Probability Of Misclassification Research Articles

Multi-label Minimax Probability Machine with Multi-manifold Regularisation

Semi-supervised learning i.e., learning from a large number of unlabelled data and exploiting a small percentage of labelled data has attracted centralised attention in recent years. Semi-supervised problem is handled mainly using graph based Laplacian and Hessian regularisation methods. However, neither the Laplacian method which leads to poor generalisation nor the Hessian energy can properly forecast the data points beyond the range of the domain. Thus, in this paper, the Laplacian-Hessian semi-supervised method is proposed, which can both predict the data points and enhance the stability of Hessian regulariser. In this paper, we propose a Laplacian-Hessian Multi-label Minimax Probability Machine, which is Multi-manifold regularisation framework. The proposed classifier requires mean and covariance information; therefore, assumptions related to the class conditional distributions are not required; rather, a upper bound on the misclassification probability of future data is obtained explicitly. Furthermore, the proposed model can effectively utilise the geometric information via a combination of Hessian-Laplacian manifold regularisation. We also show that the proposed method can be kernelised on the basis of a theorem similar to the representer theorem for handling non-linear cases. Extensive experimental comparisons of our proposed method with related multi-label algorithms on well known multi-label datasets demonstrate the validity and comparable performance of our proposed approach.

Prognosis of high-risk human papillomavirus-related cervical lesions: A hidden Markov model analysis of a single-center cohort in Japan.

IntroductionPrevious studies have shown that individuals with human papillomavirus (HPV)‐related cervical lesions have different prognoses according to the HPV genotype. However, these studies failed to account for possible diagnostic misclassification. In this retrospective cohort study, we aimed to clarify the natural course of cervical lesions according to HPV genotype to account for any diagnostic misclassification.Materials and MethodsOur cohort included 729 patients classified as having cervical intraepithelial neoplasia (CIN). HPV was genotyped in all patients, who were followed up or treated for cervical lesions at the University of Tokyo Hospital from October 1, 2008 to March 31, 2015. Hidden Markov models were applied to estimate the diagnostic misclassification probabilities of the current diagnostic practice (histology and cytology) and the transitions between true states. We then simulated two‐year transition probabilities between true cervical states according to HPV genotype.ResultsCompared with lesions in patients with other HPV genotypes, lesions in HPV 16‐positive patients were estimated to be more likely to increase in severity (i.e., CIN3/cancer); over 2 years, 17.7% (95% confidence interval [CI], 9.3%–29.3%) and 27.8% (95% CI, 16.6%–43.5%) of those with HPV 16 progressed to CIN3/cancer from the true states of CIN1 and CIN2, respectively, whereas 55%–70% of CIN1/2 patients infected with HPV 52/58 remained in the CIN1/2 category. Misclassification was estimated to occur at a rate of 3%–38% in the current diagnostic practice.ConclusionThis study contributes robust evidence to current literature on cervical lesion prognosis according to HPV genotype and quantifies the diagnostic misclassification of true cervical lesions.

Techniques to Deal with Off-Diagonal Elements in Confusion Matrices

Confusion matrices are numerical structures that deal with the distribution of errors between different classes or categories in a classification process. From a quality perspective, it is of interest to know if the confusion between the true class A and the class labelled as B is not the same as the confusion between the true class B and the class labelled as A. Otherwise, a problem with the classifier, or of identifiability between classes, may exist. In this paper two statistical methods are considered to deal with this issue. Both of them focus on the study of the off-diagonal cells in confusion matrices. First, McNemar-type tests to test the marginal homogeneity are considered, which must be followed from a one versus all study for every pair of categories. Second, a Bayesian proposal based on the Dirichlet distribution is introduced. This allows us to assess the probabilities of misclassification in a confusion matrix. Three applications, including a set of omic data, have been carried out by using the software R.

