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Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…
Irregular functional data in which densely sampled curves are observed over different ranges pose a challenge for modeling and inference, and sensitivity to outlier curves is a concern in applications. Motivated by applications in…
Efficient and accurate state estimation is essential for the optimal management of the future smart grid. However, to meet the requirements of deploying the future grid at a large scale, the state estimation algorithm must be able to…
State estimation constitutes a core task in monitoring, supervision, and control of dynamic systems. This paper proposes a data-driven framework for the design of state observers for descriptor systems. Necessary and sufficient conditions…
Many statistical estimators are defined as the fixed point of a data-dependent operator, with estimators based on minimizing a cost function being an important special case. The limiting performance of such estimators depends on the…
A generic out-of-sample error estimate is proposed for robust $M$-estimators regularized with a convex penalty in high-dimensional linear regression where $(X,y)$ is observed and $p,n$ are of the same order. If $\psi$ is the derivative of…
This paper develops a general asymptotic theory of series estimators for spatial data collected at irregularly spaced locations within a sampling region $R_n \subset \mathbb{R}^d$. We employ a stochastic sampling design that can flexibly…
Estimating the values of unknown parameters from corrupted measured data faces a lot of challenges in ill-posed problems. In such problems, many fundamental estimation methods fail to provide a meaningful stabilized solution. In this work,…
Accurate platform localization is an integral component of most robotic systems. As these robotic systems become more ubiquitous, it is necessary to develop robust state estimation algorithms that are able to withstand novel and…
In this paper, a first sample-based formulation of the recently considered population observers, or ensemble observers, which estimate the state distribution of dynamic populations from measurements of the output distribution is…
Sampling is often a necessary evil to reduce the processing and storage costs of distributed tracing. In this work, we describe a scalable and adaptive sampling approach that can preserve events of interest better than the widely used…
Continuous-time multi-state survival models can be used to describe health-related processes over time. In the presence of interval-censored times for transitions between the living states, the likelihood is constructed using transition…
This paper addresses the problem of resilient state estimation and attack reconstruction for bounded-error nonlinear discrete-time systems with nonlinear observations/ constraints, where both sensors and actuators can be compromised by…
Impulsive systems are a very flexible class of systems that can be used to represent switched and sampled-data systems. We propose to extend here the previously obtained results on deterministic impulsive systems to the stochastic setting.…
We study the problem of robust mean estimation and introduce a novel Hamming distance-based measure of distribution shift for coordinate-level corruptions. We show that this measure yields adversary models that capture more realistic…
Given a random sample of points from some unknown distribution, we propose a new data-driven method for estimating its probability support $S$. Under the mild assumption that $S$ is $r$-convex, the smallest $r$-convex set which contains the…
The need to estimate a particular quantile of a distribution is an important problem which frequently arises in many computer vision and signal processing applications. For example, our work was motivated by the requirements of many…
This paper proposes a data-driven set-based estimation algorithm for a class of nonlinear systems with polynomial nonlinearities. Using the system's input-output data, the proposed method computes a set that guarantees the inclusion of the…
We consider an additive partially linear framework for modelling massive heterogeneous data. The major goal is to extract multiple common features simultaneously across all sub-populations while exploring heterogeneity of each…
Existing methods for the estimation of stable distribution parameters, such as those based on sample quantiles, sample characteristic functions or maximum likelihood generally assume an independent sample. Little attention has been paid to…