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This paper concerns the adaptive control problem for a class of nonlinear stochastic systems in which the state update is given by a nonlinear function of linear dynamics plus additive stochastic noise. Such systems arise in a wide range of…
A recently developed measure-theoretic framework solves a stochastic inverse problem (SIP) for models where uncertainties in model output data are predominantly due to aleatoric (i.e., irreducible) uncertainties in model inputs (i.e.,…
Models are expected to engage in invariance learning, which involves distinguishing the core relations that remain consistent across varying environments to ensure the predictions are safe, robust and fair. While existing works consider…
In this paper, we propose a filtering algorithm for simultaneously estimating the mode, input and state of hidden mode switched linear stochastic systems with unknown inputs. Using a multiple-model approach with a bank of linear input and…
Stochastic Differential Equations (SDEs) serve as a powerful modeling tool in various scientific domains, including systems science, engineering, and ecological science. While the specific form of SDEs is typically known for a given…
We propose an online learning algorithm for a class of machine learning models under a separable stochastic approximation framework. The essence of our idea lies in the observation that certain parameters in the models are easier to…
We introduce a score-filter-enhanced data assimilation framework designed to reduce predictive uncertainty in machine learning (ML) models for data-driven dynamical system forecasting. Machine learning serves as an efficient numerical model…
The equations of complex dynamical systems may not be identified by expert knowledge, especially if the underlying mechanisms are unknown. Data-driven discovery methods address this challenge by inferring governing equations from…
Score-based modeling through stochastic differential equations (SDEs) has provided a new perspective on diffusion models, and demonstrated superior performance on continuous data. However, the gradient of the log-likelihood function, i.e.,…
Simulating parameter-dependent stochastic differential equations (SDEs) presents significant computational challenges, as separate high-fidelity simulations are typically required for each parameter value of interest. Despite the success of…
The Ensemble Score Filter (EnSF) has emerged as a promising approach to leverage score-based diffusion models for solving high-dimensional and nonlinear data assimilation problems. While initial applications of EnSF to the Lorenz-96 model…
The paper studies the problem of filtering a discrete-time linear system observed by a network of sensors. The sensors share a common communication medium to the estimator and transmission is bit and power budgeted. Under the assumption of…
In spite of advances in understanding lazy training, recent work attributes the practical success of deep learning to the rich regime with complex inductive bias. In this paper, we study rich regime training empirically with benchmark…
Sequential Bayesian Filtering aims to estimate the current state distribution of a Hidden Markov Model, given the past observations. The problem is well-known to be intractable for most application domains, except in notable cases such as…
We formulate and analyze an inverse problem using derivatives prices to obtain an implied filtering density on volatility's hidden state. Stochastic volatility is the unobserved state in a hidden Markov model (HMM) and can be tracked using…
Experimental data is often affected by uncontrolled variables that make analysis and interpretation difficult. For spatiotemporal systems, this problem is further exacerbated by their intricate dynamics. Modern machine learning methods are…
One of the most well-established applications of machine learning is in deciding what content to show website visitors. When observation data comes from high-velocity, user-generated data streams, machine learning methods perform a…
We develop a variational Bayes approach for dynamic variable selection in high-dimensional regression models with time-varying parameters and predictors that exhibit a predefined group structure. Through comprehensive simulation studies, we…
We introduce a new version of deep state-space models (DSSMs) that combines a recurrent neural network with a state-space framework to forecast time series data. The model estimates the observed series as functions of latent variables that…
Vision-based imitation learning has enabled impressive robotic manipulation skills, but its reliance on object appearance while ignoring the underlying 3D scene structure leads to low training efficiency and poor generalization. To address…