LR-based Methods Research Articles

Constructing Prediction Intervals Using the Likelihood Ratio Statistic

Statistical prediction plays an important role in many decision processes, such as university budgeting (depending on the number of students who will enroll), capital budgeting (depending on the remaining lifetime of a fleet of systems), the needed amount of cash reserves for warranty expenses (depending on the number of warranty returns), and whether a product recall is needed (depending on the number of potentially life-threatening product failures). In statistical inference, likelihood ratios have a long history of use for decision making relating to model parameters (e.g., in evidence-based medicine and forensics). We propose a general prediction method, based on a likelihood ratio (LR) involving both the data and a future random variable. This general approach provides a way to identify prediction interval methods that have excellent statistical properties. For example, if a prediction method can be based on a pivotal quantity, our LR-based method will often identify it. For applications where a pivotal quantity does not exist, the LR-based method provides a procedure with good coverage properties for both continuous or discrete-data prediction applications.

A Two-Branch Network Combined With Robust Principal Component Analysis for Hyperspectral Image Classification

Noise in hyperspectral images (HSIs) may degrade the HSI classification result. Robust principal component analysis (RPCA) is an excellent method to obtain low-rank (LR) representation of data and is widely used in image denoising and also in HSI classification. However, data are drawn as a union from multiple subspaces in HSIs, so LR subspace estimation (LRSE) is necessary when using RPCA, which is complicated and time-consuming. To solve this problem, this letter proposes a novel LR-based method for HSI classification called two-branch network combined with RPCA, which combines RPCA with a neural network. Specifically, both the LR component and the sparse component are preserved and used for feature extraction in two independent convolutional branches. This way, we can avoid information loss without using accurate LRSE. A concatenate operation and a pointwise convolution are then adopted to realize the feature fusion. Finally, fused features are constructed to indicate the ground truth of each pixel in the classification process. The proposed method constructs a convenient model for HSI classification by discarding the LRSE and combining denoising, feature extraction, feature fusion, and classification into an end-to-end network. The experimental results on three data sets demonstrate that the proposed method outperforms many state-of-the-art methods including ones based on LR representation and ones based on deep learning. In addition, it maintains good classification performance for the cases of small samples and class imbalance.

Prediction of the diet energy digestion using kernel extreme learning machine: A case study with Holstein dry cows

In order to effectively evaluate the diet nutritional and feeding value, it is essential to accurately predict the indicators of diet energy digestion of dairy cows, thus further optimizing feed formulation and improving feeding management. Traditional mathematical models used to predict the main indicators of diet energy digestion of dairy cows are usually based on linear regression (LR) method. However, as a typical parametric model, the LR-based method is limited by regression function assumption, and the inaccurate assumed function sometimes leads to the learned regression model biased from the ground-truth one. In this study, we propose a kernel extreme learning machine (KELM) technique to predict the indicators of Holstein dry cows' diet digestible energy (DE) and energy digestibility (ED). KELM is a typical non-parametric machine learning model, which does not require any specific assumptions about the regression function in advance. The learned modal by KELM can well fit the actual one only by learning the training sample data in most cases. To evaluate prediction accuracy effectively, we compared the KELM technique with traditional parametric prediction LR model and other commonly used non-parametric models such as radial basis function artificial neural network, support vector machine and standard extreme learning machine methods. The required sample data is obtained from actual feeding and digestion experiments. The prediction results indicate that the proposed KELM-based prediction technique is superior to other methods in most performance metrics for prediction of the DE and ED indicators of diet energy digestion of Holstein dry cows. In particular, it has higher prediction accuracy than traditional LR-based prediction method, and can predict DE and ED better under small samples conditions. The developed KELM-based prediction model may be utilized to provide key decision support information to animal nutrition experts, livestock farmers and feed suppliers. The presented model is also exploited as a potential tool for accurate evaluation of dairy cows diet feeding effect.

