Related papers: A new method for fast computing unbiased estimator…
Clustering is one of the most important tools for analysis of large datasets, and perhaps the most popular clustering algorithm is Lloyd's algorithm for $k$-means. This algorithm takes $n$ vectors $V=[v_1,\dots,v_n]\in\mathbb{R}^{d\times…
We provide an unifying polynomial expression giving moments in terms of cumulants, and viceversa, holding in the classical, boolean and free setting. This is done by using a symbolic treatment of Abel polynomials. As a by-product, we show…
We analyze a systematic algorithm for the exact computation of the current cumulants in stochastic nonequilibrium systems, recently discussed in the framework of full counting statistics for mesoscopic systems. This method is based on…
We present multivariate unbiased estimators for second, third, and fourth order cumulants $C_2(x,y)$, $C_3(x,y,z)$, and $C_4(x,y,z,w)$. Many relevant new estimators are derived for cases where some variables are average-free or pairs of…
We develop an algorithm for sampling from the unitary invariant random matrix ensembles. The algorithm is based on the representation of their eigenvalues as a determinantal point process whose kernel is given in terms of orthogonal…
Comparing the differences in outcomes (that is, in "dependent variables") between two subpopulations is often most informative when comparing outcomes only for individuals from the subpopulations who are similar according to "independent…
A novel sequential inferential method for Bayesian dynamic generalised linear models is presented, addressing both univariate and multivariate $k$-parametric exponential families. It efficiently handles diverse responses, including…
Cumulants linearize convolution of measures. We use a formula of Good to define noncommutative cumulants in a very general setting.It turns out that the essential property needed is exchangeability of random variables. Roughly speaking the…
The aim of this article is to define some new families of the special numbers. These numbers provide some further motivation for computation of combinatorial sums involving binomial coefficients and the Euler kind numbers of negative order.…
Focusing on the discrete probabilistic setting we generalize the combinatorial definition of cumulants to L-cumulants. This generalization keeps all the desired properties of the classical cumulants like semi-invariance and vanishing for…
This article aims to reinforce the broad applicability of the umbral approach to address complex mathematical challenges and contribute to various scientific and engineering endeavors. The umbral methods are used to reformulate the…
Spherical k-means is a widely used clustering algorithm for sparse and high-dimensional data such as document vectors. While several improvements and accelerations have been introduced for the original k-means algorithm, not all easily…
We introduce a novel, fast, and efficient generative model built upon scattering covariances, the most recent iteration of the scattering transforms statistics. This model is designed to augment by several orders of magnitude the number of…
Algorithms with unitary oracles can be nested, which makes them extremely versatile. An example is the phase estimation algorithm used in many candidate algorithms for quantum speed-up. The search for new quantum algorithms benefits from…
The Classical Tukey-Huber Contamination Model (CCM) is a usual framework to describe the mechanism of outliers generation in robust statistics. In a data set with $n$ observations and $p$ variables, under the CCM, an outlier is a unit, even…
We develop a stochastic calculus that makes it easy to capture a variety of predictable transformations of semimartingales such as changes of variables, stochastic integrals, and their compositions. The framework offers a unified treatment…
We propose a novel sampling framework for inference in probabilistic models: an active learning approach that converges more quickly (in wall-clock time) than Markov chain Monte Carlo (MCMC) benchmarks. The central challenge in…
Recent advances in neural recording technology allow simultaneously recording action potentials from hundreds to thousands of neurons in awake, behaving animals. However, characterizing spike patterns in the resulting data, and linking…
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…
We prove the following conjecture, raised by Aaronson and Ambainis in 2008: Let $f:\{-1,1\}^n \rightarrow [-1,1]$ be a multilinear polynomial of degree $d$. Then there exists a variable $x_i$ whose influence on $f$ is at least…