Research ArticleMulti-task Learning For Cross-platform SiRNA Efficacy .

Liu et al. BMC Bioinformatics 2010, 1Page 4 of 16Table 2: Feature weights for siRNA design derived from multi-task learningNo.FeatureWeight1position-dependent nucleotide consensus: sum0.19542Δ G difference between positions 1 and 180.09873Δ G of sense-antisense siRNA duplexes0.07744position-dependent nucleotide consensus: preferred0.07335preferred dinucleotide content index0.07266local target mRNA stabilities (Δ G)0.06517position-dependent nucleotide consensus: avoided0.06408nucleotide content: U0.06039stability (Δ G) of dimers of siRNAs antisense strands0.053710stability profile for each two neighboring base pairs in the siRNA sense-antisense in position 10.038411siRNA antisense strand intra-molecular structure stability (Δ G)0.032712avoid dinucleotide content index0.032413stability profile for each two neighboring base pairs in the siRNA sense-antisense in position 130.029814stability profile for each two neighboring base pairs in the siRNA sense-antisense in position 180.027915nucleotide content: G0.026716stability profile for each two neighboring base pairs in the siRNA sense-antisense in position 20.022217stability profile for each two neighboring base pairs in the siRNA sense-antisense in position 60.015918stability profile for each two neighboring base pairs in the siRNA sense-antisense in position 140.013819frequency of potential targets for siRNA0.0000learning paradigm, a quantitative evaluation of these 19features will be provided to reveal the relevance of these19 features to siRNA design, as shown in the next section.We should explain the reasons for why this particulardata source is chosen: First, the data source containsnearly all the RNAi experiments with numerical siRNAefficacy values reported in recent studies, thus proven tobe a complete dataset for training regression models forsiRNA efficacy prediction. Second, the data source is amixture dataset with cross-platform experiments statedin P?l Sæ trom dataset, a dataset misused by several computational siRNA efficacy prediction models where itsdata diversity is not considered [30,31]. We want to usethe multi-task learning paradigm to address this crossplatform issue by comparing our test results with those oftraditional studies. We noted that in the current study, weonly focused on the regression model rather than thegeneral classification models, since the siRNA efficacyvalues are in nature continuously valued under differentexperimental platforms and we don't want to waste anydata information in using our model. Though our modelis designed for regression problem, it's actually also suitable for the classification problem with categorical data asinput. To support our argument, we applied our model inmulti-task classification with the siRecords dataset [22],which normally standardized siRNA with consistent efficacy ratings across different platforms. The results arelisted in the supplementary materials [Additional file 1],and they also indicate that our multi-task classificationmodel is significantly better the single-task classificationmodels.Linear ridge regression modelGiven a representation of siRNAs as feature vectors, a linear ridge regression model was applied [35] to predict thenovel siRNA efficacy from a set of siRNAs with knownefficacy. Linear ridge regression is a classical statisticaltechnique that aims to find a linear function that modelsthe dependencies between covariances {x i}in 1 in d andresponse variables {y i}in 1 in , where d is the number ofdata features. The standard way to handle this problem isusing the ordinary least square (OLS) method, whichminimizes the squared loss: (yi w T x i )2(1)iHowever, due to limited training examples, the varianceof the estimated w by OLS may be large, and thus the estimation is not reliable. An effective way to overcome this

