Predicting microRNA precursors with a generalized Gaussian components based density estimation algorithm
© Hsieh et al; licensee BioMed Central Ltd. 2010
Published: 18 January 2010
MicroRNAs (miRNAs) are short non-coding RNA molecules, which play an important role in post-transcriptional regulation of gene expression. There have been many efforts to discover miRNA precursors (pre-miRNAs) over the years. Recently, ab initio approaches have attracted more attention because they do not depend on homology information and provide broader applications than comparative approaches. Kernel based classifiers such as support vector machine (SVM) are extensively adopted in these ab initio approaches due to the prediction performance they achieved. On the other hand, logic based classifiers such as decision tree, of which the constructed model is interpretable, have attracted less attention.
This article reports the design of a predictor of pre-miRNAs with a novel kernel based classifier named the generalized Gaussian density estimator (G2DE) based classifier. The G2DE is a kernel based algorithm designed to provide interpretability by utilizing a few but representative kernels for constructing the classification model. The performance of the proposed predictor has been evaluated with 692 human pre-miRNAs and has been compared with two kernel based and two logic based classifiers. The experimental results show that the proposed predictor is capable of achieving prediction performance comparable to those delivered by the prevailing kernel based classification algorithms, while providing the user with an overall picture of the distribution of the data set.
Software predictors that identify pre-miRNAs in genomic sequences have been exploited by biologists to facilitate molecular biology research in recent years. The G2DE employed in this study can deliver prediction accuracy comparable with the state-of-the-art kernel based machine learning algorithms. Furthermore, biologists can obtain valuable insights about the different characteristics of the sequences of pre-miRNAs with the models generated by the G2DE based predictor.
MicroRNAs (miRNAs) are short RNAs (~20-22 nt) that direct post-transcriptional regulation of target genes by arresting the translation of mRNAs or by inducing their cleavage . Since the initial discovery of miRNAs in Caenorhabditis elegans, RNA molecules are regarded as not only a carrier of gene information, but also a mediator of gene expression [2, 3]. Currently, 9539 experimentally verified miRNAs have been collected in the miRBase database .
Experimental miRNA identification is accomplished by directional cloning of endogenous small RNAs . Considering both the time and cost of experimental methods, many computational approaches have been proposed . The mature miRNAs is cleaved from a 70-120 nt precursor (pre-miRNA) with a stable hairpin structure. Identifying this specific structure has became an important step in analyzing miRNAs . The earliest computational approaches for discovering pre-miRNAs are mainly based on comparative techniques and can only discover pre-miRNAs that are closely homologous to known miRNAs [7–10]. Alternatively, scientists have resorted to ab initio approaches to discover pre-miRNAs based on the characteristics of their secondary structures [11–15]. The ab initio approaches based predictors are more generally applicable than those that are based on homology searches, since the ab initio approaches do not rely on the existence of homologues. As a result, design of the ab initio approaches based predictors has attracted more attention in recent years.
The basis of the ab initio approaches is to design a coding scheme that maps the sequence and structure characteristics of pre-miRNAs into distinguishable patterns of feature vectors. Then, a supervised learning algorithm, also commonly referred to as data classification, is invoked to discover pre-miRNAs in the query RNA sequence based on the associated feature vectors. In recent years, the design of the coding scheme for characterizing pre-miRNAs has been extensively studied and several different schemes, including base pairing propensity , folding energy , base pair distance , and degree of compactness , have been proposed. On the other hand, most people working on this subject have employed the existing kernel based data classification algorithms such as the hidden Markov model (HMM) [20, 21], the support vector machine (SVM) [22, 23], and the kernel density estimator  to build the predictors due to the superior prediction performance delivered by these algorithms . Nevertheless, conventional logic based data classification algorithms such as decision trees [25, 26] and decision rules [27, 28] continue to play a major role in some applications due to the interpretability of the logic rules identified by these algorithms. Such a summarized view of the characteristics and distribution of the data set further provides valuable insights about the relations among different features and is highly desirable for in-depth analysis of pre-miRNAs.
Aiming to provide the desirable functionalities of both the kernel based and the logic based data classification algorithms, the study presented in this article has exploited the generalized Gaussian density estimator (G2DE) that we have recently proposed . The G2DE identifies a small number of generalized Gaussian components to model the distribution of the data set in the vector space. As a result, the user can examine the parameter values associated with these of Gaussian components to obtain an overview picture of the distribution of the data set. Furthermore, through in-depth analysis of the parameter values, the user can obtain valuable insights about the relations among different features.
Results and discussion
This section first describes the overall scheme of using G2DE to analyze pre-miRNAs. Each step of the analysis procedure is further elaborated in the Methods section. Next, the prediction performance of the employed classification algorithm is evaluated and compared with four classification algorithms. A demonstrative analysis is also presented to investigate the interpretability of the employed classification algorithm.
