Second Order Dimensionality Reduction Using Minimum and Maximum Mutual Information Models

Conventional methods used to characterize multidimensional neural feature selectivity, such as spike-triggered covariance (STC) or maximally informative dimensions (MID), are limited to Gaussian stimuli or are only able to identify a small number of features due to the curse of dimensionality. To overcome these issues, we propose two new dimensionality reduction methods that use minimum and maximum information models. These methods are information theoretic extensions of STC that can be used with non-Gaussian stimulus distributions to find relevant linear subspaces of arbitrary dimensionality. We compare these new methods to the conventional methods in two ways: with biologically-inspired simulated neurons responding to natural images and with recordings from macaque retinal and thalamic cells responding to naturalistic time-varying stimuli. With non-Gaussian stimuli, the minimum and maximum information methods significantly outperform STC in all cases, whereas MID performs best in the regime of low dimensional feature spaces

HIERARCHICAL NEURAL COMPUTATION IN THE MAMMALIAN VISUAL SYSTEM

Our visual system can efficiently extract behaviorally relevant information from ambiguous and noisy luminance patterns. Although we know much about the anatomy and physiology of the visual system, it remains obscure how the computation performed by individual visual neurons is constructed from the neural circuits. In this thesis, I designed novel statistical modeling approaches to study hierarchical neural computation, using electrophysiological recordings from several stages of the mammalian visual system. In Chapter 2, I describe a two-stage nonlinear model that characterized both synaptic current and spike response of retinal ganglion cells with unprecedented accuracy. I found that excitatory synaptic currents to ganglion cells are well described by excitatory inputs multiplied by divisive suppression, and that spike responses can be explained with the addition of a second stage of spiking nonlinearity and refractoriness. The structure of the model was inspired by known elements of the retinal circuit, and implies that presynaptic inhibition from amacrine cells is an important mechanism underlying ganglion cell computation. In Chapter 3, I describe a hierarchical stimulus-processing model of MT neurons in the context of a naturalistic optic flow stimulus. The model incorporates relevant nonlinear properties of upstream V1 processing and explained MT neuron responses to complex motion stimuli. MT neuron responses are shown to be best predicted from distinct excitatory and suppressive components. The direction-selective suppression can impart selectivity of MT neurons to complex velocity fields, and contribute to improved estimation of the three-dimensional velocity of moving objects. In Chapter 4, I present an extended model of MT neurons that includes both the stimulus-processing component and network activity reflected in local field potentials (LFPs). A significant fraction of the trial-to-trial variability of MT neuron responses is predictable from the LFPs in both passive fixation and a motion discrimination task. Moreover, the choice-related variability of MT neuron responses can be explained by their phase preferences in low-frequency band LFPs. These results suggest an important role of network activity in cortical function. Together, these results demonstrated that it is possible to infer the nature of neural computation from physiological recordings using statistical modeling approaches

Functional connectivity and dendritic integration of feedback in visual cortex

A fundamental question in neuroscience is how different brain regions communicate with each other. Sensory processing engages distributed circuits across many brain areas and involves information flow in the feedforward and feedback direction. While feedforward processing is conceptually well understood, feedback processing has remained mysterious. Cortico-cortical feedback axons are enriched in layer 1, where they form synapses with the apical dendrites of pyramidal neurons. The organization and dendritic integration of information conveyed by these axons, however, are unknown. This thesis describes my efforts to link the circuit-level and dendritic-level organization of cortico-cortical feedback in the mouse visual system. First, using cellular resolution all-optical interrogation across cortical areas, I characterized the functional connectivity between the lateromedial higher visual area (LM) and primary visual cortex (V1). Feedback influence had both facilitating and suppressive effects on visually-evoked activity in V1 neurons, and was spatially organized: retinotopically aligned feedback was relatively more suppressive, while retinotopically offset feedback was relatively more facilitating. Second, to examine how feedback inputs are integrated in apical dendrites, I optogenetically stimulated presynaptic neurons in LM while using 2-photon calcium imaging to map feedback-recipient spines in the apical tufts of layer 5 neurons in V1. Activation of a single feedback-providing input was sufficient to boost calcium signals and recruit branch-specific local events in the recipient dendrite, suggesting that feedback can engage dendritic nonlinearities directly. Finally, I measured the recruitment of apical dendrites during visual stimulus processing. Surround visual stimuli, which should recruit relatively more facilitating feedback, drove local calcium events in apical tuft branches. Moreover, global dendritic event size was not purely determined by somatic activity but modulated by visual stimuli and behavioural state, in a manner consistent with the spatial organization of feedback. In summary, these results point toward a possible involvement of active dendritic processing in the integration of feedback signals. Active dendrites could thus provide a biophysical substrate for the integration of essential top-down information streams, including contextual or predictive processing

