Related papers: Selective information exchange in collaborative cl…
We consider a problem of optimal swarm tracking which can be formulated as a tracking problem for distributions in the Wasserstein space. Optimal solutions to this problem are non-causal and require knowing the time-trajectory of the…
This paper presents an adaptive online distributed optimal control approach that is applicable to optimal planning for very-large-scale robotics systems in highly uncertain environments. This approach is developed based on the optimal mass…
Cooperative driving at isolated intersections attracted great interest and had been well discussed in recent years. However, cooperative driving in multi-intersection road networks remains to be further investigated, because many algorithms…
This paper proposes a data-driven distributionally robust shortest path (DRSP) model where the distribution of the travel time in the transportation network can only be partially observed through a finite number of samples. Specifically, we…
We present a study of the application of a variant of a recently introduced heuristic algorithm for the optimization of transport routes on complex networks to the problem of finding the optimal routes of communication between nodes on…
Mutual information has been successfully adopted in filter feature-selection methods to assess both the relevancy of a subset of features in predicting the target variable and the redundancy with respect to other variables. However,…
We introduce the problem of transporting vector-valued distributions. In this, a salient feature is that mass may flow between vectorial entries as well as across space (discrete or continuous). The theory relies on a first step taken to…
Discriminating between distributions is an important problem in a number of scientific fields. This motivated the introduction of Linear Optimal Transportation (LOT), which embeds the space of distributions into an $L^2$-space. The…
In many applications in statistics and machine learning, the availability of data samples from multiple possibly heterogeneous sources has become increasingly prevalent. On the other hand, in distributionally robust optimization, we seek…
Context detection involves labeling segments of an online stream of data as belonging to different tasks. Task labels are used in lifelong learning algorithms to perform consolidation or other procedures that prevent catastrophic…
This work investigates several aspects related to quantitative stability in optimal transport, as well as uniqueness of the dual transport problem. Our main contributions are as follows. Chapter 1: Observations regarding the quantitative…
Variational problems that involve Wasserstein distances and more generally optimal transport (OT) theory are playing an increasingly important role in data sciences. Such problems can be used to form an examplar measure out of various…
Split conformal prediction provides finite-sample marginal coverage under exchangeability, but this guarantee averages over the random calibration sample. We study instead the law of the calibration-conditional coverage induced by a…
We propose a new approach to measuring the agreement between two oscillatory time series, such as seismic waveforms, and demonstrate that it can be employed effectively in inverse problems. Our approach is based on Optimal Transport theory…
This paper presents a Wasserstein attraction approach for solving dynamic mass transport problems over networks. In the transport problem over networks, we start with a distribution over the set of nodes that needs to be "transported" to a…
We formulate and solve a regression problem with time-stamped distributional data. Distributions are considered as points in the Wasserstein space of probability measures, metrized by the 2-Wasserstein metric, and may represent images,…
In recent years, two prominent paradigms have shaped distributionally robust optimization (DRO), modeling distributional ambiguity through $\phi$-divergences and Wasserstein distances, respectively. While the former focuses on ambiguity in…
Generating samples given a specific label requires estimating conditional distributions. We derive a tractable upper bound of the Wasserstein distance between conditional distributions to lay the theoretical groundwork to learn conditional…
In this paper, we introduce a variant of optimal transport adapted to the causal structure given by an underlying directed graph $G$. Different graph structures lead to different specifications of the optimal transport problem. For…
Word embeddings are high dimensional vector representations of words that capture their semantic similarity in the vector space. There exist several algorithms for learning such embeddings both for a single language as well as for several…