Related papers: Empirical complexity of comparator-based nearest n…
We recently proposed a general algorithm for approximating nonstandard Bayesian posterior distributions by minimization of their Kullback-Leibler divergence with respect to a more convenient approximating distribution. In this note we offer…
We present a new approach to approximate nearest-neighbor queries in fixed dimension under a variety of non-Euclidean distances. We are given a set $S$ of $n$ points in $\mathbb{R}^d$, an approximation parameter $\varepsilon > 0$, and a…
The continuation method is a popular approach in non-convex optimization and computer vision. The main idea is to start from a simple function that can be minimized efficiently, and gradually transform it to the more complicated original…
We study the problem of nonnegative rank-one approximation of a nonnegative tensor, and show that the globally optimal solution that minimizes the generalized Kullback-Leibler divergence can be efficiently obtained, i.e., it is not NP-hard.…
The k Nearest Neighbors (kNN) method has received much attention in the past decades, where some theoretical bounds on its performance were identified and where practical optimizations were proposed for making it work fairly well in high…
The k-Nearest Neighbor (kNN) classification approach is conceptually simple - yet widely applied since it often performs well in practical applications. However, using a global constant k does not always provide an optimal solution, e.g.,…
K-nearest neighbors (KNN) is one of the earliest and most established algorithms in machine learning. For regression tasks, KNN averages the targets within a neighborhood which poses a number of challenges: the neighborhood definition is…
Many distributed learning techniques have been motivated by the increasing size of datasets and their inability to fit into main memory on a single machine. We propose an algorithm that finds the nearest neighbor in a graph locally without…
We propose a general algorithm for approximating nonstandard Bayesian posterior distributions. The algorithm minimizes the Kullback-Leibler divergence of an approximating distribution to the intractable posterior distribution. Our method…
In the panoply of pattern classification techniques, few enjoy the intuitive appeal and simplicity of the nearest neighbor rule: given a set of samples in some metric domain space whose value under some function is known, we estimate the…
We show how to sample in parallel from a distribution $\pi$ over $\mathbb R^d$ that satisfies a log-Sobolev inequality and has a smooth log-density, by parallelizing the Langevin (resp. underdamped Langevin) algorithms. We show that our…
The k-nearest neighbors (kNN) algorithm is a cornerstone of non-parametric classification in artificial intelligence, yet its deployment in large-scale applications is persistently constrained by the computational trade-off between…
We study the approximation of arbitrary distributions $P$ on $d$-dimensional space by distributions with log-concave density. Approximation means minimizing a Kullback--Leibler-type functional. We show that such an approximation exists if…
We propose algorithms to approximate directed information graphs. Directed information graphs are probabilistic graphical models that depict causal dependencies between stochastic processes in a network. The proposed algorithms identify…
This paper addresses the problem of approximating an unknown probability distribution with density $f$ -- which can only be evaluated up to an unknown scaling factor -- with the help of a sequential algorithm that produces at each iteration…
Accelerated algorithms for maximum likelihood image reconstruction are essential for emerging applications such as 3D tomography, dynamic tomographic imaging, and other high dimensional inverse problems. In this paper, we introduce and…
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…
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…
We consider the problem of finding high dimensional approximate nearest neighbors. Suppose there are d independent rare features, each having its own independent statistics. A point x will have x_{i}=0 denote the absence of feature i, and…
A triplet comparison oracle on a set $S$ takes an object $x \in S$ and for any pair $\{y, z\} \subset S \setminus \{x\}$ declares which of $y$ and $z$ is more similar to $x$. Partitioned Local Depth (PaLD) supplies a principled…