Point Process Observations Research Articles

Eye tracking is more sensitive than skin conductance response in detecting mild environmental stimuli.

The skin conductance (SC) and eye tracking data are two potential arousal-related psychophysiological signals that can serve as the interoceptive unconditioned response to aversive stimuli (e.g. electric shocks). The current research investigates the sensitivity of these signals in detecting mild electric shock by decoding the hidden arousal and interoceptive awareness (IA) states. While well-established frameworks exist to decode the arousal state from the SC signal, there is a lack of a systematic approach that decodes the IA state from pupillometry and eye gaze measurements. We extract the physiological-based features from eye tracking data to recover the IA-related neural activity. Employing a Bayesian filtering framework, we decode the IA state in fear conditioning and extinction experiments where mild electric shock is used. We independently decode the underlying arousal state using binary and marked point process (MPP) observations derived from concurrently collected SC data. Eight of 11 subjects present a significantly (P-value ) higher IA state in trials that were always accompanied by electric shock ( ) compared to trials that were never accompanied by electric shock ( ). According to the decoded SC-based arousal state, only five (binary observation) and four (MPP observation) subjects present a significantly higher arousal state in trials than trials. In conclusion, the decoded hidden brain state from eye tracking data better agrees with the presented mild stimuli. Tracking IA state from eye tracking data can lead to the development of contactless monitors for neuropsychiatric and neurodegenerative disorders.

A Splitting Method for Nonlinear Filtering Problems with Diffusive and Point Process Observations

A Splitting Method for Nonlinear Filtering Problems with Diffusive and Point Process Observations

Event detection and classification from multimodal time series with application to neural data

The detection of events in time-series data is a common signal-processing problem. When the data can be modeled as a known template signal with an unknown delay in Gaussian noise, detection of the template signal can be done with a traditional matched filter. However, in many applications, the event of interest is represented in multimodal data consisting of both Gaussian and point-process time series. Neuroscience experiments, for example, can simultaneously record multimodal neural signals such as local field potentials (LFPs), which can be modeled as Gaussian, and neuronal spikes, which can be modeled as point processes. Currently, no method exists for event detection from such multimodal data, and as such our objective in this work is to develop a method to meet this need. Here we address this challenge by developing the multimodal event detector (MED) algorithm which simultaneously estimates event times and classes. To do this, we write a multimodal likelihood function for Gaussian and point-process observations and derive the associated maximum likelihood estimator of simultaneous event times and classes. We additionally introduce a cross-modal scaling parameter to account for model mismatch in real datasets. We validate this method in extensive simulations as well as in a neural spike-LFP dataset recorded during an eye-movement task, where the events of interest are eye movements with unknown times and directions. We show that the MED can successfully detect eye movement onset and classify eye movement direction. Further, the MED successfully combines information across data modalities, with multimodal performance exceeding unimodal performance. This method can facilitate applications such as the discovery of latent events in multimodal neural population activity and the development of brain-computer interfaces for naturalistic settings without constrained tasks or prior knowledge of event times.

Online Estimating Pairwise Neuronal Functional Connectivity in Brain-Machine Interface.

Neurons respond to external stimuli and form functional networks through pairwise interactions. A neural encoding model can describe a single neuron's behavior, and brain-machine interfaces (BMIs) provide a platform to investigate how neurons adapt, functionally connect, and encode movement. Movement modulation and pairwise functional connectivity are modeled as high-dimensional tuning states, estimated from neural spike train observations. However, accurate estimation of this neural state vector can be challenging as pairwise neural interactions are highly dimensional, change in different temporal scales from movement, and could be non-stationary. We propose an Adam-based gradient descent method to online estimate high-dimensional pairwise neuronal functional connectivity and single neuronal tuning adaptation simultaneously. By minimizing negative log-likelihood based on point process observation, the proposed method adaptively adjusts the learning rate for each dimension of the neural state vectors by employing momentum and regularizer. We test the method on real recordings of two rats performing the brain control mode of a two-lever discrimination task. Our results show that our method outperforms existing methods, especially when the state is sparse. Our method is more stable and faster for an online scenario regardless of the parameter initializations. Our method provides a promising tool to track and build the time-variant functional neural connectivity, which dynamically forms the functional network and results in better brain control.

Hybrid Decoders for Marked Point Process Observations and External Influences.

