Maximization Algorithm For Estimation Research Articles

Dynamic Expectation Maximization Algorithm for Estimation of Linear Systems with Colored Noise

The free energy principle from neuroscience has recently gained traction as one of the most prominent brain theories that can emulate the brain’s perception and action in a bio-inspired manner. This renders the theory with the potential to hold the key for general artificial intelligence. Leveraging this potential, this paper aims to bridge the gap between neuroscience and robotics by reformulating an FEP-based inference scheme—Dynamic Expectation Maximization—into an algorithm that can perform simultaneous state, input, parameter, and noise hyperparameter estimation of any stable linear state space system subjected to colored noises. The resulting estimator was proved to be of the form of an augmented coupled linear estimator. Using this mathematical formulation, we proved that the estimation steps have theoretical guarantees of convergence. The algorithm was rigorously tested in simulation on a wide variety of linear systems with colored noises. The paper concludes by demonstrating the superior performance of DEM for parameter estimation under colored noise in simulation, when compared to the state-of-the-art estimators like Sub Space method, Prediction Error Minimization (PEM), and Expectation Maximization (EM) algorithm. These results contribute to the applicability of DEM as a robust learning algorithm for safe robotic applications.

Estimating basis functions in massive fields under the spatial mixed effects model

AbstractSpatial prediction is commonly achieved under the assumption of a Gaussian random field by obtaining maximum likelihood estimates of parameters, and then using the kriging equations to arrive at predicted values. For massive datasets, fixed rank kriging using the expectation–maximization algorithm for estimation has been proposed as an alternative to the usual but computationally prohibitive kriging method. The method reduces computation cost of estimation by redefining the spatial process as a linear combination of basis functions and spatial random effects. A disadvantage of this method is that it imposes constraints on the relationship between the observed locations and the knots. We develop an alternative method that utilizes the spatial mixed effects model, but allows for additional flexibility by estimating the range of the spatial dependence between the observations and the knots via an alternating expectation conditional maximization algorithm. Experiments show that our methodology improves estimation without sacrificing prediction accuracy while also minimizing the additional computational burden of extra parameter estimation. The methodology is applied to a temperature dataset archived by the United States National Climate Data Center, with improved results over previous methodology.

A second-generation virtual-pinhole PET device for enhancing contrast recovery and improving lesion detectability of a whole-body PET/CT scanner.

We have developed a second-generation virtual-pinhole (VP) positron emission tomography (PET) device that can position a flat-panel PET detector around a patient's body using a robotic arm to enhance the contrast recovery coefficient (CRC) and detectability of lesions in any region-of-interest using a whole-body PET/computed tomography (CT) scanner. We constructed a flat-panel VP-PET device using 32 high-resolution detectors, each containing a 4 4 MPPC array and 16 16 LYSO crystals of 1.0 1.0 3.0mm3 each. The flat-panel detectors can be positioned around a patient's body anywhere in the imaging field-of-view (FOV) of a Siemens Biograph 40 PET/CT scanner by a robotic arm. New hardware, firmware and software have been developed to support the additional detector signals without compromising a scanner's native functions. We stepped a 22 Na point source across the axial FOV of the scanner to measure the sensitivity profile of the VP-PET device. We also recorded the coincidence events measured by the scanner detectors and by the VP-PET detectors when imaging phantoms of different sizes. To assess the improvement in the CRC of small lesions, we imaged an elliptical torso phantom measuring 316 228 162mm3 that contains spherical tumors with diameters ranging from 3.3 to 11.4mm with and without the VP-PET device. Images were reconstructed using a list mode Maximum-Likelihood Estimation-Maximization algorithm implemented on multiple graphics processing units (GPUs) to support the unconventional geometries enabled by a VP-PET system. The mean and standard deviation of the CRC were calculated for tumors of different sizes. Monte Carlo simulation was also conducted to image clusters of lesions in a torso phantom using a PET/CT scanner alone or the same scanner equipped with VP-PET devices. Receiver operating characteristic (ROC) curves were analyzed for three system configurations to evaluate the improvement in lesion detectability by the VP-PET device over the native PET/CT scanner. The repeatability in positioning the flat-panel detectors using a robotic arm is better than 0.15mm in all three directions. Experimental results show that the average CRC of 3.3, 4.3, and 6.0mm diameter tumors was 0.82%, 2.90%, and 5.25%, respectively, when measured by the native scanner. The corresponding CRC was 2.73%, 6.21% and 10.13% when imaged by the VP-PET insert device with the flat-panel detector under the torso phantom. These values may be further improved to 4.31%, 9.65% and 18.01% by a future dual-panel VP-PET insert device if DOI detectors are employed to triple its detector efficiency. Monte Carlo simulation results show that the tumor detectability can be improved by a VP-PET device that has a single flat-panel detector. The improvement is greater if the VP-PET device employs a dual-panel design. We have developed a prototype flat-panel VP-PET device and integrated it with a clinical PET/CT scanner. It significantly enhances the contrast of lesions, especially for those that are borderline detectable by the native scanner, within regions-of-interest specified by users. Simulation demonstrated the enhancement in lesion detectability with the VP-PET device. This technology may become a cost-effective solution for organ-specific imaging tasks.

