arXiv:2606. 15679v1 Announce Type: cross Abstract: Stochastic trace estimation is a standard tool for approximating the trace of a large-scale matrix available only through matrix-vector products.
arXiv:2606. 27298v1 Announce Type: cross Abstract: We study the fundamental problem of learning a high-dimensional Gaussian truncated to an unknown halfspace.
arXiv:2609. 18577v1 Announce Type: new Abstract: We consider the problem of estimating the trace of an implicit matrix $\mathbf{A} \in \mathbb{R}^{d^p\times d^p}$ that can only be accessed through matrix-vector products queries.
arXiv:2609.39855v1 Announce Type: new Abstract: We study the width required for a randomly initialized hidden layer of a neural network to achieve rank lifting. Namely, given a dataset $X \in \mathbb...
\texttt{TensorSketch} by~\cite{pham2013fast,kar2012random} provides efficient sketching algorithms for high-dimensional polynomial kernels $\vec{x}^{\otimes p} \in \R^{d^p}$. \cite{kar2012random} uses dense Johnson-Lindenstrauss (JL)-type projections with computational cost $O(pDd)$, where $D$ denotes the sketch dimension, whereas~\cite{pham2013fast} extends the sparse \texttt{CountSketch}~\citep{count_sketch} algorithm, yielding a faster algorithm for high-dimensional sparse inputs with running time $O\big(p(\nnz{\vec{x}} + D \log D)\big)$.
arXiv:2609. 13954v1 Announce Type: new Abstract: Ensemble sampling offers a practical approach to randomized exploration by maintaining a collection of models, but how small an ensemble can be while retaining strong regret guarantees remains unresolved.
arXiv:2602. 13906v2 Announce Type: replace-cross Abstract: Stochastic approximation (SA) is a method for finding the root of an operator perturbed by noise.
arXiv:2608. 10523v1 Announce Type: cross Abstract: \texttt{TensorSketch} by~\cite{pham2013fast,kar2012random} provides efficient sketching algorithms for high-dimensional polynomial kernels $\vec{x}^{\otimes p} \in \R^{d^p}$.
arXiv:2609. 02155v1 Announce Type: new Abstract: The Johnson-Lindenstrauss (JL) lemma guarantees that a random projection of $n$ points to $m=O(\varepsilon^{-2}\log n)$ dimensions preserves pairwise squared distances within relative error $\varepsilon$ with high probability, and this dimension order is asymptotically optimal.
arXiv:2602. 05869v2 Announce Type: replace-cross Abstract: We introduce Wedge Sampling, a new non-adaptive sampling scheme for low-rank tensor completion.
arXiv:2608. 26552v1 Announce Type: cross Abstract: Randomized sketch-and-solve algorithms accelerate overconstrained $\ell_2$ regression by replacing the input with a smaller problem.
arXiv:2603. 16798v2 Announce Type: replace Abstract: We study mean estimation for a Gaussian distribution with identity covariance in $\mathbb{R}^d$ under a missing data scheme termed realizable $\epsilon$-contamination model.
arXiv:2608. 13922v1 Announce Type: new Abstract: Detecting distributional changes in high dimension is difficult when neither the pre-change nor post-change density is parametrically specified.