Internal physiological processes govern multiple state variables within the human body. Estimating these from point process-type bioelectric and biochemical observations is a challenge. Here we seek to estimate cortisol-related energy production and sympathetic arousal based on point process and continuous-valued data while permitting an external influence to affect the state estimates. Traditional point process state-space methods, such as those used for estimating the aforementioned quantities from cortisol and skin conductance measurements respectively, suffer from the inability to permit the state estimates to also fit to an external influence (e.g. labels) or be guided by it. Here we modify an existing recurrent neural network (RNN) approach for state-space estimation through a weighted cost-function to enable a hybrid estimator that has this capability. Results on cortisol data based on a hypothetical sleep-wake influence term show how energy production can be estimated by permitting the estimates to fit to the external influence as much as desired. We further show how overfitting may be reduced by using circadian rhythm-based influence terms. Results on skin conductance data also indicate how the method can be used to estimate sympathetic arousal in an experiment containing stressors and relaxation, and permit an external influence as well. The RNN-based hybrid method is thus able to recover internal physiological states from point process and continuous-valued observations while permitting an external influence to guide the estimates. The hybrid estimator could be embedded within wearable monitors that can be tailored based on domain expertise or individual feedback.

A Bayesian Filtering Approach for Tracking Sympathetic Arousal and Cortisol-Related Energy From Marked Point Process and Continuous-Valued Observations

A Bayesian Filtering Approach for Tracking Sympathetic Arousal and Cortisol-Related Energy From Marked Point Process and Continuous-Valued Observations

Reliability and maintenance modeling for a production system by means of point process observations

Reliability and maintenance modeling for a production system by means of point process observations

A unified framework on defining depth for point process using function smoothing

The notion of statistical depth has been extensively studied in multivariate and functional data over the past few decades. In contrast, the depth on temporal point process is still under-explored. The problem is challenging because a point process has two types of randomness: 1) the number of events in a process, and 2) the distribution of these events. Recent studies proposed depths in a weighted product of two terms, describing the above two types of randomness, respectively. Under a new framework through a smoothing procedure, these two randomnesses can be unified. Basically, the point process observations are transformed into functions using conventional kernel smoothing methods, and then the well-known functional h-depth and its modified, center-based version are adopted to describe the center-outward rank in the original data. To do so, a proper metric is defined on the point processes with smoothed functions. Then an efficient algorithm is provided to estimate the defined “center”. The mathematical properties of the newly defined depths are explored and the asymptotic theories are studied. Simulation results show that the proposed depths can properly rank point process observations. Finally, the new methods are demonstrated in a classification task using a real neuronal spike train dataset.

Real-Time Point Process Filter for Multidimensional Decoding Problems Using Mixture Models

There is an increasing demand for a computationally efficient and accurate point process filter solution for real-time decoding of population spiking activity in multidimensional spaces. Real-time tools for neural data analysis, specifically real-time neural decoding solutions open doors for developing experiments in a closed-loop setting and more versatile brain-machine interfaces. Over the past decade, the point process filter has been successfully applied in the decoding of behavioral and biological signals using spiking activity of an ensemble of cells; however, the filter solution is computationally expensive in multi-dimensional filtering problems. Here, we propose an approximate filter solution for a general point-process filter problem when the conditional intensity of a cell’s spiking activity is characterized using a Mixture of Gaussians. We propose the filter solution for a broader class of point process observation called marked point-process, which encompasses both clustered – mainly, called sorted – and clusterless – generally called unsorted or raw– spiking activity. We assume that the posterior distribution on each filtering time-step can be approximated using a Gaussian Mixture Model and propose a computationally efficient algorithm to estimate the optimal number of mixture components and their corresponding weights, mean, and covariance estimates. This algorithm provides a real-time solution for multi-dimensional point-process filter problem and attains accuracy comparable to the exact solution. Our solution takes advantage of mixture dropping and merging algorithms, which collectively control the growth of mixture components on each filtering time-step. We apply this methodology in decoding a rat’s position in both 1-D and 2-D spaces using clusterless spiking data of an ensemble of rat hippocampus place cells. The approximate solution in 1-D and 2-D decoding is more than 20 and 4,000 times faster than the exact solution, while their accuracy in decoding a rat position only drops by less than 9% and 4% in RMSE and 95% highest probability coverage area (HPD) performance metrics. Though the marked-point filter solution is better suited for real-time decoding problems, we discuss how the filter solution can be applied to sorted spike data to better reflect the proposed methodology versatility.

A BSDE-based approach for the optimal reinsurance problem under partial information

We investigate the optimal reinsurance problem under the criterion of maximizing the expected utility of terminal wealth when the insurance company has restricted information on the loss process. We propose a risk model with claim arrival intensity and claim sizes distribution affected by an unobservable environmental stochastic factor. By filtering techniques (with marked point process observations), we reduce the original problem to an equivalent stochastic control problem under full information. Since the classical Hamilton–Jacobi–Bellman approach does not apply, due to the infinite dimensionality of the filter, we choose an alternative approach based on Backward Stochastic Differential Equations (BSDEs). Precisely, we characterize the value process and the optimal reinsurance strategy in terms of the unique solution to a BSDE driven by a marked point process.

