Iterative Expectation Maximization Research Articles

A unified EM framework for estimation and inference of normal ogive item response models.

Normal ogive (NO) models have contributed substantially to the advancement of item response theory (IRT) and have become popular educational and psychological measurement models. However, estimating NO models remains computationally challenging. The purpose of this paper is to propose an efficient and reliable computational method for fitting NO models. Specifically, we introduce a novel and unified expectation-maximization (EM) algorithm for estimating NO models, including two-parameter, three-parameter, and four-parameter NO models. A key improvement in our EM algorithm lies in augmenting the NO model to be a complete data model within the exponential family, thereby substantially streamlining the implementation of the EM iteration and avoiding the numerical optimization computation in the M-step. Additionally, we propose a two-step expectation procedure for implementing the E-step, which reduces the dimensionality of the integration and effectively enables numerical integration. Moreover, we develop a computing procedure for estimating the standard errors (SEs) of the estimated parameters. Simulation results demonstrate the superior performance of our algorithm in terms of its recovery accuracy, robustness, and computational efficiency. To further validate our methods, we apply them to real data from the Programme for International Student Assessment (PISA). The results affirm the reliability of the parameter estimates obtained using our method.

Addressing dispersion in mis-measured multivariate binomial outcomes: A novel statistical approach for detecting differentially methylated regions in bisulfite sequencing data.

Motivated by a DNA methylation application, this article addresses the problem of fitting and inferring a multivariate binomial regression model for outcomes that are contaminated by errors and exhibit extra-parametric variations, also known as dispersion. While dispersion in univariate binomial regression has been extensively studied, addressing dispersion in the context of multivariate outcomes remains a complex and relatively unexplored task. The complexity arises from a noteworthy data characteristic observed in our motivating dataset: non-constant yet correlated dispersion across outcomes. To address this challenge and account for possible measurement error, we propose a novel hierarchical quasi-binomial varying coefficient mixed model, which enables flexible dispersion patterns through a combination of additive and multiplicative dispersion components. To maximize the Laplace-approximated quasi-likelihood of our model, we further develop a specialized two-stage expectation-maximization (EM) algorithm, where a plug-in estimate for the multiplicative scale parameter enhances the speed and stability of the EM iterations. Simulations demonstrated that our approach yields accurate inference for smooth covariate effects and exhibits excellent power in detecting non-zero effects. Additionally, we applied our proposed method to investigate the association between DNA methylation, measured across the genome through targeted custom capture sequencing of whole blood, and levels of anti-citrullinated protein antibodies (ACPA), a preclinical marker for rheumatoid arthritis (RA) risk. Our analysis revealed 23 significant genes that potentially contribute to ACPA-related differential methylation, highlighting the relevance of cell signaling and collagen metabolism in RA. We implemented our method in the R Bioconductor package called "SOMNiBUS."

Online state and unknown inputs estimation for nonlinear systems with particle filter based recursive expectation‐maximization algorithm

AbstractThe article presents an innovative approach to simultaneously estimate states and unknown inputs (UIs) in nonlinear systems using a particle filter (PF) based recursive expectation‐maximization (EM) algorithm. This method is distinct from traditional iterative EM algorithms. During the E‐step, it calculates the Q‐function recursively within the maximum likelihood framework, while the PF estimates the system states. The M‐step involves local maximization of the recursive Q‐function to online estimate the UIs. The effectiveness of the PF‐based recursive EM algorithm is demonstrated with a numerical example, and comparisons with the augmented state PF are made to highlight its advantages. Finally, the proposed algorithm is implemented in a real application for the estimation of the continuous fermentation process.

Enhancing water quality prediction for fluctuating missing data scenarios: A dynamic Bayesian network-based processing system to monitor cyanobacteria proliferation

Tackling the impact of missing data in water management is crucial to ensure the reliability of scientific research that informs decision-making processes in public health. The goal of this study is to ascertain the root causes associated with cyanobacteria proliferation under major missing data scenarios. For this purpose, a dynamic missing data management methodology is proposed using Bayesian Machine Learning for accurate surface water quality prediction of a river from Limia basin (Spain). The methodology used entails a sequence of analytical steps, starting with data pre-processing, followed by the selection of a reliable dynamic Bayesian missing value prediction system, leading finally to a supervised analysis of the behavioral patterns exhibited by cyanobacteria. For that, a total of 2,118,844 data points were used, with 205,316 (9.69 %) missing values identified. The machine learning testing showed the iterative structural expectation maximization (SEM) as the best performing algorithm, above the dynamic imputation (DI) and entropy-based dynamic imputation methods (EBDI), enhancing in some cases the accuracy of imputations by approximately 50 % in R2, RMSE, NRMSE, and logarithmic loss values. These findings can impact how data on water quality is being processed and studied, thus, opening the door for more reliable water management strategies that better inform public health decisions.

