TY - GEN
T1 - The wrong tool for inference a critical view of Gaussian graphical models
AU - Keane, Kevin R.
AU - Corso, Jason J.
N1 - Publisher Copyright:
Copyright © 2018 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved.
PY - 2018
Y1 - 2018
N2 - Myopic reliance on a misleading first sentence in the abstract of Covariance Selectiona Dempster (1972) spawned the computationally and mathematically dysfunctional Gaussian graphical model (GGM). In stark contrast to the GGM approach, the actual (Dempster, 1972, § 3) algorithm facilitated elegant and powerful applications, including a “texture model” developed two decades ago involving arbitrary distributions of 1000+ dimensions Zhu (1996). The “Covariance Selection” algorithm proposes a greedy sequence of increasingly constrained maximum entropy hypotheses Good (1963), terminating when the observed data “fails to reject” the last proposed probability distribution. We are mathematically critical of GGM methods that address a continuous convex domain with a discrete domain “golden hammer”. Computationally, selection of the wrong tool morphs polynomial-time algorithms into exponential-time algorithms. GGMs concepts are at odds with the fundamental concept of the invariant spherical multivariate Gaussian distribution. We are critical of the Bayesian GGM approach because the model selection process derails at the start when virtually all prior mass is attributed to comically precise multi-dimensional geometric “configurations” (Dempster, 1969, Ch. 13). We propose two Bayesian alternatives. The first alternative is based upon (Dempster, 1969, Ch. 15.3) and (Hoff, 2009, Ch. 7). The second alternative is based upon Bretthorst (2012), a recent paper placing maximum entropy methods such as the “Covariance Selection” algorithm in a Bayesian framework.
AB - Myopic reliance on a misleading first sentence in the abstract of Covariance Selectiona Dempster (1972) spawned the computationally and mathematically dysfunctional Gaussian graphical model (GGM). In stark contrast to the GGM approach, the actual (Dempster, 1972, § 3) algorithm facilitated elegant and powerful applications, including a “texture model” developed two decades ago involving arbitrary distributions of 1000+ dimensions Zhu (1996). The “Covariance Selection” algorithm proposes a greedy sequence of increasingly constrained maximum entropy hypotheses Good (1963), terminating when the observed data “fails to reject” the last proposed probability distribution. We are mathematically critical of GGM methods that address a continuous convex domain with a discrete domain “golden hammer”. Computationally, selection of the wrong tool morphs polynomial-time algorithms into exponential-time algorithms. GGMs concepts are at odds with the fundamental concept of the invariant spherical multivariate Gaussian distribution. We are critical of the Bayesian GGM approach because the model selection process derails at the start when virtually all prior mass is attributed to comically precise multi-dimensional geometric “configurations” (Dempster, 1969, Ch. 13). We propose two Bayesian alternatives. The first alternative is based upon (Dempster, 1969, Ch. 15.3) and (Hoff, 2009, Ch. 7). The second alternative is based upon Bretthorst (2012), a recent paper placing maximum entropy methods such as the “Covariance Selection” algorithm in a Bayesian framework.
KW - Degenerate Priors
KW - Gaussian Graphical Models
KW - Multivariate Normal Distributions
UR - http://www.scopus.com/inward/record.url?scp=85052016115&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85052016115&partnerID=8YFLogxK
U2 - 10.5220/0006644604700477
DO - 10.5220/0006644604700477
M3 - Conference contribution
AN - SCOPUS:85052016115
T3 - ICPRAM 2018 - Proceedings of the 7th International Conference on Pattern Recognition Applications and Methods
SP - 470
EP - 477
BT - ICPRAM 2018 - Proceedings of the 7th International Conference on Pattern Recognition Applications and Methods
A2 - De Marsico, Maria
A2 - di Baja, Gabriella Sanniti
A2 - Fred, Ana
T2 - 7th International Conference on Pattern Recognition Applications and Methods, ICPRAM 2018
Y2 - 16 January 2018 through 18 January 2018
ER -