Related papers: Computation-Aware Kalman Filtering and Smoothing
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…
With extreme weather events becoming more common, the risk posed by surface water flooding is ever increasing. In this work we propose a model, and associated Bayesian inference scheme, for generating probabilistic (high-resolution…
We introduce a class of quadratic support (QS) functions, many of which play a crucial role in a variety of applications, including machine learning, robust statistical inference, sparsity promotion, and Kalman smoothing. Well known…
Recent years have seen a huge development in spatial modelling and prediction methodology, driven by the increased availability of remote-sensing data and the reduced cost of distributed-processing technology. It is well known that…
The Gaussian process state-space models (GPSSMs) represent a versatile class of data-driven nonlinear dynamical system models. However, the presence of numerous latent variables in GPSSM incurs unresolved issues for existing variational…
We present a framework to train a structured prediction model by performing smoothing on the inference algorithm it builds upon. Smoothing overcomes the non-smoothness inherent to the maximum margin structured prediction objective, and…
In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…
Advances in compact sensing devices mounted on satellites have facilitated the collection of large spatio-temporal datasets with coordinates. Since such datasets are often incomplete and noisy, it is useful to create the prediction surface…
Gaussian process emulators of computationally expensive computer codes provide fast statistical approximations to model physical processes. The training of these surrogates depends on the set of design points chosen to run the simulator.…
The focus of modern biomedical studies has gradually shifted to explanation and estimation of joint effects of high dimensional predictors on disease risks. Quantifying uncertainty in these estimates may provide valuable insight into…
This paper tackles the challenge of parameter calibration in stochastic models, particularly in scenarios where the likelihood function is unavailable in an analytical form. We introduce a gradient-based simulated parameter estimation…
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…
We combine high-dimensional factor models with fractional integration methods and derive models where nonstationary, potentially cointegrated data of different persistence is modelled as a function of common fractionally integrated factors.…
State estimation is a fundamental problem in control and signal processing, for which the Kalman Filter provides an optimal solution under linear dynamics, Gaussian noise, and known noise covariances. However, these assumptions often fail…
We introduce a scalable Gaussian process (GP) framework with deep product kernels for data-driven learning of parametrized spatio-temporal fields over fixed or parameter-dependent domains. The proposed framework learns a continuous…
The Gaussian graphical model (GGM) incorporates an undirected graph to represent the conditional dependence between variables, with the precision matrix encoding partial correlation between pair of variables given the others. To achieve…
By building upon the recent theory that established the connection between implicit generative modeling (IGM) and optimal transport, in this study, we propose a novel parameter-free algorithm for learning the underlying distributions of…
This paper presents a comprehensive algorithm for fitting generative models whose likelihood, moments, and other quantities typically used for inference are not analytically or numerically tractable. The proposed method aims to provide a…
This work introduces an algorithm for state estimation on manifolds within the framework of the Kalman filter. Its primary objective is to provide a methodology enabling the evaluation of the precision of existing Kalman filter variants…
For linear and Gaussian state space models parametrized by $\theta_0 \in \Theta \subset \mathbb{R}^r, r \geq 1$ corresponding to the vector of parameters of the model, the Kalman filter gives exactly the solution for the optimal filtering…