scholarly journals Balancing Accuracy and Parsimony in Genetic Programming

1995 ◽  
Vol 3 (1) ◽  
pp. 17-38 ◽  
Author(s):  
Byoung-Tak Zhang ◽  
Heinz Mühlenbein
Keyword(s):  
Genetic Programming ◽  
Adaptive Learning ◽  
Model Comparison ◽  
Model Complexity ◽  
Underlying Structure ◽  
Network Synthesis ◽  
Inference Problem ◽  
Bayesian Model Comparison ◽  
Fundamental Relationship ◽  
Representation Scheme

Genetic programming is distinguished from other evolutionary algorithms in that it uses tree representations of variable size instead of linear strings of fixed length. The flexible representation scheme is very important because it allows the underlying structure of the data to be discovered automatically. One primary difficulty, however, is that the solutions may grow too big without any improvement of their generalization ability. In this article we investigate the fundamental relationship between the performance and complexity of the evolved structures. The essence of the parsimony problem is demonstrated empirically by analyzing error landscapes of programs evolved for neural network synthesis. We consider genetic programming as a statistical inference problem and apply the Bayesian model-comparison framework to introduce a class of fitness functions with error and complexity terms. An adaptive learning method is then presented that automatically balances the model-complexity factor to evolve parsimonious programs without losing the diversity of the population needed for achieving the desired training accuracy. The effectiveness of this approach is empirically shown on the induction of sigma-pi neural networks for solving a real-world medical diagnosis problem as well as benchmark tasks.

scholarly journals Evaluation of quantitative models of the effect of insulin on lipolysis and glucose disposal

2008 ◽  
Vol 295 (4) ◽  
pp. R1089-R1096 ◽  
Author(s):  
Vipul Periwal ◽  
Carson C. Chow ◽  
Richard N. Bergman ◽  
Madia Ricks ◽  
Gloria L. Vega ◽  
...  
Keyword(s):  
Model Comparison ◽  
Tolerance Test ◽  
Intravenous Glucose Tolerance Test ◽  
Model Complexity ◽  
Glucose Disposal ◽  
Intravenous Glucose ◽  
Bayesian Model Comparison ◽  
Plasma Ffa ◽  
Second Category ◽  
Glucose Dynamics

The effects of insulin on the suppression of lipolysis are neither fully understood nor quantified. We examined a variety of mathematical models analogous to the minimal model of glucose disposal (MMG) to quantify the combined influence of insulin on lipolysis and glucose disposal during an insulin-modified frequently sampled intravenous glucose tolerance test. The tested models, which include two previously published ones, consisted of separate compartments for plasma free fatty acids (FFA), glucose, and insulin. They differed in the number of compartments and in the action of insulin to suppress lipolysis that decreased the plasma FFA level. In one category of models, a single insulin compartment acted on both glucose and FFA simultaneously. In a second category, there were two insulin compartments, each acting on FFA and glucose independently. For each of these two categories, we tested 11 variations of how insulin suppressed lipolysis. We also tested a model with an additional glucose compartment that acted on FFA. These 23 models were fit to the plasma FFA and glucose concentrations of 102 subjects individually. Using Bayesian model comparison methods, we selected the model that best balanced fit and minimized model complexity. In the best model, insulin suppressed lipolysis via a Hill function through a remote compartment that acted on both glucose and FFA simultaneously, and glucose dynamics obeyed the classic MMG.

scholarly journals No evidence for trait- and state-level urgency moderating the daily association between negative affect and subsequent alcohol use in two college samples

2022 ◽  
Author(s):  
Jonas Dora ◽  
Megan Elizabeth Schultz ◽  
Christine M Lee ◽  
Yuichi Shoda ◽  
Kevin Michael King
Keyword(s):  
Alcohol Use ◽  
Negative Affect ◽  
Model Comparison ◽  
Negative Reinforcement ◽  
Affective State ◽  
Secondary Data ◽  
State Level ◽  
Model Complexity ◽  
Previous Night ◽  
Bayesian Model Comparison

It remains unclear whether the negative reinforcement pathway to problematic drinking exists, and if so, for whom. One idea that has received some support recently is that people who tend to act impulsively in response to negative emotions (i.e., people high in negative urgency) may specifically respond to negative affect with increased alcohol consumption. We tested this idea in a preregistered secondary data analysis of two ecological momentary assessment studies using college samples. Participants (N = 226) reported on their current affective state multiple times per day and the following morning reported alcohol use the previous night. We assessed urgency both at baseline and during the momentary affect assessments. Results from our Bayesian model comparison procedure, which penalizes increasing model complexity, indicate that no combination of the variables of interest (negative affect, urgency, and the respective interactions) outperformed a baseline model that included two known demographic predictors of alcohol use. A non- preregistered exploratory analysis provided some evidence for the effect of daily positive affect, positive urgency, as well as their interaction on subsequent alcohol use. Taken together, our results suggest that college students’ drinking may be better described by a positive rather than negative reinforcement cycle.

scholarly journals Detecting episodes of star formation using Bayesian model selection

2021 ◽  
Vol 502 (3) ◽  
pp. 3993-4008
Author(s):  
Andrew J Lawler ◽  
Viviana Acquaviva
Keyword(s):  
Star Formation ◽  
Bayesian Model ◽  
Model Comparison ◽  
Density Ratio ◽  
Model Complexity ◽  
Spectral Energy ◽  
Analytic Approximation ◽  
Nested Models ◽  
Bayesian Model Comparison ◽  
Correct Model

