CN108509933A - A kind of spike time-varying Granger Causality accurate recognition method based on multi-wavelet bases functional expansion - Google Patents
A kind of spike time-varying Granger Causality accurate recognition method based on multi-wavelet bases functional expansion Download PDFInfo
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Abstract
The present invention proposes a kind of spike time-varying Granger Causality accurate recognition method based on multi-wavelet bases functional expansion, belongs to Digital Signal Analysis and Processing technical field.As shown in Figure 1, this method uses the corresponding best memory span of each neuron of AIC method choices first；Then, generalized L V models are established, it is unfolded using multi-wavelet bases functional based method, obtains time-invarying parameter model；It is then sparse to the progress of expansion model by OFR algorithms, and estimate sparse model parameter, the time-varying kernel function in Reverse reconstruction generalized L V models；Finally, solving model point process log-likelihood calculates the time-varying Granger Causality value of final corresponding neuron.The present invention proposes method compared with the existing time-varying Granger method of estimation based on SSPPF, fast-changing causality can preferably be tracked, time-varying causality accuracy of identification is improved, theoretical calculation frame and new solution route are provided for the identification of neuron spike time-varying function connects.
Description
Technical field
The present invention proposes a kind of spike time-varying Granger Causality accurate recognition algorithm based on multi-wavelet bases functional expansion,
It provides new solution for the time-varying Granger Causality accurate recognition towards spike sequence, belongs to Digital Signal Analysis and Processing
Technical field.
Background technology
Cluster connection performance is presented in neuron spike in nervous system, and neural cluster is mutually related and in function
Upper similar neuronal ensemble.Identification neuronal function connection is to understand how brain region neuron is organized to indicate, transmission, be located
Reason information and the steps necessary for further executing higher cognitive function.Nervous system is a dynamic system, and neuron is prominent
Touching, there is plasticity, neuronal function connection relation to show time-varying characteristics, so if used time constant method analyzes neuron
Between function connects relationship, cannot accurately disclose the time-varying characteristics between neuron.For these problems, neuron time-varying function connects
The analysis method for connecing relationship is increasingly paid attention to by researcher.
Granger-causality test (Granger Causality, GC) effectively divides as a kind of time series function connects
Analysis means, are widely used in neuroscience field, it have become between the network node in detection brain area domain with the presence or absence of because
The measurement standard that fruit influences.At present for there are mainly three types of neuron time-varying causality recognition methods：The first is to utilize to have
Time varying signal is divided into several signal segments by the time slip-window of limit certain length, by signal segment in each section
Regard stationary signal as to be handled, such method main problem is that time windows size can largely influence identification knot
Fruit, and there is no effective standard to determine Best Times window length, thus the Granger causality time point that this method acquires
Resolution is relatively low；Second method is to use frequency domain Granger method, and such method includes mainly orientation coherence (partial partially
Directed coherence, PDC) and adaptive directionality transmission function (adaptive directed transfer
Function, ADTF) etc., although such algorithm there are calculation amounts it is small, recognition effect is good the advantages that, under nonlinear situation,
It is difficult to obtain accurate Causality Analysis because of model complexity height；The third method establishes time-varying multivariable autoregression
(multivariate autoregressive, MVAR) parameter model, identification parameter model coefficient are simultaneously converted into Granger
Cause and effect converts neuron Granger Causality Solve problems to MVAR model parameter Solve problems.To neuron spike when
It becomes system modelling and discrimination method, is carried out under the frame of adaptive filter algorithm mostly.Common filtering algorithm has recurrence
Least square method, gradient algorithm, Kalman filtering algorithm and stochastic regime point process filter device (stochastic state
Point process filter, SSPPF) algorithm etc..SSPPF is constantly recorded new neuron variation characteristic and gradually loses
Old neuronal messages so that algorithm can tentatively track kernel function variation, and calculation amount is relatively small, compare other adaptive-filterings
Algorithm has significant advantage.However, SSPPF needs a large amount of iterative process that can just trace into accurate time-varying parameter, towards
Time-varying system changes faster time-varying parameter causes its time-varying uncertainty performance poor because its algorithm the convergence speed is slow, thus
Time-varying Granger Causality recognition methods result based on the slow adaptive filter algorithm of such convergence rate is inaccurate.