Hyperspectral Image Denoising via Subspace Low-rank Representation and Spatial–spectral Total Variation

Abstract Hyperspectral images (HSIs) acquired actually often contain various types of noise, such as Gaussian noise, impulse noise, and dead lines. On the basis of land covers, the spectral vectors in HSI can be separated into different classifications, which means the spectral space can be regarded as a union of several low-rank (LR) subspaces rather than a single LR subspace. Recently, LR constraint has been widely applied for denoising HSI. However, those LR-based methods do not constrain the intrinsic structure of spectral space. And these methods cannot make better use of the spatial or spectral features in an HSI cube. In this article, a framework named subspace low-rank representation combined with spatial‐spectral total variation regularization (SLRR-SSTV) is proposed for HSI denoising, where the SLRR is introduced to more precisely satisfy the low-rank property of spectral space, and the SSTV regularization is involved for the spatial and spectral smoothness enhancement. An inexact augmented Lagrange multiplier method by alternative iteration is employed for the SLRR-SSTV model solution. Both simulated and real HSI experiment results demonstrate that the proposed method can achieve a state-of-the-art performance in HSI denoising.

Double Structured Nuclear Norm-Based Matrix Decomposition for Saliency Detection

Saliency detection aims at identifying the most important and informative area in a scene. Recently low rank matrix recovery (LR) theory becomes an effective tool for saliency detection. The existing LR-based methods all work under the popular low rank and sparsity pursuit framework and perform well for images with small or homogeneous objects. However, if the image is with heterogeneous objects, the sparsity property of the object cannot be guaranteed. Moreover, as a useful tool for depicting a spatially structured matrix variable, nuclear norm (corresponding to the low rank) considers only the global structure but overlooks the inherent local structure of the data. We address these problems by proposing a double structured nuclear norm-based matrix decomposition (DSNMD) model for saliency detection. In the model, a tree-structured nuclear (TSN) norm is firstly introduced to constraint both the background and foreground regions. We also empirically demonstrate that TSN norm provides stronger performance at capturing the underlying structural information of the image regions including global structure, local structure, and internal structure of each node of the tree, and it deservedly inherits the advantages of both nuclear norm and sparsity-related norms (e.g., $\ell _{1}$ -norm, group sparsity norm) for saliency detection. Comprehensive evaluations on six benchmark datasets indicate that our method universally surpasses state-of-the-art unsupervised methods and performs favorably against supervised approaches.

Spatial–Spectral Total Variation Regularized Low-Rank Tensor Decomposition for Hyperspectral Image Denoising

Several bandwise total variation (TV) regularized low-rank (LR)-based models have been proposed to remove mixed noise in hyperspectral images (HSIs). These methods convert high-dimensional HSI data into 2-D data based on LR matrix factorization. This strategy introduces the loss of useful multiway structure information. Moreover, these bandwise TV-based methods exploit the spatial information in a separate manner. To cope with these problems, we propose a spatial–spectral TV regularized LR tensor factorization (SSTV-LRTF) method to remove mixed noise in HSIs. From one aspect, the hyperspectral data are assumed to lie in an LR tensor, which can exploit the inherent tensorial structure of hyperspectral data. The LRTF-based method can effectively separate the LR clean image from sparse noise. From another aspect, HSIs are assumed to be piecewisely smooth in the spatial domain. The TV regularization is effective in preserving the spatial piecewise smoothness and removing Gaussian noise. These facts inspire the integration of the LRTF with TV regularization. To address the limitations of bandwise TV, we use the SSTV regularization to simultaneously consider local spatial structure and spectral correlation of neighboring bands. Both simulated and real data experiments demonstrate that the proposed SSTV-LRTF method achieves superior performance for HSI mixed-noise removal, as compared to the state-of-the-art TV regularized and LR-based methods.

Synergistic Operation of Electricity and Natural Gas Networks via ADMM

The increasing growth in the installation of natural-gas fired units has raised necessitates on synergy between the electricity and natural gas networks. This paper discusses how synergistic operation of electricity and natural gas networks can be achieved in a distributed fashion using alternating direction method of multipliers (ADMM). A standard ADMM approach and a consensus-based ADMM approach are developed, respectively, to solve the gas-electric integrated optimal power flow problem with and without a coordination operator. In both cases, the optimization formulation for each operator is modeled, and the solution procedure as well as data exchange among multiple decision-makers are explained. Case studies on both small and large gas-electric integrated systems show that the two ADMM-based distributed approaches have significant efficiencies over the traditional Lagrange relaxation (LR) and augmented LR-based methods.

