相关论文: Set estimation from reflected Brownian motion
We consider the problem of Bayesian optimization of a one-dimensional Brownian motion in which the $T$ adaptively chosen observations are corrupted by Gaussian noise. We show that as the smallest possible expected cumulative regret and the…
We consider the problem of detecting the locations of targets in the far field by sending probing signals from an antenna array and recording the reflected echoes. Drawing on key concepts from the area of compressive sensing, we use an…
We define several new models for how to define anomalous regions among enormous sets of trajectories. These are based on spatial scan statistics, and identify a geometric region which captures a subset of trajectories which are…
We obtain rates of convergence to stationarity in L^1-Wasserstein distance for a d-dimensional reflected Brownian motion (RBM) in the nonnegative orthant that are explicit in the dimension and the system parameters. The results are then…
The study of motion in animals and robots has been aided by insights from geometric mechanics. In friction dominated systems, a mechanical "connection" can provide a high fidelity mechanical model. The connection is a co-vector (Lie…
Sparse reduced-rank regression is an important tool to uncover meaningful dependence structure between large numbers of predictors and responses in many big data applications such as genome-wide association studies and social media…
We study properties of the random metric space called the Brownian map. For every h>0, we consider the connected components of the complement of the open ball of radius h centered at the root, and we let N(h,r) be the number of those…
Let $\{U^N_t\}_{t\ge 0}$ be a standard Brownian motion on $\mathbb{U}(N)$. For fixed $N\in\mathbb{N}$ and $t>0$, we give explicit bounds on the $L_1$-Wasserstein distance of the empirical spectral measure of $U^N_t$ to both the…
Existing techniques for motion imitation often suffer a certain level of latency due to their computational overhead or a large set of correspondence samples to search. To achieve real-time imitation with small latency, we present a…
Conformal prediction constructs a confidence set for an unobserved response of a feature vector based on previous identically distributed and exchangeable observations of responses and features. It has a coverage guarantee at any nominal…
We develop constrained Bayesian estimation methods for small area problems: those requiring smoothness with respect to similarity across areas, such as geographic proximity or clustering by covariates; and benchmarking constraints,…
This paper continues a study on trajectories of Brownian Motion in a field of soft trap whose radius distribution is unbounded. We show here for both point-to-point and point-to-plane model the volume exponent (the exponent associated to…
Deciding what to sense is a crucial task, made harder by dependencies and by a nonadditive utility function. We develop approximation algorithms for selecting an optimal set of measurements, under a dependency structure modeled by a…
This paper considers an ergodic version of the bounded velocity follower problem, assuming that the decision maker lacks knowledge of the underlying system parameters and must learn them while simultaneously controlling. We propose…
The movement of a particle described by Brownian motion is quantified by a single parameter, $D$, the diffusion constant. The estimation of $D$ from a discrete sequence of noisy observations is a fundamental problem in biological single…
This paper addresses the nonparametric estimation of the drift function over a compact domain for a time-homogeneous diffusion process, based on high-frequency discrete observations from $N$ independent trajectories. We propose a neural…
Consider an multidimensional obliquely reflected Brownian motion in the positive orthant, or, more generally, in a convex polyhedral cone. We find sufficient conditions for existence of a stationary distribution and convergence to this…
The quality of numerically simulated spectra using real-time evolution methods for strongly correlated systems is affected by both the length of simulation time and the system size, limiting resolution in both frequency and momentum. In…
We prove the existence of the reflected diffusion on a complex of an arbitrary size for a large class of planar simple nested fractals. Such a process is obtained as a folding projection of the free Brownian motion from the unbounded…
In this work, we consider the detection of manoeuvring small objects with radars. Such objects induce low signal to noise ratio (SNR) reflections in the received signal. We consider both co-located and separated transmitter/receiver pairs,…