Related papers: Stochastic incompleteness for graphs and weak Omor…
The minimum number of observations such that the maximum likelihood estimator in a Gaussian graphical model exists with probability one is called the maximum likelihood threshold of the underlying graph G. The natural algebraic relaxation…
For a graph $G$ define the parameters $\ell(G)$ and $L(G)$ as the minimum and maximum value of $\nu(G\backslash F)$, where $F$ is a maximum matching of $G$ and $\nu(G)$ is the matching number of $G$. In this paper, we show that there is a…
We derive a consistency result, in the $L_1$-sense, for incomplete U-statistics in the non-standard case where the kernel at hand has infinite second-order moments. Assuming that the kernel has finite moments of order $p(\geq 1)$, we obtain…
Estimating missing judgements is a key component in many multi-criteria decision making techniques, especially in the Analytic Hierarchy Process. Inspired by the Koczkodaj inconsistency index and a widely used solution concept of…
We study local complexity measures for stochastic convex optimization problems, providing a local minimax theory analogous to that of H\'{a}jek and Le Cam for classical statistical problems. We give complementary optimality results,…
We prove that the hypotheses in the version of the Omori-Yau maximum principle that was given by Pigola-Rigoli-Setti are logically equivalent to the assumption that the manifold carries a $C^2$ proper function whose gradient and Hessian…
A method for compression of large graphs and matrices to a block structure is further developed. Szemer\'edi's regularity lemma is used as a generic motivation of the significance of stochastic block models. Another ingredient of the method…
A Riemannian manifold $M$ is said to satisfy the Omori-Yau maximum principle if for any $C^2$ bounded function $g:M\to \Bbb R$ there is a sequence $x_n\in M$, such that $\lim_{n\to \infty}g(x_n)=\sup_M g$, $ \lim_{n\to \infty}|\nabla…
Consider the family of all finite graphs with maximum degree $\Delta(G)<d$ and matching number $\nu(G)<m$. In this paper we give a new proof to obtain the exact upper bound for the number of edges in such graphs and also characterize all…
Stochastic incompleteness of a Riemannian manifold $M$ amounts to the nonconservation of probability for the heat semigroup on $M$. We show that this property is equivalent to the existence of nonnegative, nontrivial, bounded (sub)solutions…
This survey paper deals with upper and lower bounds on the number of $k$-matchings in regular graphs on $N$ vertices. For the upper bounds we recall the upper matching conjecture which is known to hold for perfect matchings. For the lower…
A Neumaier graph is a non-complete edge-regular graph containing a regular clique. A Neumaier graph that is not strongly regular is called a strictly Neumaier graph. In this work we present a new construction of strictly Neumaier graphs,…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
We derive, for the square operator of Yau, an analogue of the Omori-Yau maximum principle for the Laplacian. We then apply it to obtain nonexistence results concerning complete spacelike hypersurfaces with constant higher order mean…
In this note we prove an optimal volume growth condition for stochastic completeness of graphs under very mild assumptions. This is realized by proving a uniqueness class criterion for the heat equation which is an analogue to a…
In a decision problem, observations are said to be material if they must be taken into account to perform optimally. Decision problems have an underlying (graphical) causal structure, which may sometimes be used to evaluate certain…
The inconsistency of pairwise comparisons remains difficult to interpret in the absence of acceptability thresholds. The popular 10% cut-off rule proposed by Saaty has recently been applied to incomplete pairwise comparison matrices, which…
We introduce a new version of a curvature-dimension inequality for non-negative curvature. We use this inequality to prove a logarithmic Li-Yau inequality on finite graphs. To formulate this inequality, we introduce a non-linear variant of…
Theoretical analyses for graph learning methods often assume a complete observation of the input graph. Such an assumption might not be useful for handling any-size graphs due to the scalability issues in practice. In this work, we develop…
Given a pair of graphs with the same number of vertices, the inexact graph matching problem consists in finding a correspondence between the vertices of these graphs that minimizes the total number of induced edge disagreements. We study…