For above-mentioned time-varying Granger Causality recognition methods deficiency, present invention introduces the cutting edges of a knife or a sword based on multi-wavelet bases functional expansion
Current potential time-varying Granger Causality accurate discrimination method, by the weighted linear combination of multistage small echo B-spline to complicated time-varying MVAR
Model parameter is unfolded, and invariant parameter identification problem, constant when obtaining accurate when converting time-varying parameter identification problem to
Estimate parameter, and then obtains time-varying Granger Causality result.When neuron spike sequence has stronger non-stationary property, this
Kind method can connect time-varying cause and effect and accurately identify.This lives to structure neuron cause and effect connection network, announcement neuron
Dynamic plastic mechanism has important Practical significance.
Invention content
The present invention provides a kind of spike time-varying Granger Causality accurate recognition side based on multi-wavelet bases functional expansion
Method, it includes to estimate MVAR using multi-wavelet bases functional expansion method with the MVAR models not comprising triggering neuron to establish respectively
The point process log-likelihood difference of time-varying parameter in model, final solving model obtains spike time-varying Granger Causality knot
Fruit.Multi-wavelet bases function has multiple dimensioned and multi-resolution characteristics, can quickly track time-varying parameter variation, be widely used
Among the time-varying parameter identification of a variety of dynamic characteristics.Granger causality is a kind of neuronal function connection relation identification side
Method judges the connection relation between neuron by measuring the statistics dependence between neuron.It is verified by emulation experiment,
Method proposed by the present invention can effectively recognize the Granger causality between fast-changing neuron spike, overcome
Traditional adaptive approach leads to the low bottleneck of temporal resolution of estimation because algorithm the convergence speed is slow, connects for neuron time-varying function
It connects relationship identification and provides a kind of theoretical calculation frame and new solution route.
Spike time-varying Granger causality accurate recognition side proposed by the present invention based on multi-wavelet bases functional expansion
Method is included to be as follows：
1. parameter selection：Each neuron is selected to correspond to AIC (Akaike information criterion) criterion
Best memory span, and set the control parameter of Laguerre basic functions, m ultiwavelet scale and B-spline order；
Generalized Laguerre-Volterra 2. (L-V) model：Using Volterra series characterization time-varying neurodynamics system
System model, and time-varying Volterra cores are unfolded using Laguerre basic functions, obtain time-varying L-V generalized models；
3. time-varying parameter is unfolded：Time-varying parameter using multi-wavelet bases function pair time-varying generalized L-V models is unfolded, will
Invariant parameter when time-varying parameter is converted into, constant expansion parameter model when obtaining；
4. model is sparse and estimates：Using classical orthogonal forward direction regression algorithm to after multi-wavelet bases function expansion when it is constant
Parameter model optimizes, invariant parameter when rejecting redundancy, while estimating corresponding using generalized linear fitting algorithm, inversely
Initial time-varying parameter is solved, and reconstructs kernel function；
5. the time-varying cause and effect between neuron solves：Triggering neuron and oncontacting is built with respectively to go crazy the MVAR moulds of member
Type is estimated MVAR model parameters, is passed through in conjunction with the above-mentioned time-varying neurodynamics system identifying method based on multi-wavelet bases function
The parameter of estimation calculates point process log-likelihood function value, further calculate with/without triggering neuron MVAR models logarithm seemingly
Right value difference value, obtains the time-varying Granger Causality result between neuron.
Wherein, in the step 1, the best memory span of each neuron is determined according to AIC criterion.
In the step 2, Volterra series has the Taylor series of store-memory ability, can be non-thread with Efficient Characterization
Sexual system.Using Laguerre base function expansion methods, it can make Volterra cores that the parameter solved be needed to greatly reduce.
In the step 3, in the way of multi-wavelet bases functional expansion, complicated time-varying parameter identification problem can be turned
Turn to about it is polynomial when invariant parameter identification problem.
In the step 4, redundancy can be rejected using orthogonal regression algorithm forward, greatly reduces a parameter to be asked
Number, and model overfitting problem is avoided, it obtains with the time-invarying parameter model for preferably realizing performance.
In the step 5, it is desirable that solution triggering neuron needs to be established respectively with mesh to the causality of target nerve member
It is output to mark neuron, and MVAR model of other neurons as input (with/without triggering neuron) solves two MVAR models
Log-likelihood difference, and be multiplied by coefficient as its Granger Causality value.
