Collecting and aggregating information from several probability measures or histograms is a fundamental task in machine learning. One of the popular solution methods for this task is to compute the barycenter of the probability measures under the Wasserstein metric. However, approximating the Wasserstein barycenter is numerically challenging becaus...
In recent years, various state of the art autonomous vehicle systems and architectures have been introduced. These methods include planners that depend on high-definition (HD) maps and models that learn an autonomous agent's controls in an end-to-end fashion. While end-to-end models are geared towards solving the scalability constraints from HD map...
Given a location-based social network, how to find the communities that are highly relevant to query users and have top overall scores in multiple attributes according to user preferences? Typically, in the face of such a problem setting, we can model the network as a multi-attributed road-social network, in which each user is linked with location ...
Motivated by the application to German interest rates, we propose a timevarying autoregressive model for short and long term prediction of time series that exhibit a temporary non-stationary behavior but are assumed to mean revert in the long run. We use a Bayesian formulation to incorporate prior assumptions on the mean reverting process in the mo...
Federated learning (FL) is an emerging, privacy-preserving machine learning paradigm, drawing tremendous attention in both academia and industry. A unique characteristic of FL is heterogeneity, which resides in the various hardware specifications and dynamic states across the participating devices. Theoretically, heterogeneity can exert a huge infl...
In this paper, we consider robust optimization problems in high dimensions. Because a real-world dataset may contain significant noise or even specially crafted samples from some attacker, we are particularly interested in the optimization problems with arbitrary (and potentially adversarial) outliers. We focus on two fundamental optimization probl...
Suppose that $(Z_n)_{n\geq0}$ is a supercritical branching process in independent and identically distributed random environment. We study the positive tail function of the scaled growth rate for $(Z_n)_{n\geq0}$ and establish an Hoeffding type inequality.
Emerging autonomous vehicles (AV) can either supplement the public transportation (PT) system or compete with it. This study examines the competitive perspective where both AV and PT operators are profit-oriented with dynamic adjustable supply strategies under five regulatory structures regarding whether the AV operator is allowed to change the fle...
We investigate a heat engine under an adiabatic (Thouless) pumping process. In this process, the extracted work and lower bound on dissipated availability are characterized by a vector potential and a Riemannian metric tensor, respectively. We derive a trade-off relation between the power and effective efficiency. We also explicitly calculate the t...
The aim of this work is to investigate the qualitative behaviour of a financial dynamical system which contains a time delay. We investigate the dynamic response of this system of which variables are interest rate, investment demand, price index and average profit margin. We perform a stability analysis at the fixed points and show that the system ...