Non-rigid point set registration based on Gaussian mixture model with integrated feature divergence

PurposeThis paper aims to propose a robust method for non-rigid point set registration, using the Gaussian mixture model and accommodating non-rigid transformations. The posterior probabilities of the mixture model are determined through the proposed integrated feature divergence.Design/methodology/approachThe method involves an alternating two-step framework, comprising correspondence estimation and subsequent transformation updating. For correspondence estimation, integrated feature divergences including both global and local features, are coupled with deterministic annealing to address the non-convexity problem of registration. For transformation updating, the expectation-maximization iteration scheme is introduced to iteratively refine correspondence and transformation estimation until convergence.FindingsThe experiments confirm that the proposed registration approach exhibits remarkable robustness on deformation, noise, outliers and occlusion for both 2D and 3D point clouds. Furthermore, the proposed method outperforms existing analogous algorithms in terms of time complexity. Application of stabilizing and securing intermodal containers loaded on ships is performed. The results demonstrate that the proposed registration framework exhibits excellent adaptability for real-scan point clouds, and achieves comparatively superior alignments in a shorter time.Originality/valueThe integrated feature divergence, involving both global and local information of points, is proven to be an effective indicator for measuring the reliability of point correspondences. This inclusion prevents premature convergence, resulting in more robust registration results for our proposed method. Simultaneously, the total operating time is reduced due to a lower number of iterations.

Energy-based scatter estimation in clinical PET.

Scatter correction (SC) is essential in PET for accurate quantitative imaging. The state-of-the-art SC method is single-scatter simulation (SSS). Although this method is usually robust and accurate, it can fail in some situations, for example when there is motion between the CT and PET scans in PET/CT. Therefore, it is of interest to consider other SC methods. In this work, an energy-based scatter estimation (EBS) method is described in detail, tested in phantoms and patients, and compared to SSS. This version of EBS was developed for list-mode data from Biograph Vision-600 PET/CT scanner. EBS is based on digitized 2D energy histograms in each bin of a coarsely sampled PET sinogram, either with or without time of flight (TOF). The histograms are modeled as a noisy realization of a linear combination of nine basis functions whose parameters were derived from a measurement of the 511-keV photopeak spectrum as well as Monte-Carlo simulations of the scattering process. EBS uses an iterative expectation maximization approach to determine the coefficients in the linear combination, and from this estimates the scatter. The investigation was restricted to 18 F-based PET data in which the acquired number of counts was similar to the levels seen in oncological whole-body PET/CT scans. To evaluate the performance, phantom scans were used that involved the NEMA NU2-2018 protocol, a slab phantom, an NU 2-1994 phantom, a cardiac phantom in an anthropomorphic chest phantom, and a uniformly-filled torso phantom with a bladder phantom slightly outside the axial field of view. Contrast recovery (CR) and other parameters were evaluated in images reconstructed with SSS and EBS. Furthermore, FDG PET scans of seven lung cancer patients were used in the evaluation. Standardized uptake values (SUV) based on SSS and EBS were compared in 27 lesions. EBS and SSS images were visually similar in all cases except the torso + bladder phantom, where the EBS was much closer to the expected uniform image. The NU2-2018 analysis indicated a 2% scatter residual in EBS images compared to 3% with SSS, and 10% higher background variability, which is a surrogate for image noise. The cardiac phantom scan showed that CR was 98.2% with EBS and 99.6% with SSS, and that the SSS sinogram had values greater than the net-true emission sinogram, indicating a slight overcorrection in the case of SSS. In the lesion SUV comparison in patient scans, EBS correlated strongly (R2 =0.9973) with SSS, and SUV based on EBS were systematically 0.1 SUV lower. In the case of the torso + bladder phantom portion, the SSS image of the torso + bladder phantom was 299% times hotter than expected in one area, due to scatter estimation error, compared to 16% colder with EBS. In evaluating clinically relevant parameters such as SUV in focal lesions, EBS and SSS give almost the same results. In phantoms, some scatter figures of merit were slightly improved by use of EBS, though an image variability figure of merit was slightly degraded. In typical oncological whole-body PET/CT, EBS may be a suitable replacement for SSS, especially when SSS fails due to technical problems during the scan.

