Related papers: Principled model selection for stochastic dynamics

Species sampling processes have long served as the fundamental framework for modeling random discrete distributions and exchangeable sequences. However, data arising from distinct but related sources require a broader notion of…

A new method of deriving comparative statics information using generalized compensated derivatives is presented which yields constraint-free semidefiniteness results for any differentiable, constrained optimization problem. More generally,…

Stochastic differential equations have been an important tool in modeling complex financial relations, equipped with the possibility of being multidimensional to better oversee complexities inherent in finance. This multidimensionality,…

Sparse functional/longitudinal data have attracted widespread interest due to the prevalence of such data in social and life sciences. A prominent scenario where such data are routinely encountered are accelerated longitudinal studies,…

We address the problem of estimating unknown model parameters and state variables in stochastic reaction processes when only sparse and noisy measurements are available. Using an asymptotic system size expansion for the backward equation we…

We explore efficient estimation of statistical quantities, particularly rare event probabilities, for stochastic reaction networks. Consequently, we propose an importance sampling (IS) approach to improve the Monte Carlo (MC) estimator…

The macroscopic behavior of dissipative stochastic partial differential equations usually can be described by a finite dimensional system. This article proves that a macroscopic reduced model may be constructed for stochastic…

Conditional Density Estimation (CDE) models deal with estimating conditional distributions. The conditions imposed on the distribution are the inputs of the model. CDE is a challenging task as there is a fundamental trade-off between model…

We propose probabilistic Shapley inference (PSI), a novel probabilistic framework to model and infer sufficient statistics of feature attributions in flexible predictive models, via latent random variables whose mean recovers Shapley…

Set prediction is about learning to predict a collection of unordered variables with unknown interrelations. Training such models with set losses imposes the structure of a metric space over sets. We focus on stochastic and underdefined…

The reconstruction and inference of stochastic dynamical systems from data is a fundamental task in inverse problems and statistical learning. While surrogate modeling advances computational methods to approximate these dynamics, standard…

Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD)…

This thesis is about the study of complex systems through simple models. Our work evidences the relevance of this kind of modeling in science, which provides us with a better understanding of nature at minimum cost. The fundamentals tools…

This document introduces basics in data preparation, feature selection and learning basics for high energy physics tasks. The emphasis is on feature selection by principal component analysis, information gain and significance measures for…

We describe a stochastic, dynamical system capable of inference and learning in a probabilistic latent variable model. The most challenging problem in such models - sampling the posterior distribution over latent variables - is proposed to…

Ordinary differential equations (ODEs) are foundational in modeling intricate dynamics across a gamut of scientific disciplines. Yet, a possibility to represent a single phenomenon through multiple ODE models, driven by different…

The Poisson process is the most elementary continuous-time stochastic process that models a stream of repeating events. It is uniquely characterised by a single parameter called the rate. Instead of a single value for this rate, we here…

Dynamical models underpin our ability to understand and predict the behavior of natural systems. Whether dynamical models are developed from first-principles derivations or from observational data, they are predicated on our choice of state…

There has been an ever-increasing interest in multidisciplinary research on representing and reasoning with imperfect data. Possibilistic networks present one of the powerful frameworks of interest for representing uncertain and imprecise…

A general Bayesian framework for model selection on random network models regarding their features is considered. The goal is to develop a principle Bayesian model selection approach to compare different fittable, not necessarily nested,…