Related papers: Nonlinear Bayesian Filtering with Natural Gradient…
In this paper we revisit a non-linear filter for {\em non-Gaussian} noises that was introduced in [1]. Goggin proved that transforming the observations by the score function and then applying the Kalman Filter (KF) to the transformed…
We consider filtering in high-dimensional non-Gaussian state-space models with intractable transition kernels, nonlinear and possibly chaotic dynamics, and sparse observations in space and time. We propose a novel filtering methodology that…
A stochastic filter uses a series of measurements over time to produce estimates of unknown variables based on a dynamic model. For a quantum system, such an algorithm is provided by a quantum filter, which is also known as a stochastic…
Natural Gradient Descent, a second-degree optimization method motivated by the information geometry, makes use of the Fisher Information Matrix instead of the Hessian which is typically used. However, in many cases, the Fisher Information…
We look at a stochastic time-varying optimization problem and we formulate online algorithms to find and track its optimizers in expectation. The algorithms are derived from the intuition that standard prediction and correction steps can be…
Approximate Bayesian inference methods that scale to very large datasets are crucial in leveraging probabilistic models for real-world time series. Sparse Markovian Gaussian processes combine the use of inducing variables with efficient…
We present a new strategy for filtering high-dimensional multiscale systems characterized by high-order non-Gaussian statistics using observations from leading-order moments. A closed stochastic-statistical modeling framework suitable for…
This paper presents a novel Bayesian strategy for the estimation of smooth signals corrupted by Gaussian noise. The method assumes a smooth evolution of a succession of continuous signals that can have a numerical or an analytical…
To minimize the average of a set of log-convex functions, the stochastic Newton method iteratively updates its estimate using subsampled versions of the full objective's gradient and Hessian. We contextualize this optimization problem as…
This article discusses a partially adapted particle filter for estimating the likelihood of a nonlinear structural econometric state space models whose state transition density cannot be expressed in closed form. The filter generates the…
Data-informed predictive maintenance planning largely relies on stochastic deterioration models. Monitoring information can be utilized to update sequentially the knowledge on time-invariant deterioration model parameters either within an…
Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…
In this work, we consider the problem of steering the first two moments of the uncertain state of an unknown discrete-time stochastic nonlinear system to a given terminal distribution in finite time. Toward that goal, first, a…
We consider the Bayesian optimal filtering problem: i.e. estimating some conditional statistics of a latent time-series signal from an observation sequence. Classical approaches often rely on the use of assumed or estimated transition and…
Bayesian filtering serves as the mainstream framework of state estimation in dynamic systems. Its standard version utilizes total probability rule and Bayes' law alternatively, where how to define and compute conditional probability is…
In this paper, we study the problem of estimating the state of a dynamic state-space system where the output is subject to quantization. We compare some classical approaches and a new development in the literature to obtain the filtering…
Using quasi-Newton methods in stochastic optimization is not a trivial task given the difficulty of extracting curvature information from the noisy gradients. Moreover, pre-conditioning noisy gradient observations tend to amplify the noise.…
Filter methods realize a projection from a superposed quantum state onto a target state, which can be efficient if two states have sufficient overlap. Here we propose a quantum Gaussian filter (QGF) with the filter operator being a Gaussian…
A hybrid particle ensemble Kalman filter is developed for problems with medium non-Gaussianity, i.e. problems where the prior is very non-Gaussian but the posterior is approximately Gaussian. Such situations arise, e.g., when nonlinear…
We study non-linear Bayesian inverse problems arising from semilinear partial differential equations (PDEs) that can be transformed into linear Bayesian inverse problems. We are then able to extend the early stopping for Ensemble…