BACKGROUND
discovering novel disease genes is still challenging for constitutional genetic diseases  for which no prior knowledge - such as known disease genes or disease-related pathways - is available.
performing genetic studies frequently result in large lists of candidate genes of which only few can be followed up for further investigation.
gene prioritization establishes the ranking of candidate genes based on their relevance with respect to a biological process of interest, from which the most promising genes can be selected for further analysis.
several computational methods for prioritizing candidate genes have been proposed, such as endeavour  <cit> , genewanderer  <cit> , or prioritizer  <cit>  that rank candidate genes based on associations between known disease genes and candidate genes using different data sources and methodology.
lage et al.
developed a phenome-interactome network that integrates phenotypic literature information from omim with a cross species protein-protein interaction  network  <cit> .
chen et al.
applied link based strategies widely used in social and web network analyses to prioritize disease candidate genes based on ppi networks  <cit> .
subramanian et al.
developed a computational method, gene set enrichment analysis , that determines whether an a priori defined set of genes shows statistically significant concordant differences between two biological states , i.e.
whether the genes are differentially expressed or not  <cit> .
similarly, liu et al.
developed a network-based approach, gene network enrichment analysis  for the identification of transcriptionally altered biological processes between disease and normal states  <cit> .
it analyzes gene expression microarray and protein-protein interaction data to identify the affected regions in a protein-protein interaction network.
beside these methods, others can be found in the literature that prioritize candidate genes for human diseases.
among these, several were implemented as web-based applications that can be freely accessed.
in a previous study we have reviewed distinct web-based and freely accessible gene prioritization tools for human diseases  <cit> .
the aforementioned methods usually rank candidate genes by matching their information across multiple data sources against a profile derived from a set of genes, keywords, pathways, or biological processes already known to be associated with the phenotype.
however, often only little is known about the molecular basis of the phenotype, such as no known disease genes and limited knowledge about the biological cascades involved, and only few or no keywords are known which can be used either to retrieve genes or to perform text mining.
to overcome this limitation, we proposed in a previous study a computational method to identify the most promising candidates within a region for which limited or no prior knowledge is available regarding a phenotype of interest by using experimental data on differential gene expression between affected and healthy individuals  <cit> .
using a network-based approach, we assessed the relevance of a candidate gene by considering the level of differential expression in its neighborhood under the assumption that strong candidates tend to be surrounded by differentially expressed neighbors.
for several genetic diseases, however, there is no guarantee that the expression levels of the disease gene itself is affected, rather, genes ''downstream'' of the disease gene are those whose expression will be affected.
therefore, we consider the differential expression data at the network levels instead of  gene levels.
mapping expression patterns on a network, we then expect to observe a disrupted expression module around the disease gene, while other candidate genes  should not be part of such a disrupted expression module.
this approach is less biased than assessing relevant candidate genes by performing text mining, finding associations between known disease genes and candidate genes, or detecting disease relevant pathways.
we define a notion of a soft neighborhood where each gene is given a contributing weight, which decreases with the distance from the candidate gene in the network.
to account for multiple paths between genes, we defined a notion of distance using the laplacian exponential diffusion kernel.
finally, we scored candidates by aggregating the differential expression of their neighbors weighted as a function of distance.
to further improve prioritization results we have extended our previous work in this study by applying four different strategies to prioritize candidate genes based on network analysis of differential expression using distinct machine learning approaches to determine whether a gene is surrounded by highly differentially expressed genes in a functional association or protein-protein interaction network.
here, we have mainly focused on further performance improvement and determination of an appropriate neighborhood for network propagation of differential expression analysis by considering and benchmarking many variables occurring here in the presented ranking strategies.
we have further compared our prioritization results with a standard procedure in genetics that ranks candidate genes based solely on their differential expression levels.
first, we propose an alternative to our previous idea of defining a notion of distance using the laplacian exponential diffusion kernel.
instead of aggregating the differential expression of neighbors weighted as a function of distance, we have smoothed a candidate gene's differential expression levels through kernel ridge regression.
we name this strategy kernel ridge regression ranking.
second, we have applied the heat kernel diffusion ranking, introduced by chung and yau   <cit> , to our problem of disease candidate gene prioritization.
third, we have carried out network diffusion by applying the arnoldi algorithm based on a kyrlov space method as presented in  <cit> .
we name this strategy arnoldi diffusion ranking.
fourth, we have ranked the candidate genes by combining their differential expression levels with the average of the differential expression levels among their direct neighbors in a functional association or protein-protein interaction network, which we name direct neighborhood ranking.
this straightforward approach for scoring candidates is presented here for comparison purposes as a naïve strategy for network analysis of differential expression.
we have benchmarked these four strategies on  <dig> publicly available data sets originated from affymetrix chips on which mice with  knockout genes were tested against controls.
the raw cel files were downloaded from geo  <cit> .
for each data set we have computed the differential expression levels for each gene in our network based on the expression in the knockout experiment versus the expression in the control .
since we were seeking for a suitable interaction network for our application, we have considered two different types of networks: functional association networks and protein-protein interaction  networks.
as a functional association network, we have used two different string releases , which include associations and physical interactions coming from heterogeneous databases.
as ppi networks, we have used biogrid  <cit>  and i <dig> d  <cit> .
by using different networks in our ranking strategies, we evaluated their suitability as an interaction network for our application, and to what extent performance is influenced by the characteristics of the underlying network.
in the field of cancer, some methods for network analysis are available for gene expression towards identification of expression signatures or of dysregulated subnetworks as biomarkers.
however, the task we address is that of prioritization of disease causing genes in constitutional genetic disorders using expression data.
that problem is different from that of signature identification in cancer because it focuses on the ranking of candidate genes instead of the identification of subnetworks .
there is no established method to tackle the specific problem of candidate gene prioritization in constitutional disorders from expression data.
RESULTS
in this section, we have evaluated the gene prioritization results obtained using each of the presented strategies, focusing on performance improvement.
we aim to assess whether machine learning approaches based on random walks can outperform a standard procedure in genetics, the simple expression ranking