相关论文: Nested Junction Trees

Considering higher-order interactions allows for a more comprehensive understanding of network structures beyond simple pairwise connections. While leveraging all cliques in a network to handle higher-order interactions is intuitive, it…

The most fundamental problem in statistical causality is determining causal relationships from limited data. Probability trees, which combine prior causal structures with Bayesian updates, have been suggested as a possible solution. In this…

This paper presents a new approach for computing posterior probabilities in Bayesian nets, which sidesteps the triangulation problem. The current state of art is the clique tree propagation approach. When the underlying graph of a Bayesian…

Communication locality plays a key role in the performance of collective operations on large HPC systems, especially on oversubscribed networks where groups of nodes are fully connected internally but sparsely linked through global…

The problem of categorical data analysis in high dimensions is considered. A discussion of the fundamental difficulties of probability modeling is provided, and a solution to the derivation of high dimensional probability distributions…

Spanning trees are widely used in networks for broadcasting, fault-tolerance, and securely delivering messages. Hexagonal interconnection networks have a number of real life applications. Examples are cellular networks, computer graphics,…

We investigate a process of joining $k$ random spanning trees on a fixed clique $K_n$. The joined trees may not be disjoint and multiple edges are replaced by one simple edge. This process produces a simple graph $G$ on $n$~vertices with an…

Structure and parameters in a Bayesian network uniquely specify the probability distribution of the modeled domain. The locality of both structure and probabilistic information are the great benefits of Bayesian networks and require the…

As Bayesian networks are applied to larger and more complex problem domains, search for flexible modeling and more efficient inference methods is an ongoing effort. Multiply sectioned Bayesian networks (MSBNs) extend the HUGIN inference for…

It has been observed that mutualistic bipartite networks have a nested structure of interactions. In addition, the degree distributions associated with the two guilds involved in such networks (e.g. plants & pollinators or plants & seed…

Euclidean Steiner trees are relevant to model minimal networks in real-world applications ubiquitously. In this paper, we study the feasibility of a hierarchical approach embedded with bundling operations to compute multiple and mutually…

It is well known that tree-based theories can describe the properties of undirected clustered networks with extremely accurate results [S. Melnik, \textit{et al}. Phys. Rev. E 83, 036112 (2011)]. It is reasonable to suggest that a motif…

The past two decades have seen a growing interest in combining causal information, commonly represented using causal graphs, with machine learning models. Probability trees provide a simple yet powerful alternative representation of causal…

We propose a new method for hierarchical clustering based on the optimisation of a cost function over trees of limited depth, and we derive a message--passing method that allows to solve it efficiently. The method and algorithm can be…

Analyzing and understanding the structure of complex relational data is important in many applications including analysis of the connectivity in the human brain. Such networks can have prominent patterns on different scales, calling for a…

An extension to a recently introduced architecture of clique-based neural networks is presented. This extension makes it possible to store sequences with high efficiency. To obtain this property, network connections are provided with…

Based on decision trees, many fields have arguably made tremendous progress in recent years. In simple words, decision trees use the strategy of "divide-and-conquer" to divide the complex problem on the dependency between input features and…

The paper presents an iterative version of join-tree clustering that applies the message passing of join-tree clustering algorithm to join-graphs rather than to join-trees, iteratively. It is inspired by the success of Pearl's belief…

Consider the computations at a node in a message passing algorithm. Assume that the node has incoming and outgoing messages $\mathbf{x} = (x_1, x_2, \ldots, x_n)$ and $\mathbf{y} = (y_1, y_2, \ldots, y_n)$, respectively. In this paper, we…

In this work, we consider to improve the model estimation efficiency by aggregating the neighbors' information as well as identify the subgroup membership for each node in the network. A tree-based $l_1$ penalty is proposed to save the…