Estimating the Dimension of a Model

By G. Schwarz. 1978

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Citations in the corpus

Fused Lasso Additive Model (2014, methodology): “As an alternative, an approach for tuning parameter selection based on Akaike’s information criterion (AIC; Akaike 1973) or Bayesian information criterion (BIC; Schwarz 1978) could be developed.”
Learning generative models for protein fold families (2011, methodology): “The Bayesian Information Criterion (BIC) [40], is used to select parsimonious models and is known to be asymptotically consistent in selecting the true model.”
The Dantzig selector: Statistical estimation when P is much larger than n (2005, neutral): “le selection strategy—hence, the name. There is of course a huge literature on model selection, and many procedures motivated by a wide array of criteria have been proposed over the years—among which [1, 7, 26, 31, 36]. By and large, the most commonly discussed approach—the “canonical selection proc”
Community detection in graphs (2009, methodology): “There is no clear-cut recipe to select a model, but a bunch of heuristics, like Akaike Information Criterion (AIC) [310], Bayesian Information Criterion (BIC) [311], Minimum Description Length (MDL) [312,313], MinimumMessage Length (MML) [314], etc.”
Characterization and greedy learning of interventional Markov equivalence classes of directed acyclic graphs (2011, methodology): “For DAGs with p ≤ 20 vertices, the GIES algorithm could keep up with a consistent, exponential-time DP approach maximizing the BIC score.”
Exposing the probabilistic causal structure of discrimination (2015, methodology): “Our framework can be considered a hybrid approach exploiting constrained maximum likelihood estimation (MLE) as follows: (i) we first define all the possible causal relationship among the variables in D by considering only the oriented edges between events that are consistent with Suppes’ notion of ”
Causal Discovery with Reinforcement Learning (2019, background): “…the space of all directed acyclic graphs (DAGs) for the best scoring: While there have been well deﬁned score functions such as the BIC/MDL score [20, 5] and the BGe score [9] for linear-Gaussian models, problem (1) is generally NP-hard to solve [4, 6], largely due to its nonconvex and…”
Nearly unbiased variable selection under minimax concave penalty (2010, methodology): “For example, one may impose a proper penalty on the number of selected variables based on the AIC [Akaike (1973)], Cp [Mallows (1973)], BIC [Schwarz (1978)], RIC [Foster and George (1994)] or a data driven method.”
Automatic Construction and Natural-Language Description of Nonparametric Regression Models (2014, methodology): “We experimented with distributing all products over addition during the search, causing models with many additive components to be more heavily penalized by BIC.”
Reversible Jump Markov Chain Monte Carlo Strategies for Bayesian Model Selection in Autoregressive Processes (2004, methodology): “For each realization, k̂AIC, k̂BIC and k̂MMAP were evaluated.”
Evaluating the Long-Term Effects of Prisoner Reentry Services on Recidivism: What Types of Services Matter? (2016, methodology): “We tested several distributions of the time to the event (Weibull, lognormal, and exponential distributions) and found that the exponential distribution provided the best fit to the data based on comparison of the Bayesian information criterion (BIC; Schwarz, 1978).”
A dose of nature: Tree cover, stress reduction, and gender differences (2014, methodology): “BIC is a widely used tool for selecting the best fitting model among a set of plausible models (Schwarz, 1978).”
Lag Selection in Subset VAR Models with an Application to a U.S. Monetary System (2000, unknown): “…for time series model selection are AIC(i1, . . . , in) = log(SSE(i1, . . . , in)/T ) + 2n/T, (see Akaike (1974)), HQ(i1, . . . , in) = log(SSE(i1, . . . , in)/T ) + 2 log log T T n (see Hannan & Quinn (1979)) and SC(i1, . . . , in) = log(SSE(i1, . . . , in)/T ) + log T T n (see Schwarz (1978)).”