Spike time-varying Granger Causality accurate recognition method based on multi-wavelet bases functional expansion proposed by the invention
The advantages of include：
1. during pair time-varying MVAR model and parameters identifications, invariant parameter recognizes when time-varying parameter identification problem is converted to
Problem, problem greatly simplify, and classical time-invariant system discrimination method can directly be applied to solve；
2. using classical orthogonal forward recursion (OFR) algorithm sparse model, redundancy is rejected, model complexity is reduced, carries
High calculating speed, Model Distinguish accuracy is high, while can effectively avoid model over-fitting；
3. corresponding interneuronal Granger Causality value is used as using corresponding MVAR model point process log-likelihood differences, with
The granting rate of target nerve member and the granting history of triggering neuron are associated by this, and causality identification is accurate；
4. model construction process is simple, computation complexity is low.
Description of the drawings
Fig. 1 is spike time-varying Granger Causality accurate recognition method flow schematic diagram proposed by the present invention；
Fig. 2 is a multiple input single output spike simulation model kernel function in simulated example, before being followed successively by from top to bottom
Present kernel function k1、k2With values of the feedback kernel function h in its memory span；
Fig. 3 is the time-varying parameter of a multiple input single output spike simulation model in simulated example, from top to bottom successively
For the time-varying parameter a that feedovers1、a2With feedback time-varying parameter a3Change over time situation；
Fig. 4 is using the spike time-varying Granger Causality method pair proposed by the present invention based on multi-wavelet bases functional expansion
Simulated example centre forward's potential sequence carries out cause and effect identification, and (i, j) width subgraph indicates triggering neuron-j to target nerve member-i
In the causality value of different moments；
Fig. 5 be emulate spike sequence it is practical when constant Granger Causality as standard of comparison, proposition more of the present invention
Based on multi-wavelet bases functional expansion with based on SSPPF time-varying Granger causality recognition methods identification performance compared with.Fig. 5
(a)-(c) is two kinds of causality analysis methods respectively to Φ31(Granger causality of the neuron 1 to neuron 3), Φ32(god
Granger causality through first 3 pairs of neurons 2), Φ33The cause and effect of (Granger causality of the neuron 3 to neuron 3) is known
Other comparative effectiveness.Analysis result confirms that proposition method has better causality analysis result.
Specific implementation mode
Preferably to illustrate the specific embodiment of the invention, the present invention is further elaborated below in conjunction with the accompanying drawings.
Present invention aims at provide a kind of spike time-varying Granger Causality identification based on multi-wavelet bases functional expansion
Method accurately identifies time-varying MVAR model parameters by using based on multi-wavelet bases functional expansion model, and solves corresponding nerve
First Granger Causality is as a result, to solve the methods of existing neuron time-varying causality discrimination based on sliding window in time resolution
Rate is low, the problems such as being difficult to quickly track neuron cause and effect connection relation, can accurately and rapidly track the connection of neuron cause and effect and become
Change.
Fig. 1 illustrates the flow chart of spike time-varying Granger Causality accurate recognition method proposed by the present invention, including：
Solve corresponding neuron time-varying Granger causality, need to solve respectively comprising with not comprising triggering neuron
The log-likelihood of MVAR models estimates neuron time-varying MVAR model solution time-varying parameters.It is selected firstly the need of using AIC methods
The corresponding best memory span of each neuron is selected, determines Laguerre, m ultiwavelet B-spline parameter；Then, generalized L-V is established
Model characterizes corresponding emulation input and output spike sequence construct time-varying MISO system using Volterra series, uses
Time-varying Volterra cores are unfolded in Laguerre basic functions, obtain Generalized Laguerre-Volterra models；Then it uses
Generalized L-V models are unfolded in multi-wavelet bases functional based method, and time-varying parameter is transformed into time-invarying parameter model；When obtaining not
After variable parameter model expression formula, model optimization is carried out by OFR algorithms, deleting madel redundancy is fitted in conjunction with generalized linear
(GLMFIT) method, the parameter of Estimation Optimization model reconstruct the time-varying kernel function in generalized L-V models；Finally, by corresponding core letter
Numerical value substitutes into initial MVAR models, obtains MVAR model parameters, solves corresponding model point process log-likelihood, and calculate and do not wrap
Containing the difference with the log-likelihood comprising triggering neuron models, the symbol of excitation or inhibition is multiplied by as finally using the difference
The time-varying Granger Causality value of corresponding neuron.
