Related papers: Tree-based Node Aggregation in Sparse Graphical Mo…

$L_1$ regularized logistic regression has now become a workhorse of data mining and bioinformatics: it is widely used for many classification problems, particularly ones with many features. However, $L_1$ regularization typically selects…

This paper introduces a multi-way tensor generalization of the Bigraphical Lasso (BiGLasso), which uses a two-way sparse Kronecker-sum multivariate-normal model for the precision matrix to parsimoniously model conditional dependence…

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…

Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…

Graph Neural Networks (GNN) exhibit superior performance in graph representation learning, but their inference cost can be high, due to an aggregation operation that can require a memory fetch for a very large number of nodes. This…

High-dimensional compositional covariates, often derived from count data, are subject to measurement error and are frequently analyzed after aggregation along a prespecified tree to improve interpretability in applications such as…

This paper considers the problem of clustering a partially observed unweighted graph---i.e., one where for some node pairs we know there is an edge between them, for some others we know there is no edge, and for the remaining we do not know…

Daily internet communication relies heavily on tree-structured graphs, embodied by popular data formats such as XML and JSON. However, many recent generative (probabilistic) models utilize neural networks to learn a probability distribution…

While Graph Neural Network (GNN) has shown superiority in learning node representations of homogeneous graphs, leveraging GNN on heterogeneous graphs remains a challenging problem. The dominating reason is that GNN learns node…

Dynamic networks models describe a growing number of important scientific processes, from cell biology and epidemiology to sociology and finance. There are many aspects of dynamical networks that require statistical considerations. In this…

Modeling generative process of growing graphs has wide applications in social networks and recommendation systems, where cold start problem leads to new nodes isolated from existing graph. Despite the emerging literature in learning graph…

Graph neural networks (GNNs) have achieved great success on various tasks and fields that require relational modeling. GNNs aggregate node features using the graph structure as inductive biases resulting in flexible and powerful models.…

Multilayer graphs are appealing mathematical tools for modeling multiple types of relationship in the data. In this paper, we aim at analyzing multilayer graphs by properly combining the information provided by individual layers, while…

We consider a graphical model where a multivariate normal vector is associated with each node of the underlying graph and estimate the graphical structure. We minimize a loss function obtained by regressing the vector at each node on those…

Graph convolutional networks have been successful in addressing graph-based tasks such as semi-supervised node classification. Existing methods use a network structure defined by the user based on experimentation with fixed number of layers…

The network Lasso is a recently proposed convex optimization method for machine learning from massive network structured datasets, i.e., big data over networks. It is a variant of the well-known least absolute shrinkage and selection…

This work considers clustering nodes of a largely incomplete graph. Under the problem setting, only a small amount of queries about the edges can be made, but the entire graph is not observable. This problem finds applications in…

We consider a class of linear programs on graphs with total variation regularization and a budgetary constraint. For these programs, we give a characterization of basic solutions in terms of rooted spanning forests with orientation on the…

We introduce the localized Lasso, which is suited for learning models that are both interpretable and have a high predictive power in problems with high dimensionality $d$ and small sample size $n$. More specifically, we consider a function…

We consider the problem of learning high-dimensional Gaussian graphical models. The graphical lasso is one of the most popular methods for estimating Gaussian graphical models. However, it does not achieve the oracle rate of convergence. In…