Related papers: Dimensionality Collapse: Optimal Measurement Selec…
A dimension reduction method based on the "Nonlinear Level set Learning" (NLL) approach is presented for the pointwise prediction of functions which have been sparsely sampled. Leveraging geometric information provided by the Implicit…
Timely detection of abrupt anomalies is crucial for real-time monitoring and security of modern systems producing high-dimensional data. With this goal, we propose effective and scalable algorithms. Proposed algorithms are nonparametric as…
Ordinal classification has been widely applied in many high-stakes applications, e.g., medical imaging and diagnosis, where reliable uncertainty quantification (UQ) is essential for decision making. Conformal prediction (CP) is a general UQ…
This paper presents a solution for efficiently and accurately solving separable least squares problems with multiple datasets. These problems involve determining linear parameters that are specific to each dataset while ensuring that the…
This paper describes recursive algorithms for state estimation of linear dynamical systems when measurements are noisy with unknown bias and/or outliers. For situations with noisy and biased measurements, algorithms are proposed that…
In this work, we consider the notion of "criterion collapse," in which optimization of one metric implies optimality in another, with a particular focus on conditions for collapse into error probability minimizers under a wide variety of…
We address the problem of determining optimal sensor precisions for estimating the states of linear time-varying discrete-time stochastic dynamical systems, with guaranteed bounds on the estimation errors. This is performed in the Kalman…
We propose Comprehensive Robust Dynamic Mode Decomposition (CR-DMD), a novel framework that robustifies the entire DMD process - from mode extraction to dimensional reduction - against mixed noise. Although standard DMD widely used for…
Dynamic mode decomposition (DMD) is a widely used data-driven algorithm for predicting the future states of dynamical systems. However, its standard formulation often struggles with poor long-term predictive accuracy. To address this…
This paper presents a new deep learning-based framework for robust nonlinear estimation and control using the concept of a Neural Contraction Metric (NCM). The NCM uses a deep long short-term memory recurrent neural network for a global…
We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…
This paper tackles the problem of selecting among several linear estimators in non-parametric regression; this includes model selection for linear regression, the choice of a regularization parameter in kernel ridge regression, spline…
Dynamic mode decomposition (DMD) is a widely used data-driven algorithm for predicting the future states of dynamical systems. However, its standard formulation often struggles with poor long-term predictive accuracy. To address this…
In this paper we consider the numerical approximation of infinite horizon problems via the dynamic programming approach. The value function of the problem solves a Hamilton-Jacobi-Bellman (HJB) equation that is approximated by a fully…
We derive a parallel sampling algorithm for computational inverse problems that present an unknown linear forcing term and a vector of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of…
We provide a solution to the problem of receding horizon control for stochastic discrete-time systems with bounded control inputs and imperfect state measurements. For a suitable choice of control policies, we show that the finite-horizon…
Consider a problem where a set of feasible observations are provided by an expert and a cost function is defined that characterizes which of the observations dominate the others and are hence, preferred. Our goal is to find a set of linear…
Dimensionality reduction (DR) is often used as a preprocessing step in classification, but usually one first fixes the DR mapping, possibly using label information, and then learns a classifier (a filter approach). Best performance would be…
We consider change-point estimation in a sequence of high-dimensional signals given noisy observations. Classical approaches to this problem such as the filtered derivative method are useful for sequences of scalar-valued signals, but they…
For linear systems, many data-driven control methods rely on the behavioral framework, using historical data of the system to predict the future trajectories. However, measurement noise introduces errors in predictions. When the noise is…