Parameter Estimation for Spatio-Temporal Maximum Entropy Distributions: Application to Neural Spike Trains

Nasser, Hassan; Cessac, Bruno

doi:10.3390/e16042244

Cited by 22 publications

(36 citation statements)

References 47 publications

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“…Specifically, the left figure in Figure 9 illustrates the estimated kernels at different time (i.e., 300 s, 400 s, 500 s, 600 s, 700 s), where the x-axis represents time lag τ between the previous input events and the present time, and the y-axis stands for the amplitudes of kernels. Experimental results show that the kernels for the first and second input spike train signals (i.e., k (1) and k (2) ) are nonzero, and thus are significant inputs, while the kernels of the third and fourth input spike train signals (i.e., k (3) and k (4) ) are yielded to be zero-valued for the whole system memory, and therefore deemed to be insignificant inputs. The sMGLV model can effectively identify the sparsity in the experimental system.…”

Section: Application To Functional Connectivity Analysis Of Retinal Nmentioning

confidence: 97%

“…To make the tracking task more difficult, the last two kernels (k (7) , k (8) ) are designed to be zeroes as redundant inputs to the spiking neural system. The transient changes for all step changing kernels occur at 400 s. In particular, the amplitudes of k (1) and k (2) are doubled, while the amplitudes of k (3) and k (4) are decreased by half. To test the concurrent tracking performance in identifying gradual changes, k (5) and k (6) are linear time-varying kernels with different slopes, as shown in Figures 6 and 7.…”

Section: Simulation Studiesmentioning

confidence: 99%

“…Simulated system shown in Figures 5-7 is an 8-input and 1-output spiking neural system where the first four kernel functions (k (1) , k (2) , k (3) , k (4) ) undergo step changes and the other two kernels (k (5) , k (6) ) undergo slower gradual changes concurrently. To make the tracking task more difficult, the last two kernels (k (7) , k (8) ) are designed to be zeroes as redundant inputs to the spiking neural system.…”

Section: Simulation Studiesmentioning

confidence: 99%

“…If M is large, thousands of unknown coefficients have to be estimated for each input kernel in Equation (2). To alleviate computational complexity, Laguerre expansion decomposes the kernel functions k (n) (t, τ) into a set of weighted summation of the predefined orthogonal Laguerre basis functions:…”

Section: Time-varying Generalized Laguerre-volterra Modelmentioning

confidence: 99%

“…Modeling of information transmission processes across brain regions, including spike generation and synaptic transmission, is challenging because neurobiological processes can be nonstationary [1,2]. For example, studies establish that the synaptic plasticity, with specific forms of long-term potentiation (LTP) and long-term depression (LTD), occur in response to specific input patterns, which can be indicated as the system nonstationarity.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A Sparse Multiwavelet-Based Generalized Laguerre–Volterra Model for Identifying Time-Varying Neural Dynamics from Spiking Activities

Huang

et al. 2017

Entropy

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Abstract:Modeling of a time-varying dynamical system provides insights into the functions of biological neural networks and contributes to the development of next-generation neural prostheses. In this paper, we have formulated a novel sparse multiwavelet-based generalized Laguerre-Volterra (sMGLV) modeling framework to identify the time-varying neural dynamics from multiple spike train data. First, the significant inputs are selected by using a group least absolute shrinkage and selection operator (LASSO) method, which can capture the sparsity within the neural system. Second, the multiwavelet-based basis function expansion scheme with an efficient forward orthogonal regression (FOR) algorithm aided by mutual information is utilized to rapidly capture the time-varying characteristics from the sparse model. Quantitative simulation results demonstrate that the proposed sMGLV model in this paper outperforms the initial full model and the state-of-the-art modeling methods in tracking performance for various time-varying kernels. Analyses of experimental data show that the proposed sMGLV model can capture the timing of transient changes accurately. The proposed framework will be useful to the study of how, when, and where information transmission processes across brain regions evolve in behavior.

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Section: Application To Functional Connectivity Analysis Of Retinal Nmentioning

confidence: 97%

Section: Simulation Studiesmentioning

confidence: 99%

Section: Simulation Studiesmentioning

confidence: 99%

Section: Time-varying Generalized Laguerre-volterra Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Sparse Multiwavelet-Based Generalized Laguerre–Volterra Model for Identifying Time-Varying Neural Dynamics from Spiking Activities

Huang

et al. 2017

Entropy

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An introduction to the maximum entropy approach and its application to inference problems in biology

Martino

2018

Heliyon

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A cornerstone of statistical inference, the maximum entropy framework is being increasingly applied to construct descriptive and predictive models of biological systems, especially complex biological networks, from large experimental data sets. Both its broad applicability and the success it obtained in different contexts hinge upon its conceptual simplicity and mathematical soundness. Here we try to concisely review the basic elements of the maximum entropy principle, starting from the notion of ‘entropy’, and describe its usefulness for the analysis of biological systems. As examples, we focus specifically on the problem of reconstructing gene interaction networks from expression data and on recent work attempting to expand our system-level understanding of bacterial metabolism. Finally, we highlight some extensions and potential limitations of the maximum entropy approach, and point to more recent developments that are likely to play a key role in the upcoming challenges of extracting structures and information from increasingly rich, high-throughput biological data.

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Inverse statistical problems: from the inverse Ising problem to data science

Nguyen

Zecchina

Berg

2017

Advances in Physics

252

378

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Inverse problems in statistical physics are motivated by the challenges of 'big data' in different fields, in particular high-throughput experiments in biology. In inverse problems, the usual procedure of statistical physics needs to be reversed: Instead of calculating observables on the basis of model parameters, we seek to infer parameters of a model based on observations. In this review, we focus on the inverse Ising problem and closely related problems, namely how to infer the coupling strengths between spins given observed spin correlations, magnetizations, or other data. We review applications of the inverse Ising problem, including the reconstruction of neural connections, protein structure determination, and the inference of gene regulatory networks. For the inverse Ising problem in equilibrium, a number of controlled and uncontrolled approximate solutions have been developed in the statistical mechanics community. A particularly strong method, pseudolikelihood, stems from statistics. We also review the inverse Ising problem in the non-equilibrium case, where the model parameters must be reconstructed based on non-equilibrium statistics

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Parameter Estimation for Spatio-Temporal Maximum Entropy Distributions: Application to Neural Spike Trains

Cited by 22 publications

References 47 publications

A Sparse Multiwavelet-Based Generalized Laguerre–Volterra Model for Identifying Time-Varying Neural Dynamics from Spiking Activities

A Sparse Multiwavelet-Based Generalized Laguerre–Volterra Model for Identifying Time-Varying Neural Dynamics from Spiking Activities

An introduction to the maximum entropy approach and its application to inference problems in biology

Inverse statistical problems: from the inverse Ising problem to data science

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