Search Results for author: Ahmed El Alaoui

Found 10 papers, 0 papers with code

The Franz-Parisi Criterion and Computational Trade-offs in High Dimensional Statistics

no code implementations19 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.

Additive models

Algorithmic pure states for the negative spherical perceptron

no code implementations29 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

The Kikuchi Hierarchy and Tensor PCA

no code implementations8 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).

Bayesian Inference

Fundamental limits of detection in the spiked Wigner model

no code implementations25 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.

Tight Query Complexity Lower Bounds for PCA via Finite Sample Deformed Wigner Law

no code implementations4 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 $\langle \widehat{\mathsf{V}}, \mathbf{M} \widehat{\mathsf{V}}\rangle \ge (1 - \mathrm{const} \times \mathtt{gap})\sum_{i=1}^r \lambda_i(\mathbf{M})$.

Asymptotic behavior of $\ell_p$-based Laplacian regularization in semi-supervised learning

no code implementations2 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 $P$.

Fast Randomized Kernel Methods With Statistical Guarantees

no code implementations2 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.

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