相关论文: Exact Mean Computation in Dynamic Time Warping Spa…

Dynamic simulators are computational models governed by differential equations that evolve over time. They are essential for scientific and engineering applications but remain challenging to emulate because of the unpredictable behavior of…

In this paper we develop the theory of discrete averaging designed to study discrete time dynamical systems defined by iterates of a map. The discrete averaging uses weighted averages over a segment of trajectory to find an autonomous…

We propose two novel numerical schemes for approximate implementation of the dynamic programming~(DP) operation concerned with finite-horizon, optimal control of discrete-time systems with input-affine dynamics. The proposed algorithms…

We propose a novel time series averaging method based on Dynamic Time Warping (DTW). In contrast to previous methods, our algorithm preserves durational information and the distinctive durational features of the sequences due to a simple…

In this paper we provide optimal bounds for fully discrete approximations to finite horizon problems via dynamic programming. We adapt the error analysis in \cite{nos} for the infinite horizon case to the finite horizon case. We prove an a…

The parameter space of dynamical systems arising in applications is often found to be high-dimensional and difficult to explore. We construct a fast algorithm to numerically analyze "quantitative features" of dynamical systems depending on…

Analyzing numerous or long time series is difficult in practice due to the high storage costs and computational requirements. Therefore, techniques have been proposed to generate compact similarity-preserving representations of time series,…

Modern time series analysis requires the ability to handle datasets that are inherently high-dimensional; examples include applications in climatology, where measurements from numerous sensors must be taken into account, or inventory…

Time warping function provides a mathematical representation to measure phase variability in functional data. Recent studies have developed various approaches to estimate optimal warping between functions and provide non-Euclidean models.…

Continuous-time series is essential for different modern application areas, e.g. healthcare, automobile, energy, finance, Internet of things (IoT) and other related areas. Different application needs to process as well as analyse a massive…

Numerous studies have focused on learning and understanding the dynamics of physical systems from video data, such as spatial intelligence. Artificial intelligence requires quantitative assessments of the uncertainty of the model to ensure…

In a way similar to the string-to-string correction problem we address time series similarity in the light of a time-series-to-time-series-correction problem for which the similarity between two time series is measured as the minimum cost…

Stochastic mathematical models are essential tools for understanding and predicting complex phenomena. The purpose of this work is to study the exit times of a stochastic dynamical system-specifically, the mean exit time and the…

A new class of statistical deformable models is introduced to study high-dimensional curves or images. In addition to the standard measurement error term, these deformable models include an extra error term modeling the individual…

The computation of the distance of two time series is time-consuming for any elastic distance function that accounts for misalignments. Among those functions, DTW is the most prominent. However, a recent extensive evaluation has shown that…

We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with…

Computational models of human language often involve combinatorial problems. For instance, a probabilistic parser may marginalize over exponentially many trees to make predictions. Algorithms for such problems often employ dynamic…

Accurate and computationally efficient means for classifying human activities have been the subject of extensive research efforts. Most current research focuses on extracting complex features to achieve high classification accuracy. We…

Time series forecasting has become a critical task due to its high practicality in real-world applications such as traffic, energy consumption, economics and finance, and disease analysis. Recent deep-learning-based approaches have shown…

Despite the rapid progress on research in adversarial robustness of deep neural networks (DNNs), there is little principled work for the time-series domain. Since time-series data arises in diverse applications including mobile health,…