Related papers: Local Density Estimation in High Dimensions
Density Estimation is one of the central areas of statistics whose purpose is to estimate the probability density function underlying the observed data. It serves as a building block for many tasks in statistical inference, visualization,…
Locality Sensitive Hashing (LSH) is an effective method of indexing a set of items to support efficient nearest neighbors queries in high-dimensional spaces. The basic idea of LSH is that similar items should produce hash collisions with…
Embeddings are a basic initial feature extraction step in many machine learning models, particularly in natural language processing. An embedding attempts to map data tokens to a low-dimensional space where similar tokens are mapped to…
Nearest neighbor search is fundamental to a wide range of applications. Since the exact nearest neighbor search suffers from the "curse of dimensionality", approximate approaches, such as Locality-Sensitive Hashing (LSH), are widely used to…
The $c$-approximate Near Neighbor problem in high dimensional spaces has been mainly addressed by Locality Sensitive Hashing (LSH), which offers polynomial dependence on the dimension, query time sublinear in the size of the dataset, and…
In this work, we address the problem of cardinality estimation for similarity search in high-dimensional spaces. Our goal is to design a framework that is lightweight, easy to construct, and capable of providing accurate estimates with…
We propose two novel model architectures for computing continuous vector representations of words from very large data sets. The quality of these representations is measured in a word similarity task, and the results are compared to the…
This paper describes a fast speaker search system to retrieve segments of the same voice identity in the large-scale data. A recent study shows that Locality Sensitive Hashing (LSH) enables quick retrieval of a relevant voice in the…
Keyword-based search in text-rich multi-dimensional datasets facilitates many novel applications and tools. In this paper, we consider objects that are tagged with keywords and are embedded in a vector space. For these datasets, we study…
Hashing methods have been widely investigated for fast approximate nearest neighbor searching in large data sets. Most existing methods use binary vectors in lower dimensional spaces to represent data points that are usually real vectors of…
As data volumes continue to grow, searches in data are becoming increasingly time-consuming. Classical index structures for neighbor search are no longer sustainable due to the "curse of dimensionality". Instead, approximated index…
A set of vectors $S \subseteq \mathbb{R}^d$ is $(k_1,\varepsilon)$-clusterable if there are $k_1$ balls of radius $\varepsilon$ that cover $S$. A set of vectors $S \subseteq \mathbb{R}^d$ is $(k_2,\delta)$-far from being clusterable if…
Level set estimation (LSE) classifies whether an unknown function's value exceeds a specified threshold for given inputs, a fundamental problem in many real-world applications. In active learning settings with limited initial data, we aim…
We show that approximate similarity (near neighbour) search can be solved in high dimensions with performance matching state of the art (data independent) Locality Sensitive Hashing, but with a guarantee of no false negatives. Specifically,…
Similarity search queries in high-dimensional spaces are an important type of queries in many domains such as image processing, machine learning, etc. Since exact similarity search indexing techniques suffer from the well-known curse of…
Nearest neighbor (NN) search is inherently computationally expensive in high-dimensional spaces due to the curse of dimensionality. As a well-known solution, locality-sensitive hashing (LSH) is able to answer c-approximate NN (c-ANN)…
As data volumes continue to grow, clustering and outlier detection algorithms are becoming increasingly time-consuming. Classical index structures for neighbor search are no longer sustainable due to the "curse of dimensionality". Instead,…
Accurate estimation of Intrinsic Dimensionality (ID) is of crucial importance in many data mining and machine learning tasks, including dimensionality reduction, outlier detection, similarity search and subspace clustering. However, since…
Level Set Estimation (LSE) is an important problem with applications in various fields such as material design, biotechnology, machine operational testing, etc. Existing techniques suffer from the scalability issue, that is, these methods…
In a previous article, a least square regression estimation procedure was proposed: first, we condiser a family of functions and study the properties of an estimator in every unidimensionnal model defined by one of these functions; we then…