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From which world is your graph

Neural Information Processing Systems

Discovering statistical structure from links is a fundamental problem in the analysis of social networks. Choosing a misspecified model, or equivalently, an incorrect inference algorithm will result in an invalid analysis or even falsely uncover patterns that are in fact artifacts of the model. This work focuses on unifying two of the most widely used link-formation models: the stochastic block model (SBM) and the small world (or latent space) model (SWM). Integrating techniques from kernel learning, spectral graph theory, and nonlinear dimensionality reduction, we develop the first statistically sound polynomial-time algorithm to discover latent patterns in sparse graphs for both models. When the network comes from an SBM, the algorithm outputs a block structure.


Graph Algorithms, Neural Networks, and Graph Databases

#artificialintelligence

One of the world's top AI venues shows that using graphs to enhance machine learning, and vice versa, is what many sophisticated organizations are doing today. New developments in graph algorithms and analytics, and the latest graph database releases, many of which incorporate graph algorithms and machine learning features. To get the Year of the Graph Newsletter every month in your inbox, subscribe here.


Local Algorithms for Approximate Inference in Minor-Excluded Graphs

Neural Information Processing Systems

We present a new local approximation algorithm for computing MAP and log-partition function for arbitrary exponential family distribution represented by a finite-valued pair-wise Markov random field (MRF), say G. Our algorithm is based on decomposing G into appropriately chosen small components; computing estimates locally in each of these components and then producing a good global solution. We prove that the algorithm can provide approximate solution within arbitrary accuracy when $G$ excludes some finite sized graph as its minor and G has bounded degree: all Planar graphs with bounded degree are examples of such graphs. The running time of the algorithm is $\Theta(n)$ (n is the number of nodes in G), with constant dependent on accuracy, degree of graph and size of the graph that is excluded as a minor (constant for Planar graphs). Our algorithm for minor-excluded graphs uses the decomposition scheme of Klein, Plotkin and Rao (1993). In general, our algorithm works with any decomposition scheme and provides quantifiable approximation guarantee that depends on the decomposition scheme.


Dynamical And-Or Graph Learning for Object Shape Modeling and Detection

Neural Information Processing Systems

We validate the proposed method on several challenging databases (e.g., INRIA-Horse, ETHZ-Shape, and UIUC-People), and it outperforms the state-of-the-arts approaches. Papers published at the Neural Information Processing Systems Conference.


Learning Causal Graphs with Small Interventions

Neural Information Processing Systems

We consider the problem of learning causal networks with interventions, when each intervention is limited in size under Pearl's Structural Equation Model with independent errors (SEM-IE). The objective is to minimize the number of experiments to discover the causal directions of all the edges in a causal graph. Previous work has focused on the use of separating systems for complete graphs for this task. We prove that any deterministic adaptive algorithm needs to be a separating system in order to learn complete graphs in the worst case. In addition, we present a novel separating system construction, whose size is close to optimal and is arguably simpler than previous work in combinatorics.