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At present, the traditional scoring methods generally utilize laboratory measurements to predict mortality. It results in difficulties of early mortality prediction in the rural areas lack of professional laboratorians and medical laboratory equipment. To improve the efficiency, accuracy, and applicability of mortality prediction in the remote areas, a novel mortality prediction method based on machine learning algorithms is proposed, which only uses non-invasive parameters readily available from ordinary monitors and manual measurement. A new feature selection method based on the Bayes error rate is developed to select valuable features. Based on non-invasive parameters, four machine learning models were trained for early mortality prediction. The subjects contained in this study suffered from general critical diseases including but not limited to cancer, bone fracture, and diarrhea. Comparison tests among five traditional scoring methods and these four machine learning models with and without laboratory measurement variables are performed. Only using the non-invasive parameters, the LightGBM algorithms have an excellent performance with the largest accuracy of 0.797 and AUC of 0.879. There is no apparent difference between the mortality prediction performance with and without laboratory measurement variables for the four machine learning methods. After reducing the number of feature variables to no more than 50, the machine learning models still outperform the traditional scoring systems, with AUC higher than 0.83. The machine learning approaches only using non-invasive parameters achieved an excellent mortality prediction performance and can equal those using extra laboratory measurements, which can be applied in rural areas and remote battlefield for mortality risk evaluation. Graphical abstract.

In the context of supervised learning, meta learning uses features, metadata and other information to learn about the difficulty, behavior, or composition of the problem. Using this knowledge can be useful to contextualize classifier results or allow for targeted decisions about future data sampling. In this paper, we are specifically interested in learning the Bayes error rate (BER) based on a labeled data sample. Providing a tight bound on the BER that is also feasible to estimate has been a challenge. Previous work[1] has shown that a pairwise bound based on the sum of Henze-Penrose (HP) divergence over label pairs can be directly estimated using a sum of Friedman-Rafsky (FR) multivariate run test statistics. However, in situations in which the dataset and number of classes are large, this bound is computationally infeasible to calculate and may not be tight. Other multi-class bounds also suffer from computationally complex estimation procedures. In this paper, we present a generalized HP divergence measure that allows us to estimate the Bayes error rate with log-linear computation. We prove that the proposed bound is tighter than both the pairwise method and a bound proposed by Lin [2]. We also empirically show that these bounds are close to the BER. We illustrate the proposed method on the MNIST dataset, and show its utility for the evaluation of feature reduction strategies. We further demonstrate an approach for evaluation of deep learning architectures using the proposed bounds., 15 pages, 12 figures, 1 table

This paper addresses the spectrum sensing problem in an orthogonal frequency-division multiplexing (OFDM) system based on machine learning. To adapt to signal-to-noise ratio (SNR) variations, we first formulate the sensing problem into a novel SNR-related multi-class classification problem. Then, we train a naive Bayes classifier (NBC), and propose a class-reduction assisted prediction method to reduce spectrum sensing time. We derive the performance bounds by translating the Bayes error rate into spectrum sensing error rate. Compared with the conventional methods, the proposed method is shown by simulation to achieve higher spectrum sensing accuracy, in particular at critical areas of low SNRs. It offers a potential solution to the hidden node problem.

Feature selection has become a crucial part of many classification problems in which high-dimensional datasets may contain tens of thousands of features. In this paper, we propose a novel feature selection method scoring the features through estimating the Bayes error rate based on kernel density estimation. Additionally, we update the scores of features dynamically by quantitatively interpreting the effects of feature relevance and redundancy in a new way. Distinguishing from the common heuristic applied by many feature selection methods, which prefers choosing features that are not relevant to each other, our approach penalizes only monotonically correlated features and rewards any other kind of relevance among features based on Spearman's rank correlation coefficient and normalized mutual information. We conduct extensive experiments on seventeen diverse classification benchmarks and the results show that our approach overperforms other seventeen popular state-of-the-art feature selection methods in most cases.