Subgroup Analysis of Treatment Effects for Misclassified Biomarkers with Time-to-Event Data

Summary Analysing subgroups defined by biomarkers is of increasing importance in clinical research. In many situations the biomarker is subject to misclassification error, meaning that the subgroups are identified with imperfect sensitivity and specificity. In these cases, it is improper to assume the Cox proportional hazards model for the subgroup-specific treatment effects for time-to-event data with respect to the true subgroups, since the survival distributions with respect to the diagnosed subgroups will not adhere to the proportional hazards assumption. This precludes the possibility of using simple adjustment procedures. Two approaches to modelling are considered; the corrected score approach and a method based on formally modelling the data as a mixture of Cox models using an expectation–maximization algorithm for estimation. The methods are comparable for moderate-to-large sample sizes, but the expectation–maximization algorithm performs better when there are 100 patients per group. An estimate of the overall population treatment effect is obtained through the interpretation of the hazard ratio as a concordance odds. The methods are illustrated on data from a renal cell cancer trial.

An automatic algorithm to exploit the symmetries of the system response matrix in positron emission tomography iterative reconstruction

Positron emission tomography (PET) iterative 3D reconstruction is a very computational demanding task. One of the main issues of the iterative reconstruction concerns the management of the system response matrix (SRM). The SRM models the relationship between the projection and the voxel space and its memory footprint can easily exceed hundreds of GB. Moreover, in order to make the reconstruction fast enough not to hinder its practical application, the SRM must be stored in the random access memory of the workstation used for the reconstruction. This issue is normally solved by implementing efficient storage schemes and by reducing the number of redundant patterns in the SRM through symmetries. However, finding a sufficient number of symmetries is often non-trivial and is typically performed using dedicated solutions that cannot be exported to different detectors and geometries. In this paper, an automatic approach to reduce the memory footprint of a pre-computed SRM is described. The proposed approach was named symmetry search algorithm (SSA) and consists in an algorithm that searches for some of the redundant patterns present in the SRM, leading to its lossy compression. This approach was built to detect translations, reflections and coordinates swap in voxel space. Therefore, it is particularly well suited for those scanners where some of the rotational symmetries are broken, e.g. small animal scanner where the modules are arranged in a polygonal ring made of few elements, and dual head planar PET systems. In order to validate this approach, the SSA is applied to the SRM of a preclinical scanner (the IRIS PET/CT). The data acquired by the scanner were reconstructed with a dedicated maximum likelihood estimation maximization algorithm with both the uncompressed and the compressed SRMs. The results achieved show that the information lost due to the SSA compression is negligible. Compression factors up to 52 when using the SSA together with manually inserted symmetries and up to 204 when using the SSA alone, can be obtained for the IRIS SRM. These results come without significant differences in the values and in the main quality metrics of the reconstructed images, i.e. spatial resolution and noise. Although the compression factors depend on the system considered, the SSA is applicable to any SRM and therefore it can be considered a general tool to reduce the footprint of a pre-computed SRM.

Clustering Directions Based on the Estimation of a Mixture of Von Mises-Fisher Distributions

Background:In the statistical analysis of directional data, the von Mises-Fisher distribution plays an important role to model unit vectors. The estimation of the parameters of a mixture of von Mises-Fisher distributions can be done through the Estimation-Maximization algorithm.Objective:In this paper we propose a dynamic clusters type algorithm based on the estimation of the parameters of a mixture of von Mises-Fisher distributions for clustering directions, and we compare this algorithm with the Estimation-Maximization algorithm. We also define the between-groups and within-groups variability measures to compare the solutions obtained with the algorithms through these measures.Results:The comparison of the clusters obtained with both algorithms is provided for a simulation study based on samples generated from a mixture of two Fisher distributions and for an illustrative example with spherical data.

