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LeN3rd t1_jcgsjxq wrote

Reply to comment by ilrazziatore in [D] Simple Questions Thread by AutoModerator

define probabilistic. Is it model uncertainty, or data uncertainty? Either way you should get a standard deviation from your model (either as an output parameter, or implicitly by ensembles), that you can compare.

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ilrazziatore t1_jcgy9ya wrote

Model uncertainty. One model is a calibrated bnn ( i splitted the dataset in a training, a calibration and a test set), the other model is a mathematical model developed considering some physical relation. For computational reasons the bnn assume iid samples normally distributed around their true values and maximize the likelihood (modeled as a product of normal distribution), the mathematical model instead rely on 4 coefficients and is fitted using Monte Carlo with a multivariate likelihood with the full covariance matrix. I wanted to compare the quality of the model uncertainty estimates but I don't know if I should do it on the test dataset for both. Afterall, models calibrated with mcmc methods do not overfit so why split the dataset?

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LeN3rd t1_jcgzk3c wrote

If it is model uncertainty, the bnn should only assume distributions only for the model parameters, no? If you make the samples a distribution, you assume data uncertainty. Also I do not know exactly what you other model gives you, but as long as you get variances, I would just compare those at first. If the models give vastly different means, you should take that into account. There is probably some nice way to add this ensemble uncertainty with the uncertainty of the models. Also this strongly means that one model is biased and does jot give you a correct estimate of the model uncertainty.

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ilrazziatore t1_jch3vpu wrote

Uhm..... the bnn are built assuming distribution both on th parameters( ie the value assumed by the neurons weights) and on the data (the last layer has 2 outputs : the predicted mean and the predicted variance. Those 2 values are then used to model the loss function which is the likelihood and is a product of gaussians. I think its both model and data uncertainty.

Let's say I compare the variances and the mean values predicted.

Do I have to set the same calibration and test dataset apart for both models or use the entire dataset? The mcmc model can use the entire dataset without the risk of overfitting but for the bnn it will be like cheating

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LeN3rd t1_jchht71 wrote

Than I would just use a completely different test dataset. In a paper I would also expect this.

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ilrazziatore t1_jciyif4 wrote

Eh data are scarce, I have only this dataset ( it's composed by astrophysical measures, I cannot ask them to produce more data).

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