Related papers: A new method for fast computing unbiased estimator…
This paper develops forecasting methodology and application of new classes of dynamic models for time series of non-negative counts. Novel univariate models synthesise dynamic generalized linear models for binary and conditionally Poisson…
Efficient sampling from a classical Gibbs distribution is an important computational problem with applications ranging from statistical physics over Monte Carlo and optimization algorithms to machine learning. We introduce a family of…
Based on the Beylkin-Cramer summation rule, we introduce a new fast algorithm that enable us to explore the high order statistics efficiently in large data sets. Central to this technique is to make decomposition both of fields and…
Consumption of magic states promotes the stabilizer model of computation to universal quantum computation. Here, we propose three different classical algorithms for simulating such universal quantum circuits, and characterize them by…
A new empirical Bayes approach to variable selection in the context of generalized linear models is developed. The proposed algorithm scales to situations in which the number of putative explanatory variables is very large, possibly much…
The cumulant expansion is used to estimate generalized Lyapunov exponents of the random-frequency harmonic oscillator. Three stochastic processes are considered: Gaussian white noise, Ornstein-Uhlenbeck, and Poisson shot noise. In some…
Clustering with fast algorithms large samples of high dimensional data is an important challenge in computational statistics. Borrowing ideas from MacQueen (1967) who introduced a sequential version of the $k$-means algorithm, a new class…
Bayesian models offer great flexibility for clustering applications---Bayesian nonparametrics can be used for modeling infinite mixtures, and hierarchical Bayesian models can be utilized for sharing clusters across multiple data sets. For…
We propose a novel algebraic framework for treating probability distributions represented by their cumulants such as the mean and covariance matrix. As an example, we consider the unsupervised learning problem of finding the subspace on…
We propose a recursive method for the computation of the cumulants of self-exciting point processes of Hawkes type, based on standard combinatorial tools such as Bell polynomials. This closed-form approach is easier to implement on…
An alternative parametric description for discrete random variables, called muculants, is proposed. In contrast to cumulants, muculants are based on the Fourier series expansion, rather than on the Taylor series expansion, of the logarithm…
We present an iterative method to solve the multipartite quantum state estimation problem. We demonstrate convergence for any informationally complete set of generalized quantum measurements in every finite dimension. Our method exhibits…
We introduce polynomial couplings, a generalization of probabilistic couplings, to develop an algorithm for the computation of equivalence relations which can be interpreted as a lifting of probabilistic bisimulation to polynomial…
We introduce a new strategy for coupling the parallel in time (parareal) iterative methodology with multiscale integrators. Following the parareal framework, the algorithm computes a low-cost approximation of all slow variables in the…
A new cluster analysis method, $K$-quantiles clustering, is introduced. $K$-quantiles clustering can be computed by a simple greedy algorithm in the style of the classical Lloyd's algorithm for $K$-means. It can be applied to large and…
In this paper we propose an alternative to the coupling of Berkes, Liu and Wu [1] to obtain strong approximations for partial sums of dependent sequences. The main tool is a new Rosen-thal type inequality expressed in terms of the coupling…
In this paper we consider a variety of procedures for numerical statistical inference in the family of univariate and multivariate stable distributions. In connection with univariate distributions (i) we provide approximations by finite…
Shapley values have emerged as a widely accepted and trustworthy tool, grounded in theoretical axioms, for addressing challenges posed by black-box models like deep neural networks. However, computing Shapley values encounters exponential…
The two-parameter Macdonald polynomials are a central object of algebraic combinatorics and representation theory. We give a Markov chain on partitions of k with eigenfunctions the coefficients of the Macdonald polynomials when expanded in…
A novel multinomial theorem for commutative idempotents is shown to lead to new results about the moments, central moments, factorial moments, and their generating functions for any random variable $X = \sum_{i} Y_i $ expressible as a sum…