CN108509933B - Spike potential time-varying Glandue cause and effect accurate identification method based on multi-wavelet basis function expansion - Google Patents
Spike potential time-varying Glandue cause and effect accurate identification method based on multi-wavelet basis function expansion Download PDFInfo
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Abstract
The invention provides a method for accurately identifying a potential time-varying Glanzein cause and effect based on multi-wavelet basis function expansion, and belongs to the technical field of signal analysis and processing. As shown in FIG. 1, the method first selects the optimal memory length corresponding to each neuron using AIC method; then, establishing a generalized L-V model, and expanding the generalized L-V model by using a multi-wavelet basis function method to obtain a time-invariant parameter model; then, the expansion model is sparse through an OFR algorithm, sparse model parameters are estimated, and a time-varying kernel function in the generalized L-V model is reversely reconstructed; and finally, solving the log-likelihood value of the model point process, and calculating the final time-varying Grave causal value of the corresponding neuron. Compared with the existing SSPPF-based time-varying Glandum estimation method, the method provided by the invention can better track the causal relationship of rapid change, improve the identification precision of the time-varying causal relationship, and provide a theoretical calculation framework and a new solution for the neuron spike potential time-varying function connection identification.
Description
Technical Field
The invention provides a spike potential time-varying Glandum cause-and-effect accurate identification algorithm based on multi-wavelet basis function expansion, provides a new solution for spike potential sequence-oriented time-varying Glandum cause-and-effect accurate identification, and belongs to the technical field of signal analysis and processing.
Background
Neuronal spikes in the nervous system exhibit a clustering characteristic, neural clustering being a collection of neurons that are interrelated and functionally similar. Identifying neuronal functional connections is a necessary step to understand how neurons in brain regions organize representations, transmit, process information, and further perform higher cognitive functions. The nervous system is a dynamic system, synapses of neurons have plasticity, and functional connection relations of the neurons show time-varying characteristics, so that if the functional connection relations between the neurons are analyzed by a time-invariant method, the time-varying characteristics between the neurons cannot be accurately revealed. In order to solve these problems, researchers have paid more and more attention to methods for analyzing the connection relationship of the time-varying function of neurons.
Granger Causality analysis (GC), which is an effective analysis means for time series functional connectivity, is widely used in the field of neuroscience, and has become a measurement standard for detecting whether there is a causal effect between network nodes in a brain region. At present, there are three main methods for identifying time-varying causal relationship of neurons: the first method is that a limited sliding time window with a certain length is used for dividing a time-varying signal into a plurality of signal segments, and the signal segments are treated as stable signals in each interval, and the method has the main problems that the sizes of different time windows influence the identification result to a great extent, and no effective standard is available for determining the optimal time window length, so that the time resolution of the Glan causal relationship obtained by the method is low; the second method is a frequency domain granger method, which mainly comprises a Partial Directional Coherence (PDC) and an Adaptive Directional Transfer Function (ADTF), and although the algorithm has the advantages of small calculated amount, good identification effect and the like, under the nonlinear condition, accurate causal relationship analysis is difficult to obtain due to high model complexity; the third method establishes a time-varying multivariate autoregressive (MVAR) parameter model, identifies parameter model coefficients and converts the parameter model coefficients into a Glan cause-effect, and converts a neuron Glan cause-effect solving problem into an MVAR model parameter solving problem. The modeling and identification method of the time-varying system of the neuron spike potential is mostly carried out under the framework of a self-adaptive filtering algorithm. Common filtering algorithms include recursive least squares, gradient algorithms, kalman filtering algorithms, and random state point process filter (SSPPF) algorithms. SSPPF continuously records new neuron change characteristics and gradually loses old neuron information, so that the algorithm can preliminarily track kernel function change, the calculated amount is relatively small, and the algorithm has obvious advantages compared with other adaptive filtering algorithms. However, SSPPF needs a large number of iterative processes to track accurate time-varying parameters, and is oriented to time-varying parameters with fast variation in a time-varying system, and the algorithm has a slow convergence rate, which results in poor estimation performance of the time-varying parameters, so that the time-varying glargine causal identification method based on the adaptive filtering algorithm with a slow convergence rate has an inaccurate result.