Low-rank supervised and semi-supervised multi-metric learning for classification

Multi-metric learning is an important technique for improving classification performance since learning a single metric is usually insufficient for complex data. Most of the existing multi-metric learning approaches have high computational complexity. In this work, two multi-metric learning frameworks proposed to perform supervised and semi-supervised classifications respectively. Based on the frameworks, we first design a low-rank multi-metric learning model (LSMML) for supervised classification, in which multiple local class metrics as well as one global metric are jointly trained. A joint regularization scheme, composed of LogDet divergence and low-rank term, is also well-designed to incorporate prior knowledge for improving generalization. By learning appropriate metrics, LSMML not only captures the local nonlinear discriminate information of each class to reduce the probability of misclassification but also enhances the stability, alleviates the computational burden, and avoids the risk of overfitting. Then, we extend LSMML to a semi-supervised learning scenario and propose a low-rank semi-supervised multi-metric learning approach (LSeMML) to process data with scarce labels. Alternating iterative algorithms are designed to optimize both LSMML and LSeMML. At each iteration, we only require to perform geodesic convex optimizations, with closed-form solutions and low computational cost. In supervised and semi-supervised settings respectively, numerical simulations are carried out on different databases, which shows that the proposed LSMML and LSeMML have a simple form, fast training speed, and good classification performance.

Regularized twin minimax probability machine for pattern classification and regression

As an excellent discriminant classifier based on generating prior knowledge, the minimax probability machine (MPM) has been widely used and deeply researched in many fields. The core idea of minimax probability machine is to directly estimate probability accuracy bound by minimizing the maximum probability of misclassification. However, minimax probability machine does not include a regularization term for the construction of the separating hyperplane, and it needs to solve a large-scale second-order cone programming problem in the solution process, which greatly limits it development and application. In this paper, to improve the performance of minimax probability machine, we propose a novel binary classification method called regularized twin minimax probability machine classification (TMPMC). The TMPMC constructs two non-parallel hyperplanes for final classification by solving two smaller second-order cone programming problems to improve the performance of the MPM. For each hyperplane, our method is theoretically well grounded on the idea of minimizing the worst case (maximum) probability of misclassification of a class of samples while the distance to the other class is as large as possible. Our approach was first derived as linear methods, and subsequently extended as kernel-based strategies for nonlinear classification. Additionally, we extend TMPMC to the regression problem and propose a new regularized twin minimax probability machine regression (TMPMR). Experimental results on several datasets show that our methods are competitive in terms of generalization performance compared to other algorithms.

A novel αDistance Borderline-ADASYN-SMOTE algorithm for imbalanced data and its application in Alzheimer’s disease classification based on Dense Convolutional Network

The classification problem of imbalanced data has become a very important issue in the fields of machine learning and data mining. At present, relatively effective oversampling methods for processing imbalanced data include SMOTE, Borderline-SMOTE, and ADASYN. These algorithms have their own advantages; however, they do not adequately consider the distance factor, which is an important factor for balancing data precisely and reducing the misclassification probability of a minority boundary sample. Therefore, a new algorithm, αDistance Borderline-ADASYN-SMOTE algorithm, is proposed in the paper by combining the optimized Borderline-SMOTE algorithm with the optimized ADASYN algorithm. In the new algorithm, both the amount and the distance distribution of the nearest neighbor samples are considered. A few formulas are created to realize the algorithm. After being balanced by the algorithm, the data obtained from ADNI data set is trained, verified and tested by the Dense Convolutional Network. The experimental results show that the new model improves the classification performance of the Alzheimer’s disease.

Using an autonomous underwater vehicle with onboard stochastic advection‐diffusion models to map excursion sets of environmental variables

AbstractNew robotic sensor platforms have computing resources that enable a rich set of tasks for adaptive monitoring of the environment. But to substantially augment the toolbox of environmental sensing, such platforms must be embedded with realistic statistical models and coherent methodologies for designing experiments and assimilating the data. In this article, we develop myopic and hybrid strategies for autonomous underwater vehicle sampling in space and time. These strategies are based on a stochastic advection‐diffusion Gaussian process model for the mine tailings concentration in a Norwegian fjord, and the goal is to monitor the excursion set (ES) of high concentrations. Closed form expressions for the expected misclassification probabilities of the ES enable real‐time operation on board the autonomous vehicle, and this is used to guide the spatio‐temporal sampling. Simulation studies show that the suggested strategies outperform other approaches that either (i) simplify the models for spatio‐temporal variation, or (ii) simplify the design criterion. A field test shows how autonomous underwater sampling is useful for refining an initial stochastic advection‐diffusion model. These experiments further show that the vehicle can adapt to focus on regions with intermediate concentrations where it is natural to improve the ES prediction.

