Related papers: Time warping with Hellinger elasticity
We propose an adaptive finite element algorithm to approximate solutions of elliptic problems whose forcing data is locally defined and is approximated by regularization (or mollification). We show that the energy error decay is…
To quantify uncertainty, conformal prediction methods are gaining continuously more interest and have already been successfully applied to various domains. However, they are difficult to apply to time series as the autocorrelative structure…
In this paper, we study the problem of locating a predefined sequence of patterns in a time series. In particular, the studied scenario assumes a theoretical model is available that contains the expected locations of the patterns. This…
By some new recursive algorithms, in this paper, we will give some improvements on Waring's problem.
Computing the discrepancy between time series of variable sizes is notoriously challenging. While dynamic time warping (DTW) is popularly used for this purpose, it is not differentiable everywhere and is known to lead to bad local optima…
In this paper, we study several important geometric optimization problems arising in machine learning. First, we revisit the Minimum Enclosing Ball (MEB) problem in Euclidean space $\mathbb{R}^d$. The problem has been extensively studied…
We consider the safety evaluation of discrete time, stochastic systems over a finite horizon. Therefore, we discuss and link probabilistic invariance with reachability as well as reach-avoid problems. We show how to efficiently compute…
In this paper we consider a scenario where there are several algorithms for solving a given problem. Each algorithm is associated with a probability of success and a cost, and there is also a penalty for failing to solve the problem. The…
An important goal in algorithm design is determining the best running time for solving a problem (approximately). For some problems, we know the optimal running time, assuming certain conditional lower bounds. In this work, we study the…
The Huber's criterion is a useful method for robust regression. The adaptive least absolute shrinkage and selection operator (lasso) is a popular technique for simultaneous estimation and variable selection. In the case of small sample size…
Neural networks have achieved remarkable success in time series classification, but their reliance on large amounts of labeled data for training limits their applicability in cold-start scenarios. Moreover, they lack interpretability,…
Temporal graphs are graphs whose topology is subject to discrete changes over time. Given a static underlying graph $G$, a temporal graph is represented by assigning a set of integer time-labels to every edge $e$ of $G$, indicating the…
Adaptivity and local mesh refinement are crucial for the efficient numerical simulation of wave phenomena in complex geometry. Local mesh refinement, however, can impose a tiny time-step across the entire computational domain when using…
In this paper, we derive a practical, general framework for creating adaptive iterative (linearization or splitting) algorithms to solve multi-physics problems. This means that, given an iterative method, we derive \textit{a posteriori}…
This work investigates the finite-horizon optimal covariance steering problem for discrete-time linear systems subject to both additive and multiplicative uncertainties as well as state and input chance constraints. In particular, a…
In real-world, many problems can be formulated as the alignment between two geometric patterns. Previously, a great amount of research focus on the alignment of 2D or 3D patterns, especially in the field of computer vision. Recently, the…
To accelerate kernel methods, we propose a near input sparsity time algorithm for sampling the high-dimensional feature space implicitly defined by a kernel transformation. Our main contribution is an importance sampling method for…
The literature postulates that the dynamic time warping (dtw) distance can cope with temporal variations but stores and processes time series in a form as if the dtw-distance cannot cope with such variations. To address this inconsistency,…
A fast algorithm to study one-dimensional self-gravitating systems, and, more generally, systems that are Lagrangian integrable between collisions, is presented. The algorithm is event-driven, and uses a heap-ordered set of predicted future…
Super-Heisenberg scaling, which scales as $N^{-\beta}$ with $\beta>1$ in terms of the number of particles $N$ or $T^{-\beta}$ in terms of the evolution time $T$, is better than Heisenberg scaling in quantum metrology. It has been proven…