Related papers: Randomness-efficient Curve Samplers
In this paper we propose new techniques to sample arbitrary third-order tensors, with an objective of speeding up tensor algorithms that have recently gained popularity in machine learning. Our main contribution is a new way to select, in a…
A core principle in statistical learning is that smoothness of target functions allows to break the curse of dimensionality. However, learning a smooth function seems to require enough samples close to one another to get meaningful estimate…
In this chapter, we discuss recent work on learning sparse approximations to high-dimensional functions on data, where the target functions may be scalar-, vector- or even Hilbert space-valued. Our main objective is to study how the…
Graph spanners are sparse subgraphs that faithfully preserve the distances in the original graph up to small stretch. Spanner have been studied extensively as they have a wide range of applications ranging from distance oracles, labeling…
Quantum one-class support vector machines leverage the advantage of quantum kernel methods for semi-supervised anomaly detection. However, their quadratic time complexity with respect to data size poses challenges when dealing with large…
Miller et al. \cite{MPVX15} devised a distributed\footnote{They actually showed a PRAM algorithm. The distributed algorithm with these properties is implicit in \cite{MPVX15}.} algorithm in the CONGEST model, that given a parameter $k =…
Quantum circuits that generate coherent superpositions of stochastic processes are key to many downstream quantum-accelerated tasks, such as risk analysis, importance sampling, and DNA sequencing. However, traditional methods for designing…
Efficient sampling from a classical Gibbs distribution is an important computational problem with applications ranging from statistical physics over Monte Carlo and optimization algorithms to machine learning. We introduce a family of…
We consider the problem of sampling from a strongly log-concave density in $\mathbb{R}^d$, and prove an information theoretic lower bound on the number of stochastic gradient queries of the log density needed. Several popular sampling…
We consider the fundamental learning problem of estimating properties of distributions over large domains. Using a novel piecewise-polynomial approximation technique, we derive the first unified methodology for constructing sample- and…
Almost every software system provides configuration options to tailor the system to the target platform and application scenario. Often, this configurability renders the analysis of every individual system configuration infeasible. To…
We study the sample complexity of differentially private optimization of quasi-concave functions. For a fixed input domain $\mathcal{X}$, Cohen et al. (STOC 2023) proved that any generic private optimizer for low sensitive quasi-concave…
Space efficient algorithms play a central role in dealing with large amount of data. In such settings, one would like to analyse the large data using small amount of "working space". One of the key steps in many algorithms for analysing…
Signature is an infinite graded sequence of statistics known to characterize geometric rough paths, which includes the paths with bounded variation. This object has been studied successfully for machine learning with mostly applications in…
Random features (RFs) are a popular technique to scale up kernel methods in machine learning, replacing exact kernel evaluations with stochastic Monte Carlo estimates. They underpin models as diverse as efficient transformers (by…
Random dynamics in isolated quantum systems is of practical use in quantum information and is of theoretical interest in fundamental physics. Despite a large number of theoretical studies, it has not been addressed how random dynamics can…
In the problem of high-dimensional convexity testing, there is an unknown set $S \subseteq \mathbb{R}^n$ which is promised to be either convex or $\varepsilon$-far from every convex body with respect to the standard multivariate normal…
Random features are a powerful technique for rewriting positive-definite kernels as linear products. They bring linear tools to bear in important nonlinear domains like KNNs and attention. Unfortunately, practical implementations require…
The random sampling task performed by Google's Sycamore processor gave us a glimpse of the "Quantum Supremacy era". This has definitely shed some spotlight on the power of random quantum circuits in this abstract task of sampling outputs…
While it is commonly observed in practice that pruning networks to a certain level of sparsity can improve the quality of the features, a theoretical explanation of this phenomenon remains elusive. In this work, we investigate this by…