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### Active Learning Algorithms for Graphical Model Selection

**2016-02-01**

1602.00354 | stat.ML

The problem of learning the structure of a high dimensional graphical model
from data has received considerable attention in recent years. In many
applications such as sensor networks and proteomics it is often expensive to
obtain samples from all the variables involved simultaneously. For instance,
this might involve the synchronization of a large number of sensors or the
tagging of a large number of proteins. To address this important issue, we
initiate the study of a novel graphical model selection problem, where the goal
is to optimize the total number of scalar samples obtained by allowing the
collection of samples from only subsets of the variables. We propose a general
paradigm for graphical model selection where feedback is used to guide the
sampling to high degree vertices, while obtaining only few samples from the
ones with the low degrees. We instantiate this framework with two specific
active learning algorithms, one of which makes mild assumptions but is
computationally expensive, while the other is more computationally efficient
but requires stronger (nevertheless standard) assumptions. Whereas the sample
complexity of passive algorithms is typically a function of the maximum degree
of the graph, we show that the sample complexity of our algorithms is provable
smaller and that it depends on a novel local complexity measure that is akin to
the average degree of the graph. We finally demonstrate the efficacy of our
framework via simulations.

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