Local Gaussian Model Research Articles

An optimized intelligent open-source MLaaS framework for user-friendly clustering and anomaly detection

As data grow exponentially, the demand for advanced intelligent solutions has become increasingly urgent. Unfortunately, not all businesses have the expertise to utilize machine learning algorithms effectively. To bridge this gap, the present paper introduces a cost-effective, user-friendly, dependable, adaptable, and scalable solution for visualizing, analyzing, processing, and extracting valuable insights from data. The proposed solution is an optimized open-source unsupervised machine learning as a service (MLaaS) framework that caters to both experts and non-experts in machine learning. The framework aims to assist companies and organizations in solving problems related to clustering and anomaly detection, even without prior experience or internal infrastructure. With a focus on several clustering and anomaly detection techniques, the proposed framework automates data processing while allowing user intervention. The proposed framework includes default algorithms for clustering and outlier detection. In the clustering category, it features three algorithms: k-means, hierarchical clustering, and DBScan clustering. For outlier detection, it includes local outlier factor, K-nearest neighbors, and Gaussian mixture model. Furthermore, the proposed solution is expandable; it may include additional algorithms. It is versatile and capable of handling diverse datasets by generating separate rapid artificial intelligence models for each dataset and facilitating their comparison rapidly. The proposed framework provides a solution through a representational state transfer application programming interface, enabling seamless integration with various systems. Real-world testing of the proposed framework on customer segmentation and fraud detection data demonstrates that it is reliable, efficient, cost-effective, and time-saving. With the innovative MLaaS framework, companies may harness the full potential of business analysis.

Accelerated Bayesian Inference for Molecular Simulations using Local Gaussian Process Surrogate Models.

While Bayesian inference is the gold standard for uncertainty quantification and propagation, its use within physical chemistry encounters formidable computational barriers. These bottlenecks are magnified for modeling data with many independent variables, such as X-ray/neutron scattering patterns and electromagnetic spectra. To address this challenge, we employ local Gaussian process (LGP) surrogate models to accelerate Bayesian optimization over these complex thermophysical properties. The time-complexity of the LGPs scales linearly in the number of independent variables, in stark contrast to the computationally expensive cubic scaling of conventional Gaussian processes. To illustrate the method, we trained a LGP surrogate model on the radial distribution function of liquid neon and observed a 1,760,000-fold speed-up compared to molecular dynamics simulation, beating a conventional GP by three orders-of-magnitude. We conclude that LGPs are robust and efficient surrogate models poised to expand the application of Bayesian inference in molecular simulations to a broad spectrum of experimental data.

Federated Data Quality Assessment Approach: Robust Learning With Mixed Label Noise.

Federated learning (FL) has been an effective way to train a machine learning model distributedly, holding local data without exchanging them. However, due to the inaccessibility of local data, FL with label noise would be more challenging. Most existing methods assume only open-set or closed-set noise and correspondingly propose filtering or correction solutions, ignoring that label noise can be mixed in real-world scenarios. In this article, we propose a novel FL method to discriminate the type of noise and make the FL mixed noise-robust, named FedMIN. FedMIN employs a composite framework that captures local-global differences in multiparticipant distributions to model generalized noise patterns. By determining adaptive thresholds for identifying mixed label noise in each client and assigning appropriate weights during model aggregation, FedMIN enhances the performance of the global model. Furthermore, FedMIN incorporates a loss alignment mechanism using local and global Gaussian mixture models (GMMs) to mitigate the risk of revealing samplewise loss. Extensive experiments are conducted on several public datasets, which include the simulated FL testbeds, i.e., CIFAR-10, CIFAR-100, and SVHN, and the real-world ones, i.e., Camelyon17 and multiorgan nuclei challenge (MoNuSAC). Compared to FL benchmarks, FedMIN improves model accuracy by up to 9.9% due to its superior noise estimation capabilities.

Latin hypercubes for constrained design of experiments for data-driven models

Abstract The quality of data used for data-driven modeling affects the model performance significantly. Thus, design of experiments (DoE) is an important part during model development. The design space is constrained in many applications. In this work, the constrained case is investigated. An Latin hypercube based approach is applied and analyzed for strongly constrained design spaces. Contrary to commonly used optimization techniques, an incremental procedure is proposed. In every step, new data are added to the design. Each new point is selected by a distance-based criterion. The performance of the created designs is evaluated by the quality of the trained models. For different constraints, artificial data sets are created with a function generator. The performance of local model networks and Gaussian process regression models trained with those designs is evaluated and compared to models trained on data sets based on Sobol’ sequences.

