Related papers: A Note on Approximate Nearest Neighbor Methods
In [19], a general, inexact, efficient proximal quasi-Newton algorithm for composite optimization problems has been proposed and a sublinear global convergence rate has been established. In this paper, we analyze the convergence properties…
$\newcommand{\ball}{\mathbb{B}}\newcommand{\dsQ}{{\mathcal{Q}}}\newcommand{\dsS}{{\mathcal{S}}}$In this work we study a fair variant of the near neighbor problem. Namely, given a set of $n$ points $P$ and a parameter $r$, the goal is to…
Sensitivity measures how much the output of an algorithm changes, in terms of Hamming distance, when part of the input is modified. While approximation algorithms with low sensitivity have been developed for many problems, no sensitivity…
Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…
The traditional k nearest neighbor (kNN) approach uses a distance formula within a spherical region to determine the k closest training observations to a test sample point. However, this approach may not work well when test point is located…
A novel and intuitive nearest neighbours based clustering algorithm is introduced, in which a cluster is defined in terms of an equilibrium condition which balances its size and cohesiveness. The formulation of the equilibrium condition…
The facility location problem is widely used for summarizing large datasets and has additional applications in sensor placement, image retrieval, and clustering. One difficulty of this problem is that submodular optimization algorithms…
We present a new algorithm for the approximate near neighbor problem that combines classical ideas from group testing with locality-sensitive hashing (LSH). We reduce the near neighbor search problem to a group testing problem by…
In this paper, we consider several finite-horizon Bayesian multi-armed bandit problems with side constraints which are computationally intractable (NP-Hard) and for which no optimal (or near optimal) algorithms are known to exist with…
A risk-aware decision-making problem can be formulated as a chance-constrained linear program in probability measure space. Chance-constrained linear program in probability measure space is intractable, and no numerical method exists to…
This paper proposes a spatial k-nearest neighbor method for nonparametric prediction of real-valued spatial data and supervised classification for categorical spatial data. The proposed method is based on a double nearest neighbor rule…
Proximal operators are now ubiquitous in non-smooth optimization. Since their introduction in the seminal work of Moreau, many papers have shown their effectiveness on a wide variety of problems, culminating in their use to construct…
We derive a new asymptotic expansion for the global excess risk of a local-$k$-nearest neighbour classifier, where the choice of $k$ may depend upon the test point. This expansion elucidates conditions under which the dominant contribution…
In the Euclidean TSP with neighborhoods (TSPN), we are given a collection of n regions (neighborhoods) and we seek a shortest tour that visits each region. As a generalization of the classical Euclidean TSP, TSPN is also NP-hard. In this…
We survey the main results of approximation theory for adaptive piecewise polynomial functions. In such methods, the partition on which the piecewise polynomial approximation is defined is not fixed in advance, but adapted to the given…
This paper studies the design and analysis of approximation algorithms for aggregating preferences over combinatorial domains, represented using Conditional Preference Networks (CP-nets). Its focus is on aggregating preferences over…
Estimating some mathematical expectations from partially observed data and in particular missing outcomes is a central problem encountered in numerous fields such as transfer learning, counterfactual analysis or causal inference. Matching…
The adaptive constraints relaxing rule for swarm algorithms to handle with the problems with equality constraints is presented. The feasible space of such problems may be similiar to ridge function class, which is hard for applying swarm…
The problem of optimizing over random structures emerges in many areas of science and engineering, ranging from statistical physics to machine learning and artificial intelligence. For many such structures finding optimal solutions by means…
Scientists continue to develop increasingly complex mechanistic models to reflect their knowledge more realistically. Statistical inference using these models can be challenging since the corresponding likelihood function is often…