- Technical advance
- Open Access
- Open Peer Review
Combining macula clinical signs and patient characteristics for age-related macular degeneration diagnosis: a machine learning approach
© Fraccaro et al.; licensee BioMed Central. 2015
- Received: 6 May 2014
- Accepted: 3 January 2015
- Published: 27 January 2015
To investigate machine learning methods, ranging from simpler interpretable techniques to complex (non-linear) “black-box” approaches, for automated diagnosis of Age-related Macular Degeneration (AMD).
Data from healthy subjects and patients diagnosed with AMD or other retinal diseases were collected during routine visits via an Electronic Health Record (EHR) system. Patients’ attributes included demographics and, for each eye, presence/absence of major AMD-related clinical signs (soft drusen, retinal pigment epitelium, defects/pigment mottling, depigmentation area, subretinal haemorrhage, subretinal fluid, macula thickness, macular scar, subretinal fibrosis). Interpretable techniques known as white box methods including logistic regression and decision trees as well as less interpreitable techniques known as black box methods, such as support vector machines (SVM), random forests and AdaBoost, were used to develop models (trained and validated on unseen data) to diagnose AMD. The gold standard was confirmed diagnosis of AMD by physicians. Sensitivity, specificity and area under the receiver operating characteristic (AUC) were used to assess performance.
Study population included 487 patients (912 eyes). In terms of AUC, random forests, logistic regression and adaboost showed a mean performance of (0.92), followed by SVM and decision trees (0.90). All machine learning models identified soft drusen and age as the most discriminating variables in clinicians’ decision pathways to diagnose AMD.
Both black-box and white box methods performed well in identifying diagnoses of AMD and their decision pathways. Machine learning models developed through the proposed approach, relying on clinical signs identified by retinal specialists, could be embedded into EHR to provide physicians with real time (interpretable) support.
- Age related macular degeneration
- Machine learning
- Automated diagnosis
- Statistical learning
- macula disease
Age-related macular degeneration (AMD) is the leading cause of severe reduction in central visual acuity in adults aged 50 years and older in developed countries . As the prevalence of AMD is steadily increasing due to increasing life expectancy , early diagnosis and treatment becomes essential in slowing down progression of AMD and subsequent vision loss . Multimodal high-resolution imaging has had a substantial impact on diagnosis and treatment of macular diseases . Different imaging modalities can be used for AMD diagnosis . In particular, optical coherence tomography (OCT) associated with color fundus image acquisition technology is a non-contact, non-invasive, high resolution technique which produces real-time images used to derive several features of the macula . Such characteristics may allow OCT to become an effective screening instrument, employable in non-specialized environments (such as pharmacies) and by non-specialized personnel to perform automatic diagnosis of AMD without the intervention of a medical retinal specialist. However, to allow diagnosis by non-specialized personnel, OCT technology could be coupled with other clinical decision support functionalities  based on patient data which could enhance the potential of image analysis data. Currently, the majority of commercially available OCT technologies incorporate basic algorithms to automatically identify the presence of risk factors in macula images and diagnose AMD [8–10]. A recent review  showed how the majority of these algorithms mainly focus on automatic segmentation of soft drusen, previously identified as one of the most important signs for the diagnosis of AMD . But relying on just one sign to diagnose AMD can be suboptimal since AMD is a complex pathology which involves different stages of progression and requires consideration of several clinical aspects . Therefore image analysis should be used in conjunction with other clinical biomarkers to enhance diagnosis .
Machine learning techniques  have been applied successfully to identify, extract and analyze features in macula digital imaging [14–18]. In spite of potential higher accuracy in predicting disease diagnoses (as compared, for instance, to simple scoring rules on a small set of variables), many machine learning methods are usually regarded as non-transparent to the end user, and labeled as “black-boxes”. Methods that do not allow the clinician to identify a clear decision pathway for the diagnosis are often regarded with skepticism in the clinical community .
This paper describes the application of a variety of more and less interpretable machine learning algorithms with the aims of: 1) reproducing physicians’ diagnoses of AMD from patient data (demographics and clinical signs identified by retinal specialists through examination of medical images) and evaluating model performances on unseen data; 2) determining which are the diagnostic criteria followed by the physician (who may follow different routes to make a diagnosis); 3) identifying deviations or new rules that may emerge from the expected. Data were collected cross-sectionally from routine patient visits and stored in an Electronic Health Record, specifically designed for macular diseases management. The work reported in this paper is preliminary research into the potential of machine learning techniques to be used for AMD diagnostic support; from the perspective of using longitudinal data (i.e. symptoms/markers before a diagnosis is made), these decision support algorithms could be embedded in Electronic Health Records to support physicians during everyday clinical practice, and could be further refined by incorporating features from digital image processing leading to a fully-automated diagnostic tool suitable for non-specialized environments.