Prediction Accuracy Model Aiming to Improve Prediction Accuracy in Congenital Heart Anomaly Detection using Hybrid Feature Selection with Modified Particle Swarm Optimization Approach

Heart Disease is one of the primary causes of mortality and morbidity in the Globe since the 19th Century. Most of the Globalized Multi-Specialty Hospitals are not able to control and governed by emerging technologies, at the same time, the death rate escalates day by day in addition to Covid-19 is a multifaceted state. Heart disease classification involves identifying numerous health problems and sickness symptoms of ones’ individual with significant feature selection, there is misclassification probability that could be very high and priceless. There are many diverse methods were designing for heart disease prediction systems in earlier days, even though it is unsolved and rising the death rate. As observed by many research groups, PSO is an intensive computational and inspired biologically inspired algorithms like Genetic Algorithms (GA) has a proven track record to handle computationally complex problems with competence for predicting heart diseases. This research contribution through the proposed model downs the computation time and increases the accuracy. The high-level comprehensibility, predictive accuracy are good and desired through this Intelligence Hybrid Approach (IHP) to reduce Heart attacks and control the death rate.

Classification of observations into von Mises-Fisher populations with unknown parameters

The problem of classification of an observation into von Mises-Fisher populations is considered when the concentration parameters and the mean directions are unknown. For two von Mises-Fisher distributions, we propose the restricted maximum likelihood estimators (MLEs), and Bayes estimators of the concentration parameters. The MLEs and restricted MLEs of the concentration parameters are compared in terms of risks. When the concentration parameters are ordered, we propose classification rules using the restricted MLEs and Bayes estimators of the parameters. For two populations, we also derive predictive Bayes classification rules using informative priors for the concentration parameters. We derive the likelihood ratio-based classification rule. Nonparametric rules such as k-NN rule, support vector machine classifier, and kernel density-based rule are also studied. For more than two populations, we suggest classification rules. Comparisons among the proposed rules have been carried out with respect to the expected probability of misclassification. Applications of the rules are described using directional data sets.

COVRATIO Statistic as a Discrimination Method for Multivariate Normal Distribution

The COVRATIO statistic has been used to identify the presence of outlier in data, which is based on deletion approach, where the determinant of covariance matrix for the full dataset excludes i-th row. This study proposes a novel discrimination method for the multivariate normal (MVN) distribution using the idea of COVRATIO statistic, denoted as . The linear discrimination function (LDF) for MVN distribution will be compared to the statistic. Simulation results showed that the as discrimination method performs better than the LDF with lower misclassification probabilities in all cases considered. The interest in the discrimination method arose in connection with the study of an application to discriminate the shape of the human maxillary dental arches, thus statistic may be considered as an alternative.

A Monte Carlo Comparison of Two Linear Dimension Reduction Matrices for Statistical Discrimination

We compare two linear dimension-reduction methods for statisti cal discrimination in terms of average probabilities of misclassification in re duced dimensions. Using Monte Carlo simulation we compare the dimension reduction methods over several different parameter configurations of multi variate normal populations and find that the two methods yield very different results. We also apply the two dimension-reduction methods examined here to data from a study on football helmet design and neck injuries.