Information processing in visual systems

One of the goals of neuroscience is to understand how animals perceive sensory information. This thesis focuses on visual systems, to unravel how neuronal structures process aspects of the visual environment. To characterise the receptive field of a neuron, we developed spike-triggered independent component analysis. Alongside characterising the receptive field of a neuron, this method provides an insight into its underlying network structure. When applied to recordings from the H1 neuron of blowflies, it accurately recovered the sub-structure of the neuron. This sub-structure was studied further by recording H1's response to plaid stimuli. Based on the response, H1 can be classified as a component cell. We then fitted an anatomically inspired model to the response, and found the critical component to explain H1's response to be a sigmoid non-linearity at output of elementary movement detectors. The simpler blowfly visual system can help us understand elementary sensory information processing mechanisms. How does the more complex mammalian cortex implement these principles in its network? To study this, we used multi-electrode arrays to characterise the receptive field properties of neurons in the visual cortex of anaesthetised mice. Based on these recordings, we estimated the cortical limits on the performance of a visual task; the behavioural performance observed by Prusky and Douglas (2004) is within these limits. Our recordings were carried out in anaesthetised animals. During anaesthesia, cortical UP states are considered "fragments of wakefulness" and from simultaneous whole-cell and extracellular recordings, we found these states to be revealed in the phase of local field potentials. This finding was used to develop a method of detecting cortical state based on extracellular recordings, which allows us to explore information processing during different cortical states. Across this thesis, we have developed, tested and applied methods that help improve our understanding of information processing in visual systems

On the analysis and interpretation of inhomogeneous quadratic forms as receptive fields

In this paper we introduce some mathematical and numerical tools to analyze and interpret inhomogeneous quadratic forms. The resulting characterization is in some aspects similar to that given by experimental studies of cortical cells, making it particularly suitable for application to second-order approximations and theoretical models of physiological receptive fields. We first discuss two ways of analyzing a quadratic form by visualizing the coefficients of its quadratic and linear term directly and by considering the eigenvectors of its quadratic term. We then present an algorithm to compute the optimal excitatory and inhibitory stimuli, i.e. the stimuli that maximize and minimize the considered quadratic form, respectively, given a fixed energy constraint. The analysis of the optimal stimuli is completed by considering their invariances, which are the transformations to which the quadratic form is most insensitive. We introduce a test to determine which of these are statistically significant. Next we propose a way to measure the relative contribution of the quadratic and linear term to the total output of the quadratic form. Furthermore, we derive simpler versions of the above techniques in the special case of a quadratic form without linear term and discuss the analysis of such functions in previous theoretical and experimental studies. In the final part of the paper we show that for each quadratic form it is possible to build an equivalent two-layer neural network, which is compatible with (but more general than) related networks used in some recent papers and with the energy model of complex cells. We show that the neural network is unique only up to an arbitrary orthogonal transformation of the excitatory and inhibitory subunits in the first layer

Mapping the primate lateral geniculate nucleus: A review of experiments and methods

Mapping neuronal responses in the lateral geniculate nucleus (LGN) is key to understanding how visual information is processed in the brain. This paper focuses on our current knowledge of the dynamics the receptive field (RF) as broken down into the classical receptive field (CRF) and the extra-classical receptive field (ECRF) in primate LGN. CRFs in the LGN are known to be similar to those in the retinal ganglion cell layer in terms of both spatial and temporal characteristics, leading to the standard interpretation of the LGN as a relay center from retina to primary visual cortex. ECRFs have generally been found to be large and inhibitory, with some differences in magnitude between the magno-, parvo-, and koniocellular pathways. The specific contributions of the retina, thalamus, and visual cortex to LGN ECRF properties are presently unknown. Some reports suggest a retinal origin for extra-classical suppression based on latency arguments and other reports have suggested a thalamic origin for extra-classical suppression. This issue is complicated by the use of anesthetized animals, where cortical activity is likely to be altered. Thus further study of LGN ECRFs is warranted to reconcile these discrepancies. Producing descriptions of RF properties of LGN neurons could be enhanced by employing preferred naturalistic stimuli. Although there has been significant work in cats with natural scene stimuli and noise that statistically imitates natural scenes, we highlight a need for similar data from primates. Obtaining these data may be aided by recent advancements in experimental and analytical techniques that permit the efficient study of nonlinear RF characteristics in addition to traditional linear factors. In light of the reviewed topics, we conclude by suggesting experiments to more clearly elucidate the spatial and temporal structure of ECRFs of primate LGN neurons