Related papers: Learning minimal representations of stochastic pro…
Stochastic variational inference makes it possible to approximate posterior distributions induced by large datasets quickly using stochastic optimization. The algorithm relies on the use of fully factorized variational distributions.…
Typically, real-world stochastic processes are not easy to analyze. In this work we study the representation of any stochastic process as a memoryless innovation process triggering a dynamic system. We show that such a representation is…
We propose a variational autoencoder (VAE) approach for parameter estimation in nonlinear mixed-effects models based on ordinary differential equations (NLME-ODEs) using longitudinal data from multiple subjects. In moderate dimensions,…
Using variational autoencoders trained on known physics processes, we develop a one-sided threshold test to isolate previously unseen processes as outlier events. Since the autoencoder training does not depend on any specific new physics…
Statistical physics courses typically employ abstract language that describes objects too small to be seen, making the topic challenging for students to understand. In this work, we introduce a simple experiment that allows conceptualizing…
Modeling the temporal behavior of data is of primordial importance in many scientific and engineering fields. Baseline methods assume that both the dynamic and observation equations follow linear-Gaussian models. However, there are many…
In recent years, machine learning models, chiefly deep neural networks, have revealed suited to learn accurate energy-density functionals from data. However, problematic instabilities have been shown to occur in the search of ground-state…
Forecasting costs is now a front burner in empirical economics. We propose an unconventional tool for stochastic prediction of future expenses based on the individual (micro) developments of recorded events. Consider a firm, enterprise,…
In the wild, we often encounter collections of sequential data such as electrocardiograms, motion capture, genomes, and natural language, and sequences may be multichannel or symbolic with nonlinear dynamics. We introduce a new method to…
We consider initial value problems of nonlinear dynamical systems, which include physical parameters. A quantity of interest depending on the solution is observed. A discretisation yields the trajectories of the quantity of interest in many…
We apply recent methods in stochastic data analysis for discovering a set of few stochastic variables that represent the relevant information on a multivariate stochastic system, used as input for artificial neural networks models for air…
Stochastic approximation algorithm is a useful technique which has been exploited successfully in probability theory and statistics for a long time. The step sizes used in stochastic approximation are generally taken to be deterministic and…
Inference and prediction under partial knowledge of a physical system is challenging, particularly when multiple confounding sources influence the measured response. Explicitly accounting for these influences in physics-based models is…
Learning high-level causal representations together with a causal model from unstructured low-level data such as pixels is impossible from observational data alone. We prove under mild assumptions that this representation is however…
We present a new algorithm to optimize distributions defined implicitly by parameterized stochastic diffusions. Doing so allows us to modify the outcome distribution of sampling processes by optimizing over their parameters. We introduce a…
Data taken from observations of the natural world or laboratory measurements often depend on parameters which can vary in unexpected ways. In this paper we demonstrate how machine learning can be leveraged to detect changes in global…
We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete…
Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…
Automated scientific discovery aims to improve scientific understanding through machine learning. A central approach in this field is symbolic regression, which uses genetic programming or sparse regression to learn interpretable…
Stochastic processes generated by non-stationary distributions are difficult to represent with conventional models such as Gaussian processes. This work presents Recurrent Autoregressive Flows as a method toward general stochastic process…