A Marked Point Process Filtering Approach for Tracking Sympathetic Arousal From Skin Conductance

Human emotion represents a complex neural process within the brain. The ability to automatically recognize emotions from physiological signals has the potential to impact humanity in multiple ways through applications in human-machine interaction, remote health monitoring, smart living environments and entertainment. We present a marked point process-based Bayesian filtering approach to track sympathetic arousal from skin conductance features. The rate at which individual skin conductance responses (SCRs) occur and their respective amplitudes encode important information regarding an individual's psychological arousal level. We develop a state-space model relating a latent neuropsychological arousal state to the rate at which neural impulses underlying SCRs occur and the impulse amplitudes. We simultaneously estimate both arousal and the state-space model parameters within an expectation-maximization framework. We evaluate our method on both simulated and experimental data. Results on simulated data indicate the method's ability to accurately estimate an unobserved state from marked point process observations. The experimental data include studies involving mental stress artificially-induced in laboratory environments, real-world driver stress and Pavlovian fear conditioning. Results on experimental data outperform previous Bayesian filtering approaches in terms of a lower sensitivity to small impulses and avoiding overfitting. The filter is thus able to estimate emotional arousal from skin conductance features and is a promising approach for everyday emotion recognition applications.

Asymptotically Exact Unweighted Particle Filter for Manifold-Valued Hidden States and Point Process Observations

The filtering of a Markov diffusion process on a manifold from counting process observations leads to ‘large’ changes in the conditional distribution upon an observed event, corresponding to a multiplication of the density by the intensity function of the observation process. If that distribution is represented by unweighted samples or particles, they need to be jointly transformed such that they sample from the modified distribution. In previous work, this transformation has been approximated by a translation of all the particles by a common vector. However, such an operation is ill-defined on a manifold, and on a vector space, a constant gain can lead to a wrong estimate of the uncertainty over the hidden state. Here, taking inspiration from the feedback particle filter (FPF), we derive an asymptotically exact filter (called ppFPF) for point process observations, whose particles evolve according to intrinsic (i.e., parametrization-invariant) dynamics that are composed of the dynamics of the hidden state plus additional control terms. While not sharing the gain-times-error structure of the FPF, the optimal control terms are expressed as solutions to partial differential equations analogous to the weighted Poisson equation for the gain of the FPF. The proposed filter can therefore make use of existing approximation algorithms for solutions of weighted Poisson equations.

Bayesian Modelling of Marked Point Processes with Incomplete Records: Volcanic Eruptions

SummaryModelling point processes with incomplete records is a challenging problem, especially when the degree of record completeness varies over time. For volcanic eruption records, we expect the degree of missingness to depend on both the time and the size of an eruption. We propose a time-varying intensity function for a marked point process to model the non-stationary variation of the observed point process caused by missing data. We apply this model to global and regional volcanic eruption records and use Bayesian inference to obtain hazard estimates and their uncertainties based on the observed incomplete records, to carry out residual analysis and to provide forecasts.

Parameter Estimation in Synaptic Coupling Model Using a Point Process Modeling Framework.

Biophysical models are widely used to characterize temporal dynamics of the brain networks on different topological and spatial scales. In parallel, the state-space modeling framework with point process observations has been successfully applied in characterizing spiking activity of neuronal ensembles in response to different dynamical covariates. Parameter estimation in biophysical models is generally done heuristically, which hampers their applicability and interpretability. Heuristic parameter estimation becomes an intractable problem when the number of model parameters grows. Here, we propose an algorithm for estimating biophysical model parameters using point-process models and a state-space framework. The framework provides methods for parameter estimation as well as model validation. We demonstrate the application of this methodology to the problem of estimating the parameters of a dynamic synapse model. We generate simulation data for the dynamic synapse across a range of parameters values and assess the estimation accuracy of our method using a combination of goodness-of-fit measures. The proposed methodology can be applied broadly to parameter estimation problems across a broad range of biophysical models, including Hodgkin-Huxley models and network models.

Tracking the Time Varying Neural Tuning via Adam on Point Process Observations.

Brain machine interfaces(BMIs) translate the neural activity into the control of movement by understanding how the neural activity responds to the movement intension. However, the neural tuning property, where the modulation depth and preferred direction describe how a neuron responses to stimuli, is time varying gradually and abruptly during the interaction with environment. There has been some research to address such an issue considering either one of the cases, but never address them in a general framework. We propose a novel optimization algorithm based on the point process observations to capture these two changes at the same time. At each time index, the tuning parameter is updated stochastically according to the gradient based Adam searching method, which maximizes the likelihood of point process. Our algorithm is compared with the Adaptive Point Process Estimation (APPE), where the abrupt change is addressed by sampling all the possibilities globally, on synthetic neural data. The results show that our algorithm leads to a better prediction of tuning parameters as well as kinematics over 16.8% and 20% respectively.

