Constrained Adjusted Maximum a Posteriori Estimation of Bayesian Network Parameters

Maximum a posteriori estimation (MAP) with Dirichlet prior has been shown to be effective in improving the parameter learning of Bayesian networks when the available data are insufficient. Given no extra domain knowledge, uniform prior is often considered for regularization. However, when the underlying parameter distribution is non-uniform or skewed, uniform prior does not work well, and a more informative prior is required. In reality, unless the domain experts are extremely unfamiliar with the network, they would be able to provide some reliable knowledge on the studied network. With that knowledge, we can automatically refine informative priors and select reasonable equivalent sample size (ESS). In this paper, considering the parameter constraints that are transformed from the domain knowledge, we propose a Constrained adjusted Maximum a Posteriori (CaMAP) estimation method, which is featured by two novel techniques. First, to draw an informative prior distribution (or prior shape), we present a novel sampling method that can construct the prior distribution from the constraints. Then, to find the optimal ESS (or prior strength), we derive constraints on the ESS from the parameter constraints and select the optimal ESS by cross-validation. Numerical experiments show that the proposed method is superior to other learning algorithms.

ALGORITHMIC METHOD OF AUTONOMOUS CORRECTION MEASUREMENT ERRORS IN SYSTEMS AUTOMATIC CONTROL AND REGULATION

A method of autonomous a posteriori estimation of control target’s state coordinates is demonstrated. The method’s accuracy does not depend on automatic control system sensors errors. An algorithmic implementation of the method is proposed – an algorithm for processing the array of data on the control target observed inputs and outputs, obtained by passive information accumulation during the observation interval of the control target normal functioning. At the final stage of the estimation algorithm, the implemented control process is simulated with complete a priori information about the conditions for its implementation (simulation estimation method). The algorithm execution time should be negligible in relation to the duration of the observation interval (instantaneous a posteriori estimation of the control target’s state). The proposed method allows to cyclically correct instrumental errors of automatic control and regulation systems without using external sources of information.

Multi-Spectral Fusion and Denoising of Color and Near-Infrared Images Using Multi-Scale Wavelet Analysis

We formulate multi-spectral fusion and denoising for the luminance channel as a maximum a posteriori estimation problem in the wavelet domain. To deal with the discrepancy between RGB and near infrared (NIR) data in fusion, we build a discrepancy model and introduce the wavelet scale map. The scale map adjusts the wavelet coefficients of NIR data to have the same distribution as the RGB data. We use the priors of the wavelet scale map and its gradient as the contrast preservation term and gradient denoising term, respectively. Specifically, we utilize the local contrast and visibility measurements in the contrast preservation term to transfer the selected NIR data to the fusion result. We also use the gradient of NIR wavelet coefficients as the weight for the gradient denoising term in the wavelet scale map. Based on the wavelet scale map, we perform fusion of the RGB and NIR wavelet coefficients in the base and detail layers. To remove noise, we model the prior of the fused wavelet coefficients using NIR-guided Laplacian distributions. In the chrominance channels, we remove noise guided by the fused luminance channel. Based on the luminance variation after fusion, we further enhance the color of the fused image. Our experimental results demonstrated that the proposed method successfully performed the fusion of RGB and NIR images with noise reduction, detail preservation, and color enhancement.

Design and Analysis of Air Quality Monitoring System

In the adaptive noise cancellation (ANC) challenge, a novel least-mean-square (LMS) algorithm for filtering speech sounds has been created. It is focused on minimising the difference weight vector's squared Euclidean norm under a stability restriction specified over the a posteriori estimation error. The Lagrangian methodology was employed for this reason in order to propose a nonlinear adaptation rule described in terms of the product of differential inputs and errors, which is a generalisation of the normalised (N)LMS algorithm. The proposed approach improves monitoring ability in this sense, as shown by studies using the AURORA 2 and 3 speech databases. They include a thorough output assessment as well as a thorough comparison to regular LMS algorithms with nearly the same computational load, such as the NLMS and other recently published LMS algorithms including the updated (M)-NLMS, the error nonlinearity (EN)-LMS, or the normalised data nonlinearity (NDN)-LMS adaptation.

Some features of numerical diagnostics of instantaneous blow-up of the solution by the example of solving the equation of slow diffusion

В работе демонстрируется, как метод апостериорной оценки порядка точности разностной схемы по Ричардсону позволяет сделать вывод о некорректности постановки (в смысле отсутствия решения) решаемой численно начально-краевой задачи для уравнения в частных производных. Это актуально в ситуации, когда аналитическое доказательство некорректности постановки ещё не получено или принципиально невозможно. The paper demonstrates how the method of a posteriori estimation of the order of accuracy for the difference scheme according to the Richardson extrapolation method allows one to conclude that the formulation of the numerically solved initial-boundary value problem for a partial differential equation is ill-posed (in the sense of the absence of a solution). This is important in a situation when the ill-posedness of the formulation is not analytically proved yet or cannot be proved in principle.

Stress-Based FEM in the Problem of Bending of Euler–Bernoulli and Timoshenko Beams Resting on Elastic Foundation

The stress-based finite element method is proposed to solve the static bending problem for the Euler–Bernoulli and Timoshenko models of an elastic beam. Two types of elements—with five and six degrees of freedom—are proposed. The elaborated elements reproduce the exact solution in the case of the piece-wise constant distributed loading. The proposed elements do not exhibit the shear locking phenomenon for the Timoshenko model. The influence of an elastic foundation of the Winkler type is also taken into consideration. The foundation response is approximated by the piece-wise constant and piece-wise linear functions in the cases of the five-degrees-of-freedom and six-degrees-of-freedom elements, respectively. An a posteriori estimation of the approximate solution error is found using the hypercircle method with the addition of the standard displacement-based finite element solution.