A Web Service Reliability Prediction Using HMM and Fuzzy Logic Models

With the increasing popularity of using Service-Oriented Systems (SOS), the reliability is becoming a significant concern for SOS. SOS are mainly built by Web services, hence prediction of reliability of Web service(s) leads to major concern in SOS. In this paper, Hidden Markov Model (HMM) and Fuzzy logic prediction model are used to predict reliability of Web service(s). The experiments are often conducted on real time Web services. The maximum likelihood value in HMM are calculated by Estimation-Maximization algorithm. Viterbi algorithm is used to restore the hidden states in HMM. The throughput, response time, and successful invocation of Web service are used to form rules in Fuzzy logic model. This helps to model highly complex problems that have multi-dimensional data. These experimental results prove better prediction method as compared to other conventional methods.

Reliability Prediction of Web Services Using HMM and ANN Models

Service-oriented architecture (SOA) is an approach for constructing distributed business-driven frameworks. Reliability of service- oriented systems (SOS) relies on the Web services used and in addition Internet associations. Predicting reliability of Web service has turned into an imperative exploration issue. In this paper Hidden Markov Model (HMM) and Artificial Neural Network (ANN) are used to model the Web service failure model and predict Web services reliability. The forward-backward estimation-maximization algorithm is used to estimate the modeling parameters for HMM. Different methods of ANN like feed-forward, multilayer perceptron, and radial basis function neural networks are applied to predict the reliability. The accuracy for each model is calculated and the performance parameters of models are compared by considering Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) metrics.

A fast Monte Carlo expectation–maximization algorithm for estimation in latent class model analysis with an application to assess diagnostic accuracy for cervical neoplasia in women with atypical glandular cells

In this article, we use a latent class model (LCM) with prevalence modeled as a function of covariates to assess diagnostic test accuracy in situations where the true disease status is not observed, but observations on three or more conditionally independent diagnostic tests are available. A fast Monte Carlo expectation–maximization (MCEM) algorithm with binary (disease) diagnostic data is implemented to estimate parameters of interest; namely, sensitivity, specificity, and prevalence of the disease as a function of covariates. To obtain standard errors for confidence interval construction of estimated parameters, the missing information principle is applied to adjust information matrix estimates. We compare the adjusted information matrix-based standard error estimates with the bootstrap standard error estimates both obtained using the fast MCEM algorithm through an extensive Monte Carlo study. Simulation demonstrates that the adjusted information matrix approach estimates the standard error similarly with the bootstrap methods under certain scenarios. The bootstrap percentile intervals have satisfactory coverage probabilities. We then apply the LCM analysis to a real data set of 122 subjects from a Gynecologic Oncology Group study of significant cervical lesion diagnosis in women with atypical glandular cells of undetermined significance to compare the diagnostic accuracy of a histology-based evaluation, a carbonic anhydrase-IX biomarker-based test and a human papillomavirus DNA test.

Combined Polymorphisms in Oxidative Stress Genes Predict Coronary Artery Disease and Oxidative Stress in Coronary Angiography Patients

Oxidative stress has been implicated in all stages of atherosclerosis, but how inherited variations in oxidative stress genes influence the severity of cardiovascular disease is not known. We tested associations between polymorphisms in candidate oxidative stress genes, plasma oxidative stress biomarkers, and cardiovascular mortality in an angiography cohort. Single nucleotide polymorphisms (SNPs) across 15 genes were selected by linkage disequilibrium tagging. Genotyping was performed using customized arrayed primer extension micro-arrays, with automated genotype calling methods. Effects of SNPs and haplotypes on plasma oxidative stress and coronary artery disease (CAD) were estimated using a stochastic estimation maximization algorithm. Proportionate hazards analyses were used to determine effects of single and combined genetic markers on cardiovascular mortality risk, and on the following oxidative stress biomarkers: myeloperoxidase (MPO), nitrotyrosine, oxidized low-density lipoprotein, and antioxidant capacity. Oxidative stress gene SNPs associated with CAD were combined into an oxidative stress risk allele score, which predicted disease presence (1.5-fold risk increase per allele, P < 0.001). Combined risk alleles were also associated with elevated plasma MPO (P < 0.003), an oxidative stress biomarker that predicts cardiovascular mortality. Genetic markers that represent lifetime oxidative stress burden may implicate specific oxidative stress pathways in the pathogenesis of atherosclerosis, and offer therapeutic opportunities.

