PubMed · 5884127
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A Rapoport. 1965. A note on equivalent mathematical models.. https://doi.org/10.1007/bf02477273
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This work proposes an unsupervised learning process for analysis of natural images. The derivation is based on a generative model, a stochastic coin-flip process directly operating on many disjoint multivariate Gaussian distributions. Following the maximal likelihood principle and using the Potts encoding, the goodness-of-fit of the generative model to tremendous patches randomly sampled from natural images is quantitatively expressed by an objective function subject to a set of constraints. By further combination of the objective function and the minimal wiring criterion, we achieve a mixed integer and linear programming. A hybrid of the mean field annealing and the gradient descent method is applied to the mathematical framework and produces three sets of interactive dynamics for the learning process. Numerical simulations show that the learning process is effective for extraction of orientation, localization and bandpass features and the generative model can make an ensemble of a sparse code for natural images.
We study learning of probability distributions characterized by an unknown symmetry direction. Based on an entropic performance measure and the variational method of statistical mechanics we develop exact upper and lower bounds on the scaled critical number of examples below which learning of the direction is impossible. The asymptotic tightness of the bounds suggests an asymptotically optimal method for learning nonsmooth distributions.
We proposed a method of incremental projection learning which provides exactly the same generalization capability as that obtained by batch projection learning in the previous paper. However, properties of the method have not yet been investigated. In this paper, we analyze its properties from the following aspects: First, it is shown that some of the training data which is regarded as redundant in most incremental learning methods have potential effectiveness, i.e. they will contribute to better generalization capability in the future learning process. Based on this fact, an improved criterion for redundancy of additional training data is derived. Second, the relationship between prior and posterior learning results is investigated where effective training data is classified into two categories from the viewpoint of improving generalization capability. Finally, a simpler representation of incremental projection learning under certain conditions is given. The size of memory required for storing prior results in the representation is fixed and independent of the total number of training data.