Single Image Super-Resolution Algorithm based on Fixed-Point Multi-Model Gaussian Process Regression

To solve the problem of large amount of computation in matrix inversion of Gaussian process regression model, a super-resolution algorithm based on local Gaussian process regression of fixed point multi-model is proposed. Firstly, the training samples are classified by Gaussian mixture model, and image patches are randomly selected as fixed points in each type of training samples, and its K nearest neighbor patch are searched. Secondly, local Gaussian process regression model by using its low-mid-frequency components and the corresponding high frequency components. Again, low resolution test image patch is classified, only the K nearest neighbor test image patch is searched during reconstruction. And then, find the nearest fixed point in each kind of image patch, and use the local Gaussian process regression model based on the fixed point to predict its corresponding high-frequency component. Finally, corresponding high frequency information is predicted by using this trained model, which improves the reconstruction efficiency. Experimental results have demonstrated that the proposed algorithm is superior in both quantitative and qualitative aspects against other algorithms.

Local logit regression for loan recovery rate

Abstract This is the first paper to propose a flexible local logit regression for defaulted loan recoveries that lie in [0,1]. Via a simulation study, we demonstrate that the proposed model is robust to nonlinearity, and non-normality of errors. Applied to Moody’s dataset, the local logit model uncovers the intrinsic nonlinear relationship between loan recoveries and covariates, which include loan/borrower characteristics and economic conditions. We exploit the empirical features of the local logit model to improve the specification of the standard regression for the fractional response variable (RFRV) model, which we refer to as the calibrated-RFRV model. The estimation of the calibrated-RFRV model is more straightforward and faster than the local logit model. The overall out-of-sample predictive performance of the calibrated-RFRV is superior to the local logit, RFRV, neural network (NN), regression tree (RT) and Inverse Gaussian (IG) models. The local logit model outperforms others in quantile forecasting, showing the attractiveness of this model for estimating tail risks, the accurate estimation of which is beneficial to risk managers.

Bayesian space-time gap filling for inference on extreme hot-spots: an application to Red Sea surface temperatures

We develop a method for probabilistic prediction of extreme value hot-spots in a spatio-temporal framework, tailored to big datasets containing important gaps. In this setting, direct calculation of summaries from data, such as the minimum over a space-time domain, is not possible. To obtain predictive distributions for such cluster summaries, we propose a two-step approach. We first model marginal distributions with a focus on accurate modeling of the right tail and then, after transforming the data to a standard Gaussian scale, we estimate a Gaussian space-time dependence model defined locally in the time domain for the space-time subregions where we want to predict. In the first step, we detrend the mean and standard deviation of the data and fit a spatially resolved generalized Pareto distribution to apply a correction of the upper tail. To ensure spatial smoothness of the estimated trends, we either pool data using nearest-neighbor techniques, or apply generalized additive regression modeling. To cope with high space-time resolution of data, the local Gaussian models use a Markov representation of the Matern correlation function based on the stochastic partial differential equations (SPDE) approach. In the second step, they are fitted in a Bayesian framework through the integrated nested Laplace approximation implemented in R-INLA. Finally, posterior samples are generated to provide statistical inferences through Monte-Carlo estimation. Motivated by the 2019 Extreme Value Analysis data challenge, we illustrate our approach to predict the distribution of local space-time minima in anomalies of Red Sea surface temperatures, using a gridded dataset (11315 days, 16703 pixels) with artificially generated gaps. In particular, we show the improved performance of our two-step approach over a purely Gaussian model without tail transformations.

Retracted: Active Contour Image Segmentation Method for Training Talents of Computer Graphics and Image Processing Technology

Image segmentation is a key technology in the field of computer image processing. Among them, segmentation methods based on active contour models have been developed rapidly in recent years due to their effective processing of complex images such as medical images. These methods have achieved significant results in medical, military, and industrial fields. Present research work mainly introduces the training of computer graphics and image processing technology and the method of active contour image segmentation. It focuses on the study of image segmentation methods and focuses on the segmentation methods based on active contour models. Firstly, it summarizes two types of segmentation methods based on edge and region and summarizes their advantages and disadvantages. Then, the segmentation method based on the active contour model is studied, and several typical active contour models are comprehensively compared. Finally, the local binary fitting model and the local Gaussian distribution fitting energy model are improved and simulated. Furthermore, from the development of computer graphics and image processing technology to analyze some methods and means of training this professional talent. The experimental results of this article show that the active contour image segmentation algorithm can not only ensure the image segmentation algorithm but also reduce the number of iterations and shorten the image segmentation time. Compared with the CV, LBF, and LGIF models computational efficiency of Segmentation method is increased by 9.2 times, 2.64 times, and 1.44 times, respectively.