It is specifically described time-varying Granger Causality between the neuron provided by the invention based on multi-wavelet bases functional expansion below
Relationship discrimination method, specific steps include：
1. parameter selection：In neuron colony activity, the memory span of each neuron is different, true by AIC criterion
The best memory span of fixed each neuron, AIC expression formulas are as follows：
AIC=-2ln (L)+2K (1)
Wherein, K is number of parameters, and L is the likelihood function of corresponding parameter, is corresponded to by selecting different memory spans to solve
AIC values select the corresponding memory spans of minimum AIC as the best memory span of the neuron.
Laguerre basic functions are controlled by parameter L, and the larger case propagation delays that can track complexity that L is set, band is also brought along
The problem of computation complexity improves；Multi-wavelet bases function is by wavelet scale j, the m controls of B-spline order, the wavelet scale and B of bigger
Batten order can improve the accuracy of clock synchronization parameter-switching tracing, but can bring the calculating of more parameters and bigger to be estimated
Complexity.
2. generalized L-V models：In neuron colony activity, MISO (multiple input single output) system can indicate
For：
W=u (K, x)+a (H, y)+ε (σ) (2)
Wherein, x, y indicate that the spike sequence of input and output neuron, w indicate the threshold cephacoria of output neuron respectively
Current potential, w are the rear electricity of postsynaptic potential u caused by inputting neuron spike sequence, output neuron spike sequence feedback
Position a and deviation be σ white Gaussian noise ε summation.It will make output neuron spike granting when w is more than threshold θ.
Using single order Volterra models expansion feed-forward coefficients K and feedback factor H, time-varying broad sense Volterra moulds are obtained
Type：
Wherein, k0Indicate that constant coefficient, N are the length for inputting spike sequence, MkWith MhFeedforward and feedback procedure are indicated respectively
Memory span,For time-varying Volterra kernel functions, input neuron spike x is characterized respectivelynWith it is defeated
Go out the linearly dependent coefficient of u, the linearly dependent coefficient of output neuron spike y and a.
Then, time-varying broad sense Volterra kernel functions are unfolded using Laguerre basic functions, obtain generalized L-V moulds
Type：
Formula (4) is updated to formula (3), obtaining u, a expression formula becomes：
Wherein,And chRespectively Volterra kernel functionsWith the Laguerre expansion coefficients of h.Pass through
The mode of Laguerre base function expansions greatly reduces number of parameters to be asked, and solves Volterra kernel function dimension disasters
Problem, and over-fitting is avoided to a certain extent.Using the combination of systems by output feedback signal and input signal as system
System input, time-varying neurodynamics system model is characterized with Volterra series completely, builds time-varying generalized L-V models.
3. time-varying parameter is unfolded：Time-varying parameter using multi-wavelet bases function pair time-varying generalized L-V models is unfolded, will
Invariant parameter is solved when time-varying parameter is changed into：
Wherein,For multi-wavelet bases function,M is B-spline basic function BmOrder, j
Indicate wavelet scale, ГmIndicate wavelet basis function deviation ratio, Гm={ k:-m≤k≤2j- 1 }, T is observation sample length,For the when constant coefficient after multi-wavelet bases functional expansion.Formula (6) is substituted into formula (5), when obtaining not
Variable parameter model expression formula is：
4. model is sparse and estimates：Using classical OFR algorithms to the time-invarying parameter model after multi-wavelet bases functional expansion
Redundancy is rejected in optimization, and kernel function is further reconstructed, inversely when estimation is to corresponding in conjunction with generalized linear fitting algorithm
Solve the related coefficient of original Volterra kernel functions.
Model item number of the broad sense time-varying L-V models after multi-wavelet bases functional expansion is more, and there are bulk redundancy items, if
Original expansion model solution is directly used, model complexity is high, and is easy to cause model overfitting problem.Therefore, expansion
Model need to carry out model optimization and it is sparse be step very crucial in the present invention.In the present invention, using just returning forward
Reduction method obtains an effective sparse model to model topology optimization, deleting madel redundancy.
OFR algorithms are first to alternate item X in modeli(i=1,2 ..., M × L) makees orthogonalization process, obtains accordingly just
Friendshipization alternate item wi(i=1,2 ..., M × L).By using error slip standard (Error Reduction Ratio,
ERR the effective item of model) is selected successively.ERR expression formulas are as follows：
Wherein, Y is observation signal output sequence, wiFor orthogonalization alternate item sequence, MN=M × L is alternative item number,
<·,·>Indicate inner product of vectors.