This paper examines the implications of the market selection hypothesis on the accuracy of the probabilities implied by equilibrium prices and on the “learning” mechanism of markets. I use the standard machinery of dynamic general equilibrium models to generate a rich class of probabilities, price probabilities, and discuss their properties. This class includes the Bayes’ rule and known non-Bayesian rules. If the prior support is well-specified, I prove that all members of this class perform as well as Bayes’ rule in terms of likelihood. If the prior support is misspecified in that the Bayesian prior does not converge, I demonstrate that some members of price probabilities significantly outperform Bayes’. Because these members are never worse and sometimes better than Bayes, my result challenges the prevailing opinion that Bayes’ rule is the only rational way to learn.

This study wishes to apply a non-parametric estimate of the Bayes Error Rate (BER) to current Air Force problems related to target classification. Whether they be neural networks, autoencoders, or other architectures, classifiers are commonly assessed through confusion matrices and associated statistics, or visualizations of feature spaces like t-SNE plots. However, these methods depend on the test data used to assess the performance of the network, not the robustness of the classifier itself. This research incorporates a different statistic that estimates the BER, or the probability of misclassification given some data, to serve as an upper bound for potential classifier performance. This estimate leverages a Friedman-Rafsky test statistic: the number of cross labels in a minimum-spanning tree (MST) through points in the feature space. The first part of this study examines the behavior of the BER estimate over a general learning process, such as different epochs of the training process in a neural network. The second part of the study examines whether certain factors affect the separability of synthetic aperture radar (SAR) images of targets of interest. Given the fact that it is often difficult and expensive to survey real targets and generate SAR images, 3-D CAD models are frequently used to generate synthetic SAR images. However, given that many resources are devoted to perfecting these models, this study applies the BER estimate to examine whether minute changes to CAD models affect separability in the image domain. The results seem to indicate that, if the topology of the target is maintained in the CAD domain, low-fidelity versions of targets (with 25% the number of faces of highly accurate models), exhibit separability and ability to be correctly classified identical to their high-fidelity counterparts. The BER estimation also shows promising applications in other domains, serving as a way to describe the underlying structure of feature spaces intuitively but effectively.

The problem of supervised classifying of a multivariate Gaussian Markov random field (GMRF) observation into one of two populations specified by different regression mean models is considered. We focus on a multivariate conditionally autoregressive model, a subclass of GMRF with parametrical structure proposed by Pettitt et al. (2002) and generalized by Jin et al. (2005). For complete parametric certainty and with fixed training sample locations, the formula of the Bayes error rate is derived. Plug-in Bayes discriminant function obtained by replacing the regression and scale parameters with their ML estimators in the Bayes discriminant function is investigated. The novel formulas for the actual error rate and the approximation of the expected error rate (AER) associated with plug-in Bayes discriminant function are derived. These results are multivariate generalizations of the univariate ones. A numerical analysis of the derived formulas is implemented for the bivariate conditionally autoregressive model sampling on a regular 2-dimensional unit spacing lattice with the neighborhood structure based on the Euclidean distance. A comparison of the proposed classifier performance for different parametric structures of populations is done by studying the accuracy of the derived AER. Finally, the influence of the neighborhood order on the accuracy of the derived AER is examined.

We propose a supervised linear dimensionality reduction algorithm.The algorithm reduces the dimensionality of data to K1 for the K-class problem.The linearly reduced data is well-suited for Bayesian classification.Experiments on UCI datasets are performed for the proposed and existing algorithms.The applicability of the algorithm to flow meter diagnostics is also demonstrated. Supervised linear dimensionality reduction (LDR) performed prior to classification often improves the accuracy of classification by reducing overfitting and removing multicollinearity. If a Bayes classifier is to be used, then reduction to a dimensionality of K1 is necessary and sufficient to preserve the classification information in the original feature space for the K-class problem. However, most of the existing algorithms provide no optimal dimensionality to which to reduce the data, thus classification information can be lost in the reduced space if K1 dimensions are used. In this paper, we present a novel LDR technique to reduce the dimensionality of the original data to K1, such that it is well-primed for Bayesian classification. This is done by sequentially constructing linear classifiers that minimise the Bayes error via a gradient descent procedure, under an assumption of normality. We experimentally validate the proposed algorithm on 10 UCI datasets. Our algorithm is shown to be superior in terms of the classification accuracy when compared to existing algorithms including LDR based on Fishers criterion and the Chernoff criterion. The applicability of our algorithm is then demonstrated by employing it in diagnosing the health states of 2 ultrasonic flow meters. As with the UCI datasets, the proposed algorithm is found to have superior performance to the existing algorithms, achieving classification accuracies of 99.4% and 97.5% on the two flow meters. Such high classification accuracies on the flow meters promise significant cost benefits in oil and gas operations.

