scholarly journals Clusterless Decoding of Position from Multiunit Activity Using a Marked Point Process Filter

2015 ◽  
Vol 27 (7) ◽  
pp. 1438-1460 ◽  
Author(s):  
Xinyi Deng ◽  
Daniel F. Liu ◽  
Kenneth Kay ◽  
Loren M. Frank ◽  
Uri T. Eden
Keyword(s):  
Real Time ◽  
Point Process ◽  
Point Processes ◽  
Marked Point ◽  
Marked Point Processes ◽  
Marked Point Process ◽  
Spike Sorting ◽  
Decoding Algorithm ◽  
Population Activity ◽  
Spiking Activity

Point process filters have been applied successfully to decode neural signals and track neural dynamics. Traditionally these methods assume that multiunit spiking activity has already been correctly spike-sorted. As a result, these methods are not appropriate for situations where sorting cannot be performed with high precision, such as real-time decoding for brain-computer interfaces. Because the unsupervised spike-sorting problem remains unsolved, we took an alternative approach that takes advantage of recent insights into clusterless decoding. Here we present a new point process decoding algorithm that does not require multiunit signals to be sorted into individual units. We use the theory of marked point processes to construct a function that characterizes the relationship between a covariate of interest (in this case, the location of a rat on a track) and features of the spike waveforms. In our example, we use tetrode recordings, and the marks represent a four-dimensional vector of the maximum amplitudes of the spike waveform on each of the four electrodes. In general, the marks may represent any features of the spike waveform. We then use Bayes’s rule to estimate spatial location from hippocampal neural activity. We validate our approach with a simulation study and experimental data recorded in the hippocampus of a rat moving through a linear environment. Our decoding algorithm accurately reconstructs the rat’s position from unsorted multiunit spiking activity. We then compare the quality of our decoding algorithm to that of a traditional spike-sorting and decoding algorithm. Our analyses show that the proposed decoding algorithm performs equivalent to or better than algorithms based on sorted single-unit activity. These results provide a path toward accurate real-time decoding of spiking patterns that could be used to carry out content-specific manipulations of population activity in hippocampus or elsewhere in the brain.

Marked point processes as limits of Markovian arrival streams

1993 ◽  
Vol 30 (02) ◽  
pp. 365-372 ◽  
Author(s):  
Søren Asmussen ◽  
Ger Koole
Keyword(s):  
Point Process ◽  
Point Processes ◽  
Marked Point ◽  
The State ◽  
Marked Point Processes ◽  
Marked Point Process ◽  
State Transitions ◽  
Poisson Arrival ◽  
Convergence Of Moments ◽  
Environmental Process

A Markovian arrival stream is a marked point process generated by the state transitions of a given Markovian environmental process and Poisson arrival rates depending on the environment. It is shown that to a given marked point process there is a sequence of such Markovian arrival streams with the property that as m →∞. Various related corollaries (involving stationarity, convergence of moments and ergodicity) and counterexamples are discussed as well.

Marked point processes as limits of Markovian arrival streams

1993 ◽  
Vol 30 (2) ◽  
pp. 365-372 ◽  
Author(s):  
Søren Asmussen ◽  
Ger Koole
Keyword(s):  
Point Process ◽  
Point Processes ◽  
Marked Point ◽  
The State ◽  
Marked Point Processes ◽  
Marked Point Process ◽  
State Transitions ◽  
Poisson Arrival ◽  
Convergence Of Moments ◽  
Environmental Process

A Markovian arrival stream is a marked point process generated by the state transitions of a given Markovian environmental process and Poisson arrival rates depending on the environment. It is shown that to a given marked point process there is a sequence of such Markovian arrival streams with the property that as m →∞. Various related corollaries (involving stationarity, convergence of moments and ergodicity) and counterexamples are discussed as well.

scholarly journals Morpho-statistical characterization of the cosmic web using marked point processes

2014 ◽  
Vol 10 (S306) ◽  
pp. 239-242
Author(s):  
Radu S. Stoica
Keyword(s):  
Point Process ◽  
Point Processes ◽  
Probabilistic Models ◽  
Geometrical Structure ◽  
Marked Point ◽  
Marked Point Processes ◽  
Marked Point Process ◽  
Statistical Characterization

AbstractThe cosmic web is the intricate network of filaments outlined by the galaxies positions distribution in our Universe. One possible manner to break the complexity of such an elaborate geometrical structure is to assume it made of simple interacting objects. Under this hypothesis, the filamentary network can be considered as the realization of an object or a marked point process. These processes are probabilistic models dealing with configurations of random objects given by random points having random characteristics or marks. Here, the filamentary network is considered as the realization of such a process, with the objects being cylinders that align and connect in order to form the network. The paper presents the use of marked point processes to the detection and the characterization of the galactic filaments.

scholarly journals A common goodness-of-fit framework for neural population models using marked point process time-rescaling

2018 ◽  
Author(s):  
Long Tao ◽  
Karoline E. Weber ◽  
Kensuke Arai ◽  
Uri T. Eden
Keyword(s):  
Goodness Of Fit ◽  
Point Processes ◽  
Statistical Tests ◽  
Marked Point ◽  
Population Models ◽  
Marked Point Processes ◽  
Marked Point Process ◽  
Neural Population ◽  
Process Time ◽  
Spiking Activity

AbstractA critical component of any statistical modeling procedure is the ability to assess the goodness-of-fit between a model and observed data. For neural spike train models of individual neurons, many goodness-of-fit measures rely on the time-rescaling theorem to assess the statistical properties of rescaled spike times. Recently, there has been increasing interest in statistical models that describe the simultaneous spiking activity of neuron populations, either in a single brain region or across brain regions. Classically, such models have used spike sorted data to describe relationships between the identified neurons, but more recently clusterless modeling methods have been used to describe population activity using a single model. Here we develop a generalization of the time-rescaling theorem that enables comprehensive goodness-of-fit analysis for either of these classes of population models. We use the theory of marked point processes to model population spiking activity, and show that under the correct model, each spike can be rescaled individually to generate a uniformly distributed set of events in time and the space of spike marks. After rescaling, multiple well-established goodness-of-fit procedures and statistical tests are available. We demonstrate the application of these methods both to simulated data and real population spiking in rat hippocampus.

