Related papers: Stable Algorithms Lower Bounds for Estimation
In this work, we give efficient algorithms for privately estimating a Gaussian distribution in both pure and approximate differential privacy (DP) models with optimal dependence on the dimension in the sample complexity. In the pure DP…
We propose an algorithm to numerically determined whether a second-order linear PDE problem satisfying a Garding inequality is well-posed. This algorithm further provides a lower bound to the inf-sup constant of the weak formulation, which…
This paper develops several average-case reduction techniques to show new hardness results for three central high-dimensional statistics problems, implying a statistical-computational gap induced by robustness, a detection-recovery gap and…
In the current work we introduce a novel estimation of distribution algorithm to tackle a hard combinatorial optimization problem, namely the single-machine scheduling problem, with uncertain delivery times. The majority of the existing…
The representation of functions by artificial neural networks depends on a large number of parameters in a non-linear fashion. Suitable parameters of these are found by minimizing a 'loss functional', typically by stochastic gradient…
Statistical inference with bandit data presents fundamental challenges due to adaptive sampling, which violates the independence assumptions underlying classical asymptotic theory. Recent work has identified stability as a sufficient…
A variety of algorithms have been proposed to address the power system state estimation problem in the presence of uncertainties in the data. However, less emphasis has been given to handling perturbations in the model. In the context of…
Among the many ways to model signals, a recent approach that draws considerable attention is sparse representation modeling. In this model, the signal is assumed to be generated as a random linear combination of a few atoms from a…
We introduce an NP-complete graph decision problem, the "Multi-stage graph Simple Path" (abbr. MSP) problem, which focuses on determining the existence of specific "global paths" in a graph $G$. We show that the MSP problem can be solved in…
Algorithmic stability is a key characteristic to ensure the generalization ability of a learning algorithm. Among different notions of stability, \emph{uniform stability} is arguably the most popular one, which yields exponential…
When recovering an unknown signal from noisy measurements, the computational difficulty of performing optimal Bayesian MMSE (minimum mean squared error) inference often necessitates the use of maximum a posteriori (MAP) inference, a special…
STOchastic Recursive Momentum (STORM)-based algorithms have been widely developed to solve one to $K$-level ($K \geq 3$) stochastic optimization problems. Specifically, they use estimators to mitigate the biased gradient issue and achieve…
We consider the stability analysis of a large class of linear 1-D PDEs with polynomial data. This class of PDEs contains, as examples, parabolic and hyperbolic PDEs, PDEs with boundary feedback and systems of in-domain/boundary coupled…
An algorithm based on the interior-point methodology for solving continuous nonlinearly constrained optimization problems is proposed, analyzed, and tested. The distinguishing feature of the algorithm is that it presumes that only noisy…
We propose a new variational inference algorithm for learning in Gaussian Process State-Space Models (GPSSMs). Our algorithm enables learning of unstable and partially observable systems, where previous algorithms fail. Our main algorithmic…
We study $\textit{sparse singular value certificates}$ for random rectangular matrices. If $M$ is an $n \times d$ matrix with independent Gaussian entries, we give a new family of polynomial-time algorithms which can certify upper bounds on…
In this paper, we develop deterministic fully dynamic algorithms for computing approximate distances in a graph with worst-case update time guarantees. In particular, we obtain improved dynamic algorithms that, given an unweighted and…
We study a class of nonconvex nonsmooth optimization problems in which the objective is a sum of two functions: One function is the average of a large number of differentiable functions, while the other function is proper, lower…
We consider the minimum-norm-point (MNP) problem over polyhedra, a well-studied problem that encompasses linear programming. We present a general algorithmic framework that combines two fundamental approaches for this problem: active set…
Stochastic bilevel optimization (SBO) has been integrated into many machine learning paradigms recently, including hyperparameter optimization, meta learning, and reinforcement learning. Along with the wide range of applications, there have…