Related papers: Efficient Sampling from Feasible Sets of SDPs and …
With the aim of estimating the abundance map from observations only, linear unmixing approaches are not always suitable to spectral images, especially when the number of bands is too small or when the spectra of the observed data are too…
Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, but the result depends on distances, which vary continuously.…
Sampling is a fundamental problem in computer science and statistics. However, for a given task and stream, it is often not possible to choose good sampling probabilities in advance. We derive a general framework for adaptively changing the…
This paper studies high-dimensional sparse clustering, a combinatorial NP-hard problem arising from the bilinear coupling between cluster assignment and feature selection. We analyze semidefinite programming (SDP) relaxations of $K$-means…
We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…
We prove effective density of random walks on homogeneous spaces, assuming that the underlying measure is supported on matrices generating a dense subgroup and having algebraic entries. The main novelty is an argument passing from high…
Semidefinite programming (SDP) is a powerful tool for tackling a wide range of computationally hard problems such as clustering. Despite the high accuracy, semidefinite programs are often too slow in practice with poor scalability on large…
Eigenvalues of a graph are of high interest in graph analytics for Big Data due to their relevance to many important properties of the graph including network resilience, community detection and the speed of viral propagation. Accurate…
Randomized algorithms depend on accurate sampling from probability distributions, as their correctness and performance hinge on the quality of the generated samples. However, even for common distributions like Binomial, exact sampling is…
For a graph $G$ on $n$ vertices, naively sampling the position of a random walk of at time $t$ requires work $\Omega(t)$. We desire local access algorithms supporting $\text{position}(G,s,t)$ queries, which return the position of a random…
High-dimensional limit theorems have been shown useful to derive tuning rules for finding the optimal scaling in random-walk Metropolis algorithms. The assumptions under which weak convergence results are proved are however restrictive: the…
Graph embedding based on random-walks supports effective solutions for many graph-related downstream tasks. However, the abundance of embedding literature has made it increasingly difficult to compare existing methods and to identify…
Slice Sampling has emerged as a powerful Markov Chain Monte Carlo algorithm that adapts to the characteristics of the target distribution with minimal hand-tuning. However, Slice Sampling's performance is highly sensitive to the…
The random order graph streaming model has received significant attention recently, with problems such as matching size estimation, component counting, and the evaluation of bounded degree constant query testable properties shown to admit…
Graph vertex embeddings based on random walks have become increasingly influential in recent years, showing good performance in several tasks as they efficiently transform a graph into a more computationally digestible format while…
A semidefinite program (SDP) is a particular kind of convex optimization problem with applications in operations research, combinatorial optimization, quantum information science, and beyond. In this work, we propose variational quantum…
We develop, analyze, implement, and compare new algorithms for creating $\varepsilon$-samples of range spaces defined by halfspaces which have size sub-quadratic in $1/\varepsilon$, and have runtime linear in the input size and…
We propose a simple subsampling scheme for fast randomized approximate computation of optimal transport distances. This scheme operates on a random subset of the full data and can use any exact algorithm as a black-box back-end, including…
We provide dual algorithms for sampling the space of abstract simplicial complexes on a fixed number of vertices. We develop a generative and descriptive sampler designed with heuristics to help balance the combinatorial multiplicities of…
This paper considers the problem of completing a rating matrix based on sub-sampled matrix entries as well as observed social graphs and hypergraphs. We show that there exists a \emph{sharp threshold} on the sample probability for the task…