Related papers: Smoothing and parameter estimation by soft-adheren…
Standard maximum likelihood or Bayesian approaches to parameter estimation for stochastic differential equations are not robust to perturbations in the continuous-in-time data. In this paper, we give a rather elementary explanation of this…
Many dynamical systems are subjected to stochastic influences, such as random excitations, noise, and unmodeled behavior. Tracking the system's state and parameters based on a physical model is a common task for which filtering algorithms,…
Conventional recursive filtering approaches, designed for quantifying the state of an evolving uncertain dynamical system with intermittent observations, use a sequence of (i) an uncertainty propagation step followed by (ii) a step where…
A Kalman filter based sequential estimator is presented in the present work. The estimator is integrated in the structure of segregated solvers for the analysis of incompressible flows. This technique provides an augmented flow state…
Testing procedures for assessing specific parametric model forms, or for checking the plausibility of simplifying assumptions, play a central role in the mathematical treatment of the uncertain. No certain answers are obtained by testing…
Filtering is concerned with online estimation of the state of a dynamical system from partial and noisy observations. In applications where the state of the system is high dimensional, ensemble Kalman filters are often the method of choice.…
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…
We propose a new recursive estimator for linear dynamical systems under Gaussian process noise and non-Gaussian measurement noise. Specifically, we develop an approximate maximum a posteriori (MAP) estimator using dynamic programming and…
Many systems for which compressive sensing is used today are dynamical. The common approach is to neglect the dynamics and see the problem as a sequence of independent problems. This approach has two disadvantages. Firstly, the temporal…
In this article, we consider the problem of outlier-robust state estimation where the measurement noise can be correlated. Outliers in data arise due to many reasons like sensor malfunctioning, environmental behaviors, communication…
Data assimilation, defined as the fusion of data with preexisting knowledge, is particularly suited to elucidating underlying phenomena from noisy/insufficient observations. Although this approach has been widely used in diverse fields,…
Constructing confidence intervals for the value of an (unknown) optimal treatment policy is a fundamental problem in causal inference. Insight into the optimal policy value can guide the development of reward-maximizing, individualized…
We consider model selection and estimation for partial spline models and propose a new regularization method in the context of smoothing splines. The regularization method has a simple yet elegant form, consisting of roughness penalty on…
Nonlinear Kalman Filters are powerful and widely-used techniques when trying to estimate the hidden state of a stochastic nonlinear dynamic system. In this paper, we extend the Smart Sampling Kalman Filter (S2KF) with a new point symmetric…
This paper proposes a data-driven framework to learn a finite-dimensional approximation of a Koopman operator for approximating the state evolution of a dynamical system under noisy observations. To this end, our proposed solution has two…
Ensemble transform Kalman filtering (ETKF) data assimilation is often used to combine available observations with numerical simulations to obtain statistically accurate and reliable state representations in dynamical systems. However, it is…
Estimating the state of a dynamical system from partial and noisy observations is a ubiquitous problem in a large number of applications, such as probabilistic weather forecasting and prediction of epidemics. Particle filters are a widely…
Estimating parameters of a diffusion process given continuous-time observations of the process via maximum likelihood approaches or, online, via stochastic gradient descent or Kalman filter formulations constitutes a well-established…
Attaining reliable profile gradients is of utmost relevance for many physical systems. In most situations, the estimation of gradient can be inaccurate due to noise. It is common practice to first estimate the underlying system and then…
In some real world applications, such as spectrometry, functional models achieve better predictive performances if they work on the derivatives of order m of their inputs rather than on the original functions. As a consequence, the use of…