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When classical particle filtering algorithms are used for maximum likelihood parameter estimation in nonlinear state-space models, a key challenge is that estimates of the likelihood function and its derivatives are inherently noisy. The…

This paper addresses the problem of learning linear dynamical systems from noisy observations. In this setting, existing algorithms either yield biased parameter estimates or have large sample complexities. We resolve these issues by…

Nonlinear regression analysis is a popular and important tool for scientists and engineers. In this article, we introduce theories and methods of nonlinear regression and its statistical inferences using the frequentist and Bayesian…

In this paper, the problem of state estimation, in the context of both filtering and smoothing, for nonlinear state-space models is considered. Due to the nonlinear nature of the models, the state estimation problem is generally intractable…

All discretized numerical models contain modelling errors - this reality is amplified when reduced-order models are used. The ability to accurately approximate modelling errors informs statistics on model confidence and improves…

Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…

Distant and weak supervision allow to obtain large amounts of labeled training data quickly and cheaply, but these automatic annotations tend to contain a high amount of errors. A popular technique to overcome the negative effects of these…

Many real-world optimization problems contain parameters that are unknown before deployment time, either due to stochasticity or to lack of information (e.g., demand or travel times in delivery problems). A common strategy in such cases is…

While model selection is a well-studied topic in parametric and nonparametric regression or density estimation, selection of possibly high-dimensional nuisance parameters in semiparametric problems is far less developed. In this paper, we…

We here introduce a novel classification approach adopted from the nonlinear model identification framework, which jointly addresses the feature selection and classifier design tasks. The classifier is constructed as a polynomial expansion…

Motivated by the maneuvering target tracking with sensors such as radar and sonar, this paper considers the joint and recursive estimation of the dynamic state and the time-varying process noise covariance in nonlinear state space models.…

Based on neural network and adaptive subspace approximation method, we propose a new machine learning method for solving partial differential equations. The neural network is adopted to build the basis of the finite dimensional subspace.…

We develop a unified framework for automatic debiased machine learning (autoDML) for inference on a broad class of statistical parameters. The framework applies to any smooth functional of a nonparametric M-estimand, defined as the…

Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…

The representation of functions by artificial neural networks depends on a large number of parameters in a non-linear fashion. Suitable parameters of these are found by minimizing a 'loss functional', typically by stochastic gradient…

Scientific knowledge expands by observing the world, hypothesizing some theories about it, and testing them against collected data. When those theories take the form of statistical models, statistical analyses are involved in the process of…

In this work, we develop a simple algorithm for semi-supervised regression. The key idea is to use the top eigenfunctions of integral operator derived from both labeled and unlabeled examples as the basis functions and learn the prediction…

Analysis of non-asymptotic estimation error and structured statistical recovery based on norm regularized regression, such as Lasso, needs to consider four aspects: the norm, the loss function, the design matrix, and the noise model. This…

Optimization problems with the objective function in the form of weighted sum and linear equality constraints are considered. Given that the number of local cost functions can be large as well as the number of constraints, a stochastic…

In simulations of multiscale dynamical systems, not all relevant processes can be resolved explicitly. Taking the effect of the unresolved processes into account is important, which introduces the need for paramerizations. We present a…