Related papers: Adaptive Estimation for Approximate k-Nearest-Neig…

Modern neural network technologies, including large language models, have achieved remarkable success in various applied artificial intelligence applications, however, they face a range of fundamental limitations. Among them are…

We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…

This paper investigates the optimal ergodic sublinear convergence rate of the relaxed proximal point algorithm for solving monotone variational inequality problems. The exact worst case convergence rate is computed using the performance…

Nearest neighbor is a popular class of classification methods with many desirable properties. For a large data set which cannot be loaded into the memory of a single machine due to computation, communication, privacy, or ownership…

We consider a problem of multiclass classification, where the training sample $S_n = \{(X_i, Y_i)\}_{i=1}^n$ is generated from the model $\mathbb P(Y = m | X = x) = \eta_m(x)$, $1 \leq m \leq M$, and $\eta_1(x), \dots, \eta_M(x)$ are…

Given a reference set $R$ of $n$ points and a query set $Q$ of $m$ points in a metric space, this paper studies an important problem of finding $k$-nearest neighbors of every point $q \in Q$ in the set $R$ in a near-linear time. In the…

Polytrees are a subclass of Bayesian networks that seek to capture the conditional dependencies between a set of $n$ variables as a directed forest and are motivated by their more efficient inference and improved interpretability. Since the…

We consider a robust variant of the classical $k$-median problem, introduced by Anthony et al. \cite{AnthonyGGN10}. In the \emph{Robust $k$-Median problem}, we are given an $n$-vertex metric space $(V,d)$ and $m$ client sets $\set{S_i…

For very large values of $k$, we consider methods for fast $k$-means clustering of massive datasets with $10^7\sim10^9$ points in high-dimensions ($d\geq100$). All current practical methods for this problem have runtimes at least…

The problem of finding the shortest path for a vehicle visiting a given sequence of target points subject to the motion constraints of the vehicle is an important problem that arises in several monitoring and surveillance applications…

In the regime of bounded transportation costs, additive approximations for the optimal transport problem are reduced (rather simply) to relative approximations for positive linear programs, resulting in faster additive approximation…

Closeness is an important centrality measure widely used in the analysis of real-world complex networks. In particular, the problem of selecting the k most central nodes with respect to this measure has been deeply analyzed in the last…

This paper considers non-smooth optimization problems where we seek to minimize the pointwise maximum of a continuously parameterized family of functions. Since the objective function is given as the solution to a maximization problem,…

Using prototype methods to reduce the size of training datasets can drastically reduce the computational cost of classification with instance-based learning algorithms like the k-Nearest Neighbour classifier. The number and distribution of…

We give nearly-tight upper and lower bounds for the improving multi-armed bandits problem. An instance of this problem has $k$ arms, each of whose reward function is a concave and increasing function of the number of times that arm has been…

We consider a facility location problem, where the objective is to ``disperse'' a number of facilities, i.e., select a given number k of locations from a discrete set of n candidates, such that the average distance between selected…

Near neighbor search (NNS) is a powerful abstraction for data access; however, data indexing is troublesome even for approximate indexes. For intrinsically high-dimensional data, high-quality fast searches demand either indexes with…

Data valuation, the task of quantifying the contribution of individual data points to model performance, has emerged as a fundamental challenge in machine learning. Game-theoretic approaches, such as the Banzhaf value, offer principled…

In this paper, we consider the following $k$-dispersion problem. Given a set $S$ of $n$ points placed in the plane in a convex position, and an integer $k$ ($0<k<n$), the objective is to compute a subset $S'\subset S$ such that $|S'|=k$ and…

We propose a simple and efficient clustering method for high-dimensional data with a large number of clusters. Our algorithm achieves high-performance by evaluating distances of datapoints with a subset of the cluster centres. Our…