A Bayesian approach for inferring neuronal connectivity from calcium fluorescent imaging data

Deducing the structure of neural circuits is one of the central problems of modern neuroscience. Recently-introduced calcium fluorescent imaging methods permit experimentalists to observe network activity in large populations of neurons, but these techniques provide only indirect observations of neural spike trains, with limited time resolution and signal quality. In this work we present a Bayesian approach for inferring neural circuitry given this type of imaging data. We model the network activity in terms of a collection of coupled hidden Markov chains, with each chain corresponding to a single neuron in the network and the coupling between the chains reflecting the network's connectivity matrix. We derive a Monte Carlo Expectation--Maximization algorithm for fitting the model parameters; to obtain the sufficient statistics in a computationally-efficient manner, we introduce a specialized blockwise-Gibbs algorithm for sampling from the joint activity of all observed neurons given the observed fluorescence data. We perform large-scale simulations of randomly connected neuronal networks with biophysically realistic parameters and find that the proposed methods can accurately infer the connectivity in these networks given reasonable experimental and computational constraints. In addition, the estimation accuracy may be improved significantly by incorporating prior knowledge about the sparseness of connectivity in the network, via standard L$_1$ penalization methods.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS303 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

On the Inability of Markov Models to Capture Criticality in Human Mobility

We examine the non-Markovian nature of human mobility by exposing the inability of Markov models to capture criticality in human mobility. In particular, the assumed Markovian nature of mobility was used to establish a theoretical upper bound on the predictability of human mobility (expressed as a minimum error probability limit), based on temporally correlated entropy. Since its inception, this bound has been widely used and empirically validated using Markov chains. We show that recurrent-neural architectures can achieve significantly higher predictability, surpassing this widely used upper bound. In order to explain this anomaly, we shed light on several underlying assumptions in previous research works that has resulted in this bias. By evaluating the mobility predictability on real-world datasets, we show that human mobility exhibits scale-invariant long-range correlations, bearing similarity to a power-law decay. This is in contrast to the initial assumption that human mobility follows an exponential decay. This assumption of exponential decay coupled with Lempel-Ziv compression in computing Fano's inequality has led to an inaccurate estimation of the predictability upper bound. We show that this approach inflates the entropy, consequently lowering the upper bound on human mobility predictability. We finally highlight that this approach tends to overlook long-range correlations in human mobility. This explains why recurrent-neural architectures that are designed to handle long-range structural correlations surpass the previously computed upper bound on mobility predictability

Training Input-Output Recurrent Neural Networks through Spectral Methods

We consider the problem of training input-output recurrent neural networks (RNN) for sequence labeling tasks. We propose a novel spectral approach for learning the network parameters. It is based on decomposition of the cross-moment tensor between the output and a non-linear transformation of the input, based on score functions. We guarantee consistent learning with polynomial sample and computational complexity under transparent conditions such as non-degeneracy of model parameters, polynomial activations for the neurons, and a Markovian evolution of the input sequence. We also extend our results to Bidirectional RNN which uses both previous and future information to output the label at each time point, and is employed in many NLP tasks such as POS tagging

Handwritten digit recognition by bio-inspired hierarchical networks

The human brain processes information showing learning and prediction abilities but the underlying neuronal mechanisms still remain unknown. Recently, many studies prove that neuronal networks are able of both generalizations and associations of sensory inputs. In this paper, following a set of neurophysiological evidences, we propose a learning framework with a strong biological plausibility that mimics prominent functions of cortical circuitries. We developed the Inductive Conceptual Network (ICN), that is a hierarchical bio-inspired network, able to learn invariant patterns by Variable-order Markov Models implemented in its nodes. The outputs of the top-most node of ICN hierarchy, representing the highest input generalization, allow for automatic classification of inputs. We found that the ICN clusterized MNIST images with an error of 5.73% and USPS images with an error of 12.56%

BRAIN COMPUTER INTERFACE - Application of an Adaptive Bi-stage Classifier based on RBF-HMM

Brain Computer Interface is an emerging technology that allows new output paths to communicate the users intentions without the use of normal output paths, such as muscles or nerves. In order to obtain their objective, BCI devices make use of classifiers which translate inputs from the users brain signals into commands for external devices. This paper describes an adaptive bi-stage classifier. The first stage is based on Radial Basis Function neural networks, which provides sequences of pre-assignations to the second stage, that it is based on three different Hidden Markov Models, each one trained with pre-assignation sequences from the cognitive activities between classifying. The segment of EEG signal is assigned to the HMMwith the highest probability of generating the pre-assignation sequence. The algorithm is tested with real samples of electroencephalografic signal, from five healthy volunteers using the cross-validation method. The results allow to conclude that it is possible to implement this algorithm in an on-line BCI device. The results also shown the huge dependency of the percentage of the correct classification from the user and the setup parameters of the classifier

On the Equivalence Between Deep NADE and Generative Stochastic Networks

Neural Autoregressive Distribution Estimators (NADEs) have recently been shown as successful alternatives for modeling high dimensional multimodal distributions. One issue associated with NADEs is that they rely on a particular order of factorization for $P(\mathbf{x})$. This issue has been recently addressed by a variant of NADE called Orderless NADEs and its deeper version, Deep Orderless NADE. Orderless NADEs are trained based on a criterion that stochastically maximizes $P(\mathbf{x})$ with all possible orders of factorizations. Unfortunately, ancestral sampling from deep NADE is very expensive, corresponding to running through a neural net separately predicting each of the visible variables given some others. This work makes a connection between this criterion and the training criterion for Generative Stochastic Networks (GSNs). It shows that training NADEs in this way also trains a GSN, which defines a Markov chain associated with the NADE model. Based on this connection, we show an alternative way to sample from a trained Orderless NADE that allows to trade-off computing time and quality of the samples: a 3 to 10-fold speedup (taking into account the waste due to correlations between consecutive samples of the chain) can be obtained without noticeably reducing the quality of the samples. This is achieved using a novel sampling procedure for GSNs called annealed GSN sampling, similar to tempering methods that combines fast mixing (obtained thanks to steps at high noise levels) with accurate samples (obtained thanks to steps at low noise levels).Comment: ECML/PKDD 201