Computational complexity of the graph-based MML procedure scales with the number of latent variables within a conditionally independent subset, and brute-force integration scales exponentially with dimensionality¶

Claim · All claims
Evidence · 1 study (2 entries) · theoretical r2–r3 · q2
Currency · newest study 2009 · not yet checked against its sources · not reviewed by a person

Subclaims¶

q2 i? The computational complexity of a full information MML procedure exploiting the model's conditional independence relations scales with the number of latent variables within a subset, which may be substantially lower than the total number of latent variables. → Rijmen 2009 q2 i? Without imposed conditional independence structure, full information MML estimation remains infeasible as dimensionality grows. → Rijmen 2009 (2)

Evidence¶

Rijmen 2009¶

Rijmen, F. (2009). Efficient Full Information Maximum Likelihood Estimation for Multidimensional IRT Models. ETS Research Report RR-09-03. http://www.ets.org/research/contact.html doi:10.1002/j.2333-8504.2009.tb02160.x

q2 · i? · theoretical · r2

Analytical statement from the introduction, elaborated in the junction tree algorithm section where the E-step's complexity is stated to scale with "the sum of the clique state spaces", so smaller clique state spaces yield greater efficiency gains over the standard EM algorithm.

"The level of computational complexity of a full information MML procedure that exploits the conditional independence relation implied by the model scales with the number of latent variables within a subset, which may be substantially lower than the total number of latent variables."

Rijmen 2009 (2)¶

Rijmen, F. (2009). Efficient Full Information Maximum Likelihood Estimation for Multidimensional IRT Models. ETS Research Report RR-09-03. http://www.ets.org/research/contact.html. doi:10.1002/j.2333-8504.2009.tb02160.x

q2 · i? · theoretical · r3

Boundary-condition statement from the Discussion, grounding the earlier observation that with Gaussian quadrature "the number of calculations involved increases exponentially with the number of dimensions". Such unstructured models are mostly considered at an exploratory stage, where MML results are not crucial.

"When one is not willing to impose any conditional independence relations, full information MML estimation still becomes infeasible with an increasing number of dimensions."

Discussion¶

Related Claims¶

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