Results 1 
5 of
5
Neural Reconstruction with Approximate Message Passing (NeuRAMP)
"... Many functional descriptions of spiking neurons assume a cascade structure where inputs are passed through an initial linear filtering stage that produces a lowdimensional signal that drives subsequent nonlinear stages. This paper presents a novel and systematic parameter estimation procedure for su ..."
Abstract

Cited by 7 (5 self)
 Add to MetaCart
(Show Context)
Many functional descriptions of spiking neurons assume a cascade structure where inputs are passed through an initial linear filtering stage that produces a lowdimensional signal that drives subsequent nonlinear stages. This paper presents a novel and systematic parameter estimation procedure for such models and applies the method to two neural estimation problems: (i) compressedsensing based neural mapping from multineuron excitation, and (ii) estimation of neural receptive fields in sensory neurons. The proposed estimation algorithm models the neurons via a graphical model and then estimates the parameters in the model using a recentlydeveloped generalized approximate message passing (GAMP) method. The GAMP method is based on Gaussian approximations of loopy belief propagation. In the neural connectivity problem, the GAMPbased method is shown to be computational efficient, provides a more exact modeling of the sparsity, can incorporate nonlinearities in the output and significantly outperforms previous compressedsensing methods. For the receptive field estimation, the GAMP method can also exploit inherent structured sparsity in the linear weights. The method is validated on estimation of linear nonlinear Poisson (LNP) cascade models for receptive fields of salamander retinal ganglion cells. 1
unknown title
"... Ramsey theory reveals the conditions when sparse coding on subsampled data is unique ..."
Abstract
 Add to MetaCart
(Show Context)
Ramsey theory reveals the conditions when sparse coding on subsampled data is unique
1Short Term Memory Capacity in Networks via the Restricted Isometry Property
"... Cortical networks are hypothesized to rely on transient network activity to support short term memory (STM). In this paper we study the capacity of randomly connected recurrent linear networks for performing STM when the input signals are approximately sparse in some basis. We leverage results from ..."
Abstract
 Add to MetaCart
(Show Context)
Cortical networks are hypothesized to rely on transient network activity to support short term memory (STM). In this paper we study the capacity of randomly connected recurrent linear networks for performing STM when the input signals are approximately sparse in some basis. We leverage results from compressed sensing to provide rigorous nonasymptotic recovery guarantees, quantifying the impact of the input sparsity level, the input sparsity basis, and the network characteristics on the system capacity. Our analysis demonstrates that network memory capacities can scale superlinearly with the number of nodes, and in some situations can achieve STM capacities that are much larger than the network size. We provide perfect recovery guarantees for finite sequences and recovery bounds for infinite sequences. The latter analysis predicts that network STM systems may have an optimal recovery length that balances errors due to omission and recall mistakes. Furthermore, we show that the conditions yielding optimal STM capacity can be embodied in several network topologies, including networks with sparse or dense connectivities. ar X iv
1Ramsey
"... theory reveals the conditions when sparse coding on subsampled data is unique ..."
Abstract
 Add to MetaCart
(Show Context)
theory reveals the conditions when sparse coding on subsampled data is unique