Statistical models of natural stimuli provide an important tool for
researchers in the fields of machine learning and computational neuroscience. A
canonical way to quantitatively assess and compare the performance of
statistical models is given by the likelihood. One class of statistical models
which has recently gained increasing popularity and has been applied to a
variety of complex data are deep belief networks. Analyses of these models,
however, have been typically limited to qualitative analyses based on samples
due to the computationally intractable nature of the model likelihood.
Motivated by these circumstances, the present article provides a consistent
estimator for the likelihood that is both computationally tractable and simple
to apply in practice. Using this estimator, a deep belief network which has
been suggested for the modeling of natural image patches is quantitatively
investigated and compared to other models of natural image patches. Contrary to
earlier claims based on qualitative results, the results presented in this
article provide evidence that the model under investigation is not a
particularly good model for natural image
