no code implementations • 20 Feb 2018 • Ahmed El Alaoui, Michael. I. Jordan
This region is shaped by the prior in a non-trivial way.
no code implementations • 4 Apr 2018 • Max Simchowitz, Ahmed El Alaoui, Benjamin Recht
We show that for every $\mathtt{gap} \in (0, 1/2]$, there exists a distribution over matrices $\mathbf{M}$ for which 1) $\mathrm{gap}_r(\mathbf{M}) = \Omega(\mathtt{gap})$ (where $\mathrm{gap}_r(\mathbf{M})$ is the normalized gap between the $r$ and $r+1$-st largest-magnitude eigenvector of $\mathbf{M}$), and 2) any algorithm $\mathsf{Alg}$ which takes fewer than $\mathrm{const} \times \frac{r \log d}{\sqrt{\mathtt{gap}}}$ queries fails (with overwhelming probability) to identity a matrix $\widehat{\mathsf{V}} \in \mathbb{R}^{d \times r}$ with orthonormal columns for which $\langle \widehat{\mathsf{V}}, \mathbf{M} \widehat{\mathsf{V}}\rangle \ge (1 - \mathrm{const} \times \mathtt{gap})\sum_{i=1}^r \lambda_i(\mathbf{M})$.
no code implementations • 14 Apr 2017 • Max Simchowitz, Ahmed El Alaoui, Benjamin Recht
We prove a \emph{query complexity} lower bound on rank-one principal component analysis (PCA).
no code implementations • 2 Mar 2016 • Ahmed El Alaoui, Xiang Cheng, Aaditya Ramdas, Martin J. Wainwright, Michael. I. Jordan
Together, these properties show that $p = d+1$ is an optimal choice, yielding a function estimate $\hat{f}$ that is both smooth and non-degenerate, while remaining maximally sensitive to $P$.
no code implementations • 2 Nov 2014 • Ahmed El Alaoui, Michael W. Mahoney
By extending the notion of \emph{statistical leverage scores} to the setting of kernel ridge regression, our main statistical result is to identify an importance sampling distribution that reduces the size of the sketch (i. e., the required number of columns to be sampled) to the \emph{effective dimensionality} of the problem.
no code implementations • 25 Jun 2018 • Ahmed El Alaoui, Florent Krzakala, Michael. I. Jordan
We study the fundamental limits of detecting the presence of an additive rank-one perturbation, or spike, to a Wigner matrix.
no code implementations • 8 Apr 2019 • Alexander S. Wein, Ahmed El Alaoui, Cristopher Moore
Our hierarchy is analogous to the sum-of-squares (SOS) hierarchy but is instead inspired by statistical physics and related algorithms such as belief propagation and AMP (approximate message passing).
no code implementations • 24 Jan 2020 • Kabir Aladin Chandrasekher, Ahmed El Alaoui, Andrea Montanari
We study high-dimensional regression with missing entries in the covariates.
no code implementations • 29 Oct 2020 • Ahmed El Alaoui, Mark Sellke
In this paper we design an efficient algorithm which, given oracle access to the solution of the Parisi variational principle, exploits this conjectured FRSB structure for $\kappa<0$ and outputs a vector $\hat{\sigma}$ satisfying $\langle g_a , \hat{\sigma}\rangle \ge \kappa \sqrt{N}$ for all $1\le a \le M$ and lying on a sphere of non-trivial radius $\sqrt{\bar{q} N}$, where $\bar{q} \in (0, 1)$ is the right-end of the support of the associated Parisi measure.
Probability Data Structures and Algorithms Mathematical Physics Mathematical Physics
no code implementations • 19 May 2022 • Afonso S. Bandeira, Ahmed El Alaoui, Samuel B. Hopkins, Tselil Schramm, Alexander S. Wein, Ilias Zadik
We define a free-energy based criterion for hardness and formally connect it to the well-established notion of low-degree hardness for a broad class of statistical problems, namely all Gaussian additive models and certain models with a sparse planted signal.