Converting Cascade-Correlation Neural Nets into Probabilistic Generative Models

Humans are not only adept in recognizing what class an input instance belongs to (i.e., classification task), but perhaps more remarkably, they can imagine (i.e., generate) plausible instances of a desired class with ease, when prompted. Inspired by this, we propose a framework which allows transforming Cascade-Correlation Neural Networks (CCNNs) into probabilistic generative models, thereby enabling CCNNs to generate samples from a category of interest. CCNNs are a well-known class of deterministic, discriminative NNs, which autonomously construct their topology, and have been successful in giving accounts for a variety of psychological phenomena. Our proposed framework is based on a Markov Chain Monte Carlo (MCMC) method, called the Metropolis-adjusted Langevin algorithm, which capitalizes on the gradient information of the target distribution to direct its explorations towards regions of high probability, thereby achieving good mixing properties. Through extensive simulations, we demonstrate the efficacy of our proposed framework.