예이츠의 작품은 다시 찾은 시공과 재창조된 시공에 존재한다. 창조된 시공은 현대시대에서 음유시인의 역할을 재상상함으로써 자신을 위해 만든 것이다. 1937년 환상록을 완성함으로써 그의 작품은 전통적인 영원성의 시간개념(일순간 인식된 모든 시간)을 반영하기 시작할 뿐 아니라, 『창유리에 쓰인 말』과 『연옥』에서 보이는 현세적인 시간과 영원한 시간 사이에 존재하는 초자연적 시간도 반영한다. 이 초자연적 시간은 보통 우리가 살아가는 시간보다 더 유동적이다.

The Naive Bayes (NB) classifier is a popular classifier for text classification problems due to its simple, flexible framework and its reasonable performance. In this paper, we present how to effectively utilize negative class information to improve NB classification. As opposed to information retrieval, supervised learning based text classification already obtains class information, a negative class as well as a positive class, from a labeled training dataset. Since the negative class can also provide significant information to improve the NB classifier, the negative class information is applied to the NB classifier through two phases of indexing and class prediction tasks. As a result, the new classifier using the negative class information consistently performs better than the traditional multinomial NB classifier.

We proposed an approach to error recovery that uses the concepts of task stratification and error classification. In our method, errors are classified according to the estimated cause into several categories, such as modeling and planning errors. When an error is classified correctly, this increases the probability that the most suitable recovery is performed. In this paper, we describe a procedure for error categorization.

We derive a linear classifier for heteroscedastic linear discriminant analysis.The proposed scheme efficiently minimises the Bayes error for binary classification.A local neighbourhood search is also proposed for non-normal distributions.The proposed schemes are experimentally validated on twelve datasets. Under normality and homoscedasticity assumptions, Linear Discriminant Analysis (LDA) is known to be optimal in terms of minimising the Bayes error for binary classification. In the heteroscedastic case, LDA is not guaranteed to minimise this error. Assuming heteroscedasticity, we derive a linear classifier, the Gaussian Linear Discriminant (GLD), that directly minimises the Bayes error for binary classification. In addition, we also propose a local neighbourhood search (LNS) algorithm to obtain a more robust classifier if the data is known to have a non-normal distribution. We evaluate the proposed classifiers on two artificial and ten real-world datasets that cut across a wide range of application areas including handwriting recognition, medical diagnosis and remote sensing, and then compare our algorithm against existing LDA approaches and other linear classifiers. The GLD is shown to outperform the original LDA procedure in terms of the classification accuracy under heteroscedasticity. While it compares favourably with other existing heteroscedastic LDA approaches, the GLD requires as much as 60 times lower training time on some datasets. Our comparison with the support vector machine (SVM) also shows that, the GLD, together with the LNS, requires as much as 150 times lower training time to achieve an equivalent classification accuracy on some of the datasets. Thus, our algorithms can provide a cheap and reliable option for classification in a lot of expert systems.

The Naive Bayes approximation (NBA) and associated classifier are widely used and offer robust performance across a large spectrum of problem domains. As it depends on a very strong assumption--independence among features--this has been somewhat puzzling. Various hypotheses have been put forward to explain its success and many generalizations have been proposed. In this paper we propose a set of "local" error measures--associated with the likelihood functions for subsets of attributes and for each class--and show explicitly how these local errors combine to give a "global" error associated to the full attribute set. By so doing we formulate a framework within which the phenomenon of error cancelation, or augmentation, can be quantified and its impact on classifier performance estimated and predicted a priori. These diagnostics allow us to develop a deeper and more quantitative understanding of why the NBA is so robust and under what circumstances one expects it to break down. We show how these diagnostics can be used to select which features to combine and use them in a simple generalization of the NBA, applying the resulting classifier to a set of real world data sets.

