Related papers: Perron-Frobenius operator filter for stochastic dy…
Nature has evolved many molecular machines such as kinesin, myosin, and the rotary flagellar motor powered by an ion current from the mitochondria. Direct observation of the step-like motion of these machines with time series from novel…
Stochastic parameterizations are increasingly being used to represent the uncertainty associated with model errors in ensemble forecasting and data assimilation. One of the challenges associated with the use of these parameterizations is…
In this paper we consider the problem of finding the minimizations of the sum of two convex functions and the composition of another convex function with a continuous linear operator. With the idea of coordinate descent, we design a…
This paper contributes to the emerging viewpoint that governing equations for dynamic state estimation, conditioned on the history of noisy measurements, can be viewed as gradient flow on the manifold of joint probability density functions…
Non-Gaussian Bayesian filtering is a core problem in stochastic filtering. The difficulty of the problem lies in parameterizing the state estimates. However the existing methods are not able to treat it well. We propose to use power moments…
This paper concerns the estimation problem of attitude, position, and linear velocity of a rigid-body autonomously navigating with six degrees of freedom (6 DoF). The navigation dynamics are highly nonlinear and are modeled on the matrix…
Parameter inference of dynamical systems is a challenging task faced by many researchers and practitioners across various fields. In many applications, it is common that only limited variables are observable. In this paper, we propose a…
This paper introduces the notion of a filtration-consistent dynamic operator with a floor, by suitably formulating four axioms. It is shown that under some suitable conditions, a filtration-consistent dynamic operator with a continuous…
The filtering equations govern the evolution of the conditional distribution of a signal process given partial, and possibly noisy, observations arriving sequentially in time. Their numerical approximation plays a central role in many…
Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…
Gaussian Processes (GPs) are powerful kernelized methods for non-parameteric regression used in many applications. However, their use is limited to a few thousand of training samples due to their cubic time complexity. In order to scale GPs…
In this paper, we propose a numerical scheme for structured population models defined on a separable and complete metric space. In particular, we consider a generalized version of a transport equation with additional growth and non-local…
We study the linear filtering problem for systems driven by continuous Gaussian processes with memory described by two parameters. The driving processes have the virtue that they possess stationary increments and simple semimartingale…
Computing accurate estimates of the Fourier transform of analog signals from discrete data points is important in many fields of science and engineering. The conventional approach of performing the discrete Fourier transform of the data…
Fermion sampling is to generate probability distribution of a many-body Slater-determinant wavefunction, which is termed "determinantal point process" in statistical analysis. For its inherently-embedded Pauli exclusion principle, its…
This paper considers data-driven chance-constrained stochastic optimization problems in a Bayesian framework. Bayesian posteriors afford a principled mechanism to incorporate data and prior knowledge into stochastic optimization problems.…
Modeled along the truncated approach in Panigrahi (2016), selection-adjusted inference in a Bayesian regime is based on a selective posterior. Such a posterior is determined together by a generative model imposed on data and the selection…
In this paper, we discuss the problem of minimizing the sum of two convex functions: a smooth function plus a non-smooth function. Further, the smooth part can be expressed by the average of a large number of smooth component functions, and…
In this project, we propose to explore the Kalman filter's performance for estimating asset prices. We begin by introducing a stochastic mean-reverting processes, the Ornstein-Uhlenbeck (OU) model. After this we discuss the Kalman filter in…
In this paper, we propose a successive pseudo-convex approximation algorithm to efficiently compute stationary points for a large class of possibly nonconvex optimization problems. The stationary points are obtained by solving a sequence of…