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

A multi-method approach to delineate and validate migratory corridors

Context: Managers are faced with numerous methods for delineating wildlife movement corridors, and often must make decisions with limited data. Delineated corridors should be robust to different data and models. Objectives: We present a multi-method approach for delineating and validating wildlife corridors using multiple data sources, which can be used conserve landscape connectivity. We used this approach to delineate and validate migration corridors for wildebeest (Connochaetes taurinus) in the Tarangire Ecosystem of northern Tanzania. Methods: We used two types of locational data (distance sampling detections and GPS collar locations), and three modeling methods (negative binomial regression, logistic regression, and Maxent), to generate resource selection functions (RSFs) and define resistance surfaces. We compared two corridor detection algorithms (cost-distance and circuit theory), to delineate corridors. We validated corridors by comparing random and wildebeest locations that fell within corridors, and cross-validated by data type. Results: Both data types produced similar RSFs. Wildebeest consistently selected migration habitat in flatter terrain farther from human settlements. Validation indicated three of the combinations of data type, modeling, and corridor detection algorithms (detection data with Maxent modeling, GPS collar data with logistic regression modeling, and GPS collar data with Maxent modeling, all using cost-distance) far outperformed the other seven. We merged the predictive corridors from these three data-method combinations to reveal habitat with highest probability of use. Conclusions: The use of multiple methods ensures that planning is able to prioritize conservation of migration corridors based on all available information

Advancing functional connectivity research from association to causation

Cognition and behavior emerge from brain network interactions, such that investigating causal interactions should be central to the study of brain function. Approaches that characterize statistical associations among neural time series-functional connectivity (FC) methods-are likely a good starting point for estimating brain network interactions. Yet only a subset of FC methods ('effective connectivity') is explicitly designed to infer causal interactions from statistical associations. Here we incorporate best practices from diverse areas of FC research to illustrate how FC methods can be refined to improve inferences about neural mechanisms, with properties of causal neural interactions as a common ontology to facilitate cumulative progress across FC approaches. We further demonstrate how the most common FC measures (correlation and coherence) reduce the set of likely causal models, facilitating causal inferences despite major limitations. Alternative FC measures are suggested to immediately start improving causal inferences beyond these common FC measures

Network perspectives on epilepsy using EEG/MEG source connectivity

The evolution of EEG/MEG source connectivity is both, a promising, and controversial advance in the characterization of epileptic brain activity. In this narrative review we elucidate the potential of this technology to provide an intuitive view of the epileptic network at its origin, the different brain regions involved in the epilepsy, without the limitation of electrodes at the scalp level. Several studies have confirmed the added value of using source connectivity to localize the seizure onset zone and irritative zone or to quantify the propagation of epileptic activity over time. It has been shown in pilot studies that source connectivity has the potential to obtain prognostic correlates, to assist in the diagnosis of the epilepsy type even in the absence of visually noticeable epileptic activity in the EEG/MEG, and to predict treatment outcome. Nevertheless, prospective validation studies in large and heterogeneous patient cohorts are still lacking and are needed to bring these techniques into clinical use. Moreover, the methodological approach is challenging, with several poorly examined parameters that most likely impact the resulting network patterns. These fundamental challenges affect all potential applications of EEG/MEG source connectivity analysis, be it in a resting, spiking, or ictal state, and also its application to cognitive activation of the eloquent area in presurgical evaluation. However, such method can allow unique insights into physiological and pathological brain functions and have great potential in (clinical) neuroscience

Neural Connectivity with Hidden Gaussian Graphical State-Model

The noninvasive procedures for neural connectivity are under questioning. Theoretical models sustain that the electromagnetic field registered at external sensors is elicited by currents at neural space. Nevertheless, what we observe at the sensor space is a superposition of projected fields, from the whole gray-matter. This is the reason for a major pitfall of noninvasive Electrophysiology methods: distorted reconstruction of neural activity and its connectivity or leakage. It has been proven that current methods produce incorrect connectomes. Somewhat related to the incorrect connectivity modelling, they disregard either Systems Theory and Bayesian Information Theory. We introduce a new formalism that attains for it, Hidden Gaussian Graphical State-Model (HIGGS). A neural Gaussian Graphical Model (GGM) hidden by the observation equation of Magneto-encephalographic (MEEG) signals. HIGGS is equivalent to a frequency domain Linear State Space Model (LSSM) but with sparse connectivity prior. The mathematical contribution here is the theory for high-dimensional and frequency-domain HIGGS solvers. We demonstrate that HIGGS can attenuate the leakage effect in the most critical case: the distortion EEG signal due to head volume conduction heterogeneities. Its application in EEG is illustrated with retrieved connectivity patterns from human Steady State Visual Evoked Potentials (SSVEP). We provide for the first time confirmatory evidence for noninvasive procedures of neural connectivity: concurrent EEG and Electrocorticography (ECoG) recordings on monkey. Open source packages are freely available online, to reproduce the results presented in this paper and to analyze external MEEG databases

Fast non-negative deconvolution for spike train inference from population calcium imaging

Calcium imaging for observing spiking activity from large populations of neurons are quickly gaining popularity. While the raw data are fluorescence movies, the underlying spike trains are of interest. This work presents a fast non-negative deconvolution filter to infer the approximately most likely spike train for each neuron, given the fluorescence observations. This algorithm outperforms optimal linear deconvolution (Wiener filtering) on both simulated and biological data. The performance gains come from restricting the inferred spike trains to be positive (using an interior-point method), unlike the Wiener filter. The algorithm is fast enough that even when imaging over 100 neurons, inference can be performed on the set of all observed traces faster than real-time. Performing optimal spatial filtering on the images further refines the estimates. Importantly, all the parameters required to perform the inference can be estimated using only the fluorescence data, obviating the need to perform joint electrophysiological and imaging calibration experiments.Comment: 22 pages, 10 figure

Model-based Reinforcement Learning with Parametrized Physical Models and Optimism-Driven Exploration

In this paper, we present a robotic model-based reinforcement learning method that combines ideas from model identification and model predictive control. We use a feature-based representation of the dynamics that allows the dynamics model to be fitted with a simple least squares procedure, and the features are identified from a high-level specification of the robot's morphology, consisting of the number and connectivity structure of its links. Model predictive control is then used to choose the actions under an optimistic model of the dynamics, which produces an efficient and goal-directed exploration strategy. We present real time experimental results on standard benchmark problems involving the pendulum, cartpole, and double pendulum systems. Experiments indicate that our method is able to learn a range of benchmark tasks substantially faster than the previous best methods. To evaluate our approach on a realistic robotic control task, we also demonstrate real time control of a simulated 7 degree of freedom arm.Comment: 8 page