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Title: On Learning Continuous Pairwise Markov Random Fields
We consider learning a sparse pairwise Markov Random Field (MRF) with continuous valued variables from i.i.d samples. We adapt the algorithm of Vuffray et al. (2019) to this setting and provide finite- sample analysis revealing sample complexity scaling logarithmically with the number of variables, as in the discrete and Gaussian settings. Our approach is applicable to a large class of pairwise MRFs with continuous variables and also has desirable asymptotic properties, including consistency and normality under mild conditions. Further, we establish that the population version of the optimization criterion employed by Vuffray et al. (2019) can be interpreted as local maximum likelihood estimation (MLE). As part of our analysis, we introduce a robust variation of sparse linear regression à la Lasso, which may be of interest in its own right.  more » « less
Award ID(s):
1816209
PAR ID:
10301907
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Proc. Int. Conf. Artif. Intell., Stat. (AISTATS-2021), Proc. Mach. Learn. Res. (PMLR)
Volume:
130
Page Range / eLocation ID:
1153 - 1161
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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