A combination of experimental and theoretical studies have postulated converging evidence for the hypothesis of sparse coding during sensory information, in that information is presented by a relatively small number of active neurons out of a large population. We first consider this hypothesis from the perspective of encoding. We investigate a filter based model of primary visual cortex (V1) and find that while some of the model neurons have physiological response properties that would be consistent with sparse encoding, on the population level there is a lack of consistency. In addition, the filter based model has very limited spatio-temporal dynamics from which to consider the range of possibilities in which a sparse encoding might be manifested. We therefore turn to a more elaborate large-scale model of V1, which is built on anatomically and physiologically realistic architecture and parameters, and which yields much more realistic and experimentally consistent responses across the entire neuronal population. We then consider the sparse coding hypothesis from the decoding perspective, namely how the sparse representation of information in the early sensory system is utilized by the rest of the brain to form decisions and mediate behavior.
Inspired by recent development in reservoir computing and compressive sensing, we develop a sparse decoding framework using an ℓ1-regularized linear classifier. The ℓ1-regularized logistic regression is mathematically challenging given the non-differentiability of the ℓ 1-norm. We implement an efficient and accurate numerical algorithm, which leverages the speed and accuracy of two types of operations. Termed the hybrid iterative shrinkage (HIS) algorithm, we solve the problem using a super-fast iterative shrinkage method followed by a more accurate interior point method. Furthermore, we show that various optimization techniques, including line search and continuation, can significantly accelerate convergence. The resultant algorithm overcomes the bottleneck of memory consumption in the interior point method, and also improves the solution quality of the iterative shrinkage method. This allows us to tackle large-scale problem, as the anatomically realistic model of V1 has posed, efficiently and accurately.
We then marry the encoding and decoding processes by sparse decoding the population activity in the large-scale spiking neuron model of V1. The sparse decoder is a linear integration followed by sigmoidal nonlinearity and can therefore be viewed as a decoding neuron integrating the spatio-temporal dynamics of the V1 network. We consider the decoding problem within the context of a perceptual decision making paradigm. Population spike trains are mapped into the decision space using the sparse decoder. From this space we generate neurometric curves, which are compared to psychometric curves from human subjects psychophysics experiments. Since sparse decoding creates an avenue for feature selection, we are able to analyze the informative dimensions critical for perceptual decision making. We find that the best decoding performance is obtained from a representation that is sparse in both space and time. Furthermore, the number of neurons required for decoding increases monotonically as signal-to-noise in the stimulus decreases. In addition, sparse decoding results in a more accurate decoding of the stimulus than distributed decoding, and is more robust, in the presence of noise, than distributed decoding.
Next we use the model and decoder as a testbed to investigate the relationship between neural circuitry and behavior, for both normal and abnormal visual perception. One avenue we investigate is considering how modulation of conductances may effect decoding performance and relate these conductance changes to attentional modulation. We find that changes to lateral geniculate nucleus (LGN) conductances produce shifts in neurometric curves which are consistent with attentional effects and might be a mechanism for bottom-up attentional modulation. Another avenue of investigation is to use this testbed for assessing the perceptual consequences of macular degeneration, a blinding disease that affects over 15 million people in the US. Currently clinical assessment of macular diseases typically relies on direct analysis of retinal imaging, which does not necessarily provide a complete picture of the expected vision loss. We use psychophysics tests coupled with our stimulus encoding/decoding models to relate pathologies, found via fundus imaging, to perceptual function for a group of aged-related macular degeneration (AMD) patients. (Abstract shortened by UMI.)
|School Location:||United States -- New York|
|Source:||DAI-B 71/11, Dissertation Abstracts International|
|Subjects:||Neurosciences, Applied Mathematics, Biomedical engineering|
|Keywords:||Machine learning, Neural activity, Perceptual decision making, Primary visual cortex, Sparse decoding|
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