Natural Image Coding in V1: How Much Use is Orientation Selectivity?

Orientation selectivity is the most striking feature of simple cell coding in V1 which has been shown to emerge from the reduction of higher-order correlations in natural images in a large variety of statistical image models. The most parsimonious one among these models is linear Independent Component Analysis (ICA), whereas second-order decorrelation transformations such as Principal Component Analysis (PCA) do not yield oriented filters. Because of this finding it has been suggested that the emergence of orientation selectivity may be explained by higher-order redundancy reduction. In order to assess the tenability of this hypothesis, it is an important empirical question how much more redundancies can be removed with ICA in comparison to PCA, or other second-order decorrelation methods. This question has not yet been settled, as over the last ten years contradicting results have been reported ranging from less than five to more than hundred percent extra gain for ICA. Here, we aim at resolving this conflict by presenting a very careful and comprehensive analysis using three evaluation criteria related to redundancy reduction: In addition to the multi-information and the average log-loss we compute, for the first time, complete rate-distortion curves for ICA in comparison with PCA. Without exception, we find that the advantage of the ICA filters is surprisingly small. Furthermore, we show that a simple spherically symmetric distribution with only two parameters can fit the data even better than the probabilistic model underlying ICA. Since spherically symmetric models are agnostic with respect to the specific filter shapes, we conlude that orientation selectivity is unlikely to play a critical role for redundancy reduction

Cortical Surround Interactions and Perceptual Salience via Natural Scene Statistics

Spatial context in images induces perceptual phenomena associated with salience and modulates the responses of neurons in primary visual cortex (V1). However, the computational and ecological principles underlying contextual effects are incompletely understood. We introduce a model of natural images that includes grouping and segmentation of neighboring features based on their joint statistics, and we interpret the firing rates of V1 neurons as performing optimal recognition in this model. We show that this leads to a substantial generalization of divisive normalization, a computation that is ubiquitous in many neural areas and systems. A main novelty in our model is that the influence of the context on a target stimulus is determined by their degree of statistical dependence. We optimized the parameters of the model on natural image patches, and then simulated neural and perceptual responses on stimuli used in classical experiments. The model reproduces some rich and complex response patterns observed in V1, such as the contrast dependence, orientation tuning and spatial asymmetry of surround suppression, while also allowing for surround facilitation under conditions of weak stimulation. It also mimics the perceptual salience produced by simple displays, and leads to readily testable predictions. Our results provide a principled account of orientation-based contextual modulation in early vision and its sensitivity to the homogeneity and spatial arrangement of inputs, and lends statistical support to the theory that V1 computes visual salience

Correlated topographic analysis: estimating an ordering of correlated components

Abstract This paper describes a novel method, which we call correlated topographic analysis (CTA), to estimate non-Gaussian components and their ordering (topography). The method is inspired by a central motivation of recent variants of independent component analysis (ICA), namely, to make use of the residual statistical dependency which ICA cannot remove. We assume that components nearby on the topographic arrangement have both linear and energy correlations, while far-away components are statistically independent. We use these dependencies to fix the ordering of the components. We start by proposing the generative model for the components. Then, we derive an approximation of the likelihood based on the model. Furthermore, since gradient methods tend to get stuck in local optima, we propose a three-step optimization method which dramatically improves topographic estimation. Using simulated data, we show that CTA estimates an ordering of the components and generalizes a previous method in terms of topography estimation. Finally, to demonstrate that CTA is widely applicable, we learn topographic representations for three kinds of real data: natural images, outputs of simulated complex cells and text data

Charles Bonnet Syndrome:Evidence for a Generative Model in the Cortex?

Several theories propose that the cortex implements an internal model to explain, predict, and learn about sensory data, but the nature of this model is unclear. One condition that could be highly informative here is Charles Bonnet syndrome (CBS), where loss of vision leads to complex, vivid visual hallucinations of objects, people, and whole scenes. CBS could be taken as indication that there is a generative model in the brain, specifically one that can synthesise rich, consistent visual representations even in the absence of actual visual input. The processes that lead to CBS are poorly understood. Here, we argue that a model recently introduced in machine learning, the deep Boltzmann machine (DBM), could capture the relevant aspects of (hypothetical) generative processing in the cortex. The DBM carries both the semantics of a probabilistic generative model and of a neural network. The latter allows us to model a concrete neural mechanism that could underlie CBS, namely, homeostatic regulation of neuronal activity. We show that homeostatic plasticity could serve to make the learnt internal model robust against e.g. degradation of sensory input, but overcompensate in the case of CBS, leading to hallucinations. We demonstrate how a wide range of features of CBS can be explained in the model and suggest a potential role for the neuromodulator acetylcholine. This work constitutes the first concrete computational model of CBS and the first application of the DBM as a model in computational neuroscience. Our results lend further credence to the hypothesis of a generative model in the brain

Unsupervised discovery of nonlinear structure using contrastive backpropagation.

We describe a way of modeling high-dimensional data vectors by using an unsupervised, nonlinear, multilayer neural network in which the activity of each neuron-like unit makes an additive contribution to a global energy score that indicates how surprised the network is by the data vector. The connection weights that determine how the activity of each unit depends on the activities in earlier layers are learned by minimizing the energy assigned to data vectors that are actually observed and maximizing the energy assigned to "confabulations" that are generated by perturbing an observed data vector in a direction that decreases its energy under the current model

Learning Causally Linked Markov Random Fields

We describe a learning procedure for a generative model that contains a hidden Markov Random Field (MRF) which has directed connections to the observable variables. The learning procedure uses a variational approximation for the posterior distribution over the hidden variables. Despite the intractable partition function of the MRF, the weights on the directed connections and the variational approximation itself can be learned by maximizing a lower bound on the log probability of the observed data. The parameters of the MRF are learned by using the mean field version of contrastive divergence [1]. We show that this hybrid model simultaneously learns parts of objects and their inter-relationships from intensity images. We discuss the extension to multiple MRF's linked into in a chain graph by directed connections

Combining discriminative features to infer complex trajectories

We propose a new model for the probabilistic estimation of continuous state variables from a sequence of observations, such as tracking the position of an object in video. This mapping is modeled as a product of dynamics experts (features relating the state at adjacent time-steps) and observation experts (features relating the state to the image sequence). Individual features are flexible in that they can switch on or off at each time-step depending on their inferred relevance (or on additional side information), and discriminative in that they need not model the full generative likelihood of the data. When trained conditionally, this permits the inclusion of a broad range of rich features (for example, features relying on observations from multiple time-steps), and allows the relevance of features to be learned from labeled sequences. 1

Energy-based models for sparse overcomplete representations

We present a new way of extending independent components analysis (ICA) to overcomplete representations. In contrast to the causal generative extensions of ICA which maintain marginal independence of sources, we define features as deterministic (linear) functions of the inputs. This assumption results in marginal dependencies among the features, but conditional independence of the features given the inputs. By assigning energies to the features a probability distribution over the input states is defined through the Boltzmann distribution. Free parameters of this model are trained using the contrastive divergence objective (Hinton, 2002). When the number of features is equal to the number of input dimensions this energy-based model reduces to noiseless ICA and we show experimentally that the proposed learning algorithm is able to perform blind source separation on speech data. In additional experiments we train overcomplete energy-based models to extract features from various standard data-sets containing speech, natural images, hand-written digits and faces