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In this report, we propose a new adaptive time filter algorithm for the unsteady Stokes/Darcy model. First we present a first order ${\theta}$-scheme with the variable time step which is one parameter family of Linear Multi-step methods and…
Accurate uncertainty measurement is a key step to building robust and reliable machine learning systems. Conformal prediction is a distribution-free uncertainty quantification algorithm popular for its ease of implementation, statistical…
In this paper, we consider the time-inhomogeneous nonlinear time series regression for a general class of locally stationary time series. On one hand, we propose sieve nonparametric estimators for the time-varying regression functions which…
We develop a stochastic algorithm for independent component analysis that incorporates multi-trial supervision, which is available in many scientific contexts. The method blends a proximal gradient-type algorithm in the space of invertible…
Stochastic parametrisations are used in weather and climate models to improve the representation of unpredictable unresolved processes. When compared to a deterministic model, a stochastic model represents `model uncertainty', i.e., sources…
The sparse factorization of a large matrix is fundamental in modern statistical learning. In particular, the sparse singular value decomposition and its variants have been utilized in multivariate regression, factor analysis, biclustering,…
We propose a two phase time dependent vehicle routing and scheduling optimization model that identifies the safest routes, as a substitute for the classical objectives given in the literature such as shortest distance or travel time,…
We consider the problem of multivariate location and scatter matrix estimation when the data contain cellwise and casewise outliers. Agostinelli et al. (2015) propose a two-step approach to deal with this problem: first, apply a univariate…
In this paper, we propose a robust Kalman filtering framework for systems with probabilistic uncertainty in system parameters. We consider two cases, namely discrete time systems, and continuous time systems with discrete measurements. The…
Inverse problems are more challenging when only partial data are available in general. In this paper, we propose a two-step approach combining the extended sampling method and the ensemble Kalman filter to reconstruct an elastic rigid…
An extremely common bottleneck encountered in statistical learning algorithms is inversion of huge covariance matrices, examples being in evaluating Gaussian likelihoods for a large number of data points. We propose general parallel…
Causal inference is a fundamental research topic for discovering the cause-effect relationships in many disciplines. However, not all algorithms are equally well-suited for a given dataset. For instance, some approaches may only be able to…
We present a unified probabilistic framework for simultaneous trajectory estimation and planning (STEAP). Estimation and planning problems are usually considered separately, however, within our framework we show that solving them…
Accurate travel time estimation is essential for navigation and itinerary planning. While existing research employs probabilistic modeling to assess travel time uncertainty and account for correlations between multiple trips, modeling the…
We exploit knowledge of linear substructure in the linear-regression Kalman filters (LRKFs) to simplify the problem of moment matching. The theoretical results yield quantifiable and significant computational speedups at no cost of…
Bayesian computation for filtering and forecasting analysis is developed for a broad class of dynamic models. The ability to scale-up such analyses in non-Gaussian, nonlinear multivariate time series models is advanced through the…
We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…
While generally considered computationally expensive, Uncertainty Quantification using Monte Carlo sampling remains beneficial for applications with uncertainties of high dimension. As an extension of the naive Monte Carlo method, the…
An influential step in weather forecasting was the introduction of ensemble forecasts in operational use due to their capability to account for the uncertainties in the future state of the atmosphere. However, ensemble weather forecasts are…
In this paper, we introduce a new approach to constructing unbiased estimators when computing expectations of path functionals associated with stochastic differential equations (SDEs). Our randomization idea is closely related to…