Data-Space Validation of High-Dimensional Models by Comparing Sample Quantiles
arxiv(2024)
摘要
We present a simple method for assessing the predictive performance of
high-dimensional models directly in data space when only samples are available.
Our approach is to compare the quantiles of observables predicted by a model to
those of the observables themselves. In cases where the dimensionality of the
observables is large (e.g. multiband galaxy photometry), we advocate that the
comparison is made after projection onto a set of principal axes to reduce the
dimensionality. We demonstrate our method on a series of two-dimensional
examples. We then apply it to results from a state-of-the-art generative model
for galaxy photometry (pop-cosmos) that generates predictions of colors and
magnitudes by forward simulating from a 16-dimensional distribution of physical
parameters represented by a score-based diffusion model. We validate the
predictive performance of this model directly in a space of nine broadband
colors. Although motivated by this specific example, the techniques we present
will be broadly useful for evaluating the performance of flexible,
non-parametric population models of this kind, and can be readily applied to
any setting where two sets of samples are to be compared.
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