The web Electronic Health Record system , data collection methods  and related observational studies were approved by an ethics committee (San Martino Hospital, Genoa, Italy) and patients signed informed consent for data storage and usage for clinical/research purposes.
Study population and case selection
Data on study participants, healthy subjects (those with normal macula) as well as patients with macular diseases (both referred to as “patients” in the text), were collected from March 2013 to January 2014 during routine clinical practice at the Medical Retina Center of the University Eye Clinic of Genoa (Italy).
Primary diagnosis (AMD or other macular diseases);
Relevant clinical signs  identified by clinicians during the visit as binary variables (positive if identified):
o Soft drusen;
o Retinal Pigment Epitelium (RPE) defects/pigment mottling;
o Depigmentation area(s);
o Subretinal haemorrhage;
o Subretinal fluid;
o Macula thickness;
o Macular scar;
o Subretinal fibrosis;
The macula of all eyes included in the study was evaluated by two different ophthalmologist (10 and 2 years of experience) using a spectral domain OCT machine (Topcon 3D OCT-2000, Topcon Medical Systems, Inc., Oakland, NJ, USA). Data records were stored per single eye.
The study population included a total of 487patients (912 eyes, with information on patients’ two eyes not always available).
Primary diagnosis of AMD is the study outcome (dependent variable). Accordingly, each eye observation diagnosed as AMD was assigned to one class, while eyes diagnosed with other macular diseases were assigned to another class. The covariate set (input variables) included all the other attributes listed above and referred to the same eye.
There is evidence in support of the hypothesis of disease correlation between different eyes of the same patient . A preliminary screening on our data confirmed this hypothesis. However, information on the fellow eye may not be available when diagnoses are performed during a visit (for example, it may be the first encounter). Therefore, we performed the analysis in this paper without taking into account the information about the presence of AMD in the fellow eye.
Machine learning techniques
The purpose of this section is not to provide a detailed explanation of machine learning methods, which is left to referenced works, but to give some introduction about the techniques which readers may be less familiar with . All statistical analyses and graphs were done using the R software (http://www.r-project.org).
Logistic regression is used for predicting the outcome of a categorical dependent variable (i.e., a class label) based on one or more predictor variables. This “white-box” technique is widely used in automatic medical diagnosis [22, 23]. An embedded procedure within logistic regression, called the LogitBoost  (as implemented in RWeka R library ), was included to select the most relevant variables. No variable interactions were explored. For comparison purposes, a simple model based on a unique variable was employed, named “one-rule”, selecting the most discriminative variable, based on a univariable logistic regression fit.
Support Vector Machines are classifiers that divide data instances of different categories with a linear boundary supported by a very clear gap (called maximum margin). They can be optimised via different internal algorithms, therefore a parameter search is often recommended. Support vector machines can efficiently perform a non-linear classification using a so-called “kernel trick” which maps their inputs into feature spaces of higher dimensions. This solution however is more difficult to interpret. In this study we adopted a linear kernel and the nu-classification, optimizing the parameter nu in the value range [0.02, 0.4], with a step size of 0.01 for values below 0.1, and a step of 0.05 for values above 0.1, using e1071 library  in the R software.
Decision trees are non-linear graphical models that take the form of a flow chart. They are a “white-box” method because they produce multiple decision pathways in a tree form that can be easily interpretable . Decision trees consist of nodes which represent input variables, and edges branching from the nodes dependent on possible values of those input variables. Each terminal node (leaf) represents the value of the target variable given the values of the input variables after following the path from the root to the leaf. A decision tree is usually grown by starting from the whole population, looking at the most discriminative variable to predict a desired outcome (which becomes a node), and splitting the data based on a cut-off value of this variable (inducing an edge). In our analysis, we adopted the party package of decision tree learning  within the R software.
A single decision tree often does not yield satisfactory prediction performance. To improve performance, multiple different trees can be aggregated, and this takes the general name of a tree ensemble. A weel-recognised tree ensemble method is the random forest, which infers different decision trees via resampling and randomization, producing an average prediction from all trees. We used the randomForest package of R . The combination of several trees makes the method more powerful, but also more difficult to interpret than a single decision tree. Another ensemble method is the AdaBoost, which fits several “weak” learners, such as decision trees with only a small number of pathways, and weights them based on performance on data subsets. We adopted the RWeka AdaBoost version of R .