Using G2DE to analyze pre-miRNAs
This work uses only sequence information to identify pre-miRNAs from pseudo hairpins, which are RNA sequences with similar stem-loop features to pre-miRNAs but containing no mature miRNAs. In this method, each RNA sequence is represented as a feature vector. The characteristics used to generate the feature vector, including sequence composition, folding energy and stem-loop shape, have been shown to be useful for predicting pre-miRNAs in previous studies [17, 18, 30]. The main task carried out during the learning process of this method is to construct two mixture models of generalized Gaussian components for summarizing pre-miRNAs and pseudo hairpins in the vector space. We model this learning process as a large-parameter-optimization problem (LPOP) and employ an efficient optimization algorithm, Ranking-based Adaptive Mutation Evolutionary (RAME) , to decide the parameters associated with each generalized Gaussian component. Finally, the models learnt through the LPOP process are used to predict whether a query RNA sequence is a pre-miRNA. Furthermore, the constructed model of G2DE comprises a small number of generalized Gaussian components and is capable of detecting the sub-clusters or sub-classes of the data set. This study utilizes this feature of G2DE to develop a two-stage analysis where the first stage uses G2DE to partition the data set while the second stage uses G2DE to investigate each of the partitioned subsets.
The present approach is evaluated using two datasets, HU920 and HU424, combined with four feature sets. See the Methods section for details of the datasets and the feature sets. The prediction performance is compared to two kernel based classifiers, SVM and RVKDE, and two logic based classifiers, C4.5 and RIPPER. The parameters for each classifier are determined by maximizing the prediction accuracy of ten-fold cross-validation on the HU920. A prediction is performed by using the HU920 dataset to predict the HU464 dataset with the selected parameters.
The employed G2DE classifier is compared with two kernel based classifiers, SVM and the relaxed variable kernel density estimator (RVKDE) . The SVM is a commonly used classifier because of its prevailing success in diverse bioinformatics problems [14, 33, 34], while the RVKDE has been shown to have advantages for predicting species-specific pre-miRNAs . Two well-known logic based classifiers, C4.5  and RIPPER , are also included as representatives of logic based classification algorithms.
Prediction accuracies achieved by SVM, RVKDE, G2DE, C4.5 and RIPPER.
Kernel based classifiers
Logic based classifiers
G 2 DE
G 2 DE-2
Evaluation measures employed in this study.
Matthews' correlation coefficient
(TP × TN-FP × FN)/sqrt((TP+FP) × (TN+FN) × (TP+FN) × (TN+FP))
Comparison of G2DE and two existing pre-miRNA identification packages.
Interpretability of G2DE
Summary of the adopted feature sets.
AA, AC, ..., UU
Frequencies of 16 dinucleotide pairs
Percentage of nitrogenous bases which are either G or C
Ratio of dG to the number of stems
Ratio of dG to %G+C
Adjusted base pairing propensity. dP is the number of base pairs observed in the secondary structure divided by the sequence length.
Adjusted minimum free energy of folding. dG is the minimum free energy (MFE) divided by the sequence length.
Adjusted Shannon entropy. dQ measures the entropy of the base pairing probability distribution (BPPD).
Adjusted base pair distance. dD measures the average distance between all base pairs of structures inferred from the sequence.
Compactness of the tree-graph representation of the sequence.
zG, zQ, zD, zP, zF
5 normalized variants of dP, dG, dQ, dD and dF
Ratio of loop length to hairpin length
Another useful analysis provided by the learnt model of the G2DE based predictor is sub-class detection. By defining that a sample belongs to the Gaussian component reporting the maximum function value at the location of that sample, the learnt Gaussian components of G2DE suggests that "a sample that belongs to GGC2 is a pre-miRNA." This statement is similar to the normal decision rule "a sample that has mfe2 < 0.4 is a pre-miRNA," except that the conditions (belong vs. mfe2 < 0.4) within the rule inferred by G2DE is non-linear. This non-linearity of a single rule is an important feature of G2DE to describe more complicated model than traditional logic based classifiers when the number of kernels of G2DE is limited to the number of rules of logic based algorithms. One immediate application of the sub-class detection is to group samples into clusters and then construct a classifier for each of the clusters. The performance improved by applying such two-stage framework has been shown in the previous subsection.
Software predictors that identify pre-miRNAs in genomic sequences have been exploited by biologists to facilitate molecular biology research in recent years. However, design of advanced predictors of pre-miRNAs has focused mostly on coding the distinguishable sequence as well as structure characteristics of miRNAs. The study presented in this article addresses this issue from the aspect of exploiting advanced machine learning algorithms. The G2DE employed in this study has been designed to deliver prediction accuracy comparable with the state-of-the-art kernel based machine learning algorithms, while providing the user with good interpretability. As demonstrated by the experiments reported in this study, the models generated by the G2DE based classifier provide the user with crucial clues about the different characteristics of the sequences of pre-miRNAs.