Aiming at the defects of the time-varying grand cause-effect identification method, the invention introduces an accurate identification method of the spike potential time-varying grand cause-effect based on multi-wavelet basis function expansion, expands the complex time-varying MVAR model parameters through the weighted linear combination of multi-order wavelet B splines, converts the time-varying parameter identification problem into the time-varying parameter identification problem, obtains accurate time-varying estimation parameters and further obtains the time-varying grand cause-effect result. When the neuron spike potential sequence has strong non-stationary characteristics, the method can accurately identify the time-varying causal connection. The method has important practical significance for constructing a causal connection network of the neuron and disclosing a plasticity mechanism of the neuron activity.
Disclosure of Invention
The invention provides a method for accurately identifying a time-varying Glan cause and effect of a spike potential based on multi-wavelet basis function expansion, which comprises the steps of respectively establishing MVAR models containing and not containing trigger neurons, estimating time-varying parameters in the MVAR models by applying a multi-wavelet basis function expansion method, and finally solving a point process log likelihood difference value of the models to obtain a time-varying Glan cause and effect result of the spike potential. The multi-wavelet basis function has the characteristics of multi-scale and multi-resolution, can quickly track the change of time-varying parameters, and is widely applied to the identification of the time-varying parameters with various dynamic characteristics. The Glankey causal relationship is a neuron functional connection relationship identification method, and the connection relationship between neurons is judged by measuring the statistical dependence between the neurons. Through simulation experiment verification, the method provided by the invention can effectively identify the Glan cause-and-effect relationship between rapidly changing neuron spikes, overcomes the bottleneck of low estimated time resolution caused by low algorithm convergence speed in the traditional self-adaptive method, and provides a theoretical calculation framework and a new solution for identifying the neuron time-varying function connection relationship.
The method for accurately identifying the spike potential time-varying Glanberg causal relationship based on multi-wavelet basis function expansion comprises the following specific steps of:
1. parameter selection: selecting the optimal memory length corresponding to each neuron according to an AIC (Akaike information criterion) criterion, and setting control parameters, multi-wavelet scales and B-spline orders of Laguerre basis functions;
2. generalized Laguerre-Volterra (L-V) model: representing a time-varying neurodynamic system model by adopting a Volterra series, and expanding a time-varying Volterra kernel by applying a Laguerre basis function to obtain a time-varying L-V generalized model;
3. and (3) time-varying parameter expansion: unfolding time-varying parameters of the time-varying generalized L-V model by utilizing a multi-wavelet basis function, and converting the time-varying parameters into time-invariant parameters to obtain a time-invariant unfolded parameter model;
4. model sparseness and estimation: optimizing the time-invariant parameter model after the multi-wavelet basis function expansion by using a classical orthogonal forward regression algorithm, eliminating redundant items, simultaneously estimating corresponding time-invariant parameters by using a generalized linear fitting algorithm, reversely solving initial time-variant parameters and reconstructing a kernel function;
5. time-varying causal solution between neurons: the method comprises the steps of respectively constructing MVAR models with triggering neurons and non-triggering neurons, estimating parameters of the MVAR models by combining the time-varying neurodynamic system identification method based on the multi-wavelet basis function, calculating a point process log-likelihood function value through the estimated parameters, further calculating a difference value of the MVAR model log-likelihood values of the triggering neurons and the non-triggering neurons, and obtaining a time-varying Glan Jack causal result between the neurons.
Wherein, in said step 1, the optimal memory length of each neuron is determined according to the AIC criterion.
In the step 2, the Volterra series has a Taylor series with storage and memory capacity, and can effectively represent a nonlinear system. By adopting the Laguerre basis function expansion method, parameters of the Volterra kernel which need to be solved can be greatly reduced.
In the step 3, the complex time-varying parameter identification problem can be converted into a time-invariant parameter identification problem about a polynomial by using a multi-wavelet basis function expansion mode.