During effective item is chosen, what each step was all answered by comparing alternate item sequence pair after orthogonalization in the step
ERRiValue determines the effective item selected, such as in the 1st step is selected, enables wi=Xi, each single item is calculated by formula (8) and is corresponded to
ERRi, take { ERRi}maxRespective items are that the 1st step selects a p1；In kth step is selected, with the k-1 items { p chosen before1,
p2,…,pk-1It is used as orthogonal basis to remaining alternate item { Xi:I=1,2 ..., MN}\{p1,p2,…,pk-1Be orthogonalized, and
The corresponding ERR values of remaining alternate item are calculated, are selected { ERR }maxCorresponding alternate item is as k-th of effective pk.It can by formula (8)
Know, ERR standards are to weigh the degree of correlation of orthogonal rear alternate item and initial output sequence, i.e., preferentially select correlation in each step
Highest item is the effective item of the step.
5. neuron time-varying causality is estimated：For neuron spike sequence, respectively using different neurons as defeated
Go out other neurons to substitute into the aforementioned time-varying model based on multi-wavelet bases functional expansion as input, be reconstructed
After Volterra kernel functions, the coefficient in coefficient and MVAR models is corresponded, and is asked according to point process log-likelihood function
The log-likelihood of MVAR models must be corresponded to：
Li(t)=y (t) logp (t)+(1-y (t)) log (1-p (t))
Wherein, Li(t) be neuron i as export other neurons as input when model t moment log-likelihood
Value,Neuron i is represented as exporting, logarithm of the model in t moment when removing other neurons of neuron j as input
Likelihood value.By the symbol for calculating the coefficient sum of neuron j under neuron i MVAR models as inputThe granting history for distinguishing neuron j is excitation or inhibiting effect to the average influence of neuron i.It will
Li(t) withMake difference and be multiplied by the symbol of neuron j coefficient sums, obtain target nerve member i and triggers the time-varying between neuron j
Granger causality value：
Wherein, Φij(t) it is that positive value indicates that neuron j has incentive action, negative value to indicate neuron j the granting of neuron i
There is inhibiting effect to the granting of neuron i.
Particularly, neuron i and itself Granger causality are calculated as follows：
For quantitative analysis spike time-varying Granger causality identification effect, the present invention is carried out using three kinds of measurement standards
Evaluation：Mean absolute error (Mean Absolute Error, MAE), normalization root mean square error (normalized Root
Mean Squared Error, RMSE) and standard deviation (Standard deviations, Std).MAE, RMSE, Std are smaller,
Show that identification precision is higher, effect is better, and tracking variation causality speed is faster.Expression is as follows：
Wherein,For the prediction cause and effect value that this method obtains, Φ (t) when being point process constant Granger Causality value, N be
Length of sample series.
It is proposed by the present invention based on multi-wavelet bases function exhibition below based on the Example Verification of emulation neuron spike sequence
The neuron time-varying Granger causality discrimination method precision opened, and with the existing neuron time-varying Granger based on SSPPF
Causality discrimination method carries out Contrast on effect：
2 input of simulated example structure, 1 output emulation time-varying linear systems：
Time-varying parameter is：
As shown in Fig. 2, feedforward kernel function k1(τ)、k2The value difference of (τ) and feedback kernel function h (τ) are as shown in Figure 3.
Length of sample series N=200000, total duration 400s, mode input x1、x2It is pseudorandom Poisson distribution binary system sequence
Row, e (t) is the white Gaussian noise that mean value is 0, variance is 1.
By above-mentioned simulation sequence x1、x2, y be regarded as neuron 1,2,3 respectively, using it is proposed by the present invention be based on multi-wavelet bases
Functional expansion method carries out time-varying Granger causality identification, and the results are shown in Figure 4, and (m, n) pair subgraph represents triggering god
Causality through member-n to target nerve member-m in different moments, as shown in Figure 4, last column subgraph have apparent non-zero
Value.Last column indicates neuron 1,2 (x in Fig. 41、x2) pair and only there is causality with neuron 3 (y).Subgraph (3,1) table
Show signal x1Trigger signal y and causality there are Spline smoothing, and Spline smoothing is happened at 100s and 200s；Subgraph (3,
2) signal x is indicated2Trigger signal y and there are the causalities of Spline smoothing relationship, and Spline smoothing is happened at 200s；Subgraph
(3,3) causality of signal y and own signal are indicated.When then, with point process the identification of constant Granger Causality method because
Fruit value is as standard value, by the method proposed by the present invention based on multi-wavelet bases functional expansion and the existing method based on SSPPF
To Φ31(Granger causality of the neuron 1 to neuron 3), Φ32(neuron 2 closes the Granger Causality of neuron 3
System), Φ33(Granger causality of the neuron 3 to neuron 3) recognizes, and compares performance, as a result respectively as table 1 with
Shown in Fig. 5 (a)-(c).
