An L 1-regularized logistic model for detecting short-term neuronal interactions

Improved inference in coupling, encoding, and decoding models and its consequence for neuroscientific interpretation

BACKGROUND

A central goal of systems neuroscience is to understand the relationships amongst constituent units in neural populations, and their modulation by external factors, using high-dimensional and stochastic neural recordings. Parametric statistical models (e.g., coupling, encoding, and decoding models), play an instrumental role in accomplishing this goal. However, extracting conclusions from a parametric model requires that it is fit using an inference algorithm capable of selecting the correct parameters and properly estimating their values. Traditional approaches to parameter inference have been shown to suffer from failures in both selection and estimation. The recent development of algorithms that ameliorate these deficiencies raises the question of whether past work relying on such inference procedures have produced inaccurate systems neuroscience models, thereby impairing their interpretation.

NEW METHOD

We used algorithms based on Union of Intersections, a statistical inference framework based on stability principles, capable of improved selection and estimation.

COMPARISON

We fit functional coupling, encoding, and decoding models across a battery of neural datasets using both UoI and baseline inference procedures (e.g., ℓ₁-penalized GLMs), and compared the structure of their fitted parameters.

RESULTS

Across recording modality, brain region, and task, we found that UoI inferred models with increased sparsity, improved stability, and qualitatively different parameter distributions, while maintaining predictive performance. We obtained highly sparse functional coupling networks with substantially different community structure, more parsimonious encoding models, and decoding models that relied on fewer single-units.

CONCLUSIONS

Together, these results demonstrate that improved parameter inference, achieved via UoI, reshapes interpretation in diverse neuroscience contexts.

Binless Kernel Machine: Modeling Spike Train Transformation for Cognitive Neural Prostheses

Modeling spike train transformation among brain regions helps in designing a cognitive neural prosthesis that restores lost cognitive functions. Various methods analyze the nonlinear dynamic spike train transformation between two cortical areas with low computational eficiency. The application of a real-time neural prosthesis requires computational eficiency, performance stability, and better interpretation of the neural firing patterns that modulate target spike generation. We propose the binless kernel machine in the point-process framework to describe nonlinear dynamic spike train transformations. Our approach embeds the binless kernel to eficiently capture the feedforward dynamics of spike trains and maps the input spike timings into reproducing kernel Hilbert space (RKHS). An inhomogeneous Bernoulli process is designed to combine with a kernel logistic regression that operates on the binless kernel to generate an output spike train as a point process. Weights of the proposed model are estimated by maximizing the log likelihood of output spike trains in RKHS, which allows a global-optimal solution. To reduce computational complexity, we design a streaming-based clustering algorithm to extract typical and important spike train features. The cluster centers and their weights enable the visualization of the important input spike train patterns that motivate or inhibit output neuron firing. We test the proposed model on both synthetic data and real spike train data recorded from the dorsal premotor cortex and the primary motor cortex of a monkey performing a center-out task. Performances are evaluated by discrete-time rescaling Kolmogorov-Smirnov tests. Our model outperforms the existing methods with higher stability regardless of weight initialization and demonstrates higher eficiency in analyzing neural patterns from spike timing with less historical input (50%). Meanwhile, the typical spike train patterns selected according to weights are validated to encode output spike from the spike train of single-input neuron and the interaction of two input neurons.

Modeling task-specific neuronal ensembles improves decoding of grasp

OBJECTIVE

Dexterous movement involves the activation and coordination of networks of neuronal populations across multiple cortical regions. Attempts to model firing of individual neurons commonly treat the firing rate as directly modulating with motor behavior. However, motor behavior may additionally be associated with modulations in the activity and functional connectivity of neurons in a broader ensemble. Accounting for variations in neural ensemble connectivity may provide additional information about the behavior being performed.

APPROACH

In this study, we examined neural ensemble activity in primary motor cortex (M1) and premotor cortex (PM) of two male rhesus monkeys during performance of a center-out reach, grasp and manipulate task. We constructed point process encoding models of neuronal firing that incorporated task-specific variations in the baseline firing rate as well as variations in functional connectivity with the neural ensemble. Models were evaluated both in terms of their encoding capabilities and their ability to properly classify the grasp being performed.

MAIN RESULTS

Task-specific ensemble models correctly predicted the performed grasp with over 95% accuracy and were shown to outperform models of neuronal activity that assume only a variable baseline firing rate. Task-specific ensemble models exhibited superior decoding performance in 82% of units in both monkeys (p  <  0.01). Inclusion of ensemble activity also broadly improved the ability of models to describe observed spiking. Encoding performance of task-specific ensemble models, measured by spike timing predictability, improved upon baseline models in 62% of units.