A new binary level set model using L0 regularizer for image segmentation

In this paper, a new model of image segmentation is proposed by considering L0 regularizer term. A new energy function is formulated by utilizing Local Gaussian Distribution model based on binary level set function followed by introducing a L0 gradient regularizer as regularizing term. Instead of zero level set, the binary level set function is applied to differentiate between foreground and background regions. The regularization function is used to calculate the interfaces between foreground sub-regions and regularization term L0 which helps to evolve the curve. The proposed energy function is solved using minimization algorithm to achieve promising results in terms of segmentation accuracy. The different sets of experiments are performed on real and medical images. The proposed model provides higher segmentation accuracy results in less computational time compared to the other state-of-the-art models. Further, the results are found to be superior as compared to other existing models in terms of robustness to noise and intensity inhomogeneity.

Training Data Assisted Anomaly Detection of Multi-Pixel Targets In Hyperspectral Imagery

In this paper, we investigate the anomaly detection problem for widespread targets with known spacial patterns under a local Gaussian model when training data are available. Three adaptive detectors are proposed based on the principles of the generalized likelihood ratio test, the Rao test, and the Wald test, respectively. We prove that these tests are statistically equivalent to each other. In addition, analytical expressions for the probability of false alarm and probability of detection of the proposed detectors are obtained, which are verified through Monte Carlo simulations. It is shown that these detectors have a constant false alarm rate against the covariance matrix. Finally, numerical examples using synthetic and real hyperspectral data demonstrate that these training data assisted detectors have better detection performance than their counterparts without training data.

Multichannel Non-Negative Matrix Factorization Using Banded Spatial Covariance Matrices in Wavenumber Domain

Blind source separation exploiting multichannel information has long been a popular topic, and recently proposed methods based on the local Gaussian model have shown promising results despite its high computational cost for the case of many microphone signals. The low updating speed for such a model is mainly due to the inversion of a spatial covariance matrix, for which the complexity increases with the number of microphones, M, and is generally of order O(M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ). Several projection-based approaches that attempt to concentrate energy on the diagonal part of the spatial covariance matrix have been introduced to circumvent the matrix inversion, which can reduce the complexity to O(M). In this article, we focus on the fast Fourier transform as a projection method because the energy concentration on the diagonal can be efficiently achieved compared with other projection-based methods. For the case where the diagonalization is imperfect, for example, owing to discontinuities at the edge of a linear array, we also developed a more robust algorithm approximating the tri-diagonal part of the spatial covariance matrix, which requires a complexity of O(M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) for the inversion by applying the Thomas algorithm. To remove the ad-hoc integration of post clustering after the decomposition, we also examine a self-clustering algorithm. Our evaluation shows better results than other previously proposed methods in terms of the separation quality under reverberant conditions as well as higher efficiency than multichannel non-negative matrix factorization.

Comparison of spatial patterns of ammonia concentration and dry deposition flux between a regional Eulerian chemistry-transport model and a local Gaussian plume model

Agricultural activities are the principal sources of ammonia (NH3) emitted into the atmosphere. High ammonia deposition flux may impact sensitive ecosystems. Regional models of NH3 dispersion, transport and deposition may under- or overestimate NH3 fluxes. We compared NH3 dry deposition fluxes simulated with local and regional models on different theoretical scenarios characterised by varying the values of several input factors: grid cell sizes, characteristics of the NH3 sources such as location and emission rate, characteristics such as canopy resistance (Rc) or roughness length (z0) at the NH3 sinks, and meteorological conditions such as wind speed and direction. Our results showed that, for a given grid cell size, both models provide similar predictions of average NH3 concentration and dry deposition flux over the whole simulation domain. A sensitivity analysis of NH3 concentration and dry deposition flux to wind speed and to surface resistance also showed a similar behaviour between both models. However, the differences of model formalism and changes in the values of the input factors, especially grid cell size and vertical resolution, provide different spatial patterns of NH3 dry deposition flux and concentration. Our results would suggest that regional models operating with large grid cell sizes (e.g. larger than 1 km) could not predict accurately patterns of NH3 dry deposition fluxes close to the sources (e.g. a few tens or hundreds of metres) on heterogeneous landscapes in terms of NH3 fluxes.

