Computation Of Likelihood Function Research Articles

Amortized Bayesian inference on generative dynamical network models of epilepsy using deep neural density estimators

Whole-brain modeling of epilepsy combines personalized anatomical data with dynamical models of abnormal activities to generate spatio-temporal seizure patterns as observed in brain imaging data. Such a parametric simulator is equipped with a stochastic generative process, which itself provides the basis for inference and prediction of the local and global brain dynamics affected by disorders. However, the calculation of likelihood function at whole-brain scale is often intractable. Thus, likelihood-free algorithms are required to efficiently estimate the parameters pertaining to the hypothetical areas, ideally including the uncertainty. In this study, we introduce the simulation-based inference for the virtual epileptic patient model (SBI-VEP), enabling us to amortize the approximate posterior of the generative process from a low-dimensional representation of whole-brain epileptic patterns. The state-of-the-art deep learning algorithms for conditional density estimation are used to readily retrieve the statistical relationships between parameters and observations through a sequence of invertible transformations. We show that the SBI-VEP is able to efficiently estimate the posterior distribution of parameters linked to the extent of the epileptogenic and propagation zones from sparse intracranial electroencephalography recordings. The presented Bayesian methodology can deal with non-linear latent dynamics and parameter degeneracy, paving the way for fast and reliable inference on brain disorders from neuroimaging modalities.

Markov Chain Monte Carlo-based Bayesian method for nonlinear stochastic model updating

This paper proposes a Markov Chain Monte Carlo (MCMC)-based Bayesian method for nonlinear stochastic model updating by using the instantaneous characteristics of the structural dynamic responses. According to the discrete analytical mode decomposed method and Hilbert transform, the instantaneous characteristics of the mono-components are firstly extracted from the structural dynamic response and applied to the calculation of likelihood function. Then, the posterior probability density function associated with Bayesian theorem is derived under the assumption of Gaussian prior distribution by using instantaneous characteristics. Afterwards, to calculate the posterior probability density function and improve the sampling efficiency, the delayed rejection adaptive Metropolis-Hastings (DRAM) algorithm is implemented with the advantages of strong adaptive and fast convergence. In the process of Bayesian inference, the posterior samples generated by DRAM require vast quantities of finite element analysis to guarantee the accuracy. For reducing the computational cost, the response surface model is constructed to establish the mathematical regression model between the structural parameters and the theoretical dynamic responses. To validate the effectiveness and applicability of the proposed method, the numerical cases on a three-story nonlinear structure under earthquake excitation considering various noise level effects and an Iwan beam model with two types of excitations are simulated. In addition, an experimental validation on a ¼ scale, 3-story steel frame structure subjected to a series of earthquake excitations in the laboratory is also performed to further verify the proposed method. Both the numerical and experimental results demonstrate that the DRAM-based Bayesian method can be effectively used to update nonlinear stochastic models with a high accuracy.

On Blind Frame Synchronization of LDPC Codes

We consider in this letter the problem of blind frame synchronization of Low Density Parity-Check (LDPC) codes. We present and compare new methods of blind frame synchronization based on the calculation of Likelihood functions of the syndrome. Simulation results show that the four proposed synchronization techniques are effective once applied to LDPC codes. The method that involves the maximization of the Likelihood Difference (LD) function of the parity-checks, presents the best results in terms of probability of false synchronization.

Improved Discrete Optical Flow Estimation With Triple Image Matching Cost

Approaches that use more than two consecutive video frames in the optical flow estimation have a long research history. However, almost all such methods utilize extra information for a pre-processing flow prediction or for a post-processing flow correction and filtering. In contrast, this paper differs from previously developed techniques. We propose a new algorithm for the likelihood function calculation (alternatively the matching cost volume) that is used in the maximum a posteriori estimation. We exploit the fact that in general, optical flow is locally constant in the sense of time and the likelihood function depends on both the previous and the future frame. Implementation of our idea increases the robustness of optical flow estimation. As a result, our method outperforms 9% over the DCFlow technique, which we use as prototype for our CNN based computation architecture, on the most challenging MPI-Sintel dataset for the non-occluded mask metric. Furthermore, our approach considerably increases the accuracy of the flow estimation for the matching cost processing, consequently outperforming the original DCFlow algorithm results up to 50% in occluded regions and up to 9% in non-occluded regions on the MPI-Sintel dataset. The experimental section shows that the proposed method achieves state-of-the-arts results especially on the MPI-Sintel dataset.