We performed the complete cases analysis with all methods and used three different approaches for imputation of missing values: i) addition of a categorical variable encoding the presence of a missing value; ii) substitution with the overall population mode for binary attributes and mean for numeric ones; iii) non-linear imputation based on random forests .
Models’ performance was analysed by means of sensitivity (true positive rate), specificity (true negative rate), and using the area under the receiver operating characteristic (AUC), which is a combined indicator of sensitivity and specificity, equal to the probability that a classifier will rank a randomly chosen positive instance higher than a randomly chosen negative one . The robustness of performance was assessed via bootstrapping , a validation technique based on random data resampling with replacement (here, 50 times); we used the very conservative out-of-bag estimator which calculates errors on unseen data. To assess the entity of the difference between means of two performance distributions, a modified t-test was used, penalising the degrees of freedom due to sample overlap . Variable importance analysis for the different machine learning techniques was carried out as follows: odds ratio/AIC with associated p-values for both multivariable and univariable logistic regression; conditional independence split rule + pruning for decision trees as implemented in ctree function of party library in R ; Gini index for random forest; decrease in AUC by single feature elimination for AdaBoost and support vector machines.
Number of patients (%)
Number of eyes (%)
Number of healthy eyes (%)
65.3 +/− 14.9
70.5 +/− 12.7
68 +/− 14.1
Soft drusen positive (%)
Macular scar positive (%)
RPE defect/pigment mottling positive (%)
Depigmentation area positive (%)
Subretinal fluid positive (%)
Macular tickness (mean+/−std)
297.4 +/− 64.8
277 +/− 54.5
286.8 +/− 60.5
Subretinal fibrosis positive (%)
Subretinal hemorrhage positive (%)
AMD diagnosis (%)
Prevalence of diagnoses of retinal diseases in the whole population stratified by soft drusen, depigmentation area and RPE defect/pigment mottling (counting one eye as a single case)
Disease (or healthy status)
Soft drusen positive N (%)
Depigmentation area positive N (%)
RPE defect/pigment mottling positive N (%)
Central serous chorioretinopathy
Inflammatory cystoid macular edema
Retinal artery occlusion
Retinal vein occlusion
Performance of statistical learning methods
Performance of the machine learning methods in terms of average (+/− std. dev.) sensitivity, specificity and area under the receiver operating characteristic (AUC), applied to the dataset with different missing value imputation techniques (complete cases, categorical variable encoding the missingness, mean/mode imputation, and random forest imputation)
Type of imputation on the dataset (N = 444)
Support vector machine
Categorical variable encoding the missingness
We executed a formal t-test to compare shifts in the average AUCs of methods –specifically, logistic regression, support vector machine, AdaBoost and decision trees against random forest- given the current data, there was not enough evidence against the hypothesis of no difference in mean (whichever imputation method was used, all p-values were >0.3). Instead, the one-rule method had a lower mean AUC than all other methods (p < 0.0001 in all imputation scenarios).
Since logistic regression was not inferior to random forest in terms of AUC, we report the model fit in Table 4. Soft drusen, as expected, was the most important variable with an odds ratio (positive vs negative) of 19.3 (p < 0.0001). Other relevant variables were: subretinal fluid, subretinal hemorrage, subretinal fibrosisRPE defect/pigment mottling, depigmentation area, and age.
Odds ratio from fitting the LogitBoost logistic regression on the AMD diagnosis outcome (dataset imputing missing values with population’s mean/mode)
Lower 95% CI
Upper 95% CI
Age (per year older)
Gender (M vs F)
Soft drusen (pos vs neg)
Macular scar (pos vs neg)
RPE defect/pigment mottling (pos vs neg)
Depigmentation area (pos vs neg)
Subretinal fluid (pos vs neg)
Macular tickness (per unit increase)
Subretinal fibrosis (pos vs neg)
Subretinal hemorrhage (pos vs neg)
Variable importance ranking for one rule, random forest, adaboost and support vector machine (mean/mode dataset)
Support vector machine
RPE defect.pigment mottling
RPE defect.pigment mottling
RPE defect.pigment mottling
RPE defect.pigment mottling
This work investigated several machine learning approaches for deriving an automated system for AMD diagnosis, using clinical attributes identified by a medical retinal specialist during a routine visit. The study population was monitored via an Electronic Health Record employed by a single clinical practice in Genoa, Italy.
