CORRELATIVE INFORMATION MAXIMIZATION BASED BIOLOGICALLY PLAUSIBLE NEURAL NETWORKS FOR CORRELATED SOURCE SEPARATION

Abstract

The brain effortlessly extracts latent causes of stimuli, but how it does this at the network level remains unknown. Most prior attempts at this problem proposed neural networks that implement independent component analysis, which works under the limitation that latent causes are mutually independent. Here, we relax this limitation and propose a biologically plausible neural network that extracts correlated latent sources by exploiting information about their domains. To derive this network, we choose the maximum correlative information transfer from inputs to outputs as the separation objective under the constraint that the output vectors are restricted to the set where the source vectors are assumed to be located. The online formulation of this optimization problem naturally leads to neural networks with local learning rules. Our framework incorporates infinitely many set choices for the source domain and flexibly models complex latent structures. Choices of simplex or polytopic source domains result in networks with piecewise-linear activation functions. We provide numerical examples to demonstrate the superior correlated source separation capability for both synthetic and natural sources.

1. INTRODUCTION

Extraction of latent causes, or sources, of complex stimuli sensed by sensory organs is essential for survival. Due to absence of any supervision in most circumstances, this extraction must be performed in an unsupervised manner, a process which has been named blind source separation (BSS) (Comon & Jutten, 2010; Cichocki et al., 2009) . How BSS may be achieved in visual, auditory, or olfactory cortical circuits has attracted the attention of many researchers, e.g. (Bell & Sejnowski, 1995; Olshausen & Field, 1996; Bronkhorst, 2000; Lewicki, 2002; Asari et al., 2006; Narayan et al., 2007; Bee & Micheyl, 2008; McDermott, 2009; Mesgarani & Chang, 2012; Golumbic et al., 2013; Isomura et al., 2015) . Influential papers showed that visual and auditory cortical receptive fields could arise from performing BSS on natural scenes (Bell & Sejnowski, 1995; Olshausen & Field, 1996) and sounds (Lewicki, 2002) . The potential ubiquity of BSS in the brain suggests that there exists generic neural circuit motifs for BSS (Sharma et al., 2000) . Motivated by these observations, here, we present a set of novel biologically plausible neural network algorithms for BSS. BSS algorithms typically derive from normative principles. The most important one is the information maximization principle, which aims to maximize the information transferred from input mixtures to separator outputs under the restriction that the outputs satisfy a specific generative assumption about sources. However, Shannon mutual information is a challenging choice for quantifying information transfer, especially for data-driven adaptive applications, due to its reliance on the joint and conditional densities of the input and output components. This challenge is eased by the independent component analysis (ICA) framework by inducing joint densities into separable forms based on the assumption of source independence (Bell & Sejnowski, 1995) . In particular scenarios,

