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Online anomaly detection (OAD) plays a pivotal role in real-time analytics and decision-making for evolving data streams. However, existing methods often rely on costly retraining and rigid decision boundaries, limiting their ability to…
Optimal Transport (OT) is a mathematical framework that first emerged in the eighteenth century and has led to a plethora of methods for answering many theoretical and applied questions. The last decade has been a witness to the remarkable…
Optimal transport (OT) has become exceedingly popular in machine learning, data science, and computer vision. The core assumption in the OT problem is the equal total amount of mass in source and target measures, which limits its…
Computing optimal transport (OT) for general high-dimensional data has been a long-standing challenge. Despite much progress, most of the efforts including neural network methods have been focused on the static formulation of the OT…
State estimation that combines observational data with mathematical models is central to many applications and is commonly addressed through filtering methods, such as ensemble Kalman filters. In this article, we examine the signal-tracking…
In online incremental learning, data continuously arrives with substantial distributional shifts, creating a significant challenge because previous samples have limited replay value when learning a new task. Prior research has typically…
Flow-based Generative Models (FGMs) effectively transform noise into complex data distributions. Incorporating Optimal Transport (OT) to couple noise and data during FGM training has been shown to improve the straightness of flow…
Optimal Transport (OT) theory investigates the cost-minimizing transport map that moves a source distribution to a target distribution. Recently, several approaches have emerged for learning the optimal transport map for a given cost…
Continuous navigation in complex environments is critical for Unmanned Aerial Vehicle (UAV). However, the existing Vision-Language Navigation (VLN) models follow the dead-reckoning, which iteratively updates its position for the next…
Offline Reinforcement Learning (RL) addresses the problem of sequential decision-making by learning optimal policy through pre-collected data, without interacting with the environment. As yet, it has remained somewhat impractical, because…
Modern robotic platforms need a reliable localization system to operate daily beside humans. Simple pose estimation algorithms based on filtered wheel and inertial odometry often fail in the presence of abrupt kinematic changes and wheel…
Recent advancements in sensing and communication facilitate obtaining high-frequency real-time data from various physical systems like power networks, climate systems, biological networks, etc. However, since the data are recorded by…
Offline policy learning (OPL) leverages existing data collected a priori for policy optimization without any active exploration. Despite the prevalence and recent interest in this problem, its theoretical and algorithmic foundations in…
Semi-supervised learning has made remarkable strides by effectively utilizing a limited amount of labeled data while capitalizing on the abundant information present in unlabeled data. However, current algorithms often prioritize aligning…
When learning from streaming data, a change in the data distribution, also known as concept drift, can render a previously-learned model inaccurate and require training a new model. We present an adaptive learning algorithm that extends…
The Kalman filter has been adopted in acoustic echo cancellation due to its robustness to double-talk, fast convergence, and good steady-state performance. The performance of Kalman filter is closely related to the estimation accuracy of…
The optimal predictor for a linear dynamical system (with hidden state and Gaussian noise) takes the form of an autoregressive linear filter, namely the Kalman filter. However, a fundamental problem in reinforcement learning and control…
Lane-level navigation is critical for geographic information systems and navigation-based tasks, offering finer-grained guidance than road-level navigation by standard definition (SD) maps. However, it currently relies on expansive global…
We study the estimation of optimal transport (OT) maps between an arbitrary source probability measure and a log-concave target probability measure. Our contributions are twofold. First, we propose a new evolution equation in the set of…
Optimal transport (OT) provides effective tools for comparing and mapping probability measures. We propose to leverage the flexibility of neural networks to learn an approximate optimal transport map. More precisely, we present a new and…