Related papers: OneBatchPAM: A Fast and Frugal K-Medoids Algorithm

Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…

We propose two linear bandits algorithms with per-step complexity sublinear in the number of arms $K$. The algorithms are designed for applications where the arm set is extremely large and slowly changing. Our key realization is that…

Density peaks clustering has become a nova of clustering algorithm because of its simplicity and practicality. However, there is one main drawback: it is time-consuming due to its high computational complexity. Herein, a density peaks…

Weighted Hamming distance, as a similarity measure between binary codes and binary queries, provides superior accuracy in search tasks than Hamming distance. However, how to efficiently and accurately find $K$ binary codes that have the…

We study the problem of answering \emph{$k$-way marginal} queries on a database $D \in (\{0,1\}^d)^n$, while preserving differential privacy. The answer to a $k$-way marginal query is the fraction of the database's records $x \in \{0,1\}^d$…

The most well known and ubiquitous clustering problem encountered in nearly every branch of science is undoubtedly $k$-means: given a set of data points and a parameter $k$, select $k$ centres and partition the data points into $k$ clusters…

Traditional MCMC algorithms are computationally intensive and do not scale well to large data. In particular, the Metropolis-Hastings (MH) algorithm requires passing over the entire dataset to evaluate the likelihood ratio in each…

We propose a randomized version of the non-local means (NLM) algorithm for large-scale image filtering. The new algorithm, called Monte Carlo non-local means (MCNLM), speeds up the classical NLM by computing a small subset of image patch…

k-means has recently been recognized as one of the best algorithms for clustering unsupervised data. Since k-means depends mainly on distance calculation between all data points and the centers, the time cost will be high when the size of…

We study the task of differentially private clustering. For several basic clustering problems, including Euclidean DensestBall, 1-Cluster, k-means, and k-median, we give efficient differentially private algorithms that achieve essentially…

In the $k$-Cut problem, we are given an edge-weighted graph $G$ and an integer $k$, and have to remove a set of edges with minimum total weight so that $G$ has at least $k$ connected components. Prior work on this problem gives, for all $h…

We give a quantum approximation scheme (i.e., $(1 + \varepsilon)$-approximation for every $\varepsilon > 0$) for the classical $k$-means clustering problem in the QRAM model with a running time that has only polylogarithmic dependence on…

In recent years it has become popular to study machine learning problems in a setting of ordinal distance information rather than numerical distance measurements. By ordinal distance information we refer to binary answers to distance…

Decoding for many NLP tasks requires an effective heuristic algorithm for approximating exact search since the problem of searching the full output space is often intractable, or impractical in many settings. The default algorithm for this…

First, for the for the submodular $k$-secretary problem with shortlists [1], we provide a near optimal $1-1/e-\epsilon$ approximation using shortlist of size $O(k poly(1/\epsilon))$. In particular, we improve the size of shortlist used in…

Kernel-based clustering algorithms have the ability to capture the non-linear structure in real world data. Among various kernel-based clustering algorithms, kernel k-means has gained popularity due to its simple iterative nature and ease…

The Multidimensional Assignment Problem (MAP or s-AP in the case of s dimensions) is an extension of the well-known assignment problem. The most studied case of MAP is 3-AP, though the problems with larger values of s have also a number of…

We provide the first streaming algorithm for computing a provable approximation to the $k$-means of sparse Big data. Here, sparse Big Data is a set of $n$ vectors in $\mathbb{R}^d$, where each vector has $O(1)$ non-zeroes entries, and…

K-Nearest Neighbours (k-NN) is a popular classification and regression algorithm, yet one of its main limitations is the difficulty in choosing the number of neighbours. We present a Bayesian algorithm to compute the posterior probability…

Clustering is a fundamental problem in unsupervised machine learning with many applications in data analysis. Popular clustering algorithms such as Lloyd's algorithm and $k$-means++ can take $\Omega(ndk)$ time when clustering $n$ points in…