Related papers: Minimax lower bounds for function estimation on gr…
This article concerns the performance limits of strictly causal state estimation for linear systems with fixed, but uncertain, parameters belonging to a finite set. In particular, we provide upper and lower bounds on the smallest achievable…
When a parameter of interest is defined to be a nondifferentiable transform of a regular parameter, the parameter does not have an influence function, rendering the existing theory of semiparametric efficient estimation inapplicable.…
We study the problem of empirical minimization for variance-type functionals over functional classes. Sharp non-asymptotic bounds for the excess variance are derived under mild conditions. In particular, it is shown that under some…
Biased stochastic estimators, such as finite-differences for noisy gradient estimation, often contain parameters that need to be properly chosen to balance impacts from the bias and the variance. While the optimal order of these parameters…
Two classical upper bounds on the Shannon capacity of graphs are the $\vartheta$-function due to Lov\'asz and the minrank parameter due to Haemers. We provide several explicit constructions of $n$-vertex graphs with a constant…
We propose graph-dependent implicit regularisation strategies for distributed stochastic subgradient descent (Distributed SGD) for convex problems in multi-agent learning. Under the standard assumptions of convexity, Lipschitz continuity,…
We consider the problem of estimating the value of a linear functional in nonparametric instrumental regression, where in the presence of an instrument W a response Y is modeled in dependence of an endogenous explanatory variable Z. The…
Submodular functions describe a variety of discrete problems in machine learning, signal processing, and computer vision. However, minimizing submodular functions poses a number of algorithmic challenges. Recent work introduced an…
This survey provides an overview of optimal estimation of linear functionals which depend on the unknown values of a stationary stochastic sequence. Based on observations of the sequence without noise as well as observations of the sequence…
This paper is devoted to guaranteed estimation (so-called minimax estimation) of linear functions, defined on the solutions domain of the linear descriptor difference equations (LDDE) system, where right-hand part and initial condition are…
This paper presents a bias-variance tradeoff of graph Laplacian regularizer, which is widely used in graph signal processing and semi-supervised learning tasks. The scaling law of the optimal regularization parameter is specified in terms…
Variance function estimation in nonparametric regression is considered and the minimax rate of convergence is derived. We are particularly interested in the effect of the unknown mean on the estimation of the variance function. Our results…
The problem of estimating the mean of random functions based on discretely sampled data arises naturally in functional data analysis. In this paper, we study optimal estimation of the mean function under both common and independent designs.…
The Minimum Sum Coloring Problem is a variant of the Graph Vertex Coloring Problem, for which each color has a weight. This paper presents a new way to find a lower bound of this problem, based on a relaxation into an integer partition…
For any finite, undirected, non-bipartite, vertex-transitive graph, we establish an explicit lower bound for the smallest eigenvalue of its normalised adjacency operator, which depends on the graph only through its degree and its…
In this paper, we explore the approximation theory of functions defined on graphs. Our study builds upon the approximation results derived from the $K$-functional. We establish a theoretical framework to assess the lower bounds of…
Learning properties of large graphs from samples has been an important problem in statistical network analysis since the early work of Goodman \cite{Goodman1949} and Frank \cite{Frank1978}. We revisit a problem formulated by Frank…
We investigate the problem of estimating the structure factor, or spectra, of stationary spatial point processes. In the first part, we establish a minimax lower bound for this estimation problem, using an approach tailored to second-order…
The increasing availability of graph-structured data motivates the task of optimising over functions defined on the node set of graphs. Traditional graph search algorithms can be applied in this case, but they may be sample-inefficient and…
The purpose of this paper is to develop a "calculus" on graphs that allows graph theory to have new connections to analysis. For example, our framework gives rise to many new partial differential equations on graphs, most notably a new…