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End-to-end learning of dynamical systems with black-box models, such as neural ordinary differential equations (ODEs), provides a flexible framework for learning dynamics from data without prescribing a mathematical model for the dynamics.…
The paper is devoted to introducing an approach to compute the approximate minimum time function of control problems which is based on reachable set approximation and uses arithmetic operations for convex compact sets. In particular, in…
This paper studies the problem of distributed weighted least-squares (WLS) estimation for an interconnected linear measurement network with additive noise. Two types of measurements are considered: self measurements for individual nodes,…
In the heteroscedastic linear model, the weighted least squares (WLS) estimate of the model coefficients is more efficient than the ordinary least squares (OLS) esti- mate. However, the practical application of WLS is challenging because it…
Many interesting tasks in machine learning and computer vision are learned by optimising an objective function defined as a weighted linear combination of multiple losses. The final performance is sensitive to choosing the correct…
The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous…
In this paper, we consider the robustness of a basic model of a dynamical distribution network. In the first problem, i.e., optimal weight allocation, we minimize the H-inf- norm of the dynamical distribution network subject to allocation…
Real-world machine learning applications often have complex test metrics, and may have training and test data that are not identically distributed. Motivated by known connections between complex test metrics and cost-weighted learning, we…
Numerical modelling of several coupled passive linear dynamical systems (LDS) is considered. Since such component systems may arise from partial differential equations, transfer function descriptions, lumped systems, measurement data, etc.,…
Persistence diagrams are efficient descriptors of the topology of a point cloud. As they do not naturally belong to a Hilbert space, standard statistical methods cannot be directly applied to them. Instead, feature maps (or representations)…
Point-to-point and periodic motions are ubiquitous in the world of robotics. To master these motions, Autonomous Dynamic System (DS) based algorithms are fundamental in the domain of Learning from Demonstration (LfD). However, these…
Analyzing nonlinear systems with stabilizable controlled invariant sets (CISs) requires accurate estimation of their domains of stabilization (DOS) together with associated stabilizing controllers. Despite extensive research, estimating…
In this paper, we study the minimum dominating set (MDS) problem and the minimum total dominating set MTDS) problem which have many applications in real world. We propose a new idea to compute approximate MDS and MTDS. Next, we give an…
We highlight a formal and substantial analogy between Machine Learning (ML) algorithms and discrete dynamical systems (DDS) in relaxation form. The analogy offers a transparent interpretation of the weights in terms of physical…
Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…
The adjoint method, among other sensitivity analysis methods, can fail in chaotic dynamical systems. The result from these methods can be too large, often by orders of magnitude, when the result is the derivative of a long time averaged…
Least-mean squares (LMS) solvers such as Linear / Ridge / Lasso-Regression, SVD and Elastic-Net not only solve fundamental machine learning problems, but are also the building blocks in a variety of other methods, such as decision trees and…
We provide a novel characterization of augmented balancing weights, also known as automatic debiased machine learning (AutoDML). These popular doubly robust or de-biased machine learning estimators combine outcome modeling with balancing…
As one of the recently proposed algorithms for sparse system identification, $l_0$ norm constraint Least Mean Square ($l_0$-LMS) algorithm modifies the cost function of the traditional method with a penalty of tap-weight sparsity. The…
The evolution of images with physics-based dynamics is often spatially localized and nonlinear. A switching linear dynamic system (SLDS) is a natural model under which to pose such problems when the system's evolution randomly switches over…