Liu et al. BMC Bioinformatics 2010, 1Page 5 of 16problem is to penalize the norm of w as in ridge regression. Instead of minimizing squared errors, ridge regression minimizes the following cost:J ( w) (yi w T x i )2 l w2(2)Performance Measurementiwhere λ is a fixed positive number. By introducing theregularization parameter λ, the ridge regression canreduce the estimated variance at the expense of increasing training errors. The regularization parameter λ controls the trade-off between the bias and variance of theestimate. In the linear ridge regression model, it is shownthat the predicted label (i.e., wT x) of a new unlabeledexample x is:y T (K l I) 1k(3)where K is the matrix of dot products of the vectors {xi,i 1,2, ., n} in the training set:K i , j x iT x j , i, j 1, 2, , n(4)and κ is the vector of dot products of x and the vectorsin the training set:ki x iT x , i 1, 2, , n[10,100] with interval 10. Finally λ 10 was obtained byevaluation of the total cross-validation errors in the 14experiments. This parameter was kept the same throughout our study for consistent comparison.(5)It should be noted that this model could be generalizedto kernel ridge regression by using the kernel trick [36].However, model selection is not our main focus here.Various regression models can be applied, but we choosethe linear ridge regression as our regression model basedon the following reasons: (1) The performance of linearridge regression model is comparable to most of thestate-of-art regression models on siRNA efficacy prediction, and it is simple enough in representation [29]. Weapplied the sophisticated support vector regression (SVR)with both linear kernel and radial basis function kernel insiRNA efficacy prediction, and we obtained nearly thesame (even worse) prediction results as compared to linear ridge regression (See Results and Discussion). (2) Wealso want to exploit the feature importance across theplatforms for better siRNA design. This goal cannot beachieved if we use a kernel regression model since it willmap the input features as some non-meaningful highdimensional representations.In our experimental study, 5-fold cross-validation wasapplied to find the optimal regularization parameter thatminimizes the cross-validation errors. For all the 14experiments, 5-fold cross-validation is performed on 5regularization parameter regions respectively, i.e.[0.001,0.1] with interval 0.001, [0.01,0.1] with interval0.01, [0.1,1] with interval 0.1, [1,10] with interval 1 andIn our experiments, the proposed multi-task learning andtraditional single task learning were evaluated based onroot mean squared error (RMSE) [35], which is usuallyused as a measurement of the prediction ability in theregression model. The residual e is the differencebetween the observed data and the fitted model, denotedas:(6)e i y i yˆ iwhere yi is the observed siRNA efficacy and ŷ i is thepredicted siRNA efficacy. The root mean squared error isdefined as follows:RMSE 1nn e2i(7)i 1where n is the number of predicted siRNA sequences.The smaller the RMSE is, the better the predict performance is.Paired t-test for model comparisonIn our study, the paired t-test and F-test is performed tocompare multi-task learning versus single-task learningin siRNA efficacy prediction [37]. Paired t-test is provento work well by machine learning community in measuring the significance of one model outperforming anothermodel and it is suitable for the most common data distribution assumption (say, normal distribution, instead ofspecific chi-squared distribution, for example) when wedon't know the exact data distribution. To be briefly, thistest is trying to determine whether the mean of a set ofsamples, i.e., the cross-validation estimates for the various datasets (tasks) is significantly greater than, or significantly less than the mean of another, followed by theassumptions that the observed data are from a matchedsubject and are drawn from a population with nearly tonormal distribution.More specifically, given two paired sets Xi and Yi of nmeasured values, which could be the error rates evaluated by RMSE for each experiments under the single-tasklearning model and multi-task learning model in outstudy, the paired t-test determines whether this twomodel differ from each other in a significant way underthe assumptions that the paired prediction error rate differences for each experiment are independent and identically normally distributed.

Liu et al. BMC Bioinformatics 2010, 1Page 6 of 16To apply the paired t-test, let:Xˆ i ( X i X )(8)Yˆ i (Yi Y )(9)Then define t by:t (X Y)n(n 1) in 1 ( X i Yi )step. In the unsupervised step, the common representations shared by the tasks are learned and then in thesupervised step, these representations are used to learnthe regression functions for each each task. Detailed algorithm derivations can be found in supplementary file[Additional file 1]. A Matlab script package for suchmulti-task learning in siRNA efficacy prediction is provided, which is accessible freely on our website.Feature selection across tasks2(10)where n- 1 is the statistic degrees of freedom. Once a tvalue is determined, a p-value can be found using a tableof values from Student's t-distribution to determine thesignificance level at which two models differ.Multi-task learning for siRNA efficacy predictionComputational frameworkMulti-task learning has been developed in machinelearning research to situations where multiple relatedlearning tasks are accomplished together [38-46]. It hasbeen proven to be more effective than learning each taskindependently when there are explicit or hidden interrelationship among the tasks that can be exploited [47].The intuition underlying the framework is that the multiple related tasks can benefit each other by sharing thedata and features across the tasks, which can often boostthe learning performance of each single task. Such anadvantage is especially evident when the number oflabeled data in each task is limited, such that training oneach single task with insufficient labeled data may notwork well. Recently, researchers have begun to resort tothe multi-task learning model to solve biological problems, such as medical diagnosis, tumor classification anddrug screening [48-50]. However, applications of multitask learning in bioinformatics have just begun.In this study, a comprehensive computational framework for cross-platform RNAi experiment analysis is presented. The workfellow of the framework is shown inFigure 1. Extensive experimental tests were conducted tothoroughly examine the performance of the multi-tasklearning framework.AlgorithmIn this section, we demonstrate how to formulate thecross-platform siRNA efficacy prediction problem as amulti-task learning problem. A critical issue is to learn aset of sparse (regression) functions across the tasks. Inparticular, l1-norm regularization is used to control thenumber of learned features common for all the tasks, andthe whole multi-task learning problem is equivalent to aconvex optimization problem [47]. Consequently, theproblem is solved iteratively until convergence, by alternately performing an unsupervised step and a supervisedIn this section, we show that the proposed multi-tasklearning provides us an efficient way to evaluate the feature importance in siRNA design across various platforms. Based on the parameter W that are derived fromEquation (11), the optimal solution for matrix D isobtained, which can be used for feature selection. In ourcase, D is a diagonal matrix with D diag [λ1, ., λd], sinceU is defined as an identity matrix. Specifically, we havewili W2 , i 1, d2,1(11)If λi 0, the ith feature is the common feature; otherwise, the ith feature is not useful in regression learningacross the different tasks, since its regression weights arezeros for all the tasks. The value of λi indicates the weightof the corresponding feature, which gives us a quantitative way to evaluate the importance of various features forsiRNA design.Results and DiscussionIn this section, a number of experiments on multi-tasklearning for cross-platform siRNA efficacy prediction areperformed. The siRNA efficacy prediction problem is formulated as a linear ridge regression model and theparameters of this model are tuned with a 5-fold crossvalidation process. The root mean square error (RMSE) isadopted as the performance evaluation for different testresults. To verify the statistical significance of our modelover the baseline algorithms, the paired t-test on theexperimental results is also conducted [37].Multi-task learning for cross-platform siRNA efficacypredictionSTUDY 1: Single task learningIn this study, linear ridge regression was we first compared with SVR for single task siRNA efficacy prediction.As an overview, linear ridge regression was shown toachieve the same prediction results as SVR (see Table 3).As a result, linear ridge regression was taken as the chosen learning method in the following study. We show thatthe 14 cross-platform experiments that we use are indeedhave different conditional distribution. We will see thatsimple combinational or normalization methods only

