arXiv subjects

Federica Milinanni

Publications and source records attributed to Federica Milinanni.

6 recordsLinked to original sources

arXiv2026

Exploiting Exact Conditionals Improves Conditioning: Provably Fast Mixing Time Bounds By Sampling from the Marginal

The problem of sampling from a probability distribution arises in many applications such as posterior sampling in hierarchical Bayesian inverse problems and Gaussian processes for machine learning. Markov chain Monte Carlo (MCMC) algorithms are often used for sampling from a target probability distribution, but implementations can be computationally expensive, especially for large-scale problems. In certain applications, the target distribution naturally factorizes into a lower dimensional marginal distribution and a conditional distribution that allows exact sampling. We describe an MCMC algorithm called MarCo that exploits such a structure and generates a Markov chain via Metropolis-Hastings sampling from the marginal distribution, followed by sampling from the exact conditional distribution. By design, MarCo constructs a Markov chain on the joint space that inherits the convergence behavior of the marginal MCMC algorithm. This provides multiple theoretical and computational advantages. We prove that MarCo can achieve improved mixing time upper bounds compared to direct sampling from the joint distribution. Moreover, compared to one-block methods that also exploit marginal-conditional structure, we use the framework of Peskun-Tierney ordering to show that MarCo has a larger right spectral gap and smaller asymptotic variance, thus leading to superior convergence properties. Numerical results illustrate the performance benefits of MarCo and are provided for various problems, including a semi-blind image deblurring example.

math.ST↗

arXiv2026

Large deviations for Independent Metropolis Hastings and Metropolis-adjusted Langevin algorithm

In this paper, we prove large deviation principles for the empirical measures associated with the Independent Metropolis Hastings (IMH) sampler and the Metropolis-adjusted Langevin Algorithm (MALA). These are the first large deviation results for empirical measures of Markov chains arising from specific Metropolis-Hastings methods on a continuous state space. Moreover, we show that the existing large deviation framework, that we developed in a previous work (Milinanni and Nyquist, 2024), does not cover the Random Walk Metropolis sampler, even in cases when the underlying Markov chain is geometrically ergodic.

math.PR↗

arXiv2025

Large deviation-based tuning schemes for Metropolis-Hastings algorithms

Markov chain Monte Carlo (MCMC) methods are one of the most popular classes of algorithms for sampling from a target probability distribution. A rising trend in recent years consists in analyzing the convergence of MCMC algorithms using tools from the theory of large deviations. In (Milinanni & Nyquist, 2024), a new framework based on this approach has been developed to study the convergence of empirical measures associated with algorithms of Metropolis-Hastings type, a broad and popular sub-class of MCMC methods. The goal of this paper is to leverage these large deviation results to improve the efficiency of Metropolis-Hastings algorithms. Specifically, we use the large deviations rate function (a central object in large deviation theory) to quantify and characterize the algorithms' speed of convergence. We begin by extending the analysis from (Milinanni & Nyquist, 2024), deriving alternative representations of the rate function. Building on this, we establish explicit upper and lower bounds, which we then use to design schemes to tune Metropolis-Hastings algorithms.

math.PR↗

arXiv2025

UQSA -- An R-Package for Uncertainty Quantification and Sensitivity Analysis for Biochemical Reaction Network Models

Biochemical reaction models describing subcellular processes generally come with a large uncertainty. To be able to account for this during the modeling process, we have developed the R-package UQSA, performing uncertainty quantification and sensitivity analysis in an integrated fashion. UQSA is designed for fast sampling of complicated multi-dimensional parameter distributions, using efficient Markov chain Monte Carlo (MCMC) sampling techniques and Vine-copulas to model complicated joint distributions. We perform MCMC sampling both from stochastic and deterministic models, in either likelihood-free or likelihood-based settings. In the likelihood-free case, we use Approximate Bayesian Computation (ABC), while for likelihood-based sampling we provide different algorithms, including the fast geometry-informed algorithm SMMALA (Simplified Manifold Metropolis-Adjusted Langevin Algorithm). The uncertainty quantification can be followed by a variance decomposition-based global sensitivity analysis. We are aiming for biochemical models, but UQSA can be used for any type of reaction networks. The use of Vine-copulas allows us to describe, evaluate, and sample from complicated parameter distributions, as well as adding new datasets in a sequential manner without redoing the previous parameter fit. The code is written in R, with C as a backend to improve speed. We use the SBtab table format for Systems Biology projects for the model description as well as the experimental data. An event system allows the user to model complicated transient input, common within, e.g., neuroscience. UQSA has an extensive documentation with several examples describing different types of models and data. The code has been tested on up to 2000 cores on several nodes on a computing cluster, but we also include smaller examples that can be run on a laptop. Source code: https://github.com/icpm-kth/uqsa

q-bio.QM↗

arXiv2024

Sensitivity Approximation by the Peano-Baker Series

In this paper we develop a new method for numerically approximating sensitivities in parameter-dependent ordinary differential equations (ODEs). Our approach, intended for situations where the standard forward and adjoint sensitivity analyses become too computationally costly for practical purposes, is based on the Peano-Baker series from control theory. Using this series, we construct a representation of the sensitivity matrix $\mathbf{S}$ and, from this representation, a numerical method for approximating $\mathbf{S}$. We prove that, under standard regularity assumptions, the error of our method scales as $\mathcal{O}(Δt^2_{\text{max}})$, where $Δt_{\text{max}}$ is the largest time step used when numerically solving the ODE. We illustrate the performance of the method in several numerical experiments, taken from both the systems biology setting and more classical dynamical systems. The experiments show the sought-after improvement in running time of our method compared to the forward sensitivity approach. In experiments involving a random linear system, the forward approach requires roughly $\sqrt{n}$ longer computational time, where $n$ is the dimension of the parameter space, than our proposed method.

math.NA↗

arXiv2023

A large deviation principle for the empirical measures of Metropolis-Hastings chains

To sample from a given target distribution, Markov chain Monte Carlo (MCMC) sampling relies on constructing an ergodic Markov chain with the target distribution as its invariant measure. For any MCMC method, an important question is how to evaluate its efficiency. One approach is to consider the associated empirical measure and how fast it converges to the stationary distribution of the underlying Markov process. Recently, this question has been considered from the perspective of large deviation theory, for different types of MCMC methods, including, e.g., non-reversible Metropolis-Hastings on a finite state space, non-reversible Langevin samplers, the zig-zag sampler, and parallell tempering. This approach, based on large deviations, has proven successful in analysing existing methods and designing new, efficient ones. However, for the Metropolis-Hastings algorithm on more general state spaces, the workhorse of MCMC sampling, the same techniques have not been available for analysing performance, as the underlying Markov chain dynamics violate the conditions used to prove existing large deviation results for empirical measures of a Markov chain. This also extends to methods built on the same idea as Metropolis-Hastings, such as the Metropolis-Adjusted Langevin Method or ABC-MCMC. In this paper, we take the first steps towards such a large-deviations based analysis of Metropolis-Hastings-like methods, by proving a large deviation principle for the the empirical measures of Metropolis-Hastings chains. In addition, we characterize the rate function and its properties in terms of the acceptance- and rejection-part of the Metropolis-Hastings dynamics.

math.PR↗