Related papers: High-Dimensional Graphical Model Selection Using $…
I propose an estimation algorithm for Exponential Random Graph Models (ERGM), a popular statistical network model for estimating the structural parameters of strategic network formation in economics and finance. Existing methods often…
In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we…
We study the problem of detecting local geometry in random graphs. We introduce a model $\mathcal{G}(n, p, d, k)$, where a hidden community of average size $k$ has edges drawn as a random geometric graph on $\mathbb{S}^{d-1}$, while all…
In this paper, we propose a new estimation procedure for discovering the structure of Gaussian Markov random fields (MRFs) with false discovery rate (FDR) control, making use of the sorted l1-norm (SL1) regularization. A Gaussian MRF is an…
Structured prediction tasks in machine learning involve the simultaneous prediction of multiple labels. This is typically done by maximizing a score function on the space of labels, which decomposes as a sum of pairwise elements, each…
This research aims to estimate three parameters in a stochastic generalized logistic differential equation. We assume the intrinsic growth rate and shape parameters are constant but unknown. To estimate these two parameters, we use the…
Graphical continuous Lyapunov models offer a new perspective on modeling causally interpretable dependence structure in multivariate data by treating each independent observation as a one-time cross-sectional snapshot of a temporal process.…
Markov networks are widely studied and used throughout multivariate statistics and computer science. In particular, the problem of learning the structure of Markov networks from data without invoking chordality assumptions in order to…
A major line of contemporary research on complex networks is based on the development of statistical models that specify the local motifs associated with macro-structural properties observed in actual networks. This statistical approach…
We investigate the high-dimensional regression problem using adjacency matrices of unbalanced expander graphs. In this frame, we prove that the $\ell_{2}$-prediction error and the $\ell_{1}$-risk of the lasso and the Dantzig selector are…
We consider the problem of jointly estimating multiple related directed acyclic graph (DAG) models based on high-dimensional data from each graph. This problem is motivated by the task of learning gene regulatory networks based on gene…
We improve upon previous oblivious sketching and turnstile streaming results for $\ell_1$ and logistic regression, giving a much smaller sketching dimension achieving $O(1)$-approximation and yielding an efficient optimization problem in…
Consider the use of $\ell_{1}/\ell_{\infty}$-regularized regression for joint estimation of a $\pdim \times \numreg$ matrix of regression coefficients. We analyze the high-dimensional scaling of $\ell_1/\ell_\infty$-regularized quadratic…
Currently, Markov-Gibbs random field (MGRF) image models which include high-order interactions are almost always built by modelling responses of a stack of local linear filters. Actual interaction structure is specified implicitly by the…
Kernel and linear regression have been recently explored in the prediction of graph signals as the output, given arbitrary input signals that are agnostic to the graph. In many real-world problems, the graph expands over time as new nodes…
We consider the problem of learning the structure of ferromagnetic Ising models Markov on sparse Erdos-Renyi random graph. We propose simple local algorithms and analyze their performance in the regime of correlation decay. We prove that an…
Graph Neural Networks (GNNs) and their message passing framework that leverages both structural and feature information, have become a standard method for solving graph-based machine learning problems. However, these approaches still…
Unsupervised feature selection is an important method to reduce dimensions of high dimensional data without labels, which is benefit to avoid ``curse of dimensionality'' and improve the performance of subsequent machine learning tasks, like…
Logistic regression is commonly used for modeling dichotomous outcomes. In the classical setting, where the number of observations is much larger than the number of parameters, properties of the maximum likelihood estimator in logistic…
The problem of identifying geometric structure in heterogeneous, high-dimensional data is a cornerstone of representation learning. While there exists a large body of literature on the embeddability of canonical graphs, such as lattices or…