In the step 4, redundant items can be eliminated by utilizing a forward orthogonal regression algorithm, the number of parameters to be solved is greatly reduced, the problem of model overfitting is avoided, and the time-invariant parameter model with better implementation performance is obtained.
In step 5, it is required to solve the causal relationship between the trigger neuron and the target neuron, and it is required to establish MVAR models using the target neuron as an output and other neurons as inputs (with/without trigger neurons), respectively, solve the difference between the log likelihood values of the two MVAR models, and multiply the difference by a coefficient to obtain the grand causal value.
The method for accurately identifying the time-varying Glanduger cause and effect of the spike potential based on the multi-wavelet basis function expansion has the advantages that:
1. in the time-varying MVAR model parameter identification process, the time-varying parameter identification problem is converted into the time-invariant parameter identification problem, the problem is greatly simplified, and the problem can be solved by directly applying a classical time-invariant system identification method;
2. a classical Orthogonal Forward Recursion (OFR) algorithm sparse model is adopted, redundant items are removed, the complexity of the model is reduced, the calculation speed is improved, the identification accuracy of the model is high, and meanwhile, the overfitting phenomenon of the model can be effectively avoided;
3. the log-likelihood difference value of the corresponding MVAR model point process is used as a Glanberg causal value between corresponding neurons, so that the issuing rate of the target neuron is related to the issuing history of the trigger neuron, and the causal relationship is accurately identified;
4. the model construction process is simple, and the calculation complexity is low.
Drawings
FIG. 1 is a schematic flow chart of a method for accurately identifying a time-varying Gradney causal effect of a spike potential according to the present invention;
FIG. 2 is a diagram of a kernel function of a multi-input single-output spike potential simulation model in a simulation example, which is a feedforward kernel function k from top to bottom in sequence 1 、k 2 And the value of the feedback kernel function h over its memory length;
FIG. 3 is a time-varying parameter of a multi-input single-output spike potential simulation model in a simulation example, which is a feedforward time-varying parameter a from top to bottom in sequence 1 、a 2 With feedback of a time-varying parameter a 3 A time-varying condition;
FIG. 4 is a diagram showing causal identification of a spike-potential sequence in a simulation example by applying the spike-potential time-varying Glanberg causal method based on multi-wavelet basis function expansion proposed in the present invention, wherein the (i, j) th amplitude diagram shows causal relationship values of a triggering neuron-j to a target neuron-i at different times;
FIG. 5 shows an example of a simulated spike-potential sequenceThe time-invariant granger causal relationship is used as a comparison standard, and the identification performance of the time-variant granger causal relationship identification method based on the multi-wavelet basis function expansion and the SSPPF provided by the invention is compared. FIGS. 5(a) - (c) illustrate two causal analysis methods for phi 31 (Glanberg causal relationship of neuron 1 to neuron 3), Φ 32 (Glanberg causal relationship of neuron 3 to neuron 2), Φ 33 (Glanker causal relationship of neuron 3 to neuron 3) comparison of effects. The analysis results prove that the proposed method has better causal analysis results.
Detailed Description
To better illustrate the embodiments of the present invention, the present invention is further described in detail below with reference to the accompanying drawings.
The invention aims to provide a spike potential time-varying Glandum cause and effect identification method based on multi-wavelet basis function expansion, which accurately identifies time-varying MVAR model parameters by using a multi-wavelet basis function expansion model and solves the corresponding neuron Glandum cause and effect result so as to solve the problems that the existing methods for distinguishing neuron time-varying cause and effect relations based on a sliding window are low in time resolution, difficult to quickly track the neuron cause and effect connection relations and the like, and can accurately and quickly track the neuron cause and effect connection changes.