1 simulation example time-varying Granger identification precision of table compares
By the time-varying Granger Causality identification precision comparing result of simulation example it is found that using proposed by the present invention based on more
The spike time-varying Granger Causality discrimination method of wavelet basis function expansion, obtained time-varying Granger Causality identification effect are apparent
Better than the identification effect based on SSPPF methods under equal conditions.It as seen from Figure 5, can based on multi-wavelet bases functional expansion method
Accurate tracking time-varying cause and effect variation, and be then that progressive tracking cause and effect changes based on SSPPF methods, for fast-changing cause and effect
Relationship cannot obtain good identification effect.The experimental results showed that time-varying causal approach discrimination method proposed by the present invention can be with
It preferably identifies neuron time-varying causality, thus theoretical calculation is provided for identification neuron complexity time-varying cause and effect connection relation
Frame.
Claims (3)
1. the spike time-varying Granger Causality accurate recognition method based on multi-wavelet bases functional expansion, it is characterised in that including：
Step 1. parameter selection：The corresponding best memory span of each neuron spike is selected with AIC criterion, and is determined
The order of the control parameter of Laguerre basic functions, the scale of m ultiwavelet and B-spline；
Step 2. Generalized Laguerre-Volterra (L-V) model：Using Volterra series characterization time-varying neurodynamics system
System model, is unfolded time-varying Volterra cores using Laguerre basic functions, obtains time-varying L-V generalized models；
Step 3. time-varying parameter is unfolded：Time-varying parameter using multi-wavelet bases function pair time-varying generalized L-V models is unfolded, will
Invariant parameter when time-varying parameter model is converted into, constant expansion parameter model when obtaining；
Step 4. model is sparse and estimates：Using classical orthogonal forward direction regression algorithm to after multi-wavelet bases function expansion when it is constant
Parameter model optimizes, invariant parameter when rejecting redundancy, while estimating corresponding using generalized linear fitting, Converse solved
Initial time-varying parameter, and reconstruct kernel function；
Step 5. neuron spike time-varying cause and effect solves：Establishing respectively has triggering neuron spike and oncontacting to go crazy first cutting edge of a knife or a sword
The MVAR models of current potential, and corresponded to using the above-mentioned time-varying neurodynamics system identifying method estimation based on multi-wavelet bases function
MVAR model parameters calculate point process log-likelihood function value by these parameters, further calculate separately with/without triggering nerve
The MVAR model log-likelihood differences of member obtain corresponding neuron spike time-varying Granger Causality result.
2. the spike time-varying Granger Causality accurate recognition side based on multi-wavelet bases functional expansion as described in claim 1
Method, it is characterised in that：
The step 3 includes：It is approached using the time-varying parameter of multi-wavelet bases function pair time-varying generalized L-V models, by its table
It is shown as the linear weighted function form of multi-wavelet bases function, and then establishes the time-invarying parameter model extended based on m ultiwavelet B-spline, i.e.,
By time-varying Laguerre coefficients related to timeIt is converted into the when invariant polynomials form of multi-wavelet bases functionWhereinFor when invariant parameter,For multi-wavelet bases function.
3. the neuron spike time-varying Granger Causality based on multi-wavelet bases functional expansion is accurately distinguished as described in claim 1
Knowledge method, it is characterised in that：
The step 5 includes：Include and two models of the time-varying MVAR models not comprising triggering neuron and solution by establishing
Point process log-likelihood difference, triggering neuron spike is calculated to the time-varying Granger of target nerve member spike with this
Cause and effect value.
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| WO2021134315A1 (en) * | 2019-12-30 | 2021-07-08 | 瑞声声学科技(深圳)有限公司 | Motor nonlinear distortion compensation method and apparatus, and computer-readable storage medium |
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