Penalised estimation of partially linear additive zero-inflated Bernoulli regression models

We develop a practical and computationally efficient penalised estimation approach for partially linear additive models to zero-inflated binary outcome data. To facilitate estimation, B-splines are employed to approximate unknown nonparametric components. A two-stage iterative expectation-maximisation (EM) algorithm is proposed to calculate penalised spline estimates. The large-sample properties such as the uniform convergence and the optimal rate of convergence for functional estimators, and the asymptotic normality and efficiency for regression coefficient estimators are established. Further, two variance-covariance estimation approaches are proposed to provide reliable Wald-type inference for regression coefficients. We conducted an extensive Monte Carlo study to evaluate the numerical properties of the proposed penalised methodology and compare it to the competing spline method [Li and Lu. ‘Semiparametric Zero-Inflated Bernoulli Regression with Applications’, Journal of Applied Statistics, 49, 2845–2869]. The methodology is further illustrated by an egocentric network study.

Intersection of Perceived COVID-19 Risk, Preparedness, and Preventive Health Behaviors: Latent Class Segmentation Analysis.

COVID-19 risk perception is a factor that influences the pandemic spread. Understanding the potential behavioral responses to COVID-19, including preparedness and adoption of preventive measures, can inform interventions to curtail its spread. We assessed self-perceived and latent class analysis (LCA)-based risks of COVID-19 and their associations with preparedness, misconception, information gap, and preventive practices among residents of a densely populated city in Nigeria. We used data from a cross-sectional survey conducted among residents (N=140) of Onitsha, Nigeria, in March 2020, before the government-mandated lockdown. Using an iterative expectation-maximization algorithm, we applied LCA to systematically segment participants into the most likely distinct risk clusters. Furthermore, we used bivariate and multivariable logistic regression models to determine the associations among knowledge, attitude, preventive practice, perceived preparedness, misconception, COVID-19 information gap, and self-perceived and LCA-based COVID-19 risks. Most participants (85/140, 60.7%) had good knowledge and did not perceive themselves as at risk of contracting COVID-19. Three-quarters of the participants (102/137, 74.6%; P<.001) experienced COVID-19-related information gaps, while 62.9% (88/140; P=.04) of the participants had some misconceptions about the disease. Conversely, most participants (93/140, 66.4%; P<.001) indicated that they were prepared for the COVID-19 pandemic. The majority of the participants (94/138, 68.1%; P<.001) self-perceived that they were not at risk of contracting COVID-19 compared to 31.9% (44/138) who professed to be at risk of contracting COVID-19. Using the LCA, we identified 3 distinct risk clusters (P<.001), namely, prudent or low-risk takers, skeptics or high-risk takers, and carefree or very high-risk takers with prevalence rates (probabilities of cluster membership that represent the prevalence rate [γc]) of 47.5% (95% CI 40%-55%), 16.2% (95% CI 11.4%-20.9%), and 36.4% (95% CI 28.8%-43.9%), respectively. We recorded a significantly negative agreement between self-perceived risk and LCA-based segmentation of COVID-19 risk (κ=-0.218, SD 0.067; P=.01). Knowledge, attitude, and perceived need for COVID-19 information were significant predictors of COVID-19 preventive practices among the Onitsha city residents. The clustering patterns highlight the impact of modifiable risk behaviors on COVID-19 preventive practices, which can provide strong empirical support for health prevention policies. Consequently, clusters with individuals at high risk of contracting COVID-19 would benefit from multicomponent interventions delivered in diverse settings to improve the population-based response to the pandemic.

Estimation of IQI for AF Cooperative Single-Carrier Frequency Domain Equalization Systems Using Channel Decoder Feedback

The process of amplify-and-forward (AF) relaying is essential to the improvement of both current and future wireless communication standards. Nevertheless, significant performance loss may be posed by in-phase and quadrature imbalance (IQI) caused by defects in radio frequency components. Prior studies into this research problem were restricted to uncoded broadcasts, even though error-correcting codes are frequently used in real applications. To this purpose, we develop a novel approach applicable to the destination terminal for estimating and compensating for IQI that occurs at the source, relay, and destination terminals. The proposed approach is explored in the context of coded emissions of AF single-carrier frequency domain equalization (SC-FDE) systems. In contrast to other methods for mitigating this radio frequency deflection at each node, the proposed system estimates and compensates for all IQI parameters and channel impulse responses simultaneously. With the use of an iterative expectation–maximization (EM) process, a maximum-likelihood (ML) solution to the problem is computed. At each round, the soft information supplied by the channel decoder is employed to create the a posteriori expectations of the sent data symbols, which are then fed into the estimation process as if they were training symbols. In addition, we address how to use the estimated parameters to perform the task of data detection. The offered predictor and detector exchange soft information in a sequential process, boosting the overall system effectiveness. The simulation results show that the proposed method is not only practicable but superior to the established methods.

