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This study presents a novel algorithm for identifying the set of extreme points that constitute the exact convex hull of a point set in high-dimensional Euclidean space. The proposed method iteratively solves a sequence of dynamically…
Data processing systems offer an ever increasing degree of parallelism on the levels of cores, CPUs, and processing nodes. Query optimization must exploit high degrees of parallelism in order not to gradually become the bottleneck of query…
Much recent work has been devoted to approximate nearest neighbor queries. Motivated by applications in recommender systems, we consider approximate furthest neighbor (AFN) queries and present a simple, fast, and highly practical data…
Recent research on deep neural networks (DNNs) has primarily focused on improving the model accuracy. Given a proper deep learning framework, it is generally possible to increase the depth or layer width to achieve a higher level of…
In this work we study the problem of differentially private (DP) quantiles, in which given dataset $X$ and quantiles $q_1, ..., q_m \in [0,1]$, we want to output $m$ quantile estimations which are as close as possible to the true quantiles…
Existing fast algorithms for bilateral and nonlocal means filtering mostly work with grayscale images. They cannot easily be extended to high-dimensional data such as color and hyperspectral images, patch-based data, flow-fields, etc. In…
We consider the problem of finding the set of architectural parameters for a chosen deep neural network which is optimal under three metrics: parameter size, inference speed, and error rate. In this paper we state the problem formally, and…
Let $\RR$ be a real closed field (e.g. the field of real numbers) and $\mathscr{S} \subset \RR^n$ be a semi-algebraic set defined as the set of points in $\RR^n$ satisfying a system of $s$ equalities and inequalities of multivariate…
The quantum approximate optimization algorithm (QAOA) is known for its capability and universality in solving combinatorial optimization problems on near-term quantum devices. The results yielded by QAOA depend strongly on its initial…
In this work, we propose a novel cross Q-learning algorithm, aim at alleviating the well-known overestimation problem in value-based reinforcement learning methods, particularly in the deep Q-networks where the overestimation is exaggerated…
Depth imaging has largely focused on sensor and intrinsics properties. However, the accuracy of acquire pixel is largely dependent on the capture. We propose a new depth estimation and approximation algorithm which takes an arbitrary 3D…
Dimensionality reduction (DR) algorithms, which reduce the dimensionality of a given data set while preserving the information of the original data set as well as possible, play an important role in machine learning and data mining. Duan…
In this note, we develop fast and deterministic dimensionality reduction techniques for a family of subspace approximation problems. Let $P\subset \mathbbm{R}^N$ be a given set of $M$ points. The techniques developed herein find an $O(n…
We present a novel approach to adaptive optimal design of groundwater surveys - a methodology for choosing the location of the next monitoring well. Our dual-weighted approach borrows ideas from Bayesian Optimisation and goal-oriented error…
We describe a randomized algorithm that, given a set $P$ of points in the plane, computes the best location to insert a new point $p$, such that the Delaunay triangulation of $P\cup\{p\}$ has the largest possible minimum angle. The expected…
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…
This paper develops a new storage-optimal algorithm that provably solves generic semidefinite programs (SDPs) in standard form. This method is particularly effective for weakly constrained SDPs. The key idea is to formulate an approximate…
The problem of {\em efficiently} finding the best match for a query in a given set with respect to the Euclidean distance or the cosine similarity has been extensively studied in literature. However, a closely related problem of efficiently…
In this paper, we propose two simple yet efficient computational algorithms to obtain approximate optimal designs for multi-dimensional linear regression on a large variety of design spaces. We focus on the two commonly used optimal…
Inspired by the classical fractional cascading technique, we introduce new techniques to speed up the following type of iterated search in 3D: The input is a graph $\mathbf{G}$ with bounded degree together with a set $H_v$ of 3D hyperplanes…