Related papers: A Partition Function Estimator
A formula which only involves a partition number and elementary functions is derived by applying Burnside's Lemma to the set of idempotent maps from a set to itself. One side involves a summation over a set closely related to the partition…
In contrast with most Monte Carlo integration algorithms, which are used to estimate ratios, the replica gas identities recently introduced by Adib enable the estimation of absolute integrals and partition functions using multiple copies of…
This paper aims at achieving a "good" estimator for the gradient of a function on a high-dimensional space. Often such functions are not sensitive in all coordinates and the gradient of the function is almost sparse. We propose a method for…
We propose a novel method for estimating nonseparable selection models. We show that, for a given selection function, the potential outcome distributions are nonparametrically identified from the selected outcome distributions and can be…
We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…
Cardinality estimation algorithms receive a stream of elements whose order might be arbitrary, with possible repetitions, and return the number of distinct elements. Such algorithms usually seek to minimize the required storage and…
In this paper, we introduce a novel method to generate interpretable regression function estimators. The idea is based on called data-dependent coverings. The aim is to extract from the data a covering of the feature space instead of a…
Random sampling is an essential tool in the processing and transmission of data. It is used to summarize data too large to store or manipulate and meet resource constraints on bandwidth or battery power. Estimators that are applied to the…
A method is proposed for the characterisation of the entropy of cellular structures, based on the compactivity concept for granular packings. Hamiltonian-like volume functions are constructed both in two and in three dimensions, enabling…
We propose a splitting algorithm for solving a system of composite monotone inclusions formulated in the form of the extended set of solutions in real Hilbert spaces. The resluting algorithm is a an extension of the algorithm in [4]. The…
We propose in this paper an exploratory analysis algorithm for functional data. The method partitions a set of functions into $K$ clusters and represents each cluster by a simple prototype (e.g., piecewise constant). The total number of…
With the advent of surveys containing millions to billions of galaxies, it is imperative to develop analysis techniques that utilize the available statistical power. In galaxy clustering, even small sample contamination arising from…
The decision to incorporate cross-validation into validation processes of mathematical models raises an immediate question - how should one partition the data into calibration and validation sets? We answer this question systematically: we…
We evaluate using programmable superconducting flux qubit D-Wave quantum annealers to approximate the partition function of Ising models. We propose the use of two distinct quantum annealer sampling methods: chains of Monte Carlo-like…
This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the…
Although symmetry methods and analysis are a necessary ingredient in every physicist's toolkit, rather less use has been made of combinatorial methods. One exception is in the realm of Statistical Physics, where the calculation of the…
The variant of calculation of functions of set and their application is offered. In particular: the new measure of system of sets generalizing classical concept of a measure is entered; the variation of set that has allowed to construct a…
We present a universal algorithm for the optimal quantum state estimation of an arbitrary finite dimensional system. The algorithm specifies a physically realizable positive operator valued measurement (POVM) on a finite number of…
We derive exact matrix integral representations for different sums over partitions. The characteristic feature of all obtained matrix models is the presence of logarithmic (or, vice versa, exponential) terms in the potential. Our derivation…
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and…