Related papers: A General Pairwise Comparison Model for Extremely …
The convergence of expectation-maximization (EM)-based algorithms typically requires continuity of the likelihood function with respect to all the unknown parameters (optimization variables). The requirement is not met when parameters…
Variational methods are extremely popular in the analysis of network data. Statistical guarantees obtained for these methods typically provide asymptotic normality for the problem of estimation of global model parameters under the…
We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…
We study sparse linear regression over a network of agents, modeled as an undirected graph and no server node. The estimation of the $s$-sparse parameter is formulated as a constrained LASSO problem wherein each agent owns a subset of the…
Ranking problems based on pairwise comparisons, such as those arising in online gaming, often involve a large pool of items to order. In these situations, the gap in performance between any two items can be significant, and the smallest and…
Topic models provide a useful text-mining tool for learning, extracting, and discovering latent structures in large text corpora. Although a plethora of methods have been proposed for topic modeling, lacking in the literature is a formal…
Neural networks are becoming increasingly popular in applications, but our mathematical understanding of their potential and limitations is still limited. In this paper, we further this understanding by developing statistical guarantees for…
The increasing volume of ecologically and biologically relevant data has revealed a wide collection of emergent patterns in living systems. Analyzing different datasets, ranging from metabolic gene-regulatory to species interaction…
Conditional independence, graphical models and sparsity are key notions for parsimonious statistical models and for understanding the structural relationships in the data. The theory of multivariate and spatial extremes describes the risk…
We present a new inference method based on approximate Bayesian computation for estimating parameters governing an entire network based on link-traced samples of that network. To do this, we first take summary statistics from an observed…
This paper provides a necessary and sufficient condition for a random network with nodes Poissonly distributed on a unit square and a pair of nodes directly connected following a generic random connection model to be asymptotically almost…
We present new results for consistency of maximum likelihood estimators with a focus on multivariate mixed models. Our theory builds on the idea of using subsets of the full data to establish consistency of estimators based on the full…
The $\beta$-model is a powerful tool for modeling large and sparse networks driven by degree heterogeneity, where many network models become infeasible due to computational challenge and network sparsity. However, existing estimation…
This paper considers the problem of networks reconstruction from heterogeneous data using a Gaussian Graphical Mixture Model (GGMM). It is well known that parameter estimation in this context is challenging due to large numbers of variables…
This paper revisits the classical concept of network modularity and its spectral relaxations used throughout graph data analysis. We formulate and study several modularity statistic variants for which we establish asymptotic distributional…
We consider the problem of high-dimensional Gaussian graphical model selection. We identify a set of graphs for which an efficient estimation algorithm exists, and this algorithm is based on thresholding of empirical conditional…
In this paper, we study the nonparametric maximum likelihood estimator for an event time distribution function at a point in the current status model with observation times supported on a grid of potentially unknown sparsity and with…
Basic principles of statistical inference are commonly violated in network data analysis. Under the current approach, it is often impossible to identify a model that accommodates known empirical behaviors, possesses crucial inferential…
Distributed statistical inference has recently attracted immense attention. The asymptotic efficiency of the maximum likelihood estimator (MLE), the one-step MLE, and the aggregated estimating equation estimator are established for…
Gaussian graphical models are used for determining conditional relationships between variables. This is accomplished by identifying off-diagonal elements in the inverse-covariance matrix that are non-zero. When the ratio of variables (p) to…