Fig. 1 shows a flowchart of a method for accurately identifying a cause and effect of a time-varying glangel at a spike potential, which includes:
solving the causal relationship of the corresponding neuron time-varying Glanduger requires solving the log-likelihood values including and not including the trigger neuron MVAR model respectively, and estimating the solving time-varying parameters of the neuron time-varying MVAR model. Firstly, selecting the optimal memory length corresponding to each neuron by using an AIC method, and determining Laguerre and multi-wavelet B-spline parameters; then, establishing a generalized L-V model, constructing a time-varying MISO system by using a simulation input and output spike potential sequence corresponding to the representation of the Volterra series, and expanding a time-varying Volterra kernel by using a Laguerre basis function to obtain the generalized Laguerre-Volterra model; then, a generalized L-V model is expanded by using a multi-wavelet basis function method, and time-varying parameters are converted into a time-invariant parameter model; after a time invariant parameter model expression is obtained, model optimization is carried out through an OFR algorithm, model redundancy items are removed, parameters of an optimized model are estimated by combining a generalized linear fitting (GLMFIT) method, and a time varying kernel function in a generalized L-V model is reconstructed; and finally, substituting the corresponding kernel function value into the initial MVAR model to obtain MVAR model parameters, solving the log-likelihood value of the corresponding model point process, calculating the difference value which does not contain the log-likelihood value of the triggering neuron model, and taking the difference value multiplied by an excited or inhibited symbol as the final time-varying Glan causal value of the corresponding neuron.
The following specifically describes the method for identifying the time-varying glanged causal relationship between neurons based on the multi-wavelet basis function expansion, which specifically comprises the following steps:
1. parameter selection: in the neuron clustering activity, the memory length of each neuron is different, and the optimal memory length of each neuron is determined by an AIC criterion, wherein the expression of AIC is as follows:
AIC＝-2ln(L)+2K (1)
and K is the number of the parameters, L is a likelihood function of the corresponding parameters, the corresponding AIC value is solved by selecting different memory lengths, and the memory length corresponding to the minimum AIC is selected as the optimal memory length of the neuron.
The Laguerre basis function is controlled by a parameter L, and the larger L can track the complex time delay condition, so that the problem of increased computational complexity can be brought; the multi-wavelet basis function is controlled by a wavelet scale j and a B-spline order m, and the tracking accuracy of the time-varying parameters can be improved by a larger wavelet scale and the B-spline order, but more parameters to be estimated and higher calculation complexity are brought.
2. Generalized L-V model: in neuron clustering activity, a MISO (multiple input single output) system can be expressed as:
w＝u(K,x)+a(H,y)+ε(σ) (2)
wherein x and y respectively represent the spike potential sequence of the input neuron and the output neuron, w represents the pre-threshold membrane potential of the output neuron, and w is the sum of post-synaptic potential u caused by the spike potential sequence of the input neuron, post-potential a fed back by the spike potential sequence of the output neuron and white Gaussian noise epsilon with the deviation of sigma. When w is greater than the threshold θ, it will spike the output neuron.
And (3) expanding a feedforward coefficient K and a feedback coefficient H by using a first-order Volterra model to obtain a time-varying generalized Volterra model:
wherein k is 0 Representing constant coefficient, N being the length of the input spike sequence, M k And M h Respectively representing the memory lengths of the feed-forward and feedback processes,
separately characterizing an input neuron spike x as a time-varying Volterra kernel function n A linear correlation coefficient with output u, a linear correlation coefficient with output neuron spikes y and a.
Then, using a Laguerre basis function to expand a time-varying generalized Volterra kernel function to obtain a generalized L-V model:
substituting equation (4) into equation (3) yields the u, a expression that becomes:
wherein, the first and the second end of the pipe are connected with each other,
and c h Are respectively Volterra kernel functions
And Laguerre expansion coefficients for h. Through the Laguerre basis function expansion mode, the number of parameters to be solved is greatly reduced, the problem of Volterra kernel function dimension disaster is solved, and the overfitting phenomenon is avoided to a certain extent. And taking the combination of the system output feedback signal and the input signal as system input, completely representing a time-varying neurodynamic system model by a Volterra series, and constructing a time-varying generalized L-V model.