Distributed Gaussian mixture model for monitoring plant-wide processes with multiple operating modes

For large-scale plant-wide processes with multiple operating conditions, a distributed Gaussian mixture modeling and monitoring mechanism is proposed. To overcome the deficient prior modeling knowledge for complex process, a two-dimensional probabilistic topic model based technique named Bayesian co-clustering method is developed to simultaneously conduct the sub-block division and operating mode recognition. With the obtained sub-blocks and operating modes, a global Gaussian mixture model is first built and then several local Gaussian mixture models are extracted and applied for distributed monitoring of plant-wide processes. By conducting distributed modeling and monitoring, both global and local process changes can be reflected and the fault region can be localized more easily for further analyses. The feasibility and effectiveness of the proposed method is confirmed through a numerical example and the Tennessee Eastman benchmark process.

Local Gaussian Process Model for Large-Scale Dynamic Computer Experiments

ABSTRACTThe recent accelerated growth in the computing power has generated popularization of experimentation with dynamic computer models in various physical and engineering applications. Despite the extensive statistical research in computer experiments, most of the focus had been on the theoretical and algorithmic innovations for the design and analysis of computer models with scalar responses. In this article, we propose a computationally efficient statistical emulator for a large-scale dynamic computer simulator (i.e., simulator which gives time series outputs). The main idea is to first find a good local neighborhood for every input location, and then emulate the simulator output via a singular value decomposition (SVD) based Gaussian process (GP) model. We develop a new design criterion for sequentially finding this local neighborhood set of training points. Several test functions and a real-life application have been used to demonstrate the performance of the proposed approach over a naive method of choosing local neighborhood set using the Euclidean distance among design points. The supplementary material, which contains proof of the theoretical results, detailed algorithms, additional simulation results, and R codes, are available online.

Evaluation of localized region-based segmentation algorithms for CT-based delineation of organs at risk in radiotherapy.

Background and purposeIn radiation therapy, defining the precise borders of cancerous tissues and adjacent normal organs has a significant effect on the therapy outcome. Deformable models offer a unique and robust approach to medical image segmentation. The objective of this study was to investigate the reliability of segmenting organs-at-risk (OARs) using three well-known local region-based level-set techniques.Methods and materialsA total of 1340 non-enhanced and enhanced planning computed tomography (CT) slices of eight OARs (the bladder, rectum, kidney, clavicle, humeral head, femoral head, spinal cord, and lung) were segmented by using local region-based active contour, local Chan-Vese, and local Gaussian distribution models. Quantitative metrics, namely Hausdorff Distance (HD), Mean Absolute Distance (MAD), Dice coefficient (DC), Percentage Volume Difference (PVD) and Absolute Volumetric Difference (AVD), were adopted to measure the correspondence between detected contours and the manual references drawn by experts.ResultsThe results showed the feasibility of using local region-based active contour methods for defining six of the OARs (the bladder, kidney, clavicle, humeral head, spinal cord, and lung) when adequate intensity information is available. While the most accurate results were achieved for lung (DC = 0.94) and humeral head (DC = 0.92), a poor level of agreement (DC < 0.7) was obtained for both rectum and femur.ConclusionIncorporating local statistical information in level set methods yields to satisfactory results of OARs delineation when adequate intensity information exists between the organs. However, the complexity of adjacent organs and the lack of distinct boundaries would result in a considerable segmentation error.

Interactive GPU active contours for segmenting inhomogeneous objects

We present a segmentation software package primarily targeting medical and biological applications, with a high level of visual feedback and several usability enhancements over existing packages. Specifically, we provide a substantially faster GPU implementation of the local Gaussian distribution fitting energy model, which can segment inhomogeneous objects with poorly defined boundaries as often encountered in biomedical images. We also provide interactive brushes to guide the segmentation process in a semiautomated framework.The speed of our implementation allows us to visualize the active surface in real time with a built-in ray tracer, where users may halt evolution at any time step to correct implausible segmentation by painting new blocking regions or new seeds. Quantitative and qualitative validation is presented, demonstrating the practical efficacy of our interactive elements for a variety of real-world datasets.

