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Traffic flow forecasting is a crucial task in transportation management and planning. The main challenges for traffic flow forecasting are that (1) as the length of prediction time increases, the accuracy of prediction will decrease; (2)…
This article studies the Set-Membership Smoothing (SMSing) problem for non-stochastic Hidden Markov Models. By adopting the mathematical concept of uncertain variables, an optimal SMSing framework is established for the first time. This…
We study the problem of network regression, where one is interested in how the topology of a network changes as a function of Euclidean covariates. We build upon recent developments in generalized regression models on metric spaces based on…
Platooning of vehicles is a promising approach for reducing fuel consumption, increasing vehicle safety, and using road space more efficiently. We consider the important but difficult problem of assigning optimal routes and departure…
This work studies an explicit embedding of the set of probability measures into a Hilbert space, defined using optimal transport maps from a reference probability density. This embedding linearizes to some extent the 2-Wasserstein space,…
Classification of time series signals has become an important construct and has many practical applications. With existing classifiers we may be able to accurately classify signals, however that accuracy may decline if using a reduced…
We propose a simple subsampling scheme for fast randomized approximate computation of optimal transport distances. This scheme operates on a random subset of the full data and can use any exact algorithm as a black-box back-end, including…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
In general, standard necessary optimality conditions cannot be formulated in a straightforward manner for semi-smooth shape optimization problems. In this paper, we consider shape optimization problems constrained by variational…
We continue studies of the uncertainty quantification problem in emission tomographies such as PET or SPECT when additional multimodal data (e.g., anatomical MRI images) are available. To solve the aforementioned problem we adapt the…
Another facet of the elegant link between random processes on graphs and Laplacian-based numerical linear algebra is uncovered: based on random spanning forests, novel Monte-Carlo estimators for graph signal smoothing are proposed. These…
Multi-hypothesis tracking is a flexible and intuitive approach to tracking multiple nearby objects. However, the original formulation of its data association step is widely thought to scale poorly with the number of tracked objects. We…
Ensemble data assimilation is a problem in determining the most likely phase space trajectory of a model of an observed dynamical sys- tem as it receives inputs from measurements passing information to the model. Using methods developed in…
Connected vehicles disseminate detailed data, including their position and speed, at a very high frequency. Such data can be used for accurate real-time analysis, prediction and control of transportation systems. The outstanding challenge…
We consider the problem of estimating how well a model class is capable of fitting a distribution of labeled data. We show that it is often possible to accurately estimate this "learnability" even when given an amount of data that is too…
We address the problems of multi-domain and single-domain regression based on distinct and unpaired labeled training sets for each of the domains and a large unlabeled training set from all domains. We formulate these problems as a Bayesian…
We study the design of sampling trajectories for stable sampling and the reconstruction of bandlimited spatial fields using mobile sensors. The spectrum is assumed to be a symmetric convex set. As a performance metric we use the path…
Stochastic approximation (SA) that involves multiple coupled sequences, known as multiple-sequence SA (MSSA), finds diverse applications in the fields of signal processing and machine learning. However, existing theoretical understandings…
We consider stochastic optimization problems which use observed data to estimate essential characteristics of the random quantities involved. Sample average approximation (SAA) or empirical (plug-in) estimation are very popular ways to use…
Traffic volume is an indispensable ingredient to provide fine-grained information for traffic management and control. However, due to limited deployment of traffic sensors, obtaining full-scale volume information is far from easy. Existing…