Related papers: Rearranging Edgeworth-Cornish-Fisher Expansions
We generalize McDiarmid's inequality for functions with bounded differences on a high probability set, using an extension argument. Those functions concentrate around their conditional expectations. We further extend the results to…
It is known that evolution strategies in continuous domains might not converge in the presence of noise. It is also known that, under mild assumptions, and using an increasing number of resamplings, one can mitigate the effect of additive…
We propose a modification of a maximum likelihood procedure for tuning parameter values in models, based upon the comparison of their output to field data. Our methodology, which uses polynomial approximations of the sample space to…
We introduce a new parametrization for the two-parameter species sampling model with {\it finite} but {\it random} number of different species recently introduced in Gnedin (2010a). We show the reparametrization yields a representation in…
Background: Extensions of single-reference (SR) energy-density-functionals (EDFs) to multi-reference (MR) applications involve using the generalized Wick theorem (GWT), which leads to singular energy kernels that cannot be properly…
Data normalization is crucial in machine learning, usually performed by subtracting the mean and dividing by standard deviation, or by rescaling to a fixed range. In copula theory, popular in finance, there is used normalization to…
In this work, standard methods of the mixed thin-shell foramlism are refined using the framework of Colombeau's theory of generalized functions. To this end, systematic use is made of smooth generalized functions, in particular…
Classical Edgeworth expansions provide asymptotic correction terms to the Central Limit Theorem (CLT) up to an order that depends on the number of moments available. In this paper, we provide subsequent correction terms beyond those given…
Completely randomized experiments have been the gold standard for drawing causal inference because they can balance all potential confounding on average. However, they may suffer from unbalanced covariates for realized treatment…
We examine the large-order behaviour of a recently proposed renormalization-group-improved expansion of the Adler function in perturbative QCD, which sums in an analytically closed form the leading logarithms accessible from…
Despite its well-known shortcomings, $k$-means remains one of the most widely used approaches to data clustering. Current research continues to tackle its flaws while attempting to preserve its simplicity. Recently, the \textit{power…
The rearrangement inequalities of Hardy-Littlewood and Riesz say that certain integrals involving products of two or three functions increase under symmetric decreasing rearrangement. It is known that these inequalities extend to integrands…
In the absence of prior knowledge, ordinal embedding methods obtain new representation for items in a low-dimensional Euclidean space via a set of quadruple-wise comparisons. These ordinal comparisons often come from human annotators, and…
Using a renormalization approach, we study the asymptotic limit distribution of the maximum value in a set of independent and identically distributed random variables raised to a power q(n) that varies monotonically with the sample size n.…
A large class of statistics can be formulated as smooth functions of sample means of random vectors. In this paper, we propose a general partial Cram\'{e}r's condition (GPCC) and apply it to establish the validity of the Edgeworth expansion…
Data augmentation is an effective regularization strategy to alleviate the overfitting, which is an inherent drawback of the deep neural networks. However, data augmentation is rarely considered for point cloud processing despite many…
Owing to the edge preserving ability and low computational cost of the total variation (TV), variational models with the TV regularization have been widely investigated in the field of multiplicative noise removal. The key points of the…
Evaluation of likelihood functions for cosmological large scale structure data sets (including CMB, galaxy redshift surveys, etc.) naturally involves marginalization, i.e., integration, over an unknown underlying random signal field.…
We present and analyze a novel sparse polynomial technique for the simultaneous approximation of parameterized partial differential equations (PDEs) with deterministic and stochastic inputs. Our approach treats the numerical solution as a…
In this paper we present a tractable approach for regularizing randomly placed points, by splitting them into two subsets: the first is generated by means of the Mat\'ern hard-core point process, while the remaining points constitute the…