Related papers: Near-optimal bounds for phase synchronization
Scaling large models requires optimization strategies that ensure rapid convergence grounded in stability. Maximal Update Parametrization ($\boldsymbol{\mu}$P) provides a theoretical safeguard for width-invariant $\Theta(1)$ activation…
In this work, we give a new parallel algorithm for the problem of maximizing a non-monotone diminishing returns submodular function subject to a cardinality constraint. For any desired accuracy $\epsilon$, our algorithm achieves a $1/e -…
This paper addresses the problems of minimizing the sum of a quadratic function and a proximal-friendly nonconvex nonsmooth function. While the existing Proximal Dogleg Opportunistic Majorization (PDOM) algorithm for these problems offers…
Let $f(y|\theta), \; \theta \in \Omega$ be a parametric family, $\eta(\theta)$ a given function, and $G$ an unknown mixing distribution. It is desired to estimate $E_G (\eta(\theta))\equiv \eta_G$ based on independent observations…
In multiple-input multiple-output (MIMO) spatially multiplexing (SM) systems, achievable error rate performance is determined by signal detection strategy. The optimal maximum-likelihood detection (MLD) that exhaustively examines all symbol…
Group synchronization asks to recover group elements from their pairwise measurements. It has found numerous applications across various scientific disciplines. In this work, we focus on orthogonal and permutation group synchronization…
Mean field inference in probabilistic models is generally a highly nonconvex problem. Existing optimization methods, e.g., coordinate ascent algorithms, can only generate local optima. In this work we propose provable mean filed methods for…
In this paper, we address the top-$K$ ranking problem with a monotone adversary. We consider the scenario where a comparison graph is randomly generated and the adversary is allowed to add arbitrary edges. The statistician's goal is then to…
Recent advances have significantly improved our understanding of the sample complexity of learning in average-reward Markov decision processes (AMDPs) under the generative model. However, much less is known about the constrained…
This paper proposes a novel exact maximum likelihood (ML) estimation method for general Gaussian processes, where all parameters are estimated jointly. The exact ML estimator (MLE) is consistent and asymptotically normally distributed. We…
A new likelihood based AR approximation is given for ARMA models. The usual algorithms for the computation of the likelihood of an ARMA model require $O(n)$ flops per function evaluation. Using our new approximation, an algorithm is…
The Laplace approximation (LA) has been proposed as a method for approximating the marginal likelihood of statistical models with latent variables. However, the approximate maximum likelihood estimators (MLEs) based on the LA are often…
This paper addresses the problem of control synthesis for nonlinear optimal control problems in the presence of state and input constraints. The presented approach relies upon transforming the given problem into an infinite-dimensional…
In contrast to the advances in characterizing the sample complexity for solving Markov decision processes (MDPs), the optimal statistical complexity for solving constrained MDPs (CMDPs) remains unknown. We resolve this question by providing…
We study mixture of linear regression (random coefficient) models, which capture population heterogeneity by allowing the regression coefficients to follow an unknown distribution $G^*$. In contrast to common parametric methods that fix the…
We propose a theoretical framework to compute, rapidly and accurately, the signal-to-noise ratio at the output of spatial-division multiplexing (SDM) linear MIMO equalizers with arbitrary numbers of spatial modes and filter taps and…
Estimating symmetric properties of a distribution, e.g. support size, coverage, entropy, distance to uniformity, are among the most fundamental problems in algorithmic statistics. While each of these properties have been studied extensively…
We present a unified framework for the construction of localized exponential integrators that bypasses the traditional trade-off between the accuracy of global spectral methods and the efficiency of sparse finite differences. By evaluating…
Maximum likelihood estimation in nonlinear models can exhibit substantial instability in finite samples when the data provide limited information about certain parameters. Such instability is driven by rare but extreme realizations of the…
Sparse phase retrieval aims to recover a $k$-sparse signal from $m$ phaseless measurements. While the theoretically optimal sample complexity for successful recovery is $\Omega(k \log n)$, existing algorithms can only achieve this bound for…