Related papers: A Note on Approximate Nearest Neighbor Methods
Approximate Bayesian computation performs approximate inference for models where likelihood computations are expensive or impossible. Instead simulations from the model are performed for various parameter values and accepted if they are…
Neighborhood finders and nearest neighbor queries are fundamental parts of sampling based motion planning algorithms. Using different distance metrics or otherwise changing the definition of a neighborhood produces different algorithms with…
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…
Nearest neighbor is a popular nonparametric method for classification and regression with many appealing properties. In the big data era, the sheer volume and spatial/temporal disparity of big data may prohibit centrally processing and…
The property of almost every point being a Lebesgue point has proven to be crucial for the consistency of several classification algorithms based on nearest neighbors. We characterize Lebesgue points in terms of a 1-Nearest Neighbor…
A supervised learning algorithm has access to a distribution of labeled examples, and needs to return a function (hypothesis) that correctly labels the examples. The hypothesis of the learner is taken from some fixed class of functions…
It is well known that a binomial $(n,p)$ can be approximated by a Poisson distribution with parameter $np$. The typical approach in undergraduate probability texts is to show a convergence result for the distribution of the binomial as $n$…
Results on two different settings of asymptotic behavior of approximation characteristics of individual functions are presented. First, we discuss the following classical question for sparse approximation. Is it true that for any individual…
Nonresponse is a common problem in survey sampling. Appropriate treatment can be challenging, especially when dealing with detailed breakdowns of totals. Often, the nearest neighbor imputation method is used to handle such incomplete…
$K$-NN classifier is one of the most famous classification algorithms, whose performance is crucially dependent on the distance metric. When we consider the distance metric as a parameter of $K$-NN, learning an appropriate distance metric…
We compare the performance of standard nearest-neighbor propensity score matching with that of an analogous Bayesian propensity score matching procedure. We show that the Bayesian approach makes better use of available information, as it…
We study the fundamental problem of approximate nearest neighbor search in $d$-dimensional Hamming space $\{0,1\}^d$. We study the complexity of the problem in the famous cell-probe model, a classic model for data structures. We consider…
Combining the techniques of approximation algorithms and parameterized complexity has long been considered a promising research area, but relatively few results are currently known. In this paper we study the parameterized approximability…
We suggest a robust nearest-neighbor approach to classifying high-dimensional data. The method enhances sensitivity by employing a threshold and truncates to a sequence of zeros and ones in order to reduce the deleterious impact of…
Approximations of functions with finite data often do not respect certain "structural" properties of the functions. For example, if a given function is non-negative, a polynomial approximation of the function is not necessarily also…
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…
Gaussian process models are commonly used as emulators for computer experiments. However, developing a Gaussian process emulator can be computationally prohibitive when the number of experimental samples is even moderately large. Local…
This paper considers pairs of optimization problems that are defined from a single input and for which it is desired to find a good approximation to either one of the problems. In many instances, it is possible to efficiently find an…
Motivated by safety-critical applications, test-time attacks on classifiers via adversarial examples has recently received a great deal of attention. However, there is a general lack of understanding on why adversarial examples arise;…
Local search is a fundamental method in operations research and combinatorial optimisation. It has been widely applied to a variety of challenging problems, including multi-objective optimisation where multiple, often conflicting,…