Related papers: Near-Optimal Averaging Samplers and Matrix Sampler…
We propose a sampling algorithm that achieves superior complexity bounds in all the classical settings (strongly log-concave, log-concave, Logarithmic-Sobolev inequality (LSI), Poincar\'e inequality) as well as more general settings with…
An approximate sparse recovery system in $\ell_1$ norm consists of parameters $k$, $\epsilon$, $N$, an $m$-by-$N$ measurement $\Phi$, and a recovery algorithm, $\mathcal{R}$. Given a vector, $\mathbf{x}$, the system approximates $x$ by…
We study the theoretical properties of random Fourier features classification with Lipschitz continuous loss functions such as support vector machine and logistic regression. Utilizing the regularity condition, we show for the first time…
Two recent lower bounds on the compressibility of repetitive sequences, $\delta \le \gamma$, have received much attention. It has been shown that a length-$n$ string $S$ over an alphabet of size $\sigma$ can be represented within the…
For massive data, the family of subsampling algorithms is popular to downsize the data volume and reduce computational burden. Existing studies focus on approximating the ordinary least squares estimate in linear regression, where…
Finding a small spectral approximation for a tall $n \times d$ matrix $A$ is a fundamental numerical primitive. For a number of reasons, one often seeks an approximation whose rows are sampled from those of $A$. Row sampling improves…
The study of approximate matching in the Massively Parallel Computations (MPC) model has recently seen a burst of breakthroughs. Despite this progress, however, we still have a far more limited understanding of maximal matching which is one…
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…
We establish improved sample-complexity bounds for sample-based Lindbladian simulation based on the Wave Matrix Lindbladization (WML) algorithm. For a jump operator $L$ with dimension $d$, we derive an explicit non-asymptotic sample…
Many statistical applications involve models for which it is difficult to evaluate the likelihood, but from which it is relatively easy to sample. Approximate Bayesian computation is a likelihood-free method for implementing Bayesian…
The area of sublinear algorithms have recently received a lot of attention. In this setting, one has to choose specific access model for the input, as the algorithm does not have time to pre-process or even to see the whole input. A…
This paper addresses a fundamental problem in random variate generation: given access to a random source that emits a stream of independent fair bits, what is the most accurate and entropy-efficient algorithm for sampling from a discrete…
We consider several related problems of estimating the 'sparsity' or number of nonzero elements $d$ in a length $n$ vector $\mathbf{x}$ by observing only $\mathbf{b} = M \odot \mathbf{x}$, where $M$ is a predesigned test matrix independent…
Recently [Bhattacharya et al., STOC 2015] provide the first non-trivial algorithm for the densest subgraph problem in the streaming model with additions and deletions to its edges, i.e., for dynamic graph streams. They present a…
Subsampling is an effective approach to alleviate the computational burden associated with large-scale datasets. Nevertheless, existing subsampling estimators incur a substantial loss in estimation efficiency compared to estimators based on…
Importance sampling has been reported to produce algorithms with excellent empirical performance in counting problems. However, the theoretical support for its efficiency in these applications has been very limited. In this paper, we…
We study dynamic $(1-\epsilon)$-approximate rounding of fractional matchings -- a key ingredient in numerous breakthroughs in the dynamic graph algorithms literature. Our first contribution is a surprisingly simple deterministic rounding…
We revisit the sample and computational complexity of completing a rank-1 tensor in $\otimes_{i=1}^{N} \mathbb{R}^{d}$, given a uniformly sampled subset of its entries. We present a characterization of the problem (i.e. nonzero entries)…
We consider the sensitivity of algorithms for the maximum matching problem against edge and vertex modifications. Algorithms with low sensitivity are desirable because they are robust to edge failure or attack. In this work, we show a…
A fundamental issue in real-world systems, such as sensor networks, is the selection of observations which most effectively reduce uncertainty. More specifically, we address the long standing problem of nonmyopically selecting the most…