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Statistical Estimation from Dependent Data
Vardis Kandiros · Yuval Dagan · Nishanth Dikkala · Surbhi Goel · Constantinos Daskalakis

Thu Jul 22 05:35 PM -- 05:40 PM (PDT) @
in Probabilistic Methods 4 »

We consider a general statistical estimation problem wherein binary labels across different observations are not independent conditioning on their feature vectors, but dependent, capturing settings where e.g. these observations are collected on a spatial domain, a temporal domain, or a social network, which induce dependencies. We model these dependencies in the language of Markov Random Fields and, importantly, allow these dependencies to be substantial, i.e. do not assume that the Markov Random Field capturing these dependencies is in high temperature. As our main contribution we provide algorithms and statistically efficient estimation rates for this model, giving several instantiations of our bounds in logistic regression, sparse logistic regression, and neural network regression settings with dependent data. Our estimation guarantees follow from novel results for estimating the parameters (i.e. external fields and interaction strengths) of Ising models from a single sample.

Keywords: Graphical Models

Author Information

Vardis Kandiros (MIT)
Yuval Dagan (MIT)
Nishanth Dikkala (Google Research)
Surbhi Goel (Microsoft Research)
Constantinos Daskalakis (MIT)

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