Related papers: Likelihood-based Inference for Exponential-Family …
We consider convex hulls of random walks whose steps belong to the domain of attraction of a stable law in $\mathbb{R}^d$. We prove convergence of the convex hull in the space of all convex and compact subsets of $\mathbb{R}^d$, equipped…
We present randomized versions of the {\it triangle algorithm} introduced in \cite{kal14}. The triangle algorithm tests membership of a distinguished point $p \in \mathbb{R} ^m$ in the convex hull of a given set $S$ of $n$ points in…
The paper demonstrates the use of LASSO-based estimation in network models. Taking the Exponential Random Graph Model (ERGM) as a flexible and widely used model for network data analysis, the paper focuses on the question of how to specify…
In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…
Many popular models from the networks literature can be viewed through a common lens of contingency tables on network dyads, resulting in \emph{log-linear ERGMs}: exponential family models for random graphs whose sufficient statistics are…
The $\lambda$-exponential family generalizes the standard exponential family via a generalized convex duality motivated by optimal transport. It is the constant-curvature analogue of the exponential family from the information-geometric…
Certifiable, adaptive uncertainty estimates for unknown quantities are an essential ingredient of sequential decision-making algorithms. Standard approaches rely on problem-dependent concentration results and are limited to a specific…
In multiple scientific and technological applications we face the problem of having low dimensional data to be justified by a linear model defined in a high dimensional parameter space. The difference in dimensionality makes the problem…
We investigate the computational complexity of the exponential random graph model (ERGM) commonly used in social network analysis. This model represents a probability distribution on graphs by setting the log-likelihood of generating a…
The convex hull of N independent random points chosen on the boundary of a simple polytope in R^n is investigated. Asymptotic formulas for the expected number of vertices and facets, and for the expectation of the volume difference are…
We consider the problem of estimating the parameters of a Gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse. Our approach is to solve a maximum likelihood problem with an added l_1-norm…
We present new iterative algorithms for solving a square linear system $Ax=b$ in dimension $n$ by employing the {\it Triangle Algorithm} \cite{kal12}, a fully polynomial-time approximation scheme for testing if the convex hull of a finite…
Convexification techniques have gained increasing interest over the past decades. In this work, we apply a recently developed convexification technique for fractional programs by He, Liu and Tawarmalani (2024) to the problem of determining…
Statistical models for networks with complex dependencies pose particular challenges for model selection and evaluation. In particular, many well-established statistical tools for selecting between models assume conditional independence of…
Solving linear programs is often a challenging task in distributed settings. While there are good algorithms for solving packing and covering linear programs in a distributed manner (Kuhn et al.~2006), this is essentially the only class of…
In the field of computer science, the network reliability problem for evaluating the network failure probability has been extensively investigated. For a given undirected graph $G$, the network failure probability is the probability that…
Necessary and sufficient conditions for the square-integrability of recently proposed unbiased estimators are established. A geometric characterization of a distribution that optimizes the performance of these estimators is given. An…
We consider the problem of embedding the nodes of a hypergraph into Euclidean space under the assumption that the interactions arose through closeness to unknown hyperedge centres. In this way, we tackle the inverse problem associated with…
Representing networks in a low dimensional latent space is a crucial task with many interesting applications in graph learning problems, such as link prediction and node classification. A widely applied network representation learning…
We consider the problem of estimating the parameters in a pairwise graphical model in which the distribution of each node, conditioned on the others, may have a different parametric form. In particular, we assume that each node's…