We compared “white-box” (i.e. more interpretable) vs. “black-box” (i.e. less interpretable) techniques in terms of predictive performance. We found that higher complexity-higher performance does not necessarily hold in all contexts and a performance-complexity compromise may be found. For example, the simplest one-rule model yielded an average of 74% AUC in experiments, whilst the more complex, fully non-linear random forest and AdaBoost yielded 92% AUC. Whilst a single variable cannot be used for reliable diagnosis, logistic regression (average AUC of 92%) and decision tree (90% average AUC) were not inferior to random forest. These two modelling techniques combined interpretability and performance, as shown through the odds ratio table and tree diagram, which can be easily followed by a clinician during the diagnostic process.
Physicians must be involved in the decision about what type of system will be used in practice because without their agreement and trust, such a system risks not to being used. Generally, from the perspective of a fully automated system, where a computer program performs all calculations, the main driver should not be the interpretability of the model, but the overall performance. For example, if a black-box ensures an increment 10% over a white-box method and if this 10% is clinically relevant (if properly validated in a prospective trial), then the choice should be obvious. But in the case where model performances are comparable, such as the results reported in this study referring, the white-box is a preferable alternative.
The methods proved to be robust to handle missing values and obtained performances did not change significantly varying the imputation methods. Although complete cases and random forest imputation yielded better performance than the other methods, we think that the most reliable analysis is the one with mean/mode imputation. In fact, the clinicians that performed the analysis suggested that the majority of missing values are likely to be clinical signs that they did not identify during encounters, and thus negative values were not recorded in the system to save time, starting from the assumption that if a sign had been identified a positive value would have been registered in the system.
This study has some limitations. The study population itself is not large (487 subjects and 912 eyes) and includes only patients from a local regional area. Although the out of bag error estimator is very conservative, a way in which the generalisation error could be challenged is by considering the study population and the diagnostic process as regionally biased: for instance, by assuming that the population of Genoa and neighbouring areas (Liguria) is different from Italy (or worldwide) and that doctors make diagnoses differently. Accordingly, it would be interesting to see how the automated diagnostic algorithms would behave on patients from other countries. This would unveil indirectly the differences in the population characteristics and in the gold-standard diagnostic procedures. Performance would be affected only by using two different systems trained on two different populations, whilst one could infer a new integrated model which takes into account such regional differences and aims at the same diagnostic ability in different settings.
A more thorough analysis of missing values could be performed in order to identify the characteristic of missingness and their relevancy. Also, further investigation on intra-patient correlation is warranted. Using two records from the same patient (i.e. both eyes) may yield to correlated observations, thus overall performance results may be affected by this correlation (higher than in reality). We carried out a series of additional experiments, not shown in this paper, using only single-patient and single-eye data (out of 912 eyes, we selected 487 eyes pertaining to 487 different patients randomly, for 10 times). The analysis on this uncorrelated data was consistent with the main results in terms of sensitivity but yielded slightly lower specificity. This is most likely due to the smaller sample size (487 vs. 912) rather than the effect of correlation in the main dataset however a larger study population is required to verify this claim. A larger population and attribute set may also help to refine the model and allow prediction of different subtypes of AMD, for instance neurovascular AMD.
From a rationale point of view, the utility of the system -for now- is to determine which are the diagnostic processes followed by the physicians, since the data were cross-sectional and the diagnoses were made by doctors during visits. We found that even by using powerful nonlinear machine learning models, we could not exactly all the consistent sets of diagnostic pathways. Therefore, even in presence of standardised guidelines, physicians may follow different diagnostic routes (as those shown in the decision tree) which in some cases lead to ambiguities (see the proportions of patients with/without AMD in the tree leaves which correspond to specific variable strata). When longitudinal data and new background variables (e.g. other image processed data) will be available, an automated system will help not only in identifying such different decision paths (with an augmented information set), but also in making early diagnoses feasible and better differentiating those ambiguous subsets of patients.
In fact, we are in an era where diagnosis of AMD is most commonly pursued by image analysis, yet digital image processing techniques embedded in commercial OCT systems are still in their infancy. Imaging can be integrated with information coming from data collected during everyday clinical practice by medical retina specialists. From a technological perspective, implementing such a diagnostic model into a computer program would not be a hurdle, and using a multi-platform language (e.g. Java or Python) could facilitate the integration into Electronic Health Record systems coming from different vendors. If the model were also one of those white-box (logistic regression or decision tree in this case), a graphical user interface showing the diagnostic pathway or variable importance could be provided. Such a program could be used in real-time by physicians as a support to diagnosis as well as for educational purposes.
