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We prove equidistribution at shrinking scales for the monochromatic ensemble on a compact Riemannian manifold of any dimension. This ensemble on an arbitrary manifold takes a slowly growing spectral window in order to synthesize a random function. With hig ...
This paper investigates the effect of combination policies on the performance of adaptive social learning in non-stationary environments. By analyzing the relation between the error probability and the underlying graph topology, we prove that in the slow a ...
We propose a statistically optimal approach to construct data-driven decisions for stochastic optimization problems. Fundamentally, a data-driven decision is simply a function that maps the available training data to a feasible action. It can always be exp ...
Model-based methods in autonomous driving and advanced driving assistance gain importance in research and development due to their potential to contribute to higher road safety. Parameters of vehicle models, however, are hard to identify precisely or they ...
Many research questions involve time-to-event outcomes that can be prevented from occurring due to competing events. In these settings, we must be careful about the causal interpretation of classical statistical estimands. In particular, estimands on the h ...
The aim of this work is to provide bounds connecting two probability measures of the same event using Rényi α-Divergences and Sibson’s α-Mutual Information, a generalization of respectively the Kullback-Leibler Divergence and Shannon’s Mutual ...
Path integrals play a crucial role in describing the dynamics of physical systems subject to classical or quantum noise. In fact, when correctly normalized, they express the probability of transition between two states of the system. In this work, we show ...
Service-level requirements play a crucial role in eliminating stock-outs in a production pipeline. However, delivering a specific service level can become an unattainable goal given the various uncertainties influencing both the production pipeline and cus ...
Consider the surface quasi-geostrophic equation with random diffusion, white in time. We show global existence and uniqueness in high probability for the associated Cauchy problem satisfying a Gevrey type bound. This article is inspired by a recent work of ...
We present the design of a motion planning algorithm that ensures safety for an autonomous vehicle. In particular, we consider a multimodal distribution over uncertainties; for example, the uncertain predictions of future trajectories of surrounding vehicl ...