This work adopts 33 characteristic features which have been shown to be useful for miRNA detection in previous studies [16–19, 30, 39–41]. To investigate how alternative classifiers perform when using different features, these features are grouped as four different sets according to their biochemical properties. The first feature set includes 17 sequence composition variables, which comprise frequencies of 16 dinucleotide pairs and proportion of G and C in the RNA molecule. The second feature set includes seven folding measures: Minimum Free Energy (MFE) and two of its variants [17, 18, 39], base pairing propensity , Shannon entropy , base pair distance [18, 40] and degree of compactness [19, 41]. The third feature set uses the Z-score  to normalize the features in the second feature set except the two MFE variants. The fourth feature set includes four stem-loop features: hairpin length , loop length , consecutive base-pairs  and the ratio of loop length to hairpin length . Table 4 shows a summary of these features.
The process of data preparation is the same as that in the compared pre-miRNA identification packages [14, 15] for a fair comparison. 692 human miRNA precursors are collected from the miRBase registry database  (release 12.0) as the positive set. For the negative set, 8494 pseudo hairpins collected from the protein-coding regions (CDSs) according to RefSeq  and UCSC refGene  annotations are analyzed. These RNA sequences are extracted from genomic regions where no experimentally validated splicing event has been reported . The secondary structures of the 8494 RNA sequences are obtained by executing RNAfold . RNA sequences with <18 base pairs on the stem, MFE > -25 kcal/mol and multiple loops are excluded. As a result, 3988 pseudo hairpins, which are similar to genuine pre-miRNAs in terms of length, stem-loop structure, and number of bulges but not have been reported as pre-miRNAs, are used as the negative set.
Based on the positive and negative sets, one training set and one testing set are built to evaluate the pre-miRNA predictors. The training set, HU920, comprises 460 human pre-miRNAs and 460 pseudo hairpins randomly selected from the positive and negative sets, respectively. The HU920 dataset is used for parameter selection and model construction of the pre-miRNA predictors. The testing set, HU464, comprises the remaining 232 human pre-miRNAs and 232 randomly selected pseudo hairpins. Care has been taken to ensure that no pseudo hairpin is included in both datasets. Before performing any experiments on these datasets, the features are rescaled linearly by the svm-scale program  to the interval of [-1.0, 1.0].
Generalized Gaussian density estimator
where S j is the set of class-j training samples and |S j | is the number of class-j training samples.
In current G2DE implementation, the user can specify the maximum number of generalized Gaussian components that can be incorporated to generate the approximate probability density function for one class of samples. If the user sets this number to k and the total number of features of the data set is d, then the learning algorithm of G2DE needs to figure out the optimal combination of the values of the following k(d+2)(d+1)/2 parameters in order to generate one approximate probability density function: k d-dimensional vectors as the means of the generalized Gaussian components; k sets of d(d+1)/2 coefficients with each corresponding to the covariance matrix of one generalized Gaussian components; k weights. The optimal combination of parameter values are figured out using the Ranking-based Adaptive Mutation Evolutionary (RAME) algorithm .
Z is the vector formed by concatenating all the k(d+2)(d+1)/2 parameters associated with the approximate probability density function of one class of samples;
#Correct is the number of correctly classified training samples;
θ is a user-defined parameter;
The objective function adopted in the learning process of G2DE consists of two terms. Both terms have specific mathematical meanings. Maximizing term #Correct implies that the number of training samples of which the class can be correctly predicted with the decision model is maximized. Meanwhile, maximizing the second term implies that the mixture models give the maximum likelihood with the training samples.
The learnt model of G2DE is composed of a small number of Gaussian components. In this study, a sample is defined as belonging to the Gaussian component reporting the maximum function value at the location of that sample. The two-stage classification framework is performed by first grouping samples belonging to the same Gaussian component into clusters and then constructing a classifier for each of the clusters. In the first stage, all training samples would be submitted to G2DE for constructing a mixture model of generalized Gaussian components. Suppose that the learnt model contains n1 generalized Gaussian components, essentially dividing the training dataset into n1 clusters. Each training sample would then be assigned to the Gaussian component to which it belongs. In the second stage, G2DE is invoked n1 times to construct n1 mixture models for each cluster. If each of the learnt models in the second stage contains n2 generalized Gaussian components, the final classifier will contain n1 × n2 generalized Gaussian components.
The authors would like to thank the National Science Council of the Republic of China, Taiwan, for financially supporting this research under Contract Nos NSC 97-2627-P-001-002, NSC 96-2320-B-006-027-MY2 and NSC 96-2221-E-006-232-MY2.
This article has been published as part of BMC Bioinformatics Volume 11 Supplement 1, 2010: Selected articles from the Eighth Asia-Pacific Bioinformatics Conference (APBC 2010). The full contents of the supplement are available online at http://www.biomedcentral.com/1471-2105/11?issue=S1.
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