Detection of Lung Cancer Lesions Using 3D Convolutional Neural Networks and Segmentation for Accurate Detection

Lung cancer is a leading cause of death worldwide; it refers to the uncontrolled growth of abnormal cells in the lung. A computed tomography (CT) scan of the thorax is the most sensitive method for detecting cancerous lung nodules. A lung nodule is a round lesion which can be either non-cancerous or cancerous. In the CT, the lung cancer is observed as round white shadow nodules. In existing method, the candidate ROIs shape features are calculated, and some blood vessels are get rid of using rule-based according to shape features; secondly, the remainder candidates gray and texture features are calculated; finally, the shape, gray and texture features are taken as the inputs of the SVM (Support Vector Machine) classifier to classify the candidates. Experimental results show that the rule-based approach has no omission, but the misclassification probability is too large; Hence, in the proposed method the nodules were characterized by the computation of the texture features obtained from the gray level co-occurrence matrix (GLCM) in the wavelet domain and were classified using a SVM with radial basis function in order to classify CT images into two categories: with cancerous lung nodules and without lung nodules. The stages of the proposed methodology to design the CADx system are: 1) Extraction of the region of interest, 2) Wavelet transform, 3) Feature extraction, 4) Attribute and sub-band selection and 5) Classification. The same classification is implemented for the convolution neural networks. The final comparison is done between these two networks based on the accuracy.

Application of Skew-normal in Classification of Satellite Image

The aim of this paper is to investigate the flexibility of the skewnormal distribution to classify the pixels of a remotely sensed satellite image. In the most of remote sensing packages, for example ENVI and ERDAS, it is assumed that populations are distributed as a multivariate normal. Then linear discriminant function (LDF) or quadratic discriminant function (QDF) is used to classify the pixels, when the covariance matrix of populations are assumed equal or unequal, respectively. However, the data was obtained from the satellite or airplane images suffer from non-normality. In this case, skew-normal discriminant function (SDF) is one of techniques to obtain more accurate image. In this study, we compare the SDF with LDF and QDF using simulation for different scenarios. The results show that ignoring the skewness of the data increases the misclassification probability and consequently we get wrong image. An application is provided to identify the effect of wrong assumptions on the image accuracy.

Asymptotic approximation of misclassification probabilities in linear discriminant analysis with repeated measurements

We propose asymptotic approximations for the probabilities of misclassification in linear discriminant analysis when the group means follow a growth curve structure. The discriminant function can classify a new observation vector of p repeated measurements into one of several multivariate normal populations with equal covariance matrix. We derive certain relations of the statistics under consideration in order to obtain asymptotic approximation of misclassification errors for the two group case. Finally, we perform Monte Carlo simulations to evaluate the reliability of the proposed results.

Correction ofP/SAmplitude Ratios for Low-Magnitude Seismic Events Based on Bayesian Kriging Method

ABSTRACTClassification of low-magnitude seismic events is a challenging issue for the Comprehensive Nuclear-Test-Ban Treaty. Path correction of the P/S amplitude ratio is the key to identifying earthquakes and explosions. In this article, the Bayesian Kriging interpolation method is used to conduct the path correction of P/S amplitude ratios and recognition of low-magnitude seismic events. Based on a total of 5677 small earthquakes and 1769 explosions in Beijing and its adjacent areas, the Bayesian Kriging method is used to establish the path correction surface and uncertainty surface of Pg/Lg amplitude ratios measured within different frequency bands at five seismic stations, and path correction of amplitude ratios is conducted for all events. The results show that the correction surface is consistent with the observed amplitude ratios, which can reflect the differences in their propagation paths to a certain extent. The root mean square variation of the amplitude ratio is reduced by a maximum of 30% and the misclassification probability is reduced by a maximum of 8.5% after the Kriging correction. The high-frequency Pg/Lg amplitude ratios can effectively classify low-magnitude events, and the misclassification probability at each station is less than 15% and 10% based on high-frequency Pg/Lg of >7 and >9 Hz, respectively. Of the five stations, BJT (Baijiatuan, Beijing) has the best recognition, with the misclassification probability being lower than 5% after Kriging correction based on high-frequency Pg/Lg (>9 Hz). The classification ability of high-frequency amplitude ratios (>15 Hz) is weakened due to high-frequency noises. Bayesian Kriging correction can reduce the variance in the amplitude ratio of low-magnitude seismic events and hence effectively improve the ability to classify small-magnitude events, which has an important reference value for regional seismic monitoring and identification.