Autism spectrum disorders and fetal hypoxia in a population-based cohort: Accounting for missing exposures via Estimation-Maximization algorithm

BackgroundAutism spectrum disorders (ASD) are associated with complications of pregnancy that implicate fetal hypoxia (FH); the excess of ASD in male gender is poorly understood. We tested the hypothesis that risk of ASD is related to fetal hypoxia and investigated whether this effect is greater among males.MethodsProvincial delivery records (PDR) identified the cohort of all 218,890 singleton live births in the province of Alberta, Canada, between 01-01-98 and 12-31-04. These were followed-up for ASD via ICD-9 diagnostic codes assigned by physician billing until 03-31-08. Maternal and obstetric risk factors, including FH determined from blood tests of acidity (pH), were extracted from PDR. The binary FH status was missing in approximately half of subjects. Assuming that characteristics of mothers and pregnancies would be correlated with FH, we used an Estimation-Maximization algorithm to estimate HF-ASD association, allowing for both missing-at-random (MAR) and specific not-missing-at-random (NMAR) mechanisms.ResultsData indicated that there was excess risk of ASD among males who were hypoxic at birth, not materially affected by adjustment for potential confounding due to birth year and socio-economic status: OR 1.13, 95%CI: 0.96, 1.33 (MAR assumption). Limiting analysis to full-term males, the adjusted OR under specific NMAR assumptions spanned 95%CI of 1.0 to 1.6.ConclusionOur results are consistent with a weak effect of fetal hypoxia on risk of ASD among males. E-M algorithm is an efficient and flexible tool for modeling missing data in the studied setting.

Psychiatrists' Use of Shared Decision Making in the Treatment of Schizophrenia: Patient Characteristics and Decision Topics

Psychiatrists' Use of Shared Decision Making in the Treatment of Schizophrenia: Patient Characteristics and Decision Topics

Statistical choices can affect inferences about treatment efficacy: A case study from obsessive–compulsive disorder research

Longitudinal clinical trials in psychiatry have used various statistical methods to examine treatment effects. The validity of the inferences depends upon the different method’s assumptions and whether a given study violates those assumptions. The objective of this paper was to elucidate these complex issues by comparing various methods for handling missing data (e.g., last observation carried forward [LOCF], completer analysis, propensity-adjusted multiple imputation) and for analyzing outcome (e.g., end-point analysis, repeated-measures analysis of variance [RM-ANOVA], mixed-effects models [MEMs]) using data from a multi-site randomized controlled trial in obsessive–compulsive disorder (OCD). The trial compared the effects of 12 weeks of exposure and ritual prevention (EX/RP), clomipramine (CMI), their combination (EX/RP&CMI) or pill placebo in 122 adults with OCD. The primary outcome measure was the Yale-Brown Obsessive Compulsive Scale. For most comparisons, inferences about the relative efficacy of the different treatments were impervious to different methods for handling missing data and analyzing outcome. However, when EX/RP was compared to CMI and when CMI was compared to placebo, traditional methods (e.g., LOCF, RM-ANOVA) led to different inferences than currently recommended alternatives (e.g., multiple imputation based on estimation-maximization algorithm, MEMs). Thus, inferences about treatment efficacy can be affected by statistical choices. This is most likely when there are small but potentially clinically meaningful treatment differences and when sample sizes are modest. The use of appropriate statistical methods in psychiatric trials can advance public health by ensuring that valid inferences are made about treatment efficacy.

Latent Class Analysis With Sampling Weights

The authors illustrate how to perform maximum-likelihood estimation in latent class (LC) analysis when there are sampling weights. The methods are natural extensions of the approaches proposed by Clogg and Eliason (1987) and Magidson (1987) for dealing with sampling weights in the log-linear analysis of frequency tables. For the log-linear form of the LC model, the approach corresponds to a special case of Haberman's (1979) log-linear LC model with cell weights. This approach can also be applied to the probability formulation of the LC model with cell weights, which can accommodate many indicators. The authors propose an efficient estimation-maximization algorithm for estimating the parameters for this formulation. A small simulation study shows that the probability estimates obtained by this approach compare favorably to other weighting approaches. Several empirical examples are provided to illustrate various possible weighting methods in LC analysis.

Statistical analysis and modelling of turbulent fluxes in the plasma of the L-2M stellarator and the FT-2 tokamak

A comparative analysis is done of data on turbulent fluxes measured in the edge plasma in the L-2M stellarator and the FT-2 tokamak. This analysis is performed using the estimation-maximization algorithm to determine finite mixtures of normal distributions that give the best fit to the probability distributions (PDFs) of the increments of turbulent fluxes. The resulting PDFs indicate non-Brownian motion of particles, and the weight of rare transport events (heavy tails of PDFs of fluxes) can be calculated. The number of the normal processes in model mixtures, as well as their weights in the PDFs of the increments of the turbulent flux, change during L–H transition in FT-2. Characteristically, the number of normal processes for the H-regime of FT-2 is the same as for the L-2M stellarator, and the parameters of Gaussians are also similar. This fact may be interpreted as an indirect indication that the L-2M stellarator operates in the mode of improved plasma confinement (which is consistent with the neoclassical theory for stellarators).

