Related papers: Spectral Estimators for Multi-Index Models: Precis…
In a mixed generalized linear model, the goal is to learn multiple signals from unlabeled observations: each sample comes from exactly one signal, but it is not known which one. We consider the prototypical problem of estimating two…
We consider the problem of how many samples from a Gaussian multi-index model are required to weakly reconstruct the relevant index subspace. Despite its increasing popularity as a testbed for investigating the computational complexity of…
Line spectral estimation theory aims to estimate the off-the-grid spectral components of a time signal with optimal precision. Recent results have shown that it is possible to recover signals having sparse line spectra from few temporal…
We consider the problem of parameter estimation in a high-dimensional generalized linear model. Spectral methods obtained via the principal eigenvector of a suitable data-dependent matrix provide a simple yet surprisingly effective…
In this paper, we develop a novel framework to optimally design spectral estimators for phase retrieval given measurements realized from an arbitrary model. We begin by deconstructing spectral methods, and identify the fundamental…
We study a spectral initialization method that serves a key role in recent work on estimating signals in nonconvex settings. Previous analysis of this method focuses on the phase retrieval problem and provides only performance bounds. In…
Phase retrieval refers to algorithmic methods for recovering a signal from its phaseless measurements. Local search algorithms that work directly on the non-convex formulation of the problem have been very popular recently. Due to the…
Blind methods often separate or identify signals or signal subspaces up to an unknown scaling factor. Sometimes it is necessary to cope with the scaling ambiguity, which can be done through reconstructing signals as they are received by…
Spectral estimators are fundamental in lowrank matrix models and arise throughout machine learning and statistics, with applications including network analysis, matrix completion and PCA. These estimators aim to recover the leading…
In phase retrieval we want to recover an unknown signal $\boldsymbol x\in\mathbb C^d$ from $n$ quadratic measurements of the form $y_i = |\langle{\boldsymbol a}_i,{\boldsymbol x}\rangle|^2+w_i$ where $\boldsymbol a_i\in \mathbb C^d$ are…
Phase retrieval refers to the problem of recovering real- or complex-valued vectors from magnitude measurements. The best-known algorithms for this problem are iterative in nature and rely on so-called spectral initializers that provide…
Computing eigenvalues of very large matrices is a critical task in many machine learning applications, including the evaluation of log-determinants, the trace of matrix functions, and other important metrics. As datasets continue to grow in…
Phase retrieval refers to the problem of recovering a signal $\mathbf{x}_{\star}\in\mathbb{C}^n$ from its phaseless measurements $y_i=|\mathbf{a}_i^{\mathrm{H}}\mathbf{x}_{\star}|$, where $\{\mathbf{a}_i\}_{i=1}^m$ are the measurement…
We consider the problem of subspace estimation in situations where the number of available snapshots and the observation dimension are comparable in magnitude. In this context, traditional subspace methods tend to fail because the…
We present the optimal design of a spectral method widely used to initialize nonconvex optimization algorithms for solving phase retrieval and other signal recovery problems. Our work leverages recent results that provide an exact…
Supervised topic models simultaneously model the latent topic structure of large collections of documents and a response variable associated with each document. Existing inference methods are based on variational approximation or Monte…
We study matrix estimation problems arising in reinforcement learning (RL) with low-rank structure. In low-rank bandits, the matrix to be recovered specifies the expected arm rewards, and for low-rank Markov Decision Processes (MDPs), it…
Power spectrum estimation is an important tool in many applications, such as the whitening of noise. The popular multitaper method enjoys significant success, but fails for short signals with few samples. We propose a statistical model…
This paper studies two spectrum estimation methods for the case that the samples are obtained at a rate lower than the Nyquist rate. The first method is the correlogram method for undersampled data. The algorithm partitions the spectrum…
Dimensionality reduction is critical for deploying dense retrieval systems at scale, yet mainstream post-hoc methods face a fundamental trade-off: principal component analysis (PCA) preserves dominant variance but underutilizes…