Sparse functional linear discriminant analysis

Summary Functional linear discriminant analysis provides a simple yet efficient method for classification, with the possibility of achieving perfect classification. Several methods have been proposed in the literature that mostly address the dimensionality of the problem. On the other hand, there is growing interest in interpretability of the analysis, which favours a simple and sparse solution. In this paper we propose a new approach that incorporates a type of sparsity that identifies nonzero subdomains in the functional setting, yielding a solution that is easier to interpret without compromising performance. Given the need to embed additional constraints in the solution, we reformulate functional linear discriminant analysis as a regularization problem with an appropriate penalty. Inspired by the success of $\ell_1$-type regularization at inducing zero coefficients for scalar variables, we develop a new regularization method for functional linear discriminant analysis that incorporates an $L^1$-type penalty, $\int |f|$, to induce zero regions. We demonstrate that our formulation has a well-defined solution that contains zero regions, achieving functional sparsity in the sense of domain selection. In addition, the misclassification probability of the regularized solution is shown to converge to the Bayes error if the data are Gaussian. Our method does not assume that the underlying function has zero regions in the domain, but it produces a sparse estimator that consistently estimates the true function whether or not the latter is sparse. Using both simulated and real data examples, we demonstrate this property of our method in finite samples through comparisons with existing methods.

Alternative classification rules for two normal populations with a common mean and ordered variances

The problem of classification into two normal populations with a common mean and ordered variances is revisited. So far in the literature, authors have proposed classification rules which are based on either the Graybill-Deal estimator or its improved version of the common mean under order restricted variances. Surprisingly, the maximum likelihood estimator (MLE) of the common mean has not been used for classification purposes. However, it is interesting to know that the MLE has better performance than the Graybill-Deal estimator in most of the parameter ranges. In this article, utilizing the MLE and its plug-in type restricted version of the common mean, two new classification rules have been proposed. Further, a classification rule based on the generalized likelihood ratio test approach has been obtained. Moreover, certain rules based on some of the improved existing estimators of the common mean under order restricted variances have been proposed. More importantly, a simulation study has been carried out to numerically compare the probabilities of misclassification for all the classification rules, including the existing ones. It has been observed that the classification rules which are based on the MLE and its restricted version perform quite satisfactorily (if not the best) compared to other rules.

The curse of dimensionality (COD), misclassified DMUs, and Bayesian DEA

Data envelopment analysis (DEA) is used to assess the relative efficiency of a set of decision-making units (DMUs). A potential drawback to DEA is that one must include a sufficient number of observations to ensure that all input–output dimensions are adequately characterized. Employing DEA with too few DMUs for a given set of inputs/outputs generates estimates that overstate efficiency. This is known as the “curse of dimensionality (COD)”. Because production processes vary widely in technology and complexity, it is difficult to analytically characterize the effects of the COD on DEA-generated efficiency scores. This paper uses Bayesian methods to characterize and adjust for the possibility of misclassified DMUs and COD-related biases in DEA. Based on the nature of the COD bias we propose an appropriate prior distribution for the proportion of misclassified DMUs and use it to derive the concordant posterior distribution. A simulation analysis compares our model to those obtained with an ignorance prior distribution to evaluate the utility of the new model, and it is then applied to data from the Turkish electricity industry. We find that estimates of the probability of misclassification can be improved using our proposed prior distribution, especially in sample sizes of less than 40 observations. Highlights We account for the curse of dimensionality in the misclassification of DEA estimates. A left skewed (proposed) distribution is used to model prior misclassification beliefs. Simulations suggest that a left skewed prior outperforms an ignorance prior in small samples.

The development and validation of a multivariable model to predict the bleeding risk score for patients with non-valvular atrial fibrillation using direct oral anticoagulants in the Arab population.

