Related papers: Multi-Resolution Hashing for Fast Pairwise Summati…
For a set of $n$ points in $\Re^d$, and parameters $k$ and $\eps$, we present a data structure that answers $(1+\eps,k)$-\ANN queries in logarithmic time. Surprisingly, the space used by the data-structure is $\Otilde (n /k)$; that is, the…
Nearest neighbor search aims to obtain the samples in the database with the smallest distances from them to the queries, which is a basic task in a range of fields, including computer vision and data mining. Hashing is one of the most…
Given a set of points $P\subset \mathbb{R}^{d}$ and a kernel $k$, the Kernel Density Estimate at a point $x\in\mathbb{R}^{d}$ is defined as $\mathrm{KDE}_{P}(x)=\frac{1}{|P|}\sum_{y\in P} k(x,y)$. We study the problem of designing a data…
Minwise hashing is the standard technique in the context of search and databases for efficiently estimating set (e.g., high-dimensional 0/1 vector) similarities. Recently, b-bit minwise hashing was proposed which significantly improves upon…
The usefulness of Bayesian models for density and cluster estimation is well established across multiple literatures. However, there is still a known tension between the use of simpler, more interpretable models and more flexible, complex…
In processing large quantities of data, a fundamental problem is to obtain a summary which supports approximate query answering. Random sampling yields flexible summaries which naturally support subset-sum queries with unbiased estimators…
Let $X_1, ..., X_m$ be a set of $m$ statistically dependent sources over the common alphabet $\mathbb{F}_q$, that are linearly independent when considered as functions over the sample space. We consider a distributed function computation…
Supervised hashing aims to map the original features to compact binary codes that are able to preserve label based similarity in the Hamming space. Non-linear hash functions have demonstrated the advantage over linear ones due to their…
Subsampling is one of the popular methods to balance statistical efficiency and computational efficiency in the big data era. Most approaches aim at selecting informative or representative sample points to achieve good overall information…
We survey key techniques and results from approximation theory in the context of uniform approximations to real functions such as e^{-x}, 1/x, and x^k. We then present a selection of results demonstrating how such approximations can be used…
We revisit the Subset Sum problem over the finite cyclic group $\mathbb{Z}_m$ for some given integer $m$. A series of recent works has provided near-optimal algorithms for this problem under the Strong Exponential Time Hypothesis. Koiliaris…
We give a dimensionality reduction procedure to approximate the sum of distances of a given set of $n$ points in $R^d$ to any "shape" that lies in a $k$-dimensional subspace. Here, by "shape" we mean any set of points in $R^d$. Our…
We present a unified framework for quantum sensitivity sampling, extending the advantages of quantum computing to a broad class of classical approximation problems. Our unified framework provides a streamlined approach for constructing…
Pattern set mining, which is the task of finding a good set of patterns instead of all patterns, is a fundamental problem in data mining. Many different definitions of what constitutes a good set have been proposed in recent years. In this…
To get estimators that work within a certain error bound with high probability, a common strategy is to design one that works with constant probability, and then boost the probability using independent repetitions. Important examples of…
We study the Closest Pair Problem in Hamming metric, which asks to find the pair with the smallest Hamming distance in a collection of binary vectors. We give a new randomized algorithm for the problem on uniformly random input…
Mining large-scale high-throughput tandem mass spectrometry data sets is a very important problem in mass spectrometry based protein identification. One of the fundamental problems in large scale mining of spectra is to design appropriate…
We propose a simple and fast method for providing a high quality solution for the sum-interference minimization problem. As future networks are deployed in high density urban areas, improved clustering methods are needed to provide low…
Submodular functions are at the core of many machine learning and data mining tasks. The underlying submodular functions for many of these tasks are decomposable, i.e., they are sum of several simple submodular functions. In many data…
Set similarity join, as well as the corresponding indexing problem set similarity search, are fundamental primitives for managing noisy or uncertain data. For example, these primitives can be used in data cleaning to identify different…