3. And (3) time-varying parameter expansion: unfolding time-varying parameters of the time-varying generalized L-V model by using a multi-wavelet basis function, and converting the time-varying parameters into time-invariant parameters to solve:
wherein, the first and the second end of the pipe are connected with each other,
in order to be a multi-wavelet basis function,
m is B spline basis function B m Order, j representing the wavelet scale, r m Representing wavelet basis function biasShift coefficient, f m ＝{k:-m≤k≤2 j -1}, T is the observation sample length,
and (4) expanding the time-invariant coefficients of the multi-wavelet basis functions. Substituting the formula (6) into the formula (5) to obtain a time-invariant parameter model expression as follows:
4. model sparsity and estimation: and (3) optimizing the time-invariant parameter model after the multi-wavelet basis function is unfolded by adopting a classical OFR algorithm, eliminating redundant items, estimating corresponding time-invariant parameters by combining a generalized linear fitting algorithm, further reconstructing a kernel function, and reversely solving the correlation coefficient of the original Volterra kernel function.
The generalized time-varying L-V model has a large number of model terms after being expanded by a multi-wavelet basis function, a large number of redundant terms exist, if the original expansion model is directly adopted for solving, the model complexity is high, and the problem of model overfitting is easily caused. Therefore, the model optimization and the sparseness required by the expansion model are very critical steps in the present invention. In the invention, a forward orthogonal regression algorithm is adopted to optimize the model structure, and the model redundancy items are removed to obtain an effective sparse model.
The OFR algorithm first selects X as an alternative in the model i (i is 1,2, …, M × L) to obtain corresponding alternative w i (i ═ 1,2, …, M × L). Model significant terms are sequentially selected by using an Error Reduction Ratio (ERR) criterion. The ERR expression is as follows:
wherein Y is an observation signal output sequence, w i For orthogonalizing alternative sequences, M N Where M × L is the number of alternatives,<·,·>representing the vector inner product.
In the process of selecting effective items, each step is communicatedThe ERR corresponding to the orthogonalized backup option sequence in the step is compared i Value to determine the validity of the pick, e.g. let w be picked in step 1 i ＝X i Calculating the ERR corresponding to each term by the formula (8) i Taking { ERR i } max The corresponding item is the step 1 selection item p 1 (ii) a In the k-th step, the k-1 item { p obtained by the previous selection is selected 1 ,p 2 ,…,p k-1 As the remaining alternatives of the orthogonal basis pairs { X } i :i＝1,2,…,M N }\{p 1 ,p 2 ,…,p k-1 Orthogonalizing, calculating ERR values corresponding to the remaining alternatives, and selecting { ERR } max Corresponding alternative as the kth valid term p k . As can be seen from equation (8), the ERR criterion is a measure of the correlation degree between the orthogonal backup option and the initial output sequence, i.e. the item with the highest correlation in each step is preferably selected as the valid item in the step.
5. Neuron time-varying causal relationship estimation: for the neuron spike potential sequence, respectively taking different neurons as output and other neurons as input, substituting the input into the time-varying model based on the multi-wavelet basis function expansion to obtain a reconstructed Volterra kernel function, corresponding the coefficients to the coefficients in the MVAR model one by one, and solving the log-likelihood value of the corresponding MVAR model according to the point process log-likelihood function:
L i (t)＝y(t)logp(t)+(1-y(t))log(1-p(t))
wherein L is i (t) is the log-likelihood value of the model at time t for neuron i as the output of other neurons as the input,
and taking the representative neuron i as an output, and removing other neurons of the neuron j as input to obtain the log-likelihood value of the model at the time t. By computing the sign of the sum of the coefficients of neuron j under the MVAR model with neuron i as input
It is distinguished whether the average effect of the firing history of neuron j on neuron i is an excitatory or inhibitory effect. Will L i (t) and
and (3) performing difference calculation and multiplying the difference by the sign of the sum of the coefficients of the neuron j to obtain a time-varying Glandum causal relationship value between the target neuron i and the trigger neuron j:
wherein phi ij A positive value of (t) indicates that neuron j has an excitatory effect on the firing of neuron i, and a negative value indicates that neuron j has an inhibitory effect on the firing of neuron i.
