Related papers: A random map implementation of implicit filters

Many problems in the geophysical sciences demand the ability to calibrate the parameters and predict the time evolution of complex dynamical models using sequentially-collected data. Here we introduce a general methodology for the joint…

Data assimilation leads naturally to a Bayesian formulation in which the posterior probability distribution of the system state, given the observations, plays a central conceptual role. The aim of this paper is to use this Bayesian…

A particle filter is introduced to numerically approximate a solution of the global optimization problem. The theoretical significance of this work comes from its variational aspects: (i) the proposed particle filter is a controlled…

We introduce a probabilistic approach to the LMS filter. By means of an efficient approximation, this approach provides an adaptable step-size LMS algorithm together with a measure of uncertainty about the estimation. In addition, the…

Sampling from distributions of implicitly defined shapes enables analysis of various energy functionals used for image segmentation. Recent work describes a computationally efficient Metropolis-Hastings method for accomplishing this task.…

The aim of this paper is to provide a variational interpretation of the nonlinear filter in continuous time. A time-stepping procedure is introduced, consisting of successive minimization problems in the space of probability densities. The…

For oceanographic applications, probabilistic forecasts typically have to deal with i) high-dimensional complex models, and ii) very sparse spatial observations. In search-and-rescue operations at sea, for instance, the short-term…

In this paper we present a theoretical analysis to understand sparse filtering, a recent and effective algorithm for unsupervised learning. The aim of this research is not to show whether or how well sparse filtering works, but to…

We consider inference for a collection of partially observed, stochastic, interacting, nonlinear dynamic processes. Each process is identified with a label called its unit, and our primary motivation arises in biological metapopulation…

We provide a clear and concise introduction to the subjects of inverse problems and data assimilation, and their inter-relations. The first part of our notes covers inverse problems; this refers to the study of how to estimate unknown model…

In data assimilation, an ensemble provides a way to propagate the probability density of a system described by a nonlinear prediction model. Although a large ensemble size is required for statistical accuracy, the ensemble size is typically…

Understanding the decision-making process of machine learning models provides valuable insights into the task, the data, and the reasons behind a model's failures. In this work, we propose a method that performs inherently interpretable…

A new particle-based sampling and approximate inference method, based on electrostatics and Newton mechanics principles, is introduced with theoretical ground, algorithm design and experimental validation. This method simulates an…

Exact inference for hidden Markov models requires the evaluation of all distributions of interest - filtering, prediction, smoothing and likelihood - with a finite computational effort. This article provides sufficient conditions for exact…

Implicit neural representations are a promising new avenue of representing general signals by learning a continuous function that, parameterized as a neural network, maps the domain of a signal to its codomain; the mapping from spatial…

Randomized linear system solvers have become popular as they have the potential to reduce floating point complexity while still achieving desirable convergence rates. One particularly promising class of methods, random sketching solvers,…

Particle filtering is a numerical Bayesian technique that has great potential for solving sequential estimation problems involving non-linear and non-Gaussian models. Since the estimation accuracy achieved by particle filters improves as…

Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…

A major challenge facing existing sequential Monte-Carlo methods for parameter estimation in physics stems from the inability of existing approaches to robustly deal with experiments that have different mechanisms that yield the results…

Data assimilation, consisting in the combination of a dynamical model with a set of noisy and incomplete observations in order to infer the state of a system over time, involves uncertainty in most settings. Building upon an existing…