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Support consistency of direct sparse-change learning in Markov networks
- Source :
- Ann. Statist. 45, no. 3 (2017), 959-990, Liu, S, Suzuki, T, Relator, R, Jun, S, Sugiyama, M & Fukumizu, K 2017, ' Support consistency of direct sparse-change learning in Markov networks ', Annals of Statistics, vol. 45, no. 3, 3, pp. 959-990 . https://doi.org/10.1214/16-AOS1470
- Publication Year :
- 2017
- Publisher :
- Institute of Mathematical Statistics, 2017.
-
Abstract
- We study the problem of learning sparse structure changes between two Markov networks $P$ and $Q$. Rather than fitting two Markov networks separately to two sets of data and figuring out their differences, a recent work proposed to learn changes \emph{directly} via estimating the ratio between two Markov network models. In this paper, we give sufficient conditions for \emph{successful change detection} with respect to the sample size $n_p, n_q$, the dimension of data $m$, and the number of changed edges $d$. When using an unbounded density ratio model we prove that the true sparse changes can be consistently identified for $n_p = \Omega(d^2 \log \frac{m^2+m}{2})$ and $n_q = \Omega({n_p^2})$, with an exponentially decaying upper-bound on learning error. Such sample complexity can be improved to $\min(n_p, n_q) = \Omega(d^2 \log \frac{m^2+m}{2})$ when the boundedness of the density ratio model is assumed. Our theoretical guarantee can be applied to a wide range of discrete/continuous Markov networks.<br />Comment: Rerun experiments, added a new image change detection experiment. Changed some typos in the proof of Proposition 6 and 11
- Subjects :
- FOS: Computer and information sciences
Statistics and Probability
Markov kernel
Markov networks
Dimension (graph theory)
68T99
Markov process
Machine Learning (stat.ML)
02 engineering and technology
01 natural sciences
Omega
Combinatorics
density ratio estimation
010104 statistics & probability
symbols.namesake
Statistics - Machine Learning
Markov renewal process
Statistics
0202 electrical engineering, electronic engineering, information engineering
0101 mathematics
change detection
Mathematics
Markov blanket
Markov chain
020206 networking & telecommunications
symbols
Markov property
Statistics, Probability and Uncertainty
62F12
Subjects
Details
- ISSN :
- 00905364
- Volume :
- 45
- Database :
- OpenAIRE
- Journal :
- The Annals of Statistics
- Accession number :
- edsair.doi.dedup.....25c86d905e5eab4d7e7f0652f9a75eb8