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The Multiple Quantile Graphical Model
Alnur Ali · J. Zico Kolter · Ryan Tibshirani

Wed Dec 09:00 AM -- 12:30 PM PST @ Area 5+6+7+8 #3 #None

We introduce the Multiple Quantile Graphical Model (MQGM), which extends the neighborhood selection approach of Meinshausen and Buhlmann for learning sparse graphical models. The latter is defined by the basic subproblem of modeling the conditional mean of one variable as a sparse function of all others. Our approach models a set of conditional quantiles of one variable as a sparse function of all others, and hence offers a much richer, more expressive class of conditional distribution estimates. We establish that, under suitable regularity conditions, the MQGM identifies the exact conditional independencies with probability tending to one as the problem size grows, even outside of the usual homoskedastic Gaussian data model. We develop an efficient algorithm for fitting the MQGM using the alternating direction method of multipliers. We also describe a strategy for sampling from the joint distribution that underlies the MQGM estimate. Lastly, we present detailed experiments that demonstrate the flexibility and effectiveness of the MQGM in modeling hetereoskedastic non-Gaussian data.

Author Information

Alnur Ali (Carnegie Mellon University)
J. Zico Kolter (Carnegie Mellon University / Bosch Center for AI)

Zico Kolter is an Assistant Professor in the School of Computer Science at Carnegie Mellon University, and also serves as Chief Scientist of AI Research for the Bosch Center for Artificial Intelligence. His work focuses on the intersection of machine learning and optimization, with a large focus on developing more robust, explainable, and rigorous methods in deep learning. In addition, he has worked on a number of application areas, highlighted by work on sustainability and smart energy systems. He is the recipient of the DARPA Young Faculty Award, and best paper awards at KDD, IJCAI, and PESGM.

Ryan Tibshirani (Carnegie Mellon University)

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