We develop a Bayes factor-based approach for the design of non-inferiority clinical trials with a focus on controlling type I error and power. Historical data are incorporated in the Bayesian design via the power prior discussed in Ibrahim and Chen (Stat Sci 15:46–60, 2000). The properties of the proposed method are examined in detail. An efficient simulation-based computational algorithm is developed to calculate the Bayes factor, type I error, and power. The proposed methodology is applied to the design of a non-inferiority medical device clinical trial.

Classifier chains are among the most successful methods in multi-label classification due to their simplicity and promising performance. However the standard versions of classifier chains described in the literature do not usually perform feature selection. In this paper we propose an algorithm CCnet which is a combination of classifier chains and elastic-net regularization. An important advantage of the CCnet is that selection of the relevant features in an integral element of the learning process. We show the stability of our algorithm and analyse the generalization error bound. The difference between generalization error and empirical error is bounded by a term which scales as n − 1 / 2 , where n is a size of a training data. It follows from experiments that the proposed algorithm outperforms the standard versions of classifier chains as well as other state-of-the-art methods. We also show that the feature selection is stable with respect to the order of fitting the models in the chain.

Linear discriminant analysis (LDA) is a well-known classification technique that enjoyed great success in practical applications. Despite its effectiveness for traditional low-dimensional problems, extensions of LDA are necessary in order to classify high-dimensional data. Many variants of LDA have been proposed in the literature. However, most of these methods do not fully incorporate the structure information among predictors when such information is available. In this paper, we introduce a new high-dimensional LDA technique, namely graph-based sparse LDA (GSLDA), that utilizes the graph structure among the features. In particular, we use the regularized regression formulation for penalized LDA techniques, and propose to impose a structure-based sparse penalty on the discriminant vector β . The graph structure can be either given or estimated from the training data. Moreover, we explore the relationship between the within-class feature structure and the overall feature structure. Based on this relationship, we further propose a variant of our proposed GSLDA to utilize effectively unlabeled data, which can be abundant in the semi-supervised learning setting. With the new regularization, we can obtain a sparse estimate of β and more accurate and interpretable classifiers than many existing methods. Both the selection consistency of β estimation and the convergence rate of the classifier are established, and the resulting classifier has an asymptotic Bayes error rate. Finally, we demonstrate the competitive performance of the proposed GSLDA on both simulated and real data studies.

Recent experimental studies have shown that the support vector machine and the random forest are "stand out" models that outperform most other supervised learning methods in benchmarked evaluations on real-world data sets. Studies have also established that both these models are closely related to nearest neighbor classifiers. Due to this connection, one would expect a similar performance from a nearest neighbor classifier; however, the latter lags greatly behind the support vector machine and the random forest in most evaluations. On the contrary, the nearest neighbor classifier has great theoretical potential because of its ability to model complex decision boundaries with low bias. Furthermore, it theoretically guarantees an error of no more than twice the Bayes error rate on an infinite data set. In this paper, we examine this obvious disconnect between the great theoretical promise and empirical reality of the nearest neighbor classifier. An additional point is that the random forest and support vector machine can be considered eager forms of the (lazy) nearest neighbor classifier. Inspired by the connections between nearest neighbor classifiers, support vector machines and random forest models, we propose a nearest neighbor classifier that is competitive to these models.