SIGNIFICANCE

These results suggest that additional discriminative information about motor behavior found in the variations in functional connectivity of neuronal ensembles located in motor-related cortical regions is relevant to decode complex tasks such as grasping objects, and may serve the basis for more reliable and accurate neural prosthesis.

On the stability and dynamics of stochastic spiking neuron models: Nonlinear Hawkes process and point process GLMs

Point process generalized linear models (PP-GLMs) provide an important statistical framework for modeling spiking activity in single-neurons and neuronal networks. Stochastic stability is essential when sampling from these models, as done in computational neuroscience to analyze statistical properties of neuronal dynamics and in neuro-engineering to implement closed-loop applications. Here we show, however, that despite passing common goodness-of-fit tests, PP-GLMs estimated from data are often unstable, leading to divergent firing rates. The inclusion of absolute refractory periods is not a satisfactory solution since the activity then typically settles into unphysiological rates. To address these issues, we derive a framework for determining the existence and stability of fixed points of the expected conditional intensity function (CIF) for general PP-GLMs. Specifically, in nonlinear Hawkes PP-GLMs, the CIF is expressed as a function of the previous spike history and exogenous inputs. We use a mean-field quasi-renewal (QR) approximation that decomposes spike history effects into the contribution of the last spike and an average of the CIF over all spike histories prior to the last spike. Fixed points for stationary rates are derived as self-consistent solutions of integral equations. Bifurcation analysis and the number of fixed points predict that the original models can show stable, divergent, and metastable (fragile) dynamics. For fragile models, fluctuations of the single-neuron dynamics predict expected divergence times after which rates approach unphysiologically high values. This metric can be used to estimate the probability of rates to remain physiological for given time periods, e.g., for simulation purposes. We demonstrate the use of the stability framework using simulated single-neuron examples and neurophysiological recordings. Finally, we show how to adapt PP-GLM estimation procedures to guarantee model stability. Overall, our results provide a stability framework for data-driven PP-GLMs and shed new light on the stochastic dynamics of state-of-the-art statistical models of neuronal spiking activity.

Tracking Neural Modulation Depth by Dual Sequential Monte Carlo Estimation on Point Processes for Brain-Machine Interfaces

Classic brain-machine interface (BMI) approaches decode neural signals from the brain responsible for achieving specific motor movements, which subsequently command prosthetic devices. Brain activities adaptively change during the control of the neuroprosthesis in BMIs, where the alteration of the preferred direction and the modulation of the gain depth are observed. The static neural tuning models have been limited by fixed codes, resulting in a decay of decoding performance over the course of the movement and subsequent instability in motor performance. To achieve stable performance, we propose a dual sequential Monte Carlo adaptive point process method, which models and decodes the gradually changing modulation depth of individual neuron over the course of a movement. We use multichannel neural spike trains from the primary motor cortex of a monkey trained to perform a target pursuit task using a joystick. Our results show that our computational approach successfully tracks the neural modulation depth over time with better goodness-of-fit than classic static neural tuning models, resulting in smaller errors between the true kinematics and the estimations in both simulated and real data. Our novel decoding approach suggests that the brain may employ such strategies to achieve stable motor output, i.e., plastic neural tuning is a feature of neural systems. BMI users may benefit from this adaptive algorithm to achieve more complex and controlled movement outcomes.

A statistical method of identifying interactions in neuron-glia systems based on functional multicell Ca2+ imaging

Crosstalk between neurons and glia may constitute a significant part of information processing in the brain. We present a novel method of statistically identifying interactions in a neuron-glia network. We attempted to identify neuron-glia interactions from neuronal and glial activities via maximum-a-posteriori (MAP)-based parameter estimation by developing a generalized linear model (GLM) of a neuron-glia network. The interactions in our interest included functional connectivity and response functions. We evaluated the cross-validated likelihood of GLMs that resulted from the addition or removal of connections to confirm the existence of specific neuron-to-glia or glia-to-neuron connections. We only accepted addition or removal when the modification improved the cross-validated likelihood. We applied the method to a high-throughput, multicellular in vitro Ca2+ imaging dataset obtained from the CA3 region of a rat hippocampus, and then evaluated the reliability of connectivity estimates using a statistical test based on a surrogate method. Our findings based on the estimated connectivity were in good agreement with currently available physiological knowledge, suggesting our method can elucidate undiscovered functions of neuron-glia systems.