This study was supported in part by the DINOGMI and DIBRIS Fund of the University of Genova, Italy.
- Bressler NM: Age-Related Macular Degeneration Is the Leading Cause of Blindness.J Am Med Assoc 2004, 291:1900. 10.1001/jama.291.15.1900View ArticleGoogle Scholar
- Rein DB, Wittenborn JS, Zhang X, Honeycutt AA, Lesesne SB, Saaddine J: Forecasting age-related macular degeneration through the year 2050: the potential impact of new treatments.Arch Ophthalmol 2009, 127:533–40. 10.1001/archophthalmol.2009.58View ArticlePubMedGoogle Scholar
- Lamoureux EL, Mitchell P, Rees G, Cheung G, Yeo I, Lee SY, et al.: Impact of early and late age-related macular degeneration on vision-specific functioning.Br J Ophthalmol 2011, 95:666–70. 10.1136/bjo.2010.185207View ArticlePubMedGoogle Scholar
- Hee MR, Baumal CR, Puliafito CA, Duker JS, Reichel E, Wilkins JR, et al.: Optical coherence tomography of age-related macular degeneration and choroidal neovascularization.Ophthalmol 1996, 103:1260–70. 10.1016/S0161-6420(96)30512-5View ArticleGoogle Scholar
- Kanagasingam Y, Bhuiyan A, Abràmoff MD, Smith RT, Goldschmidt L, Wong TY: Progress on retinal image analysis for age related macular degeneration.Prog Retin Eye Res 2014, 38:20–42.View ArticlePubMedGoogle Scholar
- Hee MR, Puliafito CA, Duker JS, Reichel E, Coker JG, Wilkins JR, et al.: Topography of diabetic macular edema with optical coherence tomography.Ophthalmol 1998, 105:360–70. 10.1016/S0161-6420(98)93601-6View ArticleGoogle Scholar
- Pifer EA, Sittig DF: Improving Outcomes with Clinical Decision Support: An Implementer’ s Guide. Soc: In Chicago Healthc. Inf. Manag. Syst; 2005.Google Scholar
- Quellec G, Russell SR, Scheetz TE, Stone EM, Abràmoff MD: Computational quantification of complex fundus phenotypes in age-related macular degeneration and Stargardt disease.Invest Ophthalmol Vis Sci 2011, 52:2976–81. 10.1167/iovs.10-6232View ArticlePubMedPubMed CentralGoogle Scholar
- Sivasankari S, Narasimhan K, Ramya S: Automated diagnosis of ARMD.Int J Eng Technol 2013, 5:1462–4.Google Scholar
- Schlanitz FG, Baumann B, Spalek T, Schütze C, Ahlers C, Pircher M, et al.: Performance of automated drusen detection by polarization-sensitive optical coherence tomography.Investig Ophthalmol Vis Sci 2011, 52:4571–9. 10.1167/iovs.10-6846View ArticleGoogle Scholar
- Pauleikhoff D, Barondes MJ, Minassian D, Chisholm IH, Bird AC: Drusen as risk factors in age-related macular disease.Am J Ophthalmol 1990, 109:38–43. 10.1016/S0002-9394(14)75576-XView ArticlePubMedGoogle Scholar
- Ferris FL, Wilkinson CP, Bird A, Chakravarthy U, Chew E, Csaky K, et al.: Clinical classification of age-related macular degeneration.Ophthalmol 2013, 120:844–51. 10.1016/j.ophtha.2012.10.036View ArticleGoogle Scholar
- Mehryar M, Afshin R, Ameet T: Foundations of Machine Learning. Cambridge, Massachussets, London, England: The MIT Press; 2012.Google Scholar
- Zheng Y, Hijazi MHA, Coenen F: Automated “disease/no disease” grading of age-related macular degeneration by an image mining approach.Invest Ophthalmol Vis Sci 2012, 53:8310–8. 10.1167/iovs.12-9576View ArticlePubMedGoogle Scholar
- Serrano-Aguilar P, Abreu R, Antón-Canalís L, Guerra-Artal C, Ramallo-Fariña Y, Gómez-Ulla F, et al.: Development and validation of a computer-aided diagnostic tool to screen for age-related macular degeneration by optical coherence tomography.Br J Ophthalmol 2012, 96:503–7. 10.1136/bjophthalmol-2011-300660View ArticlePubMedGoogle Scholar
