Related papers: Efficient Probabilistic Collision Detection for No…

We study the approximability of general convex sets in $\mathbb{R}^n$ by intersections of halfspaces, where the approximation quality is measured with respect to the standard Gaussian distribution $N(0,I_n)$ and the complexity of an…

Agent behavior is arguably the greatest source of uncertainty in trajectory planning for autonomous vehicles. This problem has motivated significant amounts of work in the behavior prediction community on learning rich distributions of the…

This work presents a probabilistic deep neural network that combines LiDAR point clouds and RGB camera images for robust, accurate 3D object detection. We explicitly model uncertainties in the classification and regression tasks, and…

It has recently been shown that many of the existing quasi-Newton algorithms can be formulated as learning algorithms, capable of learning local models of the cost functions. Importantly, this understanding allows us to safely start…

Many motion planning algorithms for automated driving require estimating the probability of collision (POC) to account for uncertainties in the measurement and estimation of the motion of road users. Common POC estimation techniques often…

Locating a target is key in many applications, namely in high-stakes real-world scenarios, like detecting humans or obstacles in vehicular networks. In scenarios where precise statistics of the measurement noise are unavailable,…

For solving large-scale non-convex problems, we propose inexact variants of trust region and adaptive cubic regularization methods, which, to increase efficiency, incorporate various approximations. In particular, in addition to approximate…

Gaussian mixture filters for nonlinear systems usually rely on severe approximations when calculating mixtures in the prediction and filtering step. Thus, offline approximations of noise densities by Gaussian mixture densities to reduce the…

In a previous paper (gr-qc/0105100) we derived a set of near-optimal signal detection techniques for gravitational wave detectors whose noise probability distributions contain non-Gaussian tails. The methods modify standard methods by…

Accurate noise modelling is important for training of deep learning reconstruction algorithms. While noise models are well known for traditional imaging techniques, the noise distribution of a novel sensor may be difficult to determine a…

We consider the problem of trajectory planning in an environment comprised of a set of obstacles with uncertain locations. While previous approaches model the uncertainties with a prescribed Gaussian distribution, we consider the realistic…

This paper proposes a stochastic gradient descent method with an adaptive Gaussian noise term for the global minimization of nearly convex functions, which are nonconvex and possess multiple strict local minimizers. The noise term,…

Bayesian learning provides a unified skeleton to solve the electrophysiological source imaging task. From this perspective, existing source imaging algorithms utilize the Gaussian assumption for the observation noise to build the likelihood…

We present a method for guaranteed collision detection with toleranced motions. The basic idea is to consider the motion as a curve in the 12-dimensional space of affine displacements, endowed with an object-oriented Euclidean metric, and…

Providing non-conservative uncertainty quantification for function estimates derived from noisy observations remains a fundamental challenge in statistical machine learning, particularly for applications in safety-critical domains. In this…

In this paper, we derive a novel procedure for set-membership estimation of dynamical systems affected by stochastic noise with unbounded support. Employing a bound on the sample covariance matrix, we are able to provide a finite- sample…

A linear Gaussian state-space smoothing algorithm is presented for estimation of derivatives from a sequence of noisy measurements. The algorithm uses numerically stable square-root formulas, can handle simultaneous independent measurements…

The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the…

In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…

We propose a novel Bayesian approach to solve stochastic optimization problems that involve finding extrema of noisy, nonlinear functions. Previous work has focused on representing possible functions explicitly, which leads to a two-step…