New possibilities for the mathematical modeling of turbulent transport processes in plasma

A new mathematical model is proposed for the probability distributions of the characteristics of the processes observed in turbulent plasmas. The model is based on formal theoretical considerations related to probabilistic limit theorems for a nonhomogeneous random walk and has the form of a finite mixture of Gaussian distributions. The reliability of the model is confirmed by the results of a statistical analysis of the experimental data on density fluctuations in high-temperature plasmas of the L-2M, LHD, and TJ-II stellarators and the local fluctuating flux in the TAU-1 linear device and in the edge plasma of the L-2M stellarator with the use of the estimation-maximization algorithm. It is shown that low-frequency structural turbulence in a magnetized plasma is related to non-Brownian transport, which is determined by the characteristic temporal and spatial scales of the ensembles of stochastic plasma structures. Mechanisms that could be responsible for the random nature of time samples of the local turbulent flux in TAU-1 are indicated. A new physical concept of the intermittence of plasma turbulent pulsations is developed on the basis of the statistical separation of mixtures in terms of the model proposed. The intermittence of plasma pulsations is shown to be associated with the generation of plasma structures (solitons and vortices) and their nonlinear interaction, as well as with their damping and drift.

A custom-made two-photon microscope and deconvolution system.

We describe in detail a custom-built two-photon microscope based on a modified confocal scanhead (Olympus Fluoview) and mode-locked Ti:sapphire laser (Coherent Mira 900). This system has internal detectors as well as external whole-field detection and an electrooptical modulator for blanking the beam on flyback and effecting fast changes in excitation intensity. This microscope can be used in deep, scattering samples for quantitative measurements with a wide range of fluorophores (GFP, fura, calcium green, calcium orange, fluo-3, DiI, DiO, fluorescein, rhodamine), for fluorescent photobleaching recovery and for uncaging. Images obtained with this system can be deconvolved with the Estimation Maximization algorithm using the program XCOSM (freeware available at: http://www.ibc.wustl.edu/bcl/ xcosm/).

Neural ensemble states in prefrontal cortex identified using a hidden Markov model with a modified EM algorithm

A modification to the standard estimation–maximization algorithm is presented, that allows the identification of neural ensemble states without predetermination of the number of states. Since the actual number of states a neural ensemble goes through in a given time period may vary from trial to trial, this represents a better description than using a predetermined, fixed number of states. The algorithm is used to identify ensemble states of simultaneously recorded neurons in the prefrontal cortex of behaving monkeys while they were freely viewing scenes containing multiple objects. We demonstrate that state transitions are correlated with behavioral and trial events.

Analysis of fragmented time series data using box-jenkins models

Throughout ecology, fragmented time series data have remained largely unanalyzed even though numerous methods exist for both structural and Box-Jenkins time series models. We evaluated four fragmented-data techniques for Box-Jenkins models using a data set of Peromyscus leucopus densities that spans 248 months and contains 15% missing data. We (1) approximated missing data using a linear interpolation between available observations (interpolation model), (2) estimated missing data according to the autocorrelation pattern identified with available data (estimation model), (3) forecasted missing data and re-estimated the model until the forecasts converged using an estimation maximization algorithm (maximization model), and (4) omitted missing data during parameter estimation (omission model). We compared overall model fit using the Schwarz information criterion and outlieranalysis. We found that the estimation and omission models fit the data better than the maximization model and far better than the interpolation model. In addition, the estimation model created more biologically realistic estimates of missing data than either the interpolation or maximization model. These results are directly applicable to multivariate Box-Jenkins time series models.

Input-output HMMs for sequence processing

We consider problems of sequence processing and propose a solution based on a discrete-state model in order to represent past context. We introduce a recurrent connectionist architecture having a modular structure that associates a subnetwork to each state. The model has a statistical interpretation we call input-output hidden Markov model (IOHMM). It can be trained by the estimation-maximization (EM) or generalized EM (GEM) algorithms, considering state trajectories as missing data, which decouples temporal credit assignment and actual parameter estimation. The model presents similarities to hidden Markov models (HMMs), but allows us to map input sequences to output sequences, using the same processing style as recurrent neural networks. IOHMMs are trained using a more discriminant learning paradigm than HMMs, while potentially taking advantage of the EM algorithm. We demonstrate that IOHMMs are well suited for solving grammatical inference problems on a benchmark problem. Experimental results are presented for the seven Tomita grammars, showing that these adaptive models can attain excellent generalization.