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A standard approach for assessing the performance of partition models is to create synthetic data sets with a prespecified clustering structure, and assess how well the model reveals this structure. A common format is that subjects are…
Psychological network approaches propose to see symptoms or questionnaire items as interconnected nodes, with links between them reflecting pairwise statistical dependencies evaluated cross-sectional, time-series, or panel data. These…
We consider the problem of learning a causal graph over a set of variables with interventions. We study the cost-optimal causal graph learning problem: For a given skeleton (undirected version of the causal graph), design the set of…
Simplicial complexes are now a popular alternative to networks when it comes to describing the structure of complex systems, primarily because they encode multi-node interactions explicitly. With this new description comes the need for…
We propose a Markov chain simulation method to generate simple connected random graphs with a specified degree sequence and level of clustering. The networks generated by our algorithm are random in all other respects and can thus serve as…
Probabilistic Graphical Models are often used to understand dynamics of a system. They can model relationships between features (nodes) and the underlying distribution. Theoretically these models can represent very complex dependency…
This paper presents the foundational ideas for a new way of modeling social aggregation. Traditional approaches have been using network theory, and the theory of random networks. Under that paradigm, every social agent is represented by a…
Photonic lanterns allow the decomposition of highly multimodal light into a simplified modal basis such as single-moded and/or few-moded. They are increasingly finding uses in astronomy, optics and telecommunications. Calculating…
A method for model reduction in nonlinear ODE systems is demonstrated through computational examples. The method does not require an implicit separation of time-scales in the fine dynamics to be effective. From the computational standpoint,…
The homological scaffold leverages persistent homology to construct a topologically sound summary of a weighted network. However, its crucial dependency on the choice of representative cycles hinders the ability to trace back global…
Real-world complex systems such as ecological communities and neuron networks are essential parts of our everyday lives. These systems are composed of units which interact through intricate networks. The ability to predict sudden changes in…
Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms of ordinary or…
The solving of least square systems is a useful operation in neurocomputational modeling of learning, pattern matching, and pattern recognition. In these last two cases, the solution must be obtained on-line, thus the time required to solve…
Networks observed in real world like social networks, collaboration networks etc., exhibit temporal dynamics, i.e. nodes and edges appear and/or disappear over time. In this paper, we propose a generative, latent space based, statistical…
Surrogate networks can constitute suitable replacements for real networks, in particular to study dynamical processes on networks, when only incomplete or limited datasets are available. As empirical datasets most often present complex…
Time-varying networks are fast emerging in a wide range of scientific and business disciplines. Most existing dynamic network models are limited to a single-subject and discrete-time setting. In this article, we propose a mixed-effect…
Any function can be constructed using a hierarchy of simpler functions through compositions. Such a hierarchy can be characterized by a binary rooted tree. Each node of this tree is associated with a function which takes as inputs two…
Dynamic networks are commonly used in applications where relational data is observed over time. Statistical models for such data should capture not only the temporal dependencies between networks observed in time, but also the structural…
This monograph is about discrete energy minimization for discrete graphical models. It considers graphical models, or, more precisely, maximum a posteriori inference for graphical models, purely as a combinatorial optimization problem.…
Dependency parsing is an important NLP task. A popular approach for dependency parsing is structured perceptron. Still, graph-based dependency parsing has the time complexity of $O(n^3)$, and it suffers from slow training. To deal with this…