相关论文: Spiked Covariance Estimation from Modulo-Reduced M…

Model-based reinforcement learning algorithms tend to achieve higher sample efficiency than model-free methods. However, due to the inevitable errors of learned models, model-based methods struggle to achieve the same asymptotic performance…

This paper proposes maximum (quasi)likelihood estimation for high dimensional factor models with regime switching in the loadings. The model parameters are estimated jointly by the EM (expectation maximization) algorithm, which in the…

We consider the matrix completion problem under a form of row/column weighted entrywise sampling, including the case of uniform entrywise sampling as a special case. We analyze the associated random observation operator, and prove that with…

We use tools from random matrix theory to study the multi-spiked tensor model, i.e., a rank-$r$ deformation of a symmetric random Gaussian tensor. In particular, thanks to the nature of local optimization methods used to find the maximum…

Estimation of low-rank matrices is of significant interest in a range of contemporary applications. In this paper, we introduce a rank-one projection model for low-rank matrix recovery and propose a constrained nuclear norm minimization…

We consider fast algorithms for monotone submodular maximization with a general matroid constraint. We present a randomized $(1 - 1/e - \epsilon)$-approximation algorithm that requires $\tilde{O}_{\epsilon}(\sqrt{r} n)$ independence oracle…

To interpret observations of astrophysical disks it is essential to understand the formation process of the emitted light. If the disk is optically thick, scattering dominated and permeated by a Keplerian velocity field, Non-Local…

We study the task of high-dimensional entangled mean estimation in the subset-of-signals model. Specifically, given $N$ independent random points $x_1,\ldots,x_N$ in $\mathbb{R}^D$ and a parameter $\alpha \in (0, 1)$ such that each $x_i$ is…

This paper considers the recovery of a rank $r$ positive semidefinite matrix $X X^T\in\mathbb{R}^{n\times n}$ from $m$ scalar measurements of the form $y_i := a_i^T X X^T a_i$ (i.e., quadratic measurements of $X$). Such problems arise in a…

We propose and analyse randomized cubature formulae for the numerical integration of functions with respect to a given probability measure $\mu$ defined on a domain $\Gamma \subseteq \mathbb{R}^d$, in any dimension $d$. Each cubature…

We consider the Sherrington-Kirkpatrick model of spin glasses at high-temperature and no external field, and study the problem of sampling from the Gibbs distribution $\mu$ in polynomial time. We prove that, for any inverse temperature…

This article studies the \emph{robust covariance matrix estimation} of a data collection $X = (x_1,\ldots,x_n)$ with $x_i = \sqrt \tau_i z_i + m$, where $z_i \in \mathbb R^p$ is a \textit{concentrated vector} (e.g., an elliptical random…

Recently, many machine learning and statistical models such as non-linear regressions, the Single Index, Multi-index, Varying Coefficient Index Models and Two-layer Neural Networks can be reduced to or be seen as a special case of a new…

The spiking activity of single neurons can be well described by a nonlinear integrate-and-fire model that includes somatic adaptation. When exposed to fluctuating inputs sparsely coupled populations of these model neurons exhibit stochastic…

We propose a new random pruning method (called "submodular sparsification (SS)") to reduce the cost of submodular maximization. The pruning is applied via a "submodularity graph" over the $n$ ground elements, where each directed edge is…

The phase retrieval problem is a fundamental problem in many fields, which is appealing for investigation. It is to recover the signal vector $\tilde{x}\in\mathbb{C}^d$ from a set of $N$ measurements $b_n=|f^*_n\tilde{x}|^2,\ n=1,\cdots,…

Implantable brain-machine interfaces (iBMIs) are evolving to record from thousands of neurons wirelessly but face challenges in data bandwidth, power consumption, and implant size. We propose a novel Spiking Neural Network Spike Detector…

We consider the inverse problem of reconstructing the scattering and absorption coefficients using boundary measurements for a time dependent radiative transfer equation (RTE). As the measurement is mostly polluted by errors, both…

This paper is concerned with a numerical method for a 3D coefficient inverse problem with phaseless scattering data. These are multi-frequency data generated by a single direction of the incident plane wave. Our numerical procedure consists…

A fundamental problem in neuroscience is to characterize the dynamics of spiking from the neurons in a circuit that is involved in learning about a stimulus or a contingency. A key limitation of current methods to analyze neural spiking…