Related papers: Stable Algorithms Lower Bounds for Estimation
We study the minimum number of constraints needed to formulate random instances of the maximum stable set problem via linear programs (LPs), in two distinct models. In the uniform model, the constraints of the LP are not allowed to depend…
Stochastic nested optimization, including stochastic compositional, min-max and bilevel optimization, is gaining popularity in many machine learning applications. While the three problems share the nested structure, existing works often…
In this note we study the numerical stability problem that may take place when calculating the cumulative distribution function of the {\it Hypoexponential} random variable. This computation is extensively used during the execution of Monte…
This paper develops a new approach to the estimation of the degree of boundedness or stability of multidimensional nonlinear systems with time-dependent nonperiodic coefficients-an essential task in various engineering and natural science…
Graph Neural Networks have achieved impressive results across diverse network modeling tasks, but accurately estimating uncertainty on graphs remains difficult, especially under distributional shifts. Unlike traditional uncertainty…
Stochastic optimization has found wide applications in minimizing objective functions in machine learning, which motivates a lot of theoretical studies to understand its practical success. Most of existing studies focus on the convergence…
Numerical analysis for linear constant-coefficients Finite Difference schemes was developed approximately fifty years ago. It relies on the assumption of scheme stability and in particular -- for the $L^2$ setting -- on the absence of…
In power system steady-state estimation (PSSE), one needs to consider (1) the need for robust statistics, (2) the nonconvex transmission constraints, (3) the fast-varying nature of the inputs, and the corresponding need to track optimal…
Recently, it has been observed that a sparse trigonometric polynomial, i.e. having only a small number of non-zero coefficients, can be reconstructed exactly from a small number of random samples using Basis Pursuit (BP) or Orthogonal…
We introduce a notion of algorithmic stability of learning algorithms---that we term \emph{argument stability}---that captures stability of the hypothesis output by the learning algorithm in the normed space of functions from which…
Gradient Descent (GD) is a powerful workhorse of modern machine learning thanks to its scalability and efficiency in high-dimensional spaces. Its ability to find local minimisers is only guaranteed for losses with Lipschitz gradients, where…
We consider the stable matching problem when the preference lists are not given explicitly but are represented in a succinct way and ask whether the problem becomes computationally easier and investigate other implications. We give…
The overall performance or expected excess risk of an iterative machine learning algorithm can be decomposed into training error and generalization error. While the former is controlled by its convergence analysis, the latter can be tightly…
In machine learning, it is commonly assumed that training and test data share the same population distribution. However, this assumption is often violated in practice because the sample selection bias may induce the distribution shift from…
We consider algorithms for load balancing on unreliable machines. The objective is to optimize the two criteria of minimizing the makespan and minimizing job reassignments in response to machine failures. We assume that the set of jobs is…
We consider the problem of counting (stable) equilibriums of an important family of algebraic differential equations modeling multistable biological regulatory systems. The problem can be solved, in principle, using real quantifier…
In Bayesian probabilistic programming, a central problem is to estimate the normalised posterior distribution (NPD) of a probabilistic program with conditioning via score (a.k.a. observe) statements. Most previous approaches address this…
Stable gonality is a multigraph parameter that measures the complexity of a graph. It is defined using maps to trees. Those maps, in some sense, divide the edges equally over the edges of the tree; stable gonality asks for the map with the…
The paper addresses parametric inequality systems described by polynomial functions in finite dimensions, where state-dependent infinite parameter sets are given by finitely many polynomial inequalities and equalities. Such systems can be…
Classical optimisation theory guarantees monotonic objective decrease for gradient descent (GD) when employed in a small step size, or ``stable", regime. In contrast, gradient descent on neural networks is frequently performed in a large…