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Dynamic Mode Decomposition (DMD) is a data-driven technique to identify a low dimensional linear time invariant dynamics underlying high-dimensional data. For systems in which such underlying low-dimensional dynamics is time-varying, a…
Because reinforcement learning suffers from a lack of scalability, online value (and Q-) function approximation has received increasing interest this last decade. This contribution introduces a novel approximation scheme, namely the Kalman…
The purpose of this paper is twofold. On a technical side, we propose an extension of the Hausdorff distance from metric spaces to spaces equipped with asymmetric distance measures. Specifically, we focus on the family of Bregman…
Time series remains one of the most challenging modalities in machine learning research. The out-of-distribution (OOD) detection and generalization on time series tend to suffer due to its non-stationary property, i.e., the distribution…
Dynamic programming (DP) is one of the fundamental paradigms in algorithm design. However, many DP algorithms have to fill in large DP tables, represented by two-dimensional arrays, which causes at least quadratic running times and space…
Linear time-periodic (LTP) dynamical systems frequently appear in the modeling of phenomena related to fluid dynamics, electronic circuits, and structural mechanics via linearization centered around known periodic orbits of nonlinear…
Differential Dynamic Programming (DDP) has become a well established method for unconstrained trajectory optimization. Despite its several applications in robotics and controls however, a widely successful constrained version of the…
Stability of persistence diagrams under slight perturbations is a key characteristic behind the validity and growing popularity of topological data analysis in exploring real-world data. Central to this stability is the use of Bottleneck…
The contributions of the paper span theoretical and implementational results. First, we prove that Kd-trees can be extended to spaces in which the distance is measured with an arbitrary Bregman divergence. Perhaps surprisingly, this shows…
Temporal difference (TD) methods constitute a class of methods for learning predictions in multi-step prediction problems, parameterized by a recency factor lambda. Currently the most important application of these methods is to temporal…
Detecting outliers which are grossly different from or inconsistent with the remaining dataset is a major challenge in real-world KDD applications. Existing outlier detection methods are ineffective on scattered real-world datasets due to…
Ultra-wideband (UWB) time-difference-of-arrival (TDOA)-based localization has emerged as a promising, low-cost, and scalable indoor localization solution, which is especially suited for multi-robot applications. However, there is a lack of…
Time Difference of Arrival (TDOA) is widely used in wireless localization systems. Among the enormous approaches of TDOA, high resolution TDOA algorithms have drawn much attention for its ability to resolve closely spaced signal delays in…
Despite the success of deep neural networks (DNNs) for real-world applications over time-series data such as mobile health, little is known about how to train robust DNNs for time-series domain due to its unique characteristics compared to…
We introduce the combinatorial optimization problem Time Disjoint Walks (TDW), which has applications in collision-free routing of discrete objects (e.g., autonomous vehicles) over a network. This problem takes as input a digraph $G$ with…
Distance weighted discrimination (DWD) is a linear discrimination method that is particularly well-suited for classification tasks with high-dimensional data. The DWD coefficients minimize an intuitive objective function, which can solved…
We consider box-constrained integer programs with objective $g(Wx) + c^T x$, where $g$ is a "complicated" function with an $m$ dimensional domain. Here we assume we have $n \gg m$ variables and that $W \in \mathbb Z^{m \times n}$ is an…
High dimension low sample size statistical analysis is important in a wide range of applications. In such situations, the highly appealing discrimination method, support vector machine, can be improved to alleviate data piling at the…
In this paper localization using UWB positioning system and an inertial unit containing a single accelerometer is considered. The main part of the paper describes a novel algorithm for person localization. The algorithm is based on modified…
Diffusion approximation provides weak approximation for stochastic gradient descent algorithms in a finite time horizon. In this paper, we introduce new tools motivated by the backward error analysis of numerical stochastic differential…