Optimal Decoding of Dynamic Stimuli by Heterogeneous Populations of Spiking Neurons: A Closed-Form Approximation

Neural decoding may be formulated as dynamic state estimation (filtering) based on point-process observations, a generally intractable problem. Numerical sampling techniques are often practically useful for the decoding of real neural data. However, they are less useful as theoretical tools for modeling and understanding sensory neural systems, since they lead to limited conceptual insight into optimal encoding and decoding strategies. We consider sensory neural populations characterized by a distribution over neuron parameters. We develop an analytically tractable Bayesian approximation to optimal filtering based on the observation of spiking activity that greatly facilitates the analysis of optimal encoding in situations deviating from common assumptions of uniform coding. Continuous distributions are used to approximate large populations with few parameters, resulting in a filter whose complexity does not grow with population size and allowing optimization of population parameters rather than individual tuning functions. Numerical comparison with particle filtering demonstrates the quality of the approximation. The analytic framework leads to insights that are difficult to obtain from numerical algorithms and is consistent with biological observations about the distribution of sensory cells' preferred stimuli.

A Modularized Efficient Framework for Non-Markov Time Series Estimation

We present a compartmentalized approach to finding the maximum a posteriori (MAP) estimate of a latent time series that obeys a dynamic stochastic model and is observed through noisy measurements. We specifically consider modern signal processing problems with non-Markov signal dynamics (e.g., group sparsity) and/or non-Gaussian measurement models (e.g., point process observation models used in neuroscience). Through the use of auxiliary variables in the MAP estimation problem, we show that a consensus formulation of the alternating direction method of multipliers enables iteratively computing separate estimates based on the likelihood and prior and subsequently “averaging” them in an appropriate sense using a Kalman smoother. As such, this can be applied to a broad class of problem settings and only requires modular adjustments when interchanging various aspects of the statistical model. Under broad log-concavity assumptions, we show that the separate estimation problems are convex optimization problems and that the iterative algorithm converges to the MAP estimate. As such, this framework can capture non-Markov latent time series models and non-Gaussian measurement models. We provide example applications involving 1) group-sparsity priors, within the context of electrophysiologic specrotemporal estimation, and 2) non-Gaussian measurement models, within the context of dynamic analyses of learning with neural spiking and behavioral observations.

Autoregressive Point Processes as Latent State-Space Models: A Moment-Closure Approach to Fluctuations and Autocorrelations.

Modeling and interpreting spike train data is a task of central importance in computational neuroscience, with significant translational implications. Two popular classes of data-driven models for this task are autoregressive point-process generalized linear models (PPGLM) and latent state-space models (SSM) with point-process observations. In this letter, we derive a mathematical connection between these two classes of models. By introducing an auxiliary history process, we represent exactly a PPGLM in terms of a latent, infinite-dimensional dynamical system, which can then be mapped onto an SSM by basis function projections and moment closure. This representation provides a new perspective on widely used methods for modeling spike data and also suggests novel algorithmic approaches to fitting such models. We illustrate our results on a phasic bursting neuron model, showing that our proposed approach provides an accurate and efficient way to capture neural dynamics.

Bayesian Inference via Filtering Equations for Ultrahigh Frequency Data (I): Model and Estimation

We propose a general partially observed framework of Markov processes with marked point process observations for ultrahigh frequency (UHF) data. The model fits well the stylized facts of UHF data in both macro- and micro-movements, subsumes important existing models, and incorporates the influence of other observable economic or market factors. We develop the corresponding Bayes estimation via a filtering equation to quantify parameter uncertainty. Namely, we derive the normalized filtering equation to characterize the evolution of the posterior distribution, present a weak convergence theorem, and construct consistent, easily parallelizable, recursive algorithms to calculate the joint posteriors and the Bayes estimates for streaming UHF data. Moreover, a sufficient condition for the consistency of the Bayes estimators is provided. The general estimation theory is illustrated by four specific models built for U.S. Treasury notes transactions data from GovPX. We show that in this market, both information-b...

Bayesian Inference via Filtering Equations for Ultrahigh Frequency Data (II): Model Selection

For the general partially observed framework of Markov processes with marked point process observations proposed in [G. X. Hu, D. R. Kuipers, and Y. Zeng, SIAM/ASA J. Uncertain. Quantif., 6 (2018),...