Wealth management: Modeling the nonlinear dependence

This work aims at the development of an enhanced portfolio selection method, which is based on the classical portfolio theory proposed by Markowitz (1952) and incorporates the local Gaussian correlation model for optimization. This novel method of portfolio selection incorporates two assumptions: the non-linearity of returns and the empirical observation that the relation between assets is dynamic. By selecting ten assets from those available in Yahoo Finance from S&P500, between 1985 and 2015, the performance of the new proposed model was measured and compared to the model of portfolio selection of Markowitz (1952) . The results showed that the portfolios selected using the local Gaussian correlation model performed better than the traditional Markowitz (1952) method in 63% of the cases using block bootstrap and in 71% of the cases using the standard bootstrap. Comparing the calculated Sharpe ratios, the proposed model yielded a better adjusted risk-return in the majority of the cases studied.

A robust non-rigid point set registration method based on inhomogeneous Gaussian mixture models

In this paper, we propose a novel robust non-rigid point set registration method adopting a new probability model called inhomogeneous Gaussian mixture models (IGMM), where we regard one point set as the centroids of a Gaussian mixture model and the other point set as the data. The IGMM is defined by applying local features and Gaussian mixture models. Considering the local relationship among neighboring points is stable, a neighborhood structural descriptor, named as local shape context, is first presented. On the basis of local descriptors, we can obtain a measure of compatibility between local features in the point sets. Then, the similarity of the local structure of point neighborhoods can be calculated on the basis of the matching scores. Each Gaussian mixture component is assigned a different weight depending on the feature similarity, which differs from the traditional Gaussian mixture model where each Gaussian mixture component has the same weight. The proposed IGMM makes point pairs with more similar features have bigger probability to formulate a match, while in algorithms based on GMMs, all point pairs have the same probability to construct correspondence points. Finally, we support our claims through regularization theory and formulate registration as a likelihood maximization problem, which is solved by updating transformation parameters and outlier ratios using the expectation maximization algorithm. Extensive comparison and evaluation experiments on synthetic point-sets datasets demonstrate that the proposed approach is robust and achieves superior performance in the presence of non-rigid deformation, noise, outliers and occlusion. In addition, a number of experiments on real images reveal that our proposed algorithm is more applicable than state-of-the-art algorithms.

Multilevel Thresholding Method Based on Electromagnetism for Accurate Brain MRI Segmentation to Detect White Matter, Gray Matter, and CSF.

This work explains an advanced and accurate brain MRI segmentation method. MR brain image segmentation is to know the anatomical structure, to identify the abnormalities, and to detect various tissues which help in treatment planning prior to radiation therapy. This proposed technique is a Multilevel Thresholding (MT) method based on the phenomenon of Electromagnetism and it segments the image into three tissues such as White Matter (WM), Gray Matter (GM), and CSF. The approach incorporates skull stripping and filtering using anisotropic diffusion filter in the preprocessing stage. This thresholding method uses the force of attraction-repulsion between the charged particles to increase the population. It is the combination of Electromagnetism-Like optimization algorithm with the Otsu and Kapur objective functions. The results obtained by using the proposed method are compared with the ground-truth images and have given best values for the measures sensitivity, specificity, and segmentation accuracy. The results using 10 MR brain images proved that the proposed method has accurately segmented the three brain tissues compared to the existing segmentation methods such as K-means, fuzzy C-means, OTSU MT, Particle Swarm Optimization (PSO), Bacterial Foraging Algorithm (BFA), Genetic Algorithm (GA), and Fuzzy Local Gaussian Mixture Model (FLGMM).

Adaptive Critic Design with Local Gaussian Process Models

In this paper, local Gaussian process (GP) approximation is introduced to build the critic network of adaptive dynamic programming (ADP). The sample data are partitioned into local regions, and for each region, an individual GP model is utilized. The nearest local model is used to predict a given state-action point. With the two-phase value iteration method for a Gaussian-kernel (GK)-based critic network which realizes the update of the hyper-parameters and value functions simultaneously, fast value function approximation can be achieved. Combining this critic network with an actor network, we present a local GK-based ADP approach. Simulations were carried out to demonstrate the feasibility of the proposed approach.