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We study the problem of modeling multiple symmetric, weighted networks defined on a common set of nodes, where networks arise from different groups or conditions. We propose a model in which each network is expressed as the sum of a shared…

Combining additive models and neural networks allows to broaden the scope of statistical regression and extend deep learning-based approaches by interpretable structured additive predictors at the same time. Existing attempts uniting the…

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…

Using a perturbative expansion for weak synaptic weights and weak sources of randomness, we calculate the correlation structure of neural networks with generic connectivity matrices. In detail, the perturbative parameters are the mean and…

In this paper we examine a number of methods for probing and understanding the large-scale structure of networks that evolve over time. We focus in particular on citation networks, networks of references between documents such as papers,…

Hierarchical tree structures are common in many real-world systems, from tree roots and branches to neuronal dendrites and biologically inspired artificial neural networks, as well as in technological networks for organizing and searching…

A non-local model describing the growth of a tree-like transportation network with given allocation rules is proposed. In this model we focus on tree like networks, and the network transports the very resource it needs to build itself. Some…

Many real-world networks, ranging from subway systems to polymer structures and fungal mycelia, do not form by the incremental addition of individual nodes but instead grow through the successive extension and intersection of lines or…

Traditional studies of memory for meaningful narratives focus on specific stories and their semantic structures but do not address common quantitative features of recall across different narratives. We introduce a statistical ensemble of…

The paper introduces the Hidden Tree Markov Network (HTN), a neuro-probabilistic hybrid fusing the representation power of generative models for trees with the incremental and discriminative learning capabilities of neural networks. We put…

We introduce a random graph model based on k-trees, which can be generated by applying a probabilistic preferential attachment rule, but which also has a simple combinatorial description. We carry out a precise distributional analysis of…

We develop the mathematical theory of a model, constructed by C. Gu, I. Downes, O. Gnawali, and L. Guibas, of networks that diffuse continuously acquired information from mobile sensor nodes. We prove new results on the maximum, minimum,…

Generative network models are extremely useful for understanding the mechanisms that operate in network formation and are widely used across several areas of knowledge. However, when it comes to bipartite networks -- a class of network…

We study a random fragmentation process and its associated random tree. The process has earlier been studied by Dean and Majumdar (J. Phys. A: Math. Gen., vol. 35, L501--L507), who found a phase transition: the number of fragmentations is…

This paper develops a general framework for learning interpretable data representation via Long Short-Term Memory (LSTM) recurrent neural networks over hierarchal graph structures. Instead of learning LSTM models over the pre-fixed…

Modeling of growth (or decay) curves arises in many fields such as microbiology, epidemiology, marketing, and econometrics. Parametric forms like Logistic and Gompertz are often used for modeling such monotonic patterns. While useful for…

Random forests are a statistical learning technique that use bootstrap aggregation to average high-variance and low-bias trees. Improvements to random forests, such as applying Lasso regression to the tree predictions, have been proposed in…

We investigate regression for variable length sequential data containing missing samples and introduce a novel tree architecture based on the Long Short-Term Memory (LSTM) networks. In our architecture, we employ a variable number of LSTM…

Networks are widely used in the biological, physical, and social sciences as a concise mathematical representation of the topology of systems of interacting components. Understanding the structure of these networks is one of the outstanding…

Coupled problems with various combinations of multiple physics, scales, and domains can be found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled models is to…