The hybrid approach—convolutional neural networks and expectation maximisation algorithm—for tomographic reconstruction of hyperspectral images

We present a simple, but novel, hybrid approach to hyperspectral data cube reconstruction from computed tomography imaging spectrometry (CTIS) images that sequentially combines neural networks and the iterative expectation maximisation (EM) algorithm. We train and test the ability of the method to reconstruct data cubes of 100 × 100 × 25 and 100 × 100 × 100 voxels, corresponding to 25 and 100 spectral channels, from simulated CTIS images generated by our CTIS simulator. The hybrid approach utilises the inherent strength of the Convolutional Neural Network (CNN) with regards to noise and its ability to yield consistent reconstructions and make use of the EM algorithm’s ability to generalise to spectral images of any object without training. The hybrid approach achieves better performance than both the CNNs and EM alone for seen (included in CNN training) and unseen (excluded from CNN training) cubes for both the 25- and 100-channel cases. For the 25 spectral channels, the improvements from CNN to the hybrid model (CNN + EM) in terms of the mean-squared errors are between 14 % and 26 %. For 100 spectral channels, the improvements between 19 % and 40 % are attained with the largest improvement of 40 % for the unseen data, to which the CNNs are not exposed during the training.

An EM Algorithm for Lebesgue-sampled State-space Continuous-time System Identification*

This paper concerns the identification of continuous-time systems in state-space form that are subject to Lebesgue sampling. Contrary to equidistant (Riemann) sampling, Lebesgue sampling consists of taking measurements of a continuous-time signal whenever it crosses fixed and regularly partitioned thresholds. The knowledge of the intersample behavior of the output data is exploited in this work to derive an expectation-maximization (EM) algorithm for parameter estimation of the state-space and noise covariance matrices. For this purpose, we use the incremental discrete-time equivalent of the system, which leads to EM iterations of the continuous-time state-space matrices that can be computed by standard filtering and smoothing procedures. The effectiveness of the identification method is tested via Monte Carlo simulations.

A Variational EM Acceleration for Efficient Clustering at Very Large Scales.

How can we efficiently find very large numbers of clusters C in very large datasets N of potentially high dimensionality D? Here we address the question by using a novel variational approach to optimize Gaussian mixture models (GMMs) with diagonal covariance matrices. The variational method approximates expectation maximization (EM) by applying truncated posteriors as variational distributions and partial E-steps in combination with coresets. Run time complexity to optimize the clustering objective then reduces from O(NCD) per conventional EM iteration to O(N'G2D) for a variational EM iteration on coresets (with coreset size N ' ≤ N and truncation parameter G ≪ C). Based on the strongly reduced run time complexity per iteration, which scales sublinearly with NC, we then provide a concrete, practically applicable, parallelized and highly efficient clustering algorithm. In numerical experiments on standard large-scale benchmarks we (A) show that also overall clustering times scale sublinearly with NC, and (B) observe substantial wall-clock speedups compared to already highly efficient recently reported results. The algorithm's sublinear scaling allows for applications at scales where alternative methods cease to be applicable. We demonstrate such very large-scale applicability using the YFCC100M benchmark, for which we realize with a GMM of up to 50.000 clusters an optimization of a data density model with up to 150 M parameters.

Semi-Blind Channel Estimation for RIS-Assisted MISO Systems Using Expectation Maximization

<bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Reconfigurable intelligent surface (RIS) is a passive antenna array composed of a large number of reflecting elements. In a RIS-assisted communication system, it is a challenging task to acquire accurate channel state information (CSI). In this paper, we propose a semi-blind channel estimation method for a RIS-assisted massive multiple-input single-output (MISO) system. Assuming a Gaussian</b> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <b>priori</b> </i> <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">on the data symbols, an iterative expectation maximization (EM)-based algorithm is developed to obtain the maximum likelihood (ML) estimate of the cascaded RIS channel. Different from existing pilot-based methods, the proposed semi-blind channel estimation method exploits the data symbols for channel estimation enhancement and only a fraction of full-pilot signaling overhead is required. Simulation results verify that the proposed method achieves significant improvement in the accuracy of the channel estimation while it noticeably reduces the training pilot overhead.</b>

