem of mismatched likelihood ratio test. We analyze the type-\RNum{1} and \RNum{2} error exponents when the actual distributions generating the observation are different from the distributions used in the test. We derive…
Structured prediction is used in areas such as computer vision and natural language processing to predict structured outputs such as segmentations or parse trees. In these settings, prediction is performed by MAP inference or, equivalently,…
We present a new non-parametric statistic, called the weighed $\ell_2$ divergence, based on empirical distributions for sequential change detection. We start by constructing the weighed $\ell_2$ divergence as a fundamental building block…
Learning from label proportions (LLP) aims at learning an instance-level classifier with label proportions in grouped training data. Existing deep learning based LLP methods utilize end-to-end pipelines to obtain the proportional loss with…
Low discrepancy point sets have been widely used as a tool to approximate continuous objects by discrete ones in numerical processes, for example in numerical integration. Following a century of research on the topic, it is still unclear…
This paper studies expurgated exponents for joint source-channel coding of discrete memoryless sources and channels under i.i.d. random coding. We show that a two-class partitioning of source sequences, where the codeword distribution…
In this paper we extend the well-known L-Shaped method to solve two-stage stochastic programming problems with decision-dependent uncertainty. The method is based on a novel, unifying, formulation and on distribution-specific optimality and…
Error estimation is given for a regularized Shannon's sampling formulae, which was found to be accurate and robust for numerically solving partial differential equations.
The theory of two projections is utilized to study two-component Gibbs samplers. Through this theory, previously intractable problems regarding the asymptotic variances of two-component Gibbs samplers are reduced to elementary matrix…
Knowing if a model will generalize to data 'in the wild' is crucial for safe deployment. To this end, we study model disagreement notions that consider the full predictive distribution - specifically disagreement based on Hellinger…
In discrepancy minimization problems, we are given a family of sets $\mathcal{S} = \{S_1,\dots,S_m\}$, with each $S_i \in \mathcal{S}$ a subset of some universe $U = \{u_1,\dots,u_n\}$ of $n$ elements. The goal is to find a coloring $\chi :…
This brief, aimed at practitioners, offers an analysis of the effect of sampling-time jitter, i. e., the error produced by execution-time inaccuracies. We propose reinterpreting jitter-afflicted linear time-invariant systems through…
We investigate Learning from Label Proportions (LLP), a partial information setting where examples in a training set are grouped into bags, and only aggregate label values in each bag are available. Despite the partial observability, the…
The leptonic QED radiative corrections are calculated in the next-to-leading log approximation ${\cal O}[\alpha^2 \ln(Q^2/m_e^2)]$ for unpolarized deeply inelastic $ep$--scattering in the case of mixed variables. The corrections are…
The paper is split in two parts: in the first part, we construct the exact likelihood for a discretely observed rough differential equation, driven by a piecewise linear path. In the second part, we use this likelihood in order to construct…
This paper studies the asymptotic behavior of penalized spline estimates of derivatives. In particular, we show that simply differentiating the penalized spline estimator of the mean regression function itself to estimate the corresponding…
We prove two Large deviations principles (LDP) in the zone of moderate deviation probabilities. First we establish LDP for the conditional distributions of moderate deviations of empirical bootstrap measures given empirical probability…