Liu et al. BMC Bioinformatics 2010, 1Page 7 of 16Figure 1 Computational framework in our study.provide very limited gain on the improvement of finalsiRNA efficacy prediction.In our first test scenario (Test 1), we randomly selected50% of the data from each experiment(or platform) as thetraining data to train a linear ridge regression model, andthen tested it on the remaining 50% of the data in thatexperiment. We ran the test 10 times and reported theaverage RMSE for each experiment. The result of Test 1was compared with another test scenario (Test 2), inwhich the same parameters are used under normalizationprocess. In the normalization process, we scaled all theexperimental labels (siRNA efficacy values) into [0,1] andpooled 50% of the data from each experiment together totrain a general model. Finally, we tested the model on theremaining 50% of the data for each experiment, respectively. The final RMSE was calculated based on the rescaled predicted and ground-truth labels. Results of thesetwo tests are given in Table 4.From Table 4, we can clearly see that even if the trainingdata labels are scaled to the same level, and the trainingdata are pooled together to train a general model for individual task prediction, the prediction results are still not

Liu et al. BMC Bioinformatics 2010, 1Page 8 of 16Table 3: Comparison between linear ridge regression and support vector regression for single task siRNA efficacyprediction.TestRMSET1T2T3T4T5T6T7Linear ridge 2532.9677SVR with linear .2824SVR with radial basis function .4349T8T9T10T11T12T13T14Linear ridge 3328.7044SVR with linear .7536SVR with radial basis function .8301"E" denotes "Experiment". Linear ridge regression and support vector regression(with linear kernel and radial basis function kernel) aretrained with 50% of the data from each experiment, respectively. p-value calculated by pair t-test on linear ridge regression and SVR withlinear kernel is 0.2592. p-value calculated by pair t-test on linear ridge regression and SVR with radial basis function kernel is 0.0913.improving all the time. In fact, we observe worse resultsin half of the experiments under this general model. Statistical test evaluation on these two models has shownthat there is no statistically significant difference betweenthese two prediction results (p-value 0.7043). It indicates that directly scaling the labels and increasing thenumber of training data by combining the data fromcross-platform experiments only provides limited help inimproving the prediction performance; in many cases theperformance is degraded. All tests so far reveal that thereexists a high-level of diversity across these 14 experiments, which motivates us to apply more sophisticatedmulti-task learning in this study.STUDY 2: Multi-task learningIn this study, we show that multi-task learning is able toimprove the prediction performance as compared to single-task learning. Multi-task learning is performed on the14 cross-platform experiments with the same setting asTest 1 (50% training data as well as 50% testing data foreach experiment). Furthermore, in order to examine theimpact of the size of training set on the model's performance, we compared single task learning with multi-tasklearning trained with other different percentages of datafrom each experiment. That is, we trained the modelswith 10%, 30%, 70% and 90% of the whole data, respectively. The testing results are summarized in Table 4 andFigure 2 as Test 3.From Table 5, it can be clearly seen that multi-tasklearning achieves better performance as compared to single task learning under various training data percentagesfor nearly all the experiments. An exception is for experiment 9, in which the two models obtained almost thesame level of performance. Pair t-test evaluation indicated that multi-task learning is significantly superior tosingle task learning in siRNA efficacy prediction with alldifferent percentages of training data (p-values are listedin Table 5), thanks to the joint learning strategy employedin the multi-task learning model. The prediction performance of most experiments is shown to be correlated tothe size of training data, both for single task learning andfor multi-task learning, as shown in Figure 2.STUDY 3: Testing on independent experimentsAnother two experiments [23] were also used as independent experiments in this study (Table 1). These experiments were tested in a very low siRNA concentration,including 6 mRNAs with 20 binding siRNAs and 4mRNAs with 12 binding siRNAs, respectively. Two different tests were performed: (1) Single task learning wascompared with multi-task learning on these two independent experiments (Test 4), and (2) Multi-task learningwas performed on the two independent experimentstoget

knowledge, our work is one of the first to apply the multi-task learning model for siRNA efficacy analysis for learn-ing regression models. To test our multi-task regression learning framework, extensive experiments were conducted to show that multi-task learning is naturally suitable for cross-plat-form siRNA efficacy prediction.