BackgroundFrequently used models, such as the HAS-BLED, ATRIA, ORBIT, and GARFIELD-AF evaluate the risk of bleeding when using an anticoagulant, for example warfarin, in patients with non-valvular atrial fibrillation. Limited studies are available reporting a model with a good discriminative ability to predict the bleeding risk score when using direct oral anticoagulants.MethodsPatient data were collected from King Abdulaziz Medical City, King Fahad Cardiac Center, and Prince Sultan Cardiac Center in Riyadh, from outpatients, inpatients, or primary care clinics. In total, 1722 patients with a prescription for a new oral anticoagulant, Dabigatran, Rivaroxaban, or Apixaban, were enrolled. A resampling approach for variable selection was used and a five-fold cross-validation to assess the model fit and misclassification probabilities. The analysis used the receiver operating characteristics curve (ROC) and the concordance (c) statistic to assess the validation models’ discriminative power. The final penalized likelihood parameters were used for the development of the risk prediction tool. The accuracy of a classification and the prediction are reported with the sensitivity, specificity, and Brier score.ResultsBleeding occurred in 11.15% of cases, of which 23.08% required a blood transfusion and 51.65% had a reduction in haemoglobin of more than 2 gm. The variable selection model identified 15 predictors associated with major bleeding. The discriminative ability of the model was good (c-statistic 0.75, p = 0.035). The Brier score of the model was 0.095. With a fixed cut-off probability value of 0.12 for the logistic regression equation, the sensitivity was 72.7%, and the specificity 66.3%.ConclusionThis model demonstrated a good performance in predicting the bleeding risk in Arab patients treated with novel oral anticoagulants. This easy to use bleeding risk score will allow the clinician to quickly classify patients according to their risk category, supporting close monitoring and follow-up for high-risk patients, without laboratory and radiological monitoring.

Simulation of Random Differential Periodontitis Outcome Misclassification with Perfect Specificity

Misclassification of clinical periodontitis can occur by partial-mouth protocols, particularly when tooth-based case definitions are applied. In these cases, the true prevalence of periodontal disease is underestimated, but specificity is perfect. In association studies of periodontal disease etiology, misclassification by this mechanism is independent of exposure status (i.e., nondifferential). Despite nondifferential mechanisms, differential misclassification may be realized by virtue of random errors. To gauge the amount of uncertainty around the expectation of differential periodontitis outcome misclassification due to random error only, we estimated the probability of differential outcome misclassification, its magnitude, and expected impacts via simulation methods using values from the periodontitis literature. We simulated data sets with a binary exposure and outcome that varied according to sample size (200, 1,000, 5,000, 10,000), exposure effect (risk ratio; 1.5, 2), exposure prevalence (0.1, 0.3), outcome incidence (0.1, 0.4), and outcome sensitivity (0.6, 0.8). Using a Bernoulli trial, we introduced misclassification by randomly sampling individuals with the outcome in each exposure group and repeated each scenario 10,000 times. The probability of differential misclassification decreased as the simulation parameter values increased and occurred at least 37% of the time across the 10,000 repetitions. Across all scenarios, the risk ratio was biased, on average, toward the null when the sensitivity was higher among the unexposed and away from the null when it was higher among the exposed. The extent of bias for absolute sensitivity differences ≥0.04 ranged from 0.05 to 0.19 regardless of simulation parameters. However, similar trends were not observed for the odds ratio where the extent and direction of bias were dependent on the outcome incidence, sensitivity of classification, and effect size. The results of this simulation provide helpful quantitative information to guide interpretation of findings in which nondifferential outcome misclassification mechanisms are known to be operational with perfect specificity. Measurement of periodontitis can suffer from classification errors, such as when partial-mouth protocols are applied. In this case, specificity is perfect and sensitivity is expected to be nondifferential, leading to an expectation for no bias when studying periodontitis etiologies. Despite expectation, differential misclassification could occur from sources of random error, the effects of which are unknown. Proper scrutiny of research findings can occur when the probability and impact of random classification errors are known.