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A fundamental task of a sensory system is to infer information about the environment. It has long been suggested that an important goal of the first stage of this process is to encode the raw sensory signal efficiently by reducing its redundancy in the neural representation. Some redundancy, however, would be expected because it can provide robustness to noise inherent in the system. Encoding the raw sensory signal itself is also problematic, because it contains distortion and noise. The optimal solution would be constrained further by limited biological resources. Here, we analyze a simple theoretical model that incorporates these key aspects of sensory coding, and apply it to conditions in the retina. The model specifies the optimal way to incorporate redundancy in a population of noisy neurons, while also optimally compensating for sensory distortion and noise. Importantly, it allows an arbitrary input-to-output cell ratio between sensory units (photoreceptors) and encoding units (retinal ganglion cells), providing predictions of retinal codes at different eccentricities. Compared to earlier models based on redundancy reduction, the proposed model conveys more information about the original signal. Interestingly, redundancy reduction can be near-optimal when the number of encoding units is limited, such as in the peripheral retina. We show that there exist multiple, equally-optimal solutions whose receptive field structure and organization vary significantly. Among these, the one which maximizes the spatial locality of the computation, but not the sparsity of either synaptic weights or neural responses, is consistent with known basic properties of retinal receptive fields. The model further predicts that receptive field structure changes less with light adaptation at higher input-to-output cell ratios, such as in the periphery.

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The problem of scene analysis has been studied in a number of different fields over the past decades. These studies have led to important insights into problems of scene analysis, but not all of these insights are widely appreciated, and there remain critical shortcomings in current approaches that hinder further progress. Here we take the view that scene analysis is a universal problem solved by all animals, and that we can gain new insight by studying the problems that animals face in complex natural environments. In particular, the jumping spider, songbird, echolocating bat, and electric fish, all exhibit behaviors that require robust solutions to scene analysis problems encountered in the natural environment. By examining the behaviors of these seemingly disparate animals, we emerge with a framework for studying scene analysis comprising four essential properties: (1) the ability to solve ill-posed problems, (2) the ability to integrate and store information across time and modality, (3) efficient recovery and representation of 3D scene structure, and (4) the use of optimal motor actions for acquiring information to progress toward behavioral goals.

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Occlusion boundaries and junctions provide important cues for inferring three-dimensional scene organization from two-dimensional images. Although several investigators in machine vision have developed algorithms for detecting occlusions and other edges in natural images, relatively few psychophysics or neurophysiology studies have investigated what features are used by the visual system to detect natural occlusions. In this study, we addressed this question using a psychophysical experiment where subjects discriminated image patches containing occlusions from patches containing surfaces. Image patches were drawn from a novel occlusion database containing labeled occlusion boundaries and textured surfaces in a variety of natural scenes. Consistent with related previous work, we found that relatively large image patches were needed to attain reliable performance, suggesting that human subjects integrate complex information over a large spatial region to detect natural occlusions. By defining machine observers using a set of previously studied features measured from natural occlusions and surfaces, we demonstrate that simple features defined at the spatial scale of the image patch are insufficient to account for human performance in the task. To define machine observers using a more biologically plausible multiscale feature set, we trained standard linear and neural network classifiers on the rectified outputs of a Gabor filter bank applied to the image patches. We found that simple linear classifiers could not match human performance, while a neural network classifier combining filter information across location and spatial scale compared well. These results demonstrate the importance of combining a variety of cues defined at multiple spatial scales for detecting natural occlusions.

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Robust coding has been proposed as a solution to the problem of minimizing decoding error in the presence of neural noise. Many real-world problems, however, have degradation in the input signal, not just in neural representations. This generalized problem is more relevant to biological sensory coding where internal noise arises from limited neural precision and external noise from distortion of sensory signal such as blurring and phototransduction noise. In this note, we show that the optimal linear encoder for this problem can be decomposed exactly into two serial processes that can be optimized separately. One is Wiener filtering, which optimally compensates for input degradation. The other is robust coding, which best uses the available representational capacity for signal transmission with a noisy population of linear neurons. We also present spectral analysis of the decomposition that characterizes how the reconstruction error is minimized under different input signal spectra, types and amounts of degradation, degrees of neural precision, and neural population sizes.

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A fundamental function of the visual system is to encode the building blocks of natural scenes-edges, textures and shapes-that subserve visual tasks such as object recognition and scene understanding. Essential to this process is the formation of abstract representations that generalize from specific instances of visual input. A common view holds that neurons in the early visual system signal conjunctions of image features, but how these produce invariant representations is poorly understood. Here we propose that to generalize over similar images, higher-level visual neurons encode statistical variations that characterize local image regions. We present a model in which neural activity encodes the probability distribution most consistent with a given image. Trained on natural images, the model generalizes by learning a compact set of dictionary elements for image distributions typically encountered in natural scenes. Model neurons show a diverse range of properties observed in cortical cells. These results provide a new functional explanation for nonlinear effects in complex cells and offer insight into coding strategies in primary visual cortex (V1) and higher visual areas.

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This paper presents a statistical data-driven method for learning intrinsic structures of impact sounds. The method applies principal and independent component analysis to learn low-dimensional representations that model the distribution of both the time-varying spectral and amplitude structure. As a result, the method is able to decompose sounds into a small number of underlying features that characterize acoustic properties such as ringing, resonance, sustain, decay, and onsets. The method is highly flexible and makes no a priori assumptions about the physics, acoustics, or dynamics of the objects. In addition, by modeling the underlying distribution, the method can capture the natural variability of ensembles of related impact sounds.

