arXiv subjects

Joaquín Miguez

Publications and source records attributed to Joaquín Miguez.

5 recordsLinked to original sources

arXiv2026

Stochastic stability of master--slave synchronization for a class of PDEs with Burgers-type nonlinearity

We investigate the stochastic stability of master--slave synchronization for a class of nonlinear evolution equations sharing a Burgers-type convective nonlinearity and a polynomial linear differential operator, including the Burgers, Kuramoto--Sivashinsky, Kawahara, Benney--Lin, and Nikolaevskiy equations. Under periodic boundary conditions, each equation is represented through a Fourier truncation of order $K$, yielding a real state of one-sided complex Fourier coefficients, which is coupled to a slave system driven by observed master data. We first establish local exponential stability of the deterministic zero-error synchronization solution under a simple condition on the coupling strength in the slave model. We then introduce observational noise in the coupling signals, which turns the slave system into an Itô diffusion and prevents exact synchronization. Comparing the stochastic synchronization error with the deterministic reference error obtained from noiseless observations, we show that bounded master and reference paths and sufficiently strong scalar coupling yield an $\mathcal O(σ^2)$ mean-square bound on their deviation, together with a tail-probability estimate; the bound becomes time-uniform when the deterministic slave field and its spatial derivative can be bounded uniformly in time. Both results use a Fourier-space norm induced by the physical-space $L^2$-norm, so Parseval's identity transfers the spectral bounds directly to the physical fields. Under additional regularity assumptions on the smoothness of the deterministic master and slave fields, we also obtain a mean-square bound on the stochastic synchronization error with respect to the infinite-dimensional (non-truncated) master system. These analytical results are illustrated by the numerical simulation of two master--slave systems, built around the Kawahara and Nikolaevskiy equations.

math-ph↗

arXiv2025

Gaussian entropic optimal transport: Schrödinger bridges and the Sinkhorn algorithm

Entropic optimal transport problems are regularized versions of optimal transport problems. These models play an increasingly important role in machine learning and generative modelling. For finite spaces, these problems are commonly solved using Sinkhorn algorithm (a.k.a. iterative proportional fitting procedure). However, in more general settings the Sinkhorn iterations are based on nonlinear conditional/conjugate transformations and exact finite-dimensional solutions cannot be computed. This article presents a finite-dimensional recursive formulation of the iterative proportional fitting procedure for general Gaussian multivariate models. As expected, this recursive formulation is closely related to the celebrated Kalman filter and related Riccati matrix difference equations, and it yields algorithms that can be implemented in practical settings without further approximations. We extend this filtering methodology to develop a refined and self-contained convergence analysis of Gaussian Sinkhorn algorithms, including closed form expressions of entropic transport maps and Schrödinger bridges.

stat.ML↗

arXiv2025

Nested importance sampling for Bayesian inference: error bounds and the role of dimension

Many Bayesian inference problems involve high dimensional models for which only a subset of the model variables are of actual interest. All other variables are just nuisance parameters that one would ideally like to integrate out analytically. Unfortunately, such integration is often impossible. There are several computational methods that have been proposed over the past 15 years that replace intractable analytical marginalization by numerical integration, typically using different flavours of importance sampling (IS). Such methods include particle Markov chain Monte Carlo, sequential Monte Carlo squared (SMC$^2$), IS$^2$, nested particle filters, and others. In this paper, we investigate the role of the dimension of the nuisance variables in the error bounds achieved by nested IS methods in Bayesian inference. We prove that, under suitable regularity assumptions on the model, the approximation errors increase at a polynomial (rather than exponential) rate w.r.t. the dimension of the nuisance variables. Our analysis relies on tools from functional analysis and measure theory, and it includes the case of polynomials of degree zero, where the approximation error remains uniformly bounded, even as the dimension of the nuisance variables grows without bound. We also show how the general analysis can be applied to specific classes of models, including linear and Gaussian settings, models with bounded observation functions, and others. These findings improve the current understanding of how the performance of IS techniques scales with dimension in Bayesian inference problems.

stat.CO↗

arXiv2023

Maximum likelihood inference for a class of discrete-time Markov-switching time series models with multiple delays

Autoregressive Markov switching (ARMS) time series models are used to represent real-world signals whose dynamics may change over time. They have found application in many areas of the natural and social sciences, as well as in engineering. In general, inference in this kind of systems involves two problems: (a) detecting the number of distinct dynamical models that the signal may adopt and (b) estimating any unknown parameters in these models. In this paper, we introduce a class of ARMS time series models that includes many systems resulting from the discretisation of stochastic delay differential equations (DDEs). Remarkably, this class includes cases in which the discretisation time grid is not necessarily aligned with the delays of the DDE, resulting in discrete-time ARMS models with real (non-integer) delays. We describe methods for the maximum likelihood detection of the number of dynamical modes and the estimation of unknown parameters (including the possibly non-integer delays) and illustrate their application with an ARMS model of El Niño--southern oscillation (ENSO) phenomenon.

stat.ME↗

arXiv2018

Multiplex decomposition of non-Markovian dynamics and the hidden layer reconstruction problem

Elements composing complex systems usually interact in several different ways and as such the interaction architecture is well modelled by a multiplex network. However often this architecture is hidden, as one usually only has experimental access to an aggregated projection. A fundamental challenge is thus to determine whether the hidden underlying architecture of complex systems is better modelled as a single interaction layer or results from the aggregation and interplay of multiple layers. Here we show that using local information provided by a random walker navigating the aggregated network one can decide in a robust way if the underlying structure is a multiplex or not and, in the former case, to determine the most probable number of hidden layers. As a byproduct, we show that the mathematical formalism also provides a principled solution for the optimal decomposition and projection of complex, non-Markovian dynamics into a Markov switching combination of diffusive modes. We validate the proposed methodology with numerical simulations of both (i) random walks navigating hidden multiplex networks (thereby reconstructing the true hidden architecture) and (ii) Markovian and non-Markovian continuous stochastic processes (thereby reconstructing an effective multiplex decomposition where each layer accounts for a different diffusive mode). We also state and prove two existence theorems guaranteeing that an exact reconstruction of the dynamics in terms of these hidden jump-Markov models is always possible for arbitrary finite-order Markovian and fully non-Markovian processes. Finally, we showcase the applicability of the method to experimental recordings from (i) the mobility dynamics of human players in an online multiplayer game and (ii) the dynamics of RNA polymerases at the single-molecule level.

physics.soc-ph↗