Related papers: Fourier Analysis of Iterative Algorithms
This paper investigates statistical inference for noisy matrix completion in a semi-supervised model when auxiliary covariates are available. The model consists of two parts. One part is a low-rank matrix induced by unobserved latent…
Bayesian approaches provide a principled solution to the exploration-exploitation trade-off in Reinforcement Learning. Typical approaches, however, either assume a fully observable environment or scale poorly. This work introduces the…
Boolean networks are powerful mathematical tools for modeling the qualitative dynamics of genetic regulation. Yet inferred models often generate spurious attractors that lack biological viability. In this paper, we propose a parsimonious…
Quantum computers provide a super-exponential speedup for performing a Fourier transform over the symmetric group, an ability for which practical use cases have remained elusive so far. In this work, we leverage this ability to unlock…
In this manuscript a factor graph approach is employed to investigate the recursive filtering problem for a mixed linear/nonlinear state-space model, i.e. for a model whose state vector can be partitioned in a linear state variable…
Recursive Bayesian inference, in which posterior beliefs are updated in light of accumulating data, is a tool for implementing Bayesian models in applications with streaming and/or very large data sets. As the posterior of one iteration…
Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose…
We introduce an efficient way, called Newton algorithm, to study arbitrary ideals in C[[x,y]], using a finite succession of Newton polygons. We codify most of the data of the algorithm in a useful combinatorial object, the Newton tree. For…
The probability that two randomly selected phylogenetic trees of the same size are isomorphic is found to be asymptotic to a decreasing exponential modulated by a polynomial factor. The number of symmetrical nodes in a random phylogenetic…
Inference for partially observed Markov process models has been a longstanding methodological challenge with many scientific and engineering applications. Iterated filtering algorithms maximize the likelihood function for partially observed…
An iterative randomness extraction algorithm which generalized the Von Neumann's extraction algorithm is detailed, analyzed and implemented in standard C++. Given a sequence of independently and identically distributed biased Bernoulli…
Bayesian filtering approximates the true underlying behavior of a time-varying system by inverting an explicit generative model to convert noisy measurements into state estimates. This process typically requires either storage, inversion,…
Fourier phase retrieval is the problem of reconstructing a signal given only the magnitude of its Fourier transformation. Optimization-based approaches, like the well-established Gerchberg-Saxton or the hybrid input output algorithm,…
We develop the theory of meta-iteration trees, that is, iteration trees whose base "model" is itself an ordinary iteration tree. We prove a comparison theorem for meta-iteration strategies parallel to the one for ordinary iteration…
Boolean matrix factorisation aims to decompose a binary data matrix into an approximate Boolean product of two low rank, binary matrices: one containing meaningful patterns, the other quantifying how the observations can be expressed as a…
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. The second paper is concerned with simultaneous approximation to functions and their…
The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical…
This work demonstrates a methodology for using deep learning to discover simple, practical criteria for classifying matrices based on abstract algebraic properties. By combining a high-performance neural network with explainable AI (XAI)…
The Asymptotic Iteration Method (AIM) is a technique for solving analytically and approximately the linear second-order differential equation, especially the eigenvalue problems that frequently appear in theoretical and mathematical…
We study the problem of recovering the structure underlying large Gaussian graphical models or, more generally, partial correlation graphs. In high-dimensional problems it is often too costly to store the entire sample covariance matrix. We…