Fast Superpixel Based Subspace Low Rank Learning Method for Hyperspectral Denoising

Sequential data, such as video frames and event data, have been widely applied in the real-world. As a special kind of sequential data, hyperspectral images (HSIs) can be regarded as a sequence of 2-D images in the spectral dimension, which can be effectively utilized for distinguishing different land-covers according to the spectral sequences. This paper presents a novel noise reduction method based on superpixel-based subspace low rank representation for hyperspectral imagery. First, under the framework of a linear mixture model, the original hyperspectral cube is assumed to be low rank in the spectral domain, which could be represented by decomposing HSI data into two sub-matrices of lower ranks. Meanwhile, due to the high correlation of neighboring pixels, the spectra within each neighborhood would also promote low rankness, and the local spatial low rankness could be exploited by enforcing the nuclear norm within superpixel-based regions in the decomposed subspace. The superpixels are easily and effectively generated by utilizing state-of-the-art superpixel segmentation algorithms in the first principal component of the original HSI. Moreover, benefiting from the subspace decomposition, the proposed method has an overwhelming superiority in computational cost than the state-of-the-art LR-based methods. The final model could be efficiently solved by the augmented Lagrangian method. Experimental results on simulated and real hyperspectral data sets validate that the proposed method produces superior performance than other state-of-the-art denoising methods in terms of quantitative assessment and visual quality.

Salient object detection via spectral graph weighted low rank matrix recovery

A novel saliency detection method via spectral graph (SG) weighted low rank matrix recovery (LR) is presented in this paper. The location, color, and boundary priors are exploited in many LR-based saliency detection methods. However, these priors do not work well when the salient objects are far away from image center, especially when the background is complicated and has low contrast with objects. Because spectral graph contains rich image contrast, it is used as an efficient weight to obtain a much reasonable high-level prior in the proposed LR-based saliency model. Compared with previous LR-based methods, low rank matrix and sparse matrix rather than only sparse matrix are used to calculate the final saliency by an integration function and an activation function. The numerical and visual results on four challenging salient object datasets show that our method performs competitively for salient object detection task against some recent state-of-the-art algorithms.

Likelihood ratio meta-analysis: New motivation and approach for an old method

A 95% confidence interval (CI) in an updated meta-analysis may not have the expected 95% coverage. If a meta-analysis is simply updated with additional data, then the resulting 95% CI will be wrong because it will not have accounted for the fact that the earlier meta-analysis failed or succeeded to exclude the null. This situation can be avoided by using the likelihood ratio (LR) as a measure of evidence that does not depend on type-1 error. We show how an LR-based approach, first advanced by Goodman, can be used in a meta-analysis to pool data from separate studies to quantitatively assess where the total evidence points. The method works by estimating the log-likelihood ratio (LogLR) function from each study. Those functions are then summed to obtain a combined function, which is then used to retrieve the total effect estimate, and a corresponding ‘intrinsic’ confidence interval. Using as illustrations the CAPRIE trial of clopidogrel versus aspirin in the prevention of ischemic events, and our own meta-analysis of higher potency statins and the risk of acute kidney injury, we show that the LR-based method yields the same point estimate as the traditional analysis, but with an intrinsic confidence interval that is appropriately wider than the traditional 95% CI. The LR-based method can be used to conduct both fixed effect and random effects meta-analyses, it can be applied to old and new meta-analyses alike, and results can be presented in a format that is familiar to a meta-analytic audience.

Native and non-native class discrimination using speech rhythm- and auditory-based cues

In recent years, the use of rhythm-based features in speech processing systems has received growing interest. This approach uses a wide array of rhythm metrics that have been developed to capture speech timing differences between and within languages. However, the reliability of rhythm metrics is being increasingly called into question. In this paper, we propose two modifications to this approach. First, we describe a model that is based on auditory cues that simulate the external, middle and inner parts of the ear. We evaluate this model by performing experiments to discriminate between native and non-native Arabic speech. Data are from the West Point Arabic Speech Corpus; testing is done on standard classifiers based on Gaussian Mixture Models (GMMs), Support Vector Machines (SVMs) and a hybrid GMM/SVM. Results show that the auditory-based model consistently outperforms a traditional rhythm-metric approach that includes both duration- and intensity-based metrics. Second, we propose a framework that combines the rhythm metrics and the auditory-based cues in the context of a Logistic Regression (LR) method that can optimize feature combination. Further results show that the proposed LR-based method improves performance over the standard classifiers in the discrimination between the native and non-native Arabic speech.