For new military aircraft a specification of sensor characteristics and performance is required at an early stage in the design cycle, well before testing of a prototype. In the early days of military aviation the Johnson criteria [1] were used to determine the sensor resolution required for target recognition by a human. In the present day sensor data are processed by computer using various Automatic Target Recognition (ATR) algorithms. However there is no accepted method for predicting the sensor resolution and SNR required for reliable ATR and hence there is risk that any chosen sensor may fail to support the required ATR performance. This paper reports a study into the use of publicly-available CAD models for aircraft to address this requirement. The study considers the worst-case confusion between two views of 15 different aircraft types. For simplicity only rotations by an angle θ about the Z (vertical) axis are considered. Firstly the sensor resolution and noise level is fixed. Then for each aircraft type and view angle an ensemble of synthetic silhouettes are generated. Using these ensembles, a-posteriori distributions of 5 standard scale-invariant shape features (eccentricity, orientation, solidity, circularity and bounding box aspect ratio) are estimated for each view angle θ. The performance of ATR at the given resolution and noise level is predicted by estimating the Bayes Error Rate [2] when deciding between each aircraft type and the 14 non-matching types using these features. The worst-case confusion in terms of erroneous aircraft type and view angle is identified. The sensor resolution is then changed and the above process repeated to investigate the effect of varying sensor resolution on performance. As expected, high sensor resolution leads to low probability of misclassification, even in the worst-case. Reduction in resolution and increasing noise level causes the Bayes Error Rate to rise quickly. The Bayes Error Rate gives a fundamental limit to the reliability of classification, irrespective of the actual type of classification algorithm used. The predictions from the model are confirmed by testing against a standard classifier for specific discrimination examples. Further development of the approach presented is expected to yield a method for specifying sensor resolution requirements for specific ATR problems.

Objectives: The time complexity of the machine learning algorithm is directly proportionate to the dimension of the dataset. In this paper, he impacts of dimensionality of the dataset on the machine learning algorithm, Naive-Bayes Classifier is evaluated with all feature subsets to analyze whether there is any variations in the performance. Methods/Statistical Analysis: Naive Bayes Classifier is taken for the study to evaluate its variations in terms of its performance in correctly classified instances and incorrectly classified instances. Pima Indian Type II diabetes dataset is taken for the experimental study. Confusion matrix will be formulated for the performance of Naive-Bayes Classifier using 10-fold cross validation for each run. The study exhibits the impact of the dimensionality on the performance of Naive-Bayes Classifier. Findings: The Naive Bayes classifier classifies the patient records either as diabetes or as non-diabetes using the values of the feature set. It is a probabilistic approach of classifying the patient records into the binary class. It is found that there is an impact on the performance of Naive Bayes Classifier due to the dimensionality of the feature set it terms of Classification accuracy, number of true positives, true negatives, false positives and false negatives. The incorrect classification is certainly dangerous. Whereas the valid classification facilitates the healthcare systems in terms of planning effective course of treatment which will save the life of the patient. The invalid classification will lead to a wrong diagnosis while formulating the treatment plan and it will lead to loss of life. Hence, the invalid classification in terms of false negative rate is to be viewed very seriously. In this paper, the study shows that there is an impact on the performance of Naive Bayes Classifier due to the higher dimensionality of the dataset. Application/Improvements: They will be used in medical Informatics for the quality diagnosis and effective treatment planning. The focus on the false positive rate in the classification accuracy of Naive Bayes Classifier will notably help the healthcare systems to diagnose the patients accurately to save life.

Bayes linear kinematics and Bayes linear Bayes graphical models provide an extension of Bayes linear methods so that full conditional updates may be combined with Bayes linear belief adjustment. In this paper we investigate the application of this approach to survival analysis with time-dependent covariate effects, a more complicated problem than previous applications. We use a piecewise-constant hazard function with a prior in which covariate effects are correlated over time. The need for computationally intensive methods is avoided and the relatively simple structure facilitates interpretation. Our approach eliminates the problem of non-commutativity which was observed in earlier work by Gamerman. We apply the technique to data on survival times for leukemia patients. We demonstrate the use Bayes linear kinematics in a more complicated problem.We use a realistically complicated case study in semi-parametric survival analysis.The previously-observed problem of non-commutativity is overcome.Attention is given to the specification of prior beliefs and its effects.

In Bayesian model selection or testing problems, default priors are typically improper; that is, the resulting Bayes factor is not well defined. To circumvent this problem, two methodologies, namely, intrinsic and fractional Bayes factors are proposed and developed. Further, these two Bayes factors are asymptotically equivalent to the ordinary Bayes factors computed with proper priors called intrinsic priors. However, it seems that there are some necessary conditions to satisfy asymptotic equivalence. Such conditions are derived and justified in this article and illustrative examples are provided. Simulations are performed to demonstrate the results.

