
On the Number of Samples Needed to Learn the Correct Structure of a Bayesian Network
Bayesian Networks (BNs) are useful tools giving a natural and compact re...
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A Brief Study of InDomain Transfer and Learning from Fewer Samples using A Few Simple Priors
Domain knowledge can often be encoded in the structure of a network, suc...
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Learning Factor Graphs in Polynomial Time & Sample Complexity
We study computational and sample complexity of parameter and structure ...
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Statistical Learning for Analysis of Networked Control Systems over Unknown Channels
Recent control trends are increasingly relying on communication networks...
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Stochastic Canonical Correlation Analysis
We tightly analyze the sample complexity of CCA, provide a learning algo...
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Learning the mapping x∑_i=1^d x_i^2: the cost of finding the needle in a haystack
The task of using machine learning to approximate the mapping x∑_i=1^d x...
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Estimating Entropy of Distributions in Constant Space
We consider the task of estimating the entropy of kary distributions fr...
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On the Sample Complexity of Learning Bayesian Networks
In recent years there has been an increasing interest in learning Bayesian networks from data. One of the most effective methods for learning such networks is based on the minimum description length (MDL) principle. Previous work has shown that this learning procedure is asymptotically successful: with probability one, it will converge to the target distribution, given a sufficient number of samples. However, the rate of this convergence has been hitherto unknown. In this work we examine the sample complexity of MDL based learning procedures for Bayesian networks. We show that the number of samples needed to learn an epsilonclose approximation (in terms of entropy distance) with confidence delta is O((1/epsilon)^(4/3)log(1/epsilon)log(1/delta)loglog (1/delta)). This means that the sample complexity is a loworder polynomial in the error threshold and sublinear in the confidence bound. We also discuss how the constants in this term depend on the complexity of the target distribution. Finally, we address questions of asymptotic minimality and propose a method for using the sample complexity results to speed up the learning process.
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