Lattice Reduction-Based MIMO Iterative Receiver Using Randomized Sampling

For iterative detection and decoding (IDD) in multiple-input multiple-output (MIMO) systems, although the maximum a posteriori probability (MAP) detector is desirable in terms of performance, it is difficult to be employed due to its prohibitively high complexity as an exhaustive search is used. In this paper, a lattice reduction (LR)-based MIMO detection method is studied to achieve near MAP performance with reasonably low complexity for IDD. The a priori information (API), which is available from a soft-input soft-output (SISO) decoder, is taken into account to generate a list with a randomized successive interference cancellation (SIC) method. More specifically, a joint Gaussian distribution is used to convert the API into the LR domain and a modified sampling distribution, which was originally adopted for near optimal LR-based detection in non-IDD MIMO systems, is derived for random sampling to build a list of candidate vectors of high a posteriori probability (APP) with low complexity. It is shown that the IDD receiver with the proposed method outperforms those with the conventional LR-based methods, where no API is taken into account to build a list. Furthermore, the trade-off between performance and complexity is exploited with varying list length.

Classification of Glass Fragments Based on Elemental Composition and Refractive Index*

The aim of this study was to assess the efficiency of likelihood ratio (LR)-based measures when they are applied to solving various classification problems for glass objects which are described by elemental composition, and refractive index (RI) values, and compare LR-based methods to other classification methods such as support vector machines (SVM) and naïve Bayes classifiers (NBC). One hundred and fifty-three glass objects (23 building windows, 25 bulbs, 32 car windows, 57 containers, and 16 headlamps) were analyzed by scanning electron microscopy coupled with an energy dispersive X-ray spectrometer. Refractive indices for building and car windows were measured before (RI(b)), and after (RI(a)) an annealing process. The proposed scheme for glass fragment(s) classification demonstrates some efficiency, although the classification of car windows (c) and building windows (w) must be treated carefully. This is because of their very similar elemental content. However, a combination of elemental content and information on the change in RI during annealing (DeltaRI = RI(a)-RI(b)) gave very promising results. A LR model for the classification of glass fragments into use-type categories for forensic purposes gives slightly higher misclassification rates than SVM and NBC. However, the observed differences between results obtained by all three approaches were very similar, especially when applied to the car window and building window classification problem. Therefore, the LR model can be recommended because of the ease of interpretation of LR-based measures of certainty.

Comparisons of Approximate Confidence Intervals for Distributions Used in Life-Data Analysis

This article evaluates the accuracy of approximate confidence intervals for parameters and quantiles of the smallest extreme value and normal distributions. The findings also apply to the Weibull and the lognormal distributions. The interval estimates are based on (a) the asymptotic normality of the maximum likelihood estimator, (b) the asymptotic x 2 distribution of the likelihood ratio (LR) statistic, (c) a mean and variance correction to the signed square roots of the LR statistic, and (d) the Bartlett correction to the LR statistic. The extensive Monte Carlo results about true error probabilities and average lengths under various degrees of censoring show advantages of the LR-based intervals. For complete or moderately censored samples, the mean and variance correction to the LR statistic gives nearly exact and symmetric error probabilities. In small samples with heavy censoring, the Bartlett correction tends to give conservative error probabilities, whereas the uncorrected LR interval is often anticonservative. The results also indicate that LR-based methods have longer interval lengths than intervals based on the asymptotic normality of the maximum likelihood estimator.

Comparisons of Approximate Confidence Intervals for Distributions Used in Life-Data Analysis

This article evaluates the accuracy of approximate confidence intervals for parameters and quantiles of the smallest extreme value and normal distributions. The findings also apply to the Weibull and the lognormal distributions. The interval estimates are based on (a) the asymptotic normality of the maximum likelihood estimator, (b) the asymptotic x 2 distribution of the likelihood ratio (LR) statistic, (c) a mean and variance correction to the signed square roots of the LR statistic, and (d) the Bartlett correction to the LR statistic. The extensive Monte Carlo results about true error probabilities and average lengths under various degrees of censoring show advantages of the LR-based intervals. For complete or moderately censored samples, the mean and variance correction to the LR statistic gives nearly exact and symmetric error probabilities. In small samples with heavy censoring, the Bartlett correction tends to give conservative error probabilities, whereas the uncorrected LR interval is often anticonservative. The results also indicate that LR-based methods have longer interval lengths than intervals based on the asymptotic normality of the maximum likelihood estimator.