Neural mixture models with expectation-maximization for end-to-end deep clustering

Any clustering algorithm must synchronously learn to model the clusters and allocate data to those clusters in the absence of labels. Mixture model-based methods model clusters with pre-defined statistical distributions and allocate data to those clusters based on the cluster likelihoods. They iteratively refine those distribution parameters and member assignments following the Expectation-Maximization (EM) algorithm. However, the cluster representability of such hand-designed distributions that employ a limited amount of parameters is not adequate for most real-world clustering tasks. In this paper, we realize mixture model-based clustering with a neural network where the final layer neurons, with the aid of an additional transformation, approximate cluster distribution outputs. The network parameters pose as the parameters of those distributions. The result is an elegant, much-generalized representation of clusters than a restricted mixture of hand-designed distributions. We train the network end-to-end via batch-wise EM iterations where the forward pass acts as the E-step and the backward pass acts as the M-step. In image clustering, the mixture-based EM objective can be used as the clustering objective along with existing representation learning methods. In particular, we show that when mixture-EM optimization is fused with consistency optimization, it improves the sole consistency optimization performance in clustering. Our trained networks outperform single-stage deep clustering methods that still depend on k-means, with unsupervised classification accuracy of 63.8% in STL10, 58% in CIFAR10, 25.9% in CIFAR100, and 98.9% in MNIST.

Cognitive Radios Equipped With Modulation and STBC Recognition Over Coded Transmissions

Signal recognition has recently emerged as a key ingredient for cognitive radios with defense and industrial uses. This letter area encompasses the recognition of a broad range of transmission aspects such as modulation format, space-time mapping, channel coding form, central frequency, and data rate. Each of these aspects has been extensively researched in the literature. Only a few works addressed co-recognition. To the best of the authors’ knowledge, there is a single study that is dedicated to the recognition of combined modulation and space-time block coding (STBC), with the constraints of having more receive antennas than transmit antennas and operating over frequency-flat channels. In this letter, we propose a novel algorithm that recognizes modulation and STBC simultaneously over unknown frequency-selective channels while relaxing the requirement of having more antennas at the receiver than at the transmitter. The mathematical treatments demonstrate how an iterative expectation-maximization strategy is simply used to create a maximum-likelihood solution for this problem. Additionally, we make use of soft information coupled with channel decoders to enhance the proposed algorithm’s recognition performance. The proposed design also incorporates the supplementary task of channel estimation as a part of its overall structure. According to the findings of the computational complexity analysis and simulation results, the proposed algorithm easily defeats the one documented in the literature.

Example-based color transfer with Gaussian mixture modeling

Color transfer, which plays a key role in image editing, has attracted noticeable attention recently. It has remained a challenge to date due to various issues such as time-consuming manual adjustments and prior segmentation issues. In this paper, we propose to model color transfer under a probability framework and cast it as a parameter estimation problem. In particular, we relate the transferred image with the example image under the Gaussian Mixture Model (GMM) and regard the transferred image color as the GMM centroids. We employ the Expectation-Maximization (EM) algorithm (E-step and M-step) for optimization. To better preserve gradient information, we introduce a Laplacian based regularization term to the objective function at the M-step which is solved by deriving a gradient descent algorithm. Given the input of a source image and an example image, our method is able to generate multiple color transfer results with increasing EM iterations. Extensive experiments show that our approach generally outperforms other competitive color transfer methods, both visually and quantitatively.

Conditionally Exponential Prior in Focal Near- and Far-Field EEG Source Localization via Randomized Multiresolution Scanning (RAMUS)