- Hijazi MHA, Coenen F, Zheng Y: Data mining techniques for the screening of age-related macular degeneration.Knowl Base Syst 2012, 29:83–92.View ArticleGoogle Scholar
- Liu YY, Ishikawa H, Chen M, Wollstein G, Duker JS, Fujimoto JG, et al.: Computerized macular pathology diagnosis in spectral domain optical coherence tomography scans based on multiscale texture and shape features.Investig. Ophthalmol. Vis. Sci 2011, 52:8316–22. 10.1167/iovs.10-7012View ArticleGoogle Scholar
- Kankanahalli S, Burlina PM, Wolfson Y, Freund DE, Bressler NM: Automated classification of severity of age-related macular degeneration from fundus photographs.Invest Ophthalmol Vis Sci 2013, 54:1789–96. 10.1167/iovs.12-10928View ArticlePubMedGoogle Scholar
- Bonetto M, Fraccaro P, Nicolo M, Giacomini M: A web-tool to manage ophthalmologic electronic health records.IEEE-EMBS Int. Conf. Biomed. Heal. Informatics 2014. IEEE; 2014:346–349Google Scholar
- Fraccaro P, Dentone C, Fenoglio D, Giacomini M: Multicentre clinical trials’ data management: a hybrid solution to exploit the strengths of electronic data capture and electronic health records systems.Inform Health Soc Care 2013, 38:313–29. 10.3109/17538157.2013.812648View ArticlePubMedGoogle Scholar
- Murdoch IE, Morris SS, Cousens SN: People and eyes: statistical approaches in ophthalmology.Br J Ophthalmol 1998, 82:971–3. 10.1136/bjo.82.8.971View ArticlePubMedPubMed CentralGoogle Scholar
- Bishop CM: Pattern Recognition and Machine Learning. Berlin, Heidelberg: Springer; 2006:738.Google Scholar
- Hosmer DW Jr, Lemeshow S: Applied Logistic Regression. Hoboken, New Jersey: John Wiley & Sons; 2004:392.Google Scholar
- Friedman J, Hastie T, Tibshirani R: Additive logistic regression: a statistical view of boosting (With discussion and a rejoinder by the authors).Ann Stat 2000, 28:337–407.View ArticleGoogle Scholar
- Hornik K, Buchta C, Zeileis A: Open-source machine learning: R meets Weka.Comput Stat 2008, 24:225–32.View ArticleGoogle Scholar
- Cortes C, Vapnik V: Support-vector networks.Mach Learn 1995, 20:273–97.Google Scholar
- Dimitriadou E, Hornik K, Leisch F, Meyer D, Weingessel A: SVM, e1071 Package, The R project for statistical computing. 2004.Google Scholar
- Breiman L, Friedman JH, Olshen RA, Stone CJ: Classification and regression trees. Advanced B. Monterey: CA; 1984.Google Scholar
- Hothorn T, Hornik K, Zeileis A: party: A Laboratory for Recursive Partytioning.http://cran.r-project.org/web/packages/party/index.html
- Breiman L: Random Forests.Mach Learn 2001, 45:5–32. 10.1023/A:1010933404324View ArticleGoogle Scholar
- Liaw A, Wiener M: Classification and Regression by randomForest.R News 2002, 2:18–22.Google Scholar
- Freund Y, Schapire RE: A Decision-Theoretic Generalization of On-Line Learning and an Application to Boosting.J Comput Syst Sci 1997, 55:119–39. 10.1006/jcss.1997.1504View ArticleGoogle Scholar
- Stekhoven DJ, Bühlmann P: MissForest–non-parametric missing value imputation for mixed-type data.Bioinformatics 2012, 28:112–8. 10.1093/bioinformatics/btr597View ArticlePubMedGoogle Scholar
- Fawcett T: An introduction to ROC analysis.Pattern Recognit Lett 2006, 27:861–74. 10.1016/j.patrec.2005.10.010View ArticleGoogle Scholar
- Breiman L: Bagging predictors.Mach Learn 1996, 24:123–40.Google Scholar
- Nadeau C, Bengio Y: Inference for the Generalization Error.Mach Learn 2003, 52:239–81. 10.1023/A:1024068626366View ArticleGoogle Scholar
- The pre-publication history for this paper can be accessed here:http://www.biomedcentral.com/1471-2415/15/10/prepub
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.