The Bayesian "evidence" approximation has recently been employed to determine the noise and weight-penalty terms used in back-propagation. This paper shows that for neural nets it is far easier to use the exact result than it is to use the evidence approximation. Moreover, unlike the evi(cid:173) dence approximation, the exact result neither has to be re-calculated for every new data set, nor requires the running of computer code (the exact result is closed form). In addition, it turns out that the evidence proce(cid:173) dure's MAP estimate for neural nets is, in toto, approximation error. An(cid:173) other advantage of the exact analysis is that it does not lead one to incor(cid:173) rect intuition, like the claim that using evidence one can "evaluate differ(cid:173) ent priors in light of the data".

We develop latent variable models for Bayesian learning based low-rank matrix completion and reconstruction from linear measurements. For under-determined systems, the developed methods are shown to reconstruct low-rank matrices when neither the rank nor the noise power is known a-priori. We derive relations between the latent variable models and several low-rank promoting penalty functions. The relations justify the use of Kronecker structured covariance matrices in a Gaussian based prior. In the methods, we use evidence approximation and expectation-maximization to learn the model parameters. The performance of the methods is evaluated through extensive numerical simulations.

The Bayesian "evidence" approximation has recently been employed to determine the noise and weight-penalty terms used in back-propagation. This paper shows that for neural nets it is far easier to use the exact result than it is to use the evidence approximation. Moreover, unlike the evidence approximation, the exact result neither has to be re-calculated for every new data set, nor requires the running of computer code (the exact result is closed form). In addition, it turns out that the evidence procedure's MAP estimate for neural nets is, in toto, approximation error. Another advantage of the exact analysis is that it does not lead one to incorrect intuition, like the claim that using evidence one can "evaluate different priors in light of the data". This paper also discusses sufficiency conditions for the evidence approximation to hold, why it can sometimes give "reasonable" results, etc.

The Bayesian "evidence" approximation has recently been employed to determine the noise and weight-penalty terms used in back-propagation. This paper shows that for neural nets it is far easier to use the exact result than it is to use the evidence approximation. Moreover, unlike the evidence approximation, the exact result neither has to be re-calculated for every new data set, nor requires the running of computer code (the exact result is closed form). In addition, it turns out that the evidence procedure's MAP estimate for neural nets is, in toto, approximation error. Another advantage of the exact analysis is that it does not lead one to incorrect intuition, like the claim that using evidence one can "evaluate different priors in light of the data". This paper also discusses sufficiency conditions for the evidence approximation to hold, why it can sometimes give "reasonable" results, etc.

The Bayesian "evidence" approximation has recently been employed to determine the noise and weight-penalty terms used in back-propagation. This paper shows that for neural nets it is far easier to use the exact result than it is to use the evidence approximation. Moreover, unlike the evidence approximation,the exact result neither has to be re-calculated for every new data set, nor requires the running of computer code (the exact result is closed form). In addition, it turns out that the evidence procedure's MAPestimate for neural nets is, in toto, approximation error. Another advantage of the exact analysis is that it does not lead one to incorrect intuition, like the claim that using evidence one can "evaluate different priors in light of the data". This paper also discusses sufficiency conditions for the evidence approximation to hold, why it can sometimes give "reasonable" results, etc.