Identification of functional synaptic plasticity from spiking activities using nonlinear dynamical modeling

This paper presents a systems identification approach for studying the long-term synaptic plasticity using natural spiking activities. This approach consists of three modeling steps. First, a multi-input, single-output (MISO), nonlinear dynamical spiking neuron model is formulated to estimate and represent the synaptic strength in means of functional connectivity between input and output neurons. Second, this MISO model is extended to a nonstationary form to track the time-varying properties of the synaptic strength. Finally, a Volterra modeling method is used to extract the synaptic learning rule, e.g., spike-timing-dependent plasticity, for the explanation of the input-output nonstationarity as the consequence of the past input-output spiking patterns. This framework is developed to study the underlying mechanisms of learning and memory formation in behaving animals, and may serve as the computational basis for building the next-generation adaptive cortical prostheses.

Long-term recordings improve the detection of weak excitatory-excitatory connections in rat prefrontal cortex

Characterization of synaptic connectivity is essential to understanding neural circuit dynamics. For extracellularly recorded spike trains, indirect evidence for connectivity can be inferred from short-latency peaks in the correlogram between two neurons. Despite their predominance in cortex, however, significant interactions between excitatory neurons (E) have been hard to detect because of their intrinsic weakness. By taking advantage of long duration recordings, up to 25 h, from rat prefrontal cortex, we found that 7.6% of the recorded pyramidal neurons are connected. This corresponds to ∼70% of the local E-E connection probability that has been reported by paired intracellular recordings (11.6%). This value is significantly higher than previous reports from extracellular recordings, but still a substantial underestimate. Our analysis showed that long recording times and strict significance thresholds are necessary to detect weak connections while avoiding false-positive results, but will likely still leave many excitatory connections undetected. In addition, we found that hyper-reciprocity of connections in prefrontal cortex that was shown previously by paired intracellular recordings was only present in short-distance, but not in long distance (∼300 micrometers or more) interactions. As hyper-reciprocity is restricted to local clusters, it might be a minicolumnar effect. Given the current surge of interest in very high-density neural spike recording (e.g., NIH BRAIN Project) it is of paramount importance that we have statistically reliable methods for estimating connectivity from cross-correlation analysis available. We provide an important step in this direction.

Likelihood Methods for Point Processes with Refractoriness

Likelihood-based encoding models founded on point processes have received significant attention in the literature because of their ability to reveal the information encoded by spiking neural populations. We propose an approximation to the likelihood of a point-process model of neurons that holds under assumptions about the continuous time process that are physiologically reasonable for neural spike trains: the presence of a refractory period, the predictability of the conditional intensity function, and its integrability. These are properties that apply to a large class of point processes arising in applications other than neuroscience. The proposed approach has several advantages over conventional ones. In particular, one can use standard fitting procedures for generalized linear models based on iteratively reweighted least squares while improving the accuracy of the approximation to the likelihood and reducing bias in the estimation of the parameters of the underlying continuous-time model. As a result, the proposed approach can use a larger bin size to achieve the same accuracy as conventional approaches would with a smaller bin size. This is particularly important when analyzing neural data with high mean and instantaneous firing rates. We demonstrate these claims on simulated and real neural spiking activity. By allowing a substantive increase in the required bin size, our algorithm has the potential to lower the barrier to the use of point-process methods in an increasing number of applications.

Identification of sparse neural functional connectivity using penalized likelihood estimation and basis functions

One key problem in computational neuroscience and neural engineering is the identification and modeling of functional connectivity in the brain using spike train data. To reduce model complexity, alleviate overfitting, and thus facilitate model interpretation, sparse representation and estimation of functional connectivity is needed. Sparsities include global sparsity, which captures the sparse connectivities between neurons, and local sparsity, which reflects the active temporal ranges of the input-output dynamical interactions. In this paper, we formulate a generalized functional additive model (GFAM) and develop the associated penalized likelihood estimation methods for such a modeling problem. A GFAM consists of a set of basis functions convolving the input signals, and a link function generating the firing probability of the output neuron from the summation of the convolutions weighted by the sought model coefficients. Model sparsities are achieved by using various penalized likelihood estimations and basis functions. Specifically, we introduce two variations of the GFAM using a global basis (e.g., Laguerre basis) and group LASSO estimation, and a local basis (e.g., B-spline basis) and group bridge estimation, respectively. We further develop an optimization method based on quadratic approximation of the likelihood function for the estimation of these models. Simulation and experimental results show that both group-LASSO-Laguerre and group-bridge-B-spline can capture faithfully the global sparsities, while the latter can replicate accurately and simultaneously both global and local sparsities. The sparse models outperform the full models estimated with the standard maximum likelihood method in out-of-sample predictions.