In particular, the causal relationship between neuron i and self glange is calculated as follows:
in order to quantitatively analyze the identification effect of the causal relationship between the spike potential and the time-varying Glanduger, the method adopts three measurement standards for evaluation: mean Absolute Error (MAE), normalized Root Mean Square Error (RMSE), and Standard deviation (Std). The smaller the MAE, the RMSE and the Std are, the higher the identification precision is, the better the effect is, and the faster the causal relationship speed of tracking change is. The specific expression is as follows:
wherein the content of the first and second substances,
for the predicted causal value obtained by the method, phi (t) is an invariant granger causal value in a point process, and N is the length of a sample sequence.
The following example based on the simulation neuron spike electric sequence verifies the accuracy of the neuron time-varying Glanberg causal relationship identification method based on multi-wavelet basis function expansion, and the effect is compared with the existing neuron time-varying Glanberg causal relationship identification method based on SSPPF:
simulation example construction 2 input 1 output simulation time-varying linear system:
the time-varying parameters are:
as shown in fig. 2, the feedforward kernel function k 1 (τ)、k 2 The values of (τ) and the feedback kernel h (τ) are shown in fig. 3, respectively.
Sample sequence length N200000, total duration 400s, model input x 1 、x 2 Is a pseudo-random poisson distribution binary sequence, and e (t) is white gaussian noise with mean 0 and variance 1.
The simulation sequence x is 1 、x 2 And y are respectively regarded as neurons 1,2 and 3, and the multi-wavelet-based basis function provided by the invention is usedAnd (3) performing time-varying Glankey causal relationship identification, wherein the result is shown in FIG. 4, the (m, n) th sub-graph represents the causal relationship of the triggering neuron-n to the target neuron-m at different moments, and as can be seen from FIG. 4, the last row of sub-graphs has an obvious nonzero value. The last row in FIG. 4 represents neurons 1,2 (x) 1 、x 2 ) All have causal relationships to and only have causal relationships with neuron 3 (y). Sub-diagram (3,1) shows a signal x 1 The trigger signal y has a causal relationship of step change, and the step change occurs in 100s and 200 s; FIG. 3,2 shows signal x 2 Triggering a signal y, wherein the causal relationship of a step change relationship exists, and the step change occurs in 200 s; the graphs (3,3) show the causal relationship of the signal y to the own signal. Then, taking the cause and effect value identified by the invariant Greenger cause and effect method in the point process as a standard value, and carrying out phi unfolding on the method based on the multi-wavelet basis function and the conventional SSPPF-based method 31 (Glanker causal relationship of neuron 1 to neuron 3), Φ 32 (Glanberg causal relationship of neuron 2 to neuron 3), Φ 33 (neuron 3-Glanberg causal relationship for neuron 3) were identified and the performance compared, with the results shown in Table 1 and FIGS. 5(a) - (c), respectively.
TABLE 1 simulation example time-varying Glanzein recognition accuracy contrast
According to the comparison result of the time-varying Glanberg cause and effect identification precision of the simulation example, the time-varying Glanberg cause and effect identification effect obtained by the spike potential time-varying Glanberg cause and effect identification method based on multi-wavelet basis function expansion provided by the invention is obviously better than the identification effect based on an SSPPF method under the same condition. As can be seen from fig. 5, the wavelet-based function expansion method can accurately track the time-varying causal change, while the SSPPF method is a method for gradually tracking the causal change, and cannot obtain a good identification effect for the causal relationship of the rapid change. Experimental results show that the identification method of the time-varying causal method can better identify the time-varying causal relationship of the neurons, so that a theoretical calculation framework is provided for identifying the complex time-varying causal connection relationship of the neurons.