In this paper, we focus on the inverse problem of reconstructing distributional brain activity with cortical and weakly detectable deep components in non-invasive Electroencephalography. We consider a recently introduced hybrid reconstruction strategy combining a hierarchical Bayesian model to incorporate a priori information and the advanced randomized multiresolution scanning (RAMUS) source space decomposition approach to reduce modelling errors, respectively. In particular, we aim to generalize the previously extensively used conditionally Gaussian prior (CGP) formalism to achieve distributional reconstructions with higher focality. For this purpose, we introduce as a hierarchical prior, a general exponential distribution, which we refer to as conditionally exponential prior (CEP). The first-degree CEP corresponds to focality enforcing Laplace prior, but it also suffers from strong depth bias, when applied in numerical modelling, making the deep activity unrecoverable. We sample over multiple resolution levels via RAMUS to reduce this bias as it is known to depend on the resolution of the source space. Moreover, we introduce a procedure based on the physiological a priori knowledge of the brain activity to obtain the shape and scale parameters of the gamma hyperprior that steer the CEP. The posterior estimates are calculated using iterative statistical methods, expectation maximization and iterative alternating sequential algorithm, which we show to be algorithmically similar and to have a close resemblance to the iterative ell _1 and ell _2 reweighting methods. The performance of CEP is compared with the recent sampling-based dipole localization method Sequential semi-analytic Monte Carlo estimation (SESAME) in numerical experiments of simulated somatosensory evoked potentials related to the human median nerve stimulation. Our results obtained using synthetic sources suggest that a hybrid of the first-degree CEP and RAMUS can achieve an accuracy comparable to the second-degree case (CGP) while being more focal. Further, the proposed hybrid is shown to be robust to noise effects and compares well with the dipole reconstructions obtained with SESAME.

The ‘ramp filter’ artifact in filtered back projection is due to attenuation not ramp filtering

Artifactually decreased counts in regions of the left ventricle adjacent to intense splanchnic activity have been described in single photon emission computed tomography imaging and attributed to the side lobes of ramp filtering, a crucial step in filtered back projection. However, filtered back projection is based on a mathematical proof that makes no assumptions about the distribution of activity implying there is another cause for this artifact. Computer simulations of a left ventricle with varying intensity, proximity and size of adjacent splanchnic activity was created with and without attenuation. Both filtered back projection and an iterative expectation maximization algorithm were performed. Volume weighted bullseyes were generated then the ratio of average activity in regions in the anterior and inferior walls of the bullseye were calculated. In the absence of attenuation, there was no effect on uptake despite intense adjacent splanchnic activity. The effect of attenuation alone was mild but was greatly amplified by adjacent splanchnic uptake. This effect varied with the intensity, proximity and size of adjacent activity. Moving the attenuation to the apex of the left ventricle produced a paradoxical increase in counts to the inferior wall. The effect on iterative reconstruction was less pronounced than with filtered back projection and the paradoxical increase with attenuation at the apex did not occur. The ramp filter artifact in single photon emission computed tomography reconstruction is due to attenuation, not ramp filtering per se. Adjacent splanchnic activity can result in either an increase or decrease in counts. These effects are less pronounced and more consistent with iterative reconstruction.

An efficient penalized estimation approach for semiparametric linear transformation models with interval-censored data.

We consider efficient estimation of flexible transformation models with interval-censored data. To reduce the dimension of semiparametric models, the unknown monotone function is approximated via a monotone B-spline. A penalization technique is used to provide computationally efficient estimation of all parameters. To accomplish model fitting and inference, an easy to implement nested iterative expectation-maximization (EM) algorithm is developed for estimation, and a simple variance-covariance estimation approach is proposed which makes large-sample inference for the regression parameters possible. Theoretically, we show that the estimator of the unknown monotone increasing function achieves the optimal rate of convergence, and the estimators of the regression parameters are asymptotically normal and efficient under the appropriate selection of the order of the smoothing parameter and the knots of the spline space. The proposed penalized procedure is assessed through extensive numerical experiments and implemented in R package PenIC. The proposed methodology is further illustrated via a signal tandmobiel study.

Power of Error Correcting Codes for SFBC-OFDM Classification Over Unknown Channels

The development of intelligent radios in wireless applications is mainly driven by the growing need for higher data rates, along with constrained spectrum resources. An intelligent radio is one that can autonomously assess the communication environment and automatically update the communication parameters to achieve optimal performance. The problem of determining the type of space-frequency block coding (SFBC) for orthogonal frequency division multiplexing (OFDM) transmissions is one of the main tasks of an intelligent receiver. Previous approaches to this problem are restricted to uncoded communications; nevertheless, existing systems typically utilize error-correcting codes. This study develops a maximum-likelihood (ML) classifier that discriminates among SFBC-OFDM signals using the soft outputs of a channel decoder. The mathematical analysis shows that the maximization of the likelihood function can be carried out by employing an iterative expectation-maximization (EM) procedure. A channel estimator is also included in the proposed classifier as a vital step. The findings show that the classification performance of the proposed algorithm is considerably better than the classical classifiers reported in the literature, at the cost of an acceptable increase in computing complexity.