Related papers: Translation invariance, exponential sums, and Wari…
The estimation of a covariance matrix from an insufficient amount of data is one of the most common problems in fields as diverse as multivariate statistics, wireless communications, signal processing, biology, learning theory and finance.…
By systematically applying ten inequivalent two-part relations between hypergeometric sums 3F2(1) to the published database of all such sums, 66 new sums are obtained. Many results extracted from the literature are shown to be special cases…
When the data do not conform to the hypothesis of a known sampling-variance, the fitting of a constant to a set of measured values is a long debated problem. Given the data, fitting would require to find what measurand value is the most…
Continuous dually epi-translation invariant valuations on convex functions are characterized in terms of the Fourier-Laplace transform of the associated Goodey-Weil distributions. This description is used to obtain integral representations…
When dealing with difficult inverse problems such as inverse rendering, using Monte Carlo estimated gradients to optimise parameters can slow down convergence due to variance. Averaging many gradient samples in each iteration reduces this…
Transfer learning aims at building robust prediction models by transferring knowledge gained from one problem to another. In the semantic Web, learning tasks are enhanced with semantic representations. We exploit their semantics to augment…
We establish effective mean-value estimates for a wide class of multiplicative arithmetic functions, thereby providing (essentially optimal) quantitative versions of Wirsing's classical estimates and extending those of Hal\'asz. Several…
We establish a rate of convergence of the two scale expansion (in the sense of homogenization theory) of the solution to a highly oscillatory elliptic partial differential equation with random coefficients that are a perturbation of…
As machine learning applications grow increasingly ubiquitous and complex, they face an increasing set of requirements beyond accuracy. The prevalent approach to handle this challenge is to aggregate a weighted combination of requirement…
Bayesian posterior inference is prevalent in various machine learning problems. Variational inference provides one way to approximate the posterior distribution, however its expressive power is limited and so is the accuracy of resulting…
This paper explores some sufficient conditions for the enhanced solvability of strong vector equilibrium problems, which can be established via a variational approach. Enhanced solvability here means existence of solutions, which are strong…
There have been several efforts to extend distributional semantics beyond individual words, to measure the similarity of word pairs, phrases, and sentences (briefly, tuples; ordered sets of words, contiguous or noncontiguous). One way to…
For Paley-Wiener functions on weighted combinatorial finite or infinite graphs we develop a weighted sampling theory in which samples are defined as inner products with weight functions (measuring devices). Three reconstruction methods are…
This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…
We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…
We introduce a method to measure uncertainty in large language models. For tasks like question answering, it is essential to know when we can trust the natural language outputs of foundation models. We show that measuring uncertainty in…
In this paper we consider a multiparametric version of Wolfgang Schmidt and Leonard Summerer's parametric geometry of numbers. We apply this approach in two settings: the first one concerns weighted Diophantine approximation, the second one…
In a variety of scientific applications we wish to characterize a physical system using measurements or observations. This often requires us to solve an inverse problem, which usually has non-unique solutions so uncertainty must be…
We prove upper and lower bounds for certain sums of products of fractional parts by using majoring and minorizing functions from Fourier analysis. In special cases the upper bounds are sharp if there exist counterexamples to the Littlewood…
We prove strong estimates for averages of shifted convolution sums consisting of quadratic twists of $\mathrm{GL}_{2}$ $L$-functions. The key input involves the circle method together with standard tools such as Vorono\u{\i}, quadratic…