Synthesis and analysis of algorithms for digital signal recognition in conditions of deforming distortions and additive noise

The problem of digital signal recognition has been considered in conditions of deforming distortions of the waveform of these signals and additive Gaussian noise. A mathematical model for introducing deformations of the known or random waveform signals is proposed for synthesizing recognition algorithms. The model is based on introducing the nonlinear deformation operator as an operator of permutations with repetitions of elements of the initial discrete signal with addition of additive noise component caused by quantization errors of continuous deformation function. Two recognition algorithms were synthesized and investigated. The first is an optimal one based on the exact calculation of likelihood functions, and the second is a quasi-optimal algorithm based on using the Gaussian approximation of likelihood functions. These algorithms were simulated for different variants of the specified values of deforming distortions in the form of determinate functions and in the form of random function realizations. The experimental error probability was compared with its theoretical estimate at different values of signal-to-noise ratio.

MINUIT package parallelization and applications using the RooFit package

The fitting procedures are based on numerical minimization of functions. The MINUIT package is the most common package used for such procedures in High Energy Physics community. The main algorithm in this package, MIGRAD, searches the minimum of a function using the gradient information. For each minimization iteration, MIGRAD requires the calculation of the derivative for each free parameter of the function to be minimized. Minimization is required for data analysis problems based on the maximum likelihood technique. The calculation of complex likelihood functions, with several free parameters, many independent variables and large data samples, can be very CPU-time consuming. Then, the minimization process requires the calculation of the likelihood functions several times for each minimization iteration. In this paper we will show how MIGRAD algorithm and the likelihood function calculation can be easily parallelized using Message Passing Interface techniques. We will present the speed-up improvements obtained in typical physics applications such as complex maximum likelihood fits using the RooFit package.

On scalarized calculation of the likelihood function in array square-root filtering algorithms

An efficient method of scalarized calculation of the logarithmic likelihood function based on the array square-root implementation methods for Kalman filtering formulas was proposed. The algorithms of this kind were shown to be more stable to the roundoff errors than the conventional Kalman filter. The measurement scalarization technique enables a substantial reduction in the computational complexity of the algorithm. Additionally, the new implementations are classified with the array filtering algorithms and thereby are oriented to the parallel calculations. Computational results corroborated effectiveness of the new algorithm.

Likelihood approximation by numerical integration on sparse grids

The calculation of likelihood functions of many econometric models requires the evaluation of integrals without analytical solutions. Approaches for extending Gaussian quadrature to multiple dimensions discussed in the literature are either very specific or suffer from exponentially rising computational costs in the number of dimensions. We propose an extension that is very general and easily implemented, and does not suffer from the curse of dimensionality. Monte Carlo experiments for the mixed logit model indicate the superior performance of the proposed method over simulation techniques.

Low-Complexity Algorithm for Near-Optimum Detection of V-BLAST Systems

For the Vertical Bell Laboratories Layered Space-Time systems, the optimum a posteriori probability detector encounters the problem of calculating Gaussian mixtures with large numbers of components. In this letter, a new detector is proposed, which consists of an minimum-mean-square-error generalized decision feedback equalization-based dominant symbol combinations selection algorithm for mixture components reduction, and a Cholesky factorization-based efficient algorithm for likelihood function calculation. The new detector can obtain near optimum performance with a complexity much lower than that of a previous sequential algorithm with Gaussian approximation.

The two source maximum likelihood function

The maximum likelihood method is designed to yield high resolution estimates in a multiple source environment. The article derive a simplified representation of the maximum likelihood function for the two source case. This case is instructive to understand when and why the full power of the maximum likelihood method should be used. This approach extends the results of a previous paper (see J. Piper, IEEE Trans. Signal Processing, vol.42, no.2, p.412, 1994) that showed how the maximum likelihood function calculation can be transformed from a matrix problem to a vector product. The maximum likelihood function for spectral estimation is given. >