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This paper applies conformal prediction techniques to compute simultaneous prediction bands and clustering trees for functional data. These tools can be used to detect outliers and clusters. Both our prediction bands and clustering trees…
The paper introduces two new aggregation functions to encode structural knowledge from tree-structured data. They leverage the Canonical and Tensor-Train decompositions to yield expressive context aggregation while limiting the number of…
Acting on time-critical events by processing ever growing social media or news streams is a major technical challenge. Many of these data sources can be modeled as multi-relational graphs. Continuous queries or techniques to search for rare…
We review old and new uses of exchangeability, emphasizing the general theme of exchangeable representations of complex random structures. Illustrations of this theme include processes of stochastic coalescence and fragmentation; continuum…
Contour trees offer an abstract representation of the level set topology in scalar fields and are widely used in topological data analysis and visualization. However, applying contour trees to large-scale scientific datasets remains…
Processing graphs with temporal information (the temporal graphs) has become increasingly important in the real world. In this paper, we study efficient solutions to temporal graph applications using new algorithms for Incremental Minimum…
Two fundamental algorithm-design paradigms are Tree Search and Dynamic Programming. The techniques used therein have been shown to complement one another when solving the complete set partitioning problem, also known as the coalition…
In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an…
How can we find a good graph clustering of a real-world network, that allows insight into its underlying structure and also potential functions? In this paper, we introduce a new graph clustering algorithm Dcut from a density point of view.…
We present a constraint model for the problem of producing a tree decomposition of a graph. The inputs to the model are a simple graph G, the number of nodes in the desired tree decomposition and the maximum cardinality of each node in that…
We propose and study a method for learning interpretable representations for the task of regression. Features are represented as networks of multi-type expression trees comprised of activation functions common in neural networks in addition…
Convolution trees, loopy belief propagation, and fast numerical p-convolution are combined for the first time to efficiently solve networks with several additive constraints between random variables. An implementation of this "convolution…
Graph Convolutional Networks (GCNs) are extensively utilized for deep learning on graphs. The large data sizes of graphs and their vertex features make scalable training algorithms and distributed memory systems necessary. Since the…
Spanning tree modulus is a generalization of effective resistance that is closely related to graph strength and fractional arboricity. The optimal edge density associated with spanning tree modulus is known to produce two hierarchical…
A novel graph-to-tree conversion mechanism called the deep-tree generation (DTG) algorithm is first proposed to predict text data represented by graphs. The DTG method can generate a richer and more accurate representation for nodes (or…
In 1996, Bodlaender showed the celebrated result that an optimal tree decomposition of a graph of bounded treewidth can be found in linear time. The algorithm is based on an algorithm of Bodlaender and Kloks that computes an optimal tree…
Motivated by performance optimization of large-scale graph processing systems that distribute the graph across multiple machines, we consider the balanced graph partitioning problem. Compared to the previous work, we study the…
There is a recent exciting line of work in distributed graph algorithms in the $\mathsf{CONGEST}$ model that exploit expanders. All these algorithms so far are based on two tools: expander decomposition and expander routing. An…
Understanding the response of an output variable to multi-dimensional inputs lies at the heart of many data exploration endeavours. Topology-based methods, in particular Morse theory and persistent homology, provide a useful framework for…
Motivated by the need to extract meaning from large amounts of complex structured data, we consider three critical problems on graphs: localization, decomposition, and dictionary learning of piecewise-constant signals. These graph-based…