Defining notion of Bayes covariance.Proving existence and uniqueness of Bayes covariant classifier of 3 categories.Explicit construction of a Bayes covariant classifier for any number of categories.A proof that previously considered methods are not Bayes covariant.Comparison of various methods for combining pairwise classifiers via MDS, and speech frame classification. We consider multi-class classification models built from complete sets of pairwise binary classifiers. The BradleyTerry model is often used to estimate posterior distributions in this setting. We introduce the notion of Bayes covariance, which holds if the multi-class classifier respects multiplicative group action on class priors. As a consequence, a Bayes covariant method yields the same result whether new priors are considered before or after combination of the individual classifiers, which has several practical advantages for systems with feedback. In the paper, we construct a Bayes covariant combining method and compare it with previously published methods in both Monte Carlo simulations as well as on a practical speech frame recognition task.

Text classification is the task of assigning predefined categories to natural language documents, and it can provide conceptual views of document collections. The Naïve Bayes (NB) classifier is a family of simple probabilistic classifiers based on a common assumption that all features are independent of each other, given the category variable, and it is often used as the baseline in text classification. However, classical NB classifiers with multinomial, Bernoulli and Gaussian event models are not fully Bayesian. This study proposes three Bayesian counterparts, where it turns out that classical NB classifier with Bernoulli event model is equivalent to Bayesian counterpart. Finally, experimental results on 20 newsgroups and WebKB data sets show that the performance of Bayesian NB classifier with multinomial event model is similar to that of classical counterpart, but Bayesian NB classifier with Gaussian event model is obviously better than classical counterpart.

Diabetes can lead to mortality and disability, so patients should be inpatient again to undergo treatment again to be saved. On previous research about feature selection with greedy stepwise forward fail to predict classification ratio inpatient of patient with the result of recall and precision 0 on data training 60%, 75%, 80%, and 90% and there is suggestion to handle unbalanced class data problem by comparison of data readmitted 6293 and the otherwise 64141. The research purposed to know the effect of choosing the best model using best first instead of greedy stepwise forward and data sampling with spreadsubsample to resolve unbalanced class data problem. The data used was patient data from 130 American Hospital in 1999 until 2008 with 70434 data. The method that used was best first search and spreadsubsample. The result of this research are precision found 0.4 and 0.333 on training dataset 75% and 90% with best first method, while spreadsubsample method found that value of precision and recall is more significantly increased. Spreadsubsample has more effect with the result of precision and recall rather than using best first method.

A linear Bayes procedure is suggested to simultaneously estimate the parameters of the uniform distribution U(θ1, θ2). The proposed linear Bayes estimator is simple and easy to use and its superiorities are established.

In this paper we deal with Bayes, E-Bayes and robust Bayes prediction under precautionary loss functions. It is well-known that in the Bayesian framework, the Bayes rule is obtained by considering a specific prior distribution over the parameter of interest but in practice, the use of a specified prior with specific hyperparameters is critical. Specially, when a problem in the Bayesian framework is behaved by two or more statisticians, they might agree on a specific prior but not on the hyperparameter choices. To deal with such an uncertainty issue, E-Bayes and robust Bayes approaches may be called, in which some classes of priors are considered and some optimal rules are derived. In this regard, we extend the idea of E-Bayes estimation to E-Bayes prediction and as a useful alternative approach, we deal with robust Bayes prediction. We also apply these approaches to the type-II censoring scheme. We conduct a simulation study and compare performance of the Bayes, E-Bayes and robust Bayes approaches. Finally, the proposed predictors are applied to a real data analysis and reporting some existing prediction methods in the literature, we illustrate practical utility of the prediction procedures.

Semi-supervised algorithms are well-known for their ability to combine both supervised and unsupervised strategies for optimizing their learning ability under the assumption that only a few examples together with their full feature set are given. In such cases, the use of weak learners as base classifiers is usually preferred, since the iterative behavior of semi-supervised schemes require the building of new temporal models during each new iteration. Locally weighted naive Bayes classifier is such a classifier that encompasses the power of NB and k-NN algorithms. In this work, we have implemented a self-labeled weighted variant of local learner which uses NB as the base classifier of self-training scheme. We performed an in depth comparison with other well-known semi-supervised classification methods on standard benchmark datasets and we reached to the conclusion that the presented technique had better accuracy in most cases.

