Related papers: CacheDiff: Fast Random Sampling
We study the differentially private top-$k$ selection problem, aiming to identify a sequence of $k$ items with approximately the highest scores from $d$ items. Recent work by Gillenwater et al. (ICML '22) employs a direct sampling approach…
The $k$-$\mathtt{means}$++ seeding algorithm (Arthur & Vassilvitskii, 2007) is widely used in practice for the $k$-means clustering problem where the goal is to cluster a dataset $\mathcal{X} \subset \mathbb{R} ^d$ into $k$ clusters. The…
This paper proposes a novel k-medoids approximation algorithm to handle large-scale datasets with reasonable computational time and memory complexity. We develop a local-search algorithm that iteratively improves the medoid selection based…
We present a quantum algorithm for sampling random spanning trees from a weighted graph in $\widetilde{O}(\sqrt{mn})$ time, where $n$ and $m$ denote the number of vertices and edges, respectively. Our algorithm has sublinear runtime for…
We consider the problem of sampling $n$ numbers from the range $\{1,\ldots,N\}$ without replacement on modern architectures. The main result is a simple divide-and-conquer scheme that makes sequential algorithms more cache efficient and…
Copies have been proposed as a viable alternative to endow machine learning models with properties and features that adapt them to changing needs. A fundamental step of the copying process is generating an unlabelled set of points to…
Diffusion models deliver high-fidelity synthesis but remain slow due to iterative sampling. We empirically observe there exists feature invariance in deterministic sampling, and present InvarDiff, a training-free acceleration method that…
We describe a very simple method for `consistent sampling' that allows for sampling with replacement. The method extends previous approaches to consistent sampling, which assign a pseudorandom real number to each element, and sample those…
We study the following distribution clustering problem: Given a hidden partition of $k$ distributions into two groups, such that the distributions within each group are the same, and the two distributions associated with the two clusters…
The task of extracting a diverse subset from a dataset, often referred to as maximum diversification, plays a pivotal role in various real-world applications that have far-reaching consequences. In this work, we delve into the realm of…
Although dense local spatial-temporal features with bag-of-features representation achieve state-of-the-art performance for action recognition, the huge feature number and feature size prevent current methods from scaling up to real size…
Described are two algorithms to find long approximate palindromes in a string, for example a DNA sequence. A simple algorithm requires O(n)-space and almost always runs in $O(k.n)$-time where n is the length of the string and k is the…
Clustering non-Euclidean data is difficult, and one of the most used algorithms besides hierarchical clustering is the popular algorithm Partitioning Around Medoids (PAM), also simply referred to as k-medoids clustering. In Euclidean…
We provide an algorithm for properly learning mixtures of two single-dimensional Gaussians without any separability assumptions. Given $\tilde{O}(1/\varepsilon^2)$ samples from an unknown mixture, our algorithm outputs a mixture that is…
Collecting the most informative data from a large dataset distributed over a network is a fundamental problem in many fields, including control, signal processing and machine learning. In this paper, we establish a connection between…
We propose the K-series estimation approach for the recovery of unknown univariate and multivariate distributions given knowledge of a finite number of their moments. Our method is directly applicable to the probabilistic analysis of…
We study the problem of robustly learning multi-dimensional histograms. A $d$-dimensional function $h: D \rightarrow \mathbb{R}$ is called a $k$-histogram if there exists a partition of the domain $D \subseteq \mathbb{R}^d$ into $k$…
In this paper we suggest analytical methods and associated algorithms for determining the sum of the subsets $X_m$ of the set $X_n$ (subset sum problem). Our algorithm has time complexity $T=O(C_{n}^{k})$ ($k=[m/2]$, which significantly…
Sampling-based algorithms are widely used for motion planning in high-dimensional configuration spaces. However, due to low sampling efficiency, their performance often diminishes in complex configuration spaces with narrow corridors.…
From a high volume stream of weighted items, we want to maintain a generic sample of a certain limited size $k$ that we can later use to estimate the total weight of arbitrary subsets. This is the classic context of on-line reservoir…