Related papers: Interpretable Gradient Descent for Kalman Gain

We present a step by step mathematical derivation of the Kalman filter using two different approaches. First, we consider the orthogonal projection method by means of vector-space optimization. Second, we derive the Kalman filter using…

We propose an online parametric estimation method of stochastic differential equations with discrete observations and misspecified modelling based on online gradient descent. Our study provides uniform upper bounds for the risks of the…

Halls exact variance decomposition [Phys. Rev. A 64, 052103 (2001)] splits the quantum variance of an observable into the ensemble variance of an optimal position based estimate and a residual nonclassical inaccuracy. We evaluate this…

Observability quantification is a key problem in dynamic network sciences. While it has been thoroughly studied for linear systems, observability quantification for nonlinear networks is less intuitive and more cumbersome. One common…

Uncertainty propagation and filtering can be interpreted as gradient flows with respect to suitable metrics in the infinite dimensional manifold of probability density functions. Such a viewpoint has been put forth in recent literature, and…

An observer is an estimator of the state of a dynamical system from noisy sensor measurements. The need for observers is ubiquitous, with applications in fields ranging from engineering to biology to economics. The most widely used observer…

This paper addresses the synthesis of an optimal fixed-gain distributed observer for discrete-time linear systems over wireless sensor networks. The proposed approach targets the steady-state estimation regime and computes fixed observer…

We propose a new robust filtering paradigm considering the situation in which model uncertainty, described through an ambiguity set, is present only in the observations. We derive the corresponding robust estimator, referred to as…

This paper considers the observer design problem for discrete-time nonlinear dynamical systems with sampled measurement data. Earlier, the recently proposed Iteratively Preconditioned Gradient-Descent (IPG) observer, a Newton-type observer,…

Solving large tensor linear systems poses significant challenges due to the high volume of data stored, and it only becomes more challenging when some of the data is missing. Recently, Ma et al. showed that this problem can be tackled using…

Performative distribution shift captures the setting where the choice of which ML model is deployed changes the data distribution. For example, a bank which uses the number of open credit lines to determine a customer's risk of default on a…

Coherent ptychographic imaging experiments often discard over 99.9 % of the flux from a light source to define the coherence of an illumination. Even when coherent flux is sufficient, the stability required during an exposure is another…

In this paper, we propose a non-parametric method for state estimation of high-dimensional nonlinear stochastic dynamical systems, which evolve according to gradient flows with isotropic diffusion. We combine diffusion maps, a manifold…

In the framework of the Keldysh technique, we formulate the nonlinear sigma model for disordered optical media with linear absorption or gain. The effective action for fluctuations of the matrix field about the saddle point acquires an…

Gradient descent methods are fundamental first-order optimization algorithms in both Euclidean spaces and Riemannian manifolds. However, the exact gradient is not readily available in many scenarios. This paper proposes a novel inexact…

We study the Stein Variational Gradient Descent (SVGD) algorithm, which optimises a set of particles to approximate a target probability distribution $\pi\propto e^{-V}$ on $\mathbb{R}^d$. In the population limit, SVGD performs gradient…

Kalman filter is a best linear unbiased state estimator. It is also comprehensible from the point view of the Bayesian estimation. However, this note gives a detailed derivation of Kalman filter from the mutual information perspective for…

Optimization is often cast as a deterministic problem, where the solution is found through some iterative procedure such as gradient descent. However, when training neural networks the loss function changes over (iteration) time due to the…

We use statistical learning methods to construct an adaptive state estimator for nonlinear stochastic systems. Optimal state estimation, in the form of a Kalman filter, requires knowledge of the system's process and measurement uncertainty.…

In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…