ABSTRACT Bayesian model comparison frameworks can be used when fitting models to data in order to infer the appropriate model complexity in a data-driven manner. We aim to use them to detect the correct number of major episodes of star formation from the analysis of the spectral energy distributions (SEDs) of galaxies, modelled after 3D-HST galaxies at z ∼ 1. Starting from the published stellar population properties of these galaxies, we use kernel density estimates to build multivariate input parameter distributions to obtain realistic simulations. We create simulated sets of spectra of varying degrees of complexity (identified by the number of parameters), and derive SED fitting results and pieces of evidence for pairs of nested models, including the correct model as well as more simplistic ones, using the bagpipes codebase with nested sampling algorithm multinest. We then ask the question: is it true – as expected in Bayesian model comparison frameworks – that the correct model has larger evidence? Our results indicate that the ratio of pieces of evidence (the Bayes factor) is able to identify the correct underlying model in the vast majority of cases. The quality of the results improves primarily as a function of the total S/N in the SED. We also compare the Bayes factors obtained using the evidence to those obtained via the Savage–Dickey density ratio (SDDR), an analytic approximation that can be calculated using samples from regular Markov Chain Monte Carlo methods. We show that the SDDR ratio can satisfactorily replace a full evidence calculation provided that the sampling density is sufficient.

Bayesian model comparison

2014 ◽  
pp. 101-117
Author(s):  
Michael D. Lee ◽  
Eric-Jan Wagenmakers
Keyword(s):  
Bayesian Model ◽  
Model Comparison ◽  
Bayesian Model Comparison

scholarly journals A complete search for redshift z ≳ 6.5 quasars in the VIKING survey

2020 ◽  
Vol 501 (2) ◽  
pp. 1663-1676
Author(s):  
R Barnett ◽  
S J Warren ◽  
N J G Cross ◽  
D J Mortlock ◽  
X Fan ◽  
...  
Keyword(s):  
Model Comparison ◽  
High Redshift ◽  
Detailed Comparison ◽  
Selection Function ◽  
Data Set ◽  
Bayesian Model Comparison ◽  
Fitting Method ◽  
Complete Search ◽  
Potential Contaminant ◽  
Ranked List

ABSTRACT We present the results of a new, deeper, and complete search for high-redshift 6.5 < z < 9.3 quasars over 977 deg2 of the VISTA Kilo-Degree Infrared Galaxy (VIKING) survey. This exploits a new list-driven data set providing photometry in all bands Z, Y, J, H, Ks, for all sources detected by VIKING in J. We use the Bayesian model comparison (BMC) selection method of Mortlock et al., producing a ranked list of just 21 candidates. The sources ranked 1, 2, 3, and 5 are the four known z > 6.5 quasars in this field. Additional observations of the other 17 candidates, primarily DESI Legacy Survey photometry and ESO FORS2 spectroscopy, confirm that none is a quasar. This is the first complete sample from the VIKING survey, and we provide the computed selection function. We include a detailed comparison of the BMC method against two other selection methods: colour cuts and minimum-χ2 SED fitting. We find that: (i) BMC produces eight times fewer false positives than colour cuts, while also reaching 0.3 mag deeper, (ii) the minimum-χ2 SED-fitting method is extremely efficient but reaches 0.7 mag less deep than the BMC method, and selects only one of the four known quasars. We show that BMC candidates, rejected because their photometric SEDs have high χ2 values, include bright examples of galaxies with very strong [O iii] λλ4959,5007 emission in the Y band, identified in fainter surveys by Matsuoka et al. This is a potential contaminant population in Euclid searches for faint z > 7 quasars, not previously accounted for, and that requires better characterization.

scholarly journals A Bayesian model comparison approach to test the specificity of visual integration impairment in schizophrenia or psychosis

2018 ◽  
Vol 265 ◽  
pp. 271-278 ◽  
Author(s):  
Tyler B. Grove ◽  
Beier Yao ◽  
Savanna A. Mueller ◽  
Merranda McLaughlin ◽  
Vicki L. Ellingrod ◽  
...  
Keyword(s):  
Bayesian Model ◽  
Model Comparison ◽  
Visual Integration ◽  
Bayesian Model Comparison ◽  
Comparison Approach

Uncertainty of prior and posterior model probability: Implications for interpreting Bayes factors

2021 ◽  
Author(s):  
John K. Kruschke
Keyword(s):  
Posterior Distribution ◽  
Bayesian Model ◽  
Model Comparison ◽  
Bayes Factor ◽  
Bayes Factors ◽  
Prior Model ◽  
Bayesian Hypothesis Testing ◽  
Bayesian Model Comparison ◽  
Posterior Model Probability ◽  
Model Probability

In most applications of Bayesian model comparison or Bayesian hypothesis testing, the results are reported in terms of the Bayes factor only, not in terms of the posterior probabilities of the models. Posterior model probabilities are not reported because researchers are reluctant to declare prior model probabilities, which in turn stems from uncertainty in the prior. Fortunately, Bayesian formalisms are designed to embrace prior uncertainty, not ignore it. This article provides a novel derivation of the posterior distribution of model probability, and shows many examples. The posterior distribution is useful for making decisions taking into account the uncertainty of the posterior model probability. Benchmark Bayes factors are provided for a spectrum of priors on model probability. R code is posted at https://osf.io/36527/. This framework and tools will improve interpretation and usefulness of Bayes factors in all their applications.

Combined-chain nested sampling for efficient Bayesian model comparison

2017 ◽  
Vol 70 ◽  
pp. 84-93 ◽  
Author(s):  
R. Wesley Henderson ◽  
Paul M. Goggans ◽  
Lei Cao
Keyword(s):  
Bayesian Model ◽  
Model Comparison ◽  
Nested Sampling ◽  
Bayesian Model Comparison
Sign in / Sign up

Export Citation Format

Share Document