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

2018 ◽  
Author(s):  
Ali Yousefi ◽  
Mohamad Reza Rezaei ◽  
Kensuke Arai ◽  
Loren M. Frank ◽  
Uri T. Eden
Keyword(s):  
Exact Solution ◽  
Real Time ◽  
Point Process ◽  
Performance Metrics ◽  
Marked Point ◽  
Marked Point Process ◽  
Computationally Efficient ◽  
Time Step ◽  
Filter Solution ◽  
Spiking Activity

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% HPD coverage 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.

State aggregation and discrete-state Markov chains embedded in a class of point processes

1995 ◽  
Vol 32 (01) ◽  
pp. 39-51
Author(s):  
Xi-Ren Cao
Keyword(s):  
Markov Chains ◽  
Poisson Process ◽  
Point Process ◽  
Point Processes ◽  
Marked Point ◽  
Practical Importance ◽  
Marked Point Process ◽  
Interarrival Time ◽  
Discrete State ◽  
State Aggregation

One result that is of both theoretical and practical importance regarding point processes is the method of thinning. The basic idea of this method is that under some conditions, there exists an embedded Poisson process in any point process such that all its arrival points form a sub-sequence of the Poisson process. We extend this result by showing that on the embedded Poisson process of a uni- or multi-variable marked point process in which interarrival time distributions may depend on the marks, one can define a Markov chain with a discrete state that characterizes the stage of the interarrival times. This implies that one can construct embedded Markov chains with countable state spaces for the state processes of many practical systems that can be modeled by such point processes.

UTILITY MAXIMIZATION IN A PURE JUMP MODEL WITH PARTIAL OBSERVATION

2010 ◽  
Vol 25 (1) ◽  
pp. 29-54 ◽  
Author(s):  
Paola Tardelli
Keyword(s):  
Utility Maximization ◽  
Point Processes ◽  
Marked Point ◽  
Asset Price ◽  
Main Tool ◽  
Risky Asset ◽  
Marked Point Processes ◽  
Marked Point Process ◽  
Underlying Event ◽  
Jump Model

This article considers the asset price movements in a financial market when risky asset prices are modeled by marked point processes. Their dynamics depend on an underlying event arrivals process—a marked point process having common jump times with the risky asset price process. The problem of utility maximization of terminal wealth is dealt with when the underlying event arrivals process is assumed to be unobserved by the market agents using, as the main tool, backward stochastic differential equations. The dual problem is studied. Explicit solutions in a particular case are given.

Reliability analysis of complex repairable systems by means of marked point processes

1980 ◽  
Vol 17 (1) ◽  
pp. 154-167 ◽  
Author(s):  
Peter Franken ◽  
Arnfried Streller
Keyword(s):  
Reliability Analysis ◽  
Point Processes ◽  
Marked Point ◽  
Regenerative Process ◽  
Marked Point Processes ◽  
Marked Point Process ◽  
Repairable Systems ◽  
Interval Reliability ◽  
Repair Facility ◽  
Markovian Systems

Starting from the theory of point processes the concept of a process with an embedded marked point process is defined. It is shown that the known formula expressing the relation between the stationary and synchronous version of a regenerative process remains valid without the assumption of independence of cycles. General formulae for stationary availability and interval reliability of complex systems with repair are also obtained. In this way generalizations of Keilson's results for Markovian systems and Ross's results for systems with separately maintained elements are presented. The formulae are applied to a two-unit parallel system with a single repair facility.

Power spectra of general shot noises and Hawkes point processes with a random excitation

2002 ◽  
Vol 34 (01) ◽  
pp. 205-222 ◽  
Author(s):  
P. Brémaud ◽  
L. Massoulié
Keyword(s):  
Point Process ◽  
Spectral Measure ◽  
Point Processes ◽  
Marked Point ◽  
Power Spectra ◽  
Random Excitation ◽  
Marked Point Process ◽  
Martingale Measure ◽  
Shot Noise Process ◽  
Power Spectral

We give (i) the Cramér power spectral measure of the general shot noise process with random excitation and non-Poisson stationary driving point processes and (ii) the Bartlett power spectral measure of the self-exciting Hawkes point process with random excitation, also called the Hawkes branching point process with random fertility rate. The latter is obtained via the isometry formula for integrals with respect to the canonical martingale measure associated with a marked point process.

Reliability analysis of complex repairable systems by means of marked point processes

1980 ◽  
Vol 17 (01) ◽  
pp. 154-167 ◽  
Author(s):  
Peter Franken ◽  
Arnfried Streller
Keyword(s):  
Reliability Analysis ◽  
Point Processes ◽  
Marked Point ◽  
Regenerative Process ◽  
Marked Point Processes ◽  
Marked Point Process ◽  
Repairable Systems ◽  
Interval Reliability ◽  
Repair Facility ◽  
Markovian Systems

Starting from the theory of point processes the concept of a process with an embedded marked point process is defined. It is shown that the known formula expressing the relation between the stationary and synchronous version of a regenerative process remains valid without the assumption of independence of cycles. General formulae for stationary availability and interval reliability of complex systems with repair are also obtained. In this way generalizations of Keilson's results for Markovian systems and Ross's results for systems with separately maintained elements are presented. The formulae are applied to a two-unit parallel system with a single repair facility.

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