Background Electroencephalogram (EEG) and electromyogram (EMG) recordings are often used in rodents to study sleep architecture and sleep-associated neural activity. These recordings must be scored to designate what sleep/wake state the animal is in at each time point. Manual sleep-scoring is very time-consuming, so machine-learning classifier algorithms have been used to automate scoring. New method Instead of using single classifiers, we implement a multiple classifier system. The multiple classifier is built from six base classifiers: decision tree, k-nearest neighbors, naive Bayes, support vector machine, neural net, and linear discriminant analysis. Decision tree and k-nearest neighbors were improved into ensemble classifiers by using bagging and random subspace. Confidence scores from each classifier were combined to determine the final classification. Ambiguous epochs can be rejected and left for a human to classify. Results Support vector machine was the most accurate base classifier, and had error rate of 0.054. The multiple classifier system reduced the error rate to 0.049, which was not significantly different from a second human scorer. When 10% of epochs were rejected, the remaining epochs’ error rate dropped to 0.018. Comparison with existing method(s) Compared with the most accurate single classifier (support vector machine), the multiple classifier reduced errors by 9.4%. The multiple classifier surpassed the accuracy of a second human scorer after rejecting only 2% of epochs. Conclusions Multiple classifier systems are an effective way to increase automated sleep scoring accuracy. Improvements in autoscoring will allow sleep researchers to increase sample sizes and recording lengths, opening new experimental possibilities.

Error spectrum is a comprehensive metric for evaluation of estimation performance in that it is an aggregation of many incomprehensive measures. However, error spectrum requires computing the expectation of the rth power of the estimation-error-norm as using it to evaluate an estimator's performance. Therefore unless the error distribution is given, it's usually not easy to obtain the error spectrum. To alleviate this difficulty, two approximation algorithms are proposed. One is the Gaussian mixture method, which calculated the error spectrum by capturing the probability density function. The other using the sample is the power means error method. Furthermore, how the Gaussian mixture method and power means error method can be used in estimation performance evaluation are analyzed not only in the large sample case but also in the small sample case. Numerical examples are provided to illustrate the effectiveness of the above two algorithms. It is shown that the two proposed algorithms can be applied easily to calculate the error spectrum in estimator performance evaluation.

Currently available (classical) testing procedures for the network autocorrelation can only be used for falsifying a precise null hypothesis of no network effect. Classical methods can be neither used for quantifying evidence for the null nor for testing multiple hypotheses simultaneously. This article presents flexible Bayes factor testing procedures that do not have these limitations. We propose Bayes factors based on an empirical and a uniform prior for the network effect, respectively, first. Next, we develop a fractional Bayes factor where a default prior is automatically constructed. Simulation results suggest that the first two Bayes factors show superior performance and are the Bayes factors we recommend. We apply the recommended Bayes factors to three data sets from the literature and compare the results to those coming from classical analyses using p values. R code for efficient computation of the Bayes factors is provided.

We study the statistical performance of semidefinite programming (SDP) relaxations for clustering under random graph models. Under the $\mathbb{Z}_{2}$ Synchronization model, Censored Block Model and Stochastic Block Model, we show that SDP achieves an error rate of the form \[ \exp\Big[-\big(1-o(1)\big)\bar{n} I^* \Big]. \] Here $\bar{n}$ is an appropriate multiple of the number of nodes and $I^*$ is an information-theoretic measure of the signal-to-noise ratio. We provide matching lower bounds on the Bayes error for each model and therefore demonstrate that the SDP approach is Bayes optimal. As a corollary, our results imply that SDP achieves the optimal exact recovery threshold under each model. Furthermore, we show that SDP is robust: the above bound remains valid under semirandom versions of the models in which the observed graph is modified by a monotone adversary. Our proof is based on a novel primal-dual analysis of SDP under a unified framework for all three models, and the analysis shows that SDP tightly approximates a joint majority voting procedure., Comment: Partial preliminary results to appear in the Conference on Learning Theory (COLT) 2019