Related papers: Cauchy-Gaussian Overbound for Heavy-tailed GNSS Me…
In recent years, various notions of capacity and complexity have been proposed for characterizing the generalization properties of stochastic gradient descent (SGD) in deep learning. Some of the popular notions that correlate well with the…
Hyperbolic neural networks (HNNs) have demonstrated notable efficacy in representing real-world data with hierarchical structures via exploiting the geometric properties of hyperbolic spaces characterized by negative curvatures. Curvature…
Training neural networks with high certified accuracy against adversarial examples remains an open challenge despite significant efforts. While certification methods can effectively leverage tight convex relaxations for bound computation,…
Various natural phenomena exhibit spatial extremal dependence at short spatial distances. However, existing models proposed in the spatial extremes literature often assume that extremal dependence persists across the entire domain. This is…
Many problems in navigation and tracking require increasingly accurate characterizations of the evolution of uncertainty in nonlinear systems. Nonlinear uncertainty propagation approaches based on Gaussian mixture density approximations…
We propose a principled algorithm for robust Bayesian filtering and smoothing in nonlinear stochastic dynamic systems when both the transition function and the measurement function are described by non-parametric Gaussian process (GP)…
We present a quasi-conjugate Bayes approach for estimating Generalized Pareto Distribution (GPD) parameters, distribution tails and extreme quantiles within the Peaks-Over-Threshold framework. Damsleth conjugate Bayes structure on Gamma…
Recent works have proposed incorporating heavy-tailed (HT) noise into diffusion- and flow-based generative models, with the goals of better recovering the tails of target distributions and improving generative diversity. This motivation is…
We revisit and refine known tail inequalities and confidence bounds for the hypergeometric distribution, i.e., for the setting where we sample without replacement from a fixed population with binary values or properties. The results are…
The maximum-marginal-a-posteriori success rate of statistical decision under multivariate Gaussian error distribution on an integer lattice is almost rigorously calculated by using union-bound approximation and Monte Carlo integration.…
Random linear mappings are widely used in modern signal processing, compressed sensing and machine learning. These mappings may be used to embed the data into a significantly lower dimension while at the same time preserving useful…
Indoor localization is critical for IoT applications, yet challenges such as non-Gaussian noise, environmental interference, and measurement outliers hinder the robustness of traditional methods. Existing approaches, including Kalman…
Estimating the parameters of compact binaries which coalesce and produce gravitational waves is a challenging Bayesian inverse problem. Gravitational-wave parameter estimation lies within the class of multifidelity problems, where a variety…
Data derived from remote sensing or numerical simulations often have a regular gridded structure and are large in volume, making it challenging to find accurate spatial models that can fill in missing grid cells or simulate the process…
The precise tuning required to observe critical phenomena in gravitational collapse poses a challenge for most numerical codes. First, threshold estimation searches may be obstructed by the appearance of coordinate singularities, indicating…
This short paper presents research findings on two learning-based methods for quantifying measurement uncertainties in global navigation satellite systems (GNSS). We investigate two learning strategies: offline learning for outlier…
Using tail bounds, we introduce a new probabilistic condition for function estimation in stochastic derivative-free optimization which leads to a reduction in the number of samples and eases algorithmic analyses. Moreover, we develop simple…
In urban environments, where line-of-sight signals from GNSS satellites are frequently blocked by high-rise objects, GNSS receivers are subject to large errors in measuring satellite ranges. Heuristic methods are commonly used to estimate…
Sparse-view satellite image surface reconstruction remains highly challenging, fundamentally because the reliability of multi-view matching under satellite imaging conditions is strongly spatially heterogeneous. Affected by large…
We propose an approach to construction of robust non-Euclidean iterative algorithms for convex composite stochastic optimization based on truncation of stochastic gradients. For such algorithms, we establish sub-Gaussian confidence bounds…