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Information-theoretic bounds on learning network dynamics
Published on Mar 07, 20161872 Views
How long should we observe the trajectory of a system before being able to characterize its underlying network dynamics? I will present a brief review of information-theoretic tools to establish low
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Chapter list
Information-theoretic Bounds on Learning Network Dynamics00:00
What is this talk about?00:16
Outline01:28
General approach01:46
General estimation in Hamming metric01:48
Entropy and conditional entropy03:18
Two properties03:58
Information-theoretic approach05:15
Some simple examples07:15
Toy example07:19
Evaluating the conditional entropy08:48
Fano’s inequality10:06
Interpretation10:49
A more ‘dynamical’ example11:06
5, T = 2011:47
5, T = 4012:07
5, T = 8012:11
5, T = 16012:15
Conditional entropy12:23
A general lemma14:09
Hence15:10
A more advanced application16:40
High-dimensional SDE16:58
Example17:48
Information-theoretic lower bound18:47
A general lower bound21:44
Application: Sparse, linear model - 125:36
Application: Sparse, linear model - 226:50
Conclusion - 128:56
Conclusion - 228:58