Related papers: ABCDepth: efficient algorithm for Tukey depth
Exploiting internal spatial geometric constraints of sparse LiDARs is beneficial to depth completion, however, has been not explored well. This paper proposes an efficient method to learn geometry-aware embedding, which encodes the local…
In deep active learning, it is especially important to choose multiple examples to markup at each step to work efficiently, especially on large datasets. At the same time, existing solutions to this problem in the Bayesian setup, such as…
One fundamental goal of high-dimensional statistics is to detect or recover planted structure (such as a low-rank matrix) hidden in noisy data. A growing body of work studies low-degree polynomials as a restricted model of computation for…
This paper presents a systematic methodology based on the algebraic theory of signal processing to classify and derive fast algorithms for linear transforms. Instead of manipulating the entries of transform matrices, our approach derives…
A new Approximate Bayesian Computation (ABC) algorithm for Bayesian updating of model parameters is proposed in this paper, which combines the ABC principles with the technique of Subset Simulation for efficient rare-event simulation, first…
Hypervolume indicator is a commonly accepted quality measure for comparing Pareto approximation set generated by multi-objective optimizers. The best known algorithm to calculate it for $n$ points in $d$-dimensional space has a run time of…
In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…
A new depth-based clustering procedure for directional data is proposed. Such method is fully non-parametric and has the advantages to be flexible and applicable even in high dimensions when a suitable notion of depth is adopted. The…
Recently, deep clustering, which is able to perform feature learning that favors clustering tasks via deep neural networks, has achieved remarkable performance in image clustering applications. However, the existing deep clustering…
Finding the k-medianin a network involves identifying a subset of k vertices that minimize the total distance to all other vertices in a graph. This problem has been extensively studied in computer science, graph theory, operations…
In the rapidly advancing domain of computer vision, accurately estimating the poses of multiple individuals from various viewpoints remains a significant challenge, especially when reliability is a key requirement. This paper introduces a…
Topological data analysis (TDA) provides a growing body of tools for computing geometric and topological information about spaces from a finite sample of points. We present a new adaptive algorithm for finding provably dense samples of…
Given a probability measure $\mu $ on ${\mathbb R}^n$, Tukey's half-space depth is defined for any $x\in {\mathbb R}^n$ by $\varphi_{\mu }(x)=\inf\{\mu (H):H\in {\cal H}(x)\}$, where ${\cal H}(x)$ is the set of all half-spaces $H$ of…
This report elaborates on approximations for the discrete Fourier transform by means of replacing the exact Cooley-Tukey algorithm twiddle-factors by low-complexity integers, such as $0, \pm \frac{1}{2}, \pm 1$.
A matching algorithm for the identification of backbones in percolation problems is introduced. Using this procedure, percolation backbones are studied in two- to five-dimensional systems containing 1.7x10^7 sites, two orders of magnitude…
Approximating the set of reachable states of a dynamical system is an algorithmic yet mathematically rigorous way to reason about its safety. Although progress has been made in the development of efficient algorithms for affine dynamical…
In this paper, we present a fast monocular depth estimation method for enabling 3D perception capabilities of low-cost underwater robots. We formulate a novel end-to-end deep visual learning pipeline named UDepth, which incorporates domain…
Depth completion aims at predicting dense pixel-wise depth from an extremely sparse map captured from a depth sensor, e.g., LiDARs. It plays an essential role in various applications such as autonomous driving, 3D reconstruction, augmented…
Over the past few years, monocular depth estimation and completion have been paid more and more attention from the computer vision community because of their widespread applications. In this paper, we introduce novel physics…
Consider a high-dimensional data set, in which for every data-point there is incomplete information. Each object in the data set represents a real entity, which is described by a point in high-dimensional space. We model the lack of…