Claims (2)
1. A spike potential time-varying Glandue cause and effect accurate identification method based on multi-wavelet basis function expansion is characterized by comprising the following steps:
step 1, parameter selection: selecting the optimal memory length corresponding to the spike potential of each neuron according to an AIC (advanced information center) rule, and determining control parameters of a Laguerre basis function, the scale of multiple wavelets and the order of a B spline;
step 2, representing a time-varying neurodynamic system model by using a Volterra series, and expanding a time-varying Volterra kernel by using a Laguerre basis function to obtain a time-varying generalized L-V model;
and 3, time-varying parameter expansion: expanding the time-varying parameters of the time-varying generalized L-V model by using a multi-wavelet basis function, and converting the time-varying parameter model into time-invariant parameters to obtain a time-invariant expanded parameter model;
and 4, model sparseness and estimation: optimizing the time-invariant parameter model after the multi-wavelet basis function expansion by using a classical orthogonal forward regression algorithm, removing redundant items, estimating corresponding time-invariant parameters by using generalized linear fitting, reversely solving initial time-variant parameters and reconstructing a kernel function;
and 5, solving a neuron spike time-varying causal solution: respectively establishing MVAR models with trigger neuron spikes and without trigger neuron spikes, estimating corresponding MVAR model parameters by using the time-varying neurodynamics system identification method based on the multi-wavelet basis function, calculating point process log-likelihood function values through the parameters, further respectively calculating MVAR model log-likelihood value difference values of the trigger neurons and the non-trigger neurons, and obtaining a time-varying Glanduger causal result of the corresponding neuron spikes;
wherein the step 3 comprises: approximating the time-varying parameters of the time-varying generalized L-V model by utilizing the multi-wavelet basis function, expressing the approximation as the linear weighting form of the multi-wavelet basis function, and further establishing a time-invariant parameter model based on multi-wavelet B-spline expansion, namely a time-varying Laguerre coefficient model related to time
Time-invariant polynomial form converted into multi-wavelet basis function
Wherein
In order to be a time-invariant parameter,
is a multi-wavelet basis function;
the step 5 comprises the following steps: calculating a time-varying Glandum causal value of a trigger neuron spike to a target neuron spike by establishing a time-varying MVAR model including and not including the trigger neuron and solving a difference between point process log-likelihood values of the two models, comprising:
for the neuron spike potential sequence, respectively taking different neurons as output and other neurons as input, substituting the output and other neurons into the time-varying model based on the multi-wavelet basis function expansion to obtain a reconstructed Volterra kernel function, corresponding the coefficients to the coefficients in the MVAR model one by one, and solving the log-likelihood value corresponding to the MVAR model according to the point process log-likelihood function:
L i (t)＝y(t)logp(t)+(1-y(t))log(1-p(t))，
wherein L is i (t) is the log-likelihood value of the model at time t when neuron i outputs other neurons as inputs;
by calculating the coefficients and signs of neuron j under the MVAR model with neuron i as input
Differentiating whether the mean impact of firing history of neuron j on neuron i is an excitation or an excitationInhibition of L i (t) and
and (3) performing difference and multiplying the difference by the coefficient and the sign of the neuron j to obtain a time-varying Glanzein causal relationship value between the target neuron i and the trigger neuron j:
wherein, the first and the second end of the pipe are connected with each other,
represents the log-likelihood value, Φ, of the model at time t when neuron i is output and the other neurons from which neuron j is removed are input ij (t) a positive value indicates that neuron j has an excitatory effect on the firing of neuron i, and phi ij A negative value of (t) indicates that neuron j has an inhibitory effect on firing of neuron i.
2. The method for accurately identifying the time-varying granger cause and effect of the spike based on the multi-wavelet basis function expansion as claimed in claim 1, wherein:
the causal relationship between neuron i and self glange is calculated as follows:
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| CN106773693A (en) * | 2016-12-21 | 2017-05-31 | 浙江大学 | A kind of sparse causality analysis method of Industry Control multi-loop oscillation behavior |
| CN107240098A (en) * | 2017-06-16 | 2017-10-10 | 大连理工大学 | A kind of sparse Bayesian network of brain function linking parsing and the double constrained procedures of Granger |
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| CN106773693A (en) * | 2016-12-21 | 2017-05-31 | 浙江大学 | A kind of sparse causality analysis method of Industry Control multi-loop oscillation behavior |
| CN107240098A (en) * | 2017-06-16 | 2017-10-10 | 大连理工大学 | A kind of sparse Bayesian network of brain function linking parsing and the double constrained procedures of Granger |
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