相关论文: Sharp threshold for alignment of graph databases w…

Considering the worst-case scenario, junction tree algorithm remains the most general solution for exact MAP inference with polynomial run-time guarantees. Unfortunately, its main tractability assumption requires the treewidth of a…

We study the problem of recovering the structure underlying large Gaussian graphical models or, more generally, partial correlation graphs. In high-dimensional problems it is often too costly to store the entire sample covariance matrix. We…

We investigate the threshold probability for connectivity of sparse graphs under weak assumptions. As a corollary this completely solve the problem for Cartesian powers of arbitrary graphs. In detail, let $G$ be a connected graph on $k$…

The problem of recovering the sparsity pattern of a fixed but unknown vector $\beta^* \in \real^p based on a set of $n$ noisy observations arises in a variety of settings, including subset selection in regression, graphical model selection,…

Graph matching refers to finding node correspondence between graphs, such that the corresponding node and edge's affinity can be maximized. In addition with its NP-completeness nature, another important challenge is effective modeling of…

MAP is the problem of finding a most probable instantiation of a set of variables in a Bayesian network given some evidence. Unlike computing posterior probabilities, or MPE (a special case of MAP), the time and space complexity of…

Gaussian graphical models can capture complex dependency structures among variables. For such models, Bayesian inference is attractive as it provides principled ways to incorporate prior information and to quantify uncertainty through the…

Graphs are ubiquitous in various fields, and deep learning methods have been successful applied in graph classification tasks. However, building large and diverse graph datasets for training can be expensive. While augmentation techniques…

Key to successfully deal with complex contemporary datasets is the development of tractable models that account for the irregular structure of the information at hand. This paper provides a comprehensive and unifying view of several…

Finding the mean of sampled data is a fundamental task in machine learning and statistics. However, in cases where the data samples are graph objects, defining a mean is an inherently difficult task. We propose a novel framework for…

Bayesian structure learning is the NP-hard problem of discovering a Bayesian network that optimally represents a given set of training data. In this paper we study the computational worst-case complexity of exact Bayesian structure learning…

This paper provides a comprehensive and detailed derivation of the backpropagation algorithm for graph convolutional neural networks using matrix calculus. The derivation is extended to include arbitrary element-wise activation functions…

Aligning a sequence to a walk in a labeled graph is a problem of fundamental importance to Computational Biology. For finding a walk in an arbitrary graph with $|E|$ edges that exactly matches a pattern of length $m$, a lower bound based on…

Graph partitioning is the problem of dividing the nodes of a graph into balanced partitions while minimizing the edge cut across the partitions. Due to its combinatorial nature, many approximate solutions have been developed, including…

There has been substantial interest in estimating the value of a graph parameter, i.e., of a real-valued function defined on the set of finite graphs, by querying a randomly sampled substructure whose size is independent of the size of the…

A major question in the study of the Erd\H{o}s--R\'enyi random graph is to understand the probability that it contains a given subgraph. This study originated in classical work of Erd\H{o}s and R\'enyi (1960). More recent work studies this…

Gaussian errors are sometimes inappropriate in a multivariate linear regression setting because, for example, the data contain outliers. In such situations, it is often assumed that the error density is a scale mixture of multivariate…

Expander graphs have been recently proposed to construct efficient compressed sensing algorithms. In particular, it has been shown that any $n$-dimensional vector that is $k$-sparse (with $k\ll n$) can be fully recovered using…

The problem of the distributed recovery of jointly sparse signals has attracted much attention recently. Let us assume that the nodes of a network observe different sparse signals with common support; starting from linear, compressed…

Probabilistic Graphical Models (PGMs) are generative models of complex systems. They rely on conditional independence assumptions between variables to learn sparse representations which can be visualized in a form of a graph. Such models…