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We address the problem of robust coding in which the signal information should be preserved in spite of intrinsic noise in the representation. We present a theoretical analysis for 1- and 2-D cases and characterize the optimal linear encoder and decoder in the mean-squared error sense. Our analysis allows for an arbitrary number of coding units, thus including both under- and over-complete representations, and provides insights into optimal coding strategies. In particular, we show how the form of the code adapts to the number of coding units and to different data and noise conditions in order to achieve robustness. We also present numerical solutions of robust coding for high-dimensional image data, demonstrating that these codes are substantially more robust than other linear image coding methods such as PCA, ICA, and wavelets.

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The auditory neural code must serve a wide range of auditory tasks that require great sensitivity in time and frequency and be effective over the diverse array of sounds present in natural acoustic environments. It has been suggested that sensory systems might have evolved highly efficient coding strategies to maximize the information conveyed to the brain while minimizing the required energy and neural resources. Here we show that, for natural sounds, the complete acoustic waveform can be represented efficiently with a nonlinear model based on a population spike code. In this model, idealized spikes encode the precise temporal positions and magnitudes of underlying acoustic features. We find that when the features are optimized for coding either natural sounds or speech, they show striking similarities to time-domain cochlear filter estimates, have a frequency-bandwidth dependence similar to that of auditory nerve fibres, and yield significantly greater coding efficiency than conventional signal representations. These results indicate that the auditory code might approach an information theoretic optimum and that the acoustic structure of speech might be adapted to the coding capacity of the mammalian auditory system.

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Capturing statistical regularities in complex, high-dimensional data is an important problem in machine learning and signal processing. Models such as principal component analysis (PCA) and independent component analysis (ICA) make few assumptions about the structure in the data and have good scaling properties, but they are limited to representing linear statistical regularities and assume that the distribution of the data is stationary. For many natural, complex signals, the latent variables often exhibit residual dependencies as well as nonstationary statistics. Here we present a hierarchical Bayesian model that is able to capture higher-order nonlinear structure and represent nonstationary data distributions. The model is a generalization of ICA in which the basis function coefficients are no longer assumed to be independent; instead, the dependencies in their magnitudes are captured by a set of density components. Each density component describes a common pattern of deviation from the marginal density of the pattern ensemble; in different combinations, they can describe nonstationary distributions. Adapting the model to image or audio data yields a nonlinear, distributed code for higher-order statistical regularities that reflect more abstract, invariant properties of the signal.

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Nonstationary acoustic features provide essential cues for many auditory tasks, including sound localization, auditory stream analysis, and speech recognition. These features can best be characterized relative to a precise point in time, such as the onset of a sound or the beginning of a harmonic periodicity. Extracting these types of features is a difficult problem. Part of the difficulty is that with standard block-based signal analysis methods, the representation is sensitive to the arbitrary alignment of the blocks with respect to the signal. Convolutional techniques such as shift-invariant transformations can reduce this sensitivity, but these do not yield a code that is efficient, that is, one that forms a nonredundant representation of the underlying structure. Here, we develop a non-block-based method for signal representation that is both time relative and efficient. Signals are represented using a linear superposition of time-shiftable kernel functions, each with an associated magnitude and temporal position. Signal decomposition in this method is a non-linear process that consists of optimizing the kernel function scaling coefficients and temporal positions to form an efficient, shift-invariant representation. We demonstrate the properties of this representation for the purpose of characterizing structure in various types of nonstationary acoustic signals. The computational problem investigated here has direct relevance to the neural coding at the auditory nerve and the more general issue of how to encode complex, time-varying signals with a population of spiking neurons.

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The theoretical principles that underlie the representation and computation of higher-order structure in natural images are poorly understood. Recently, there has been considerable interest in using information theoretic techniques, such as independent component analysis, to derive representations for natural images that are optimal in the sense of coding efficiency. Although these approaches have been successful in explaining properties of neural representations in the early visual pathway and visual cortex, because they are based on a linear model, the types of image structure that can be represented are very limited. Here, we present a hierarchical probabilistic model for learning higher-order statistical regularities in natural images. This non-linear model learns an efficient code that describes variations in the underlying probabilistic density. When applied to natural images the algorithm yields coarse-coded, sparse-distributed representations of abstract image properties such as object location, scale and texture. This model offers a novel description of higher-order image structure and could provide theoretical insight into the response properties and computational functions of lower level cortical visual areas.

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The auditory system encodes sound by decomposing the amplitude signal arriving at the ear into multiple frequency bands whose center frequencies and bandwidths are approximately exponential functions of the distance from the stapes. This organization is thought to result from the adaptation of cochlear mechanisms to the animal's auditory environment. Here we report that several basic auditory nerve fiber tuning properties can be accounted for by adapting a population of filter shapes to encode natural sounds efficiently. The form of the code depends on sound class, resembling a Fourier transformation when optimized for animal vocalizations and a wavelet transformation when optimized for non-biological environmental sounds. Only for the combined set does the optimal code follow scaling characteristics of physiological data. These results suggest that auditory nerve fibers encode a broad set of natural sounds in a manner consistent with information theoretic principles.

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An unsupervised classification algorithm is derived by modeling observed data as a mixture of several mutually exclusive classes that are each described by linear combinations of independent, non-Gaussian densities. The algorithm estimates the data density in each class by using parametric nonlinear functions that fit to the non-Gaussian structure of the data. This improves classification accuracy compared with standard Gaussian mixture models. When applied to images, the algorithm can learn efficient codes (basis functions) for images that capture the statistically significant structure intrinsic in the images. We apply this technique to the problem of unsupervised classification, segmentation, and denoising of images. We demonstrate that this method was effective in classifying complex image textures such as natural scenes and text. It was also useful for denoising and filling in missing pixels in images with complex structures. The advantage of this model is that image codes can be learned with increasing numbers of classes thus providing greater flexibility in modeling structure and in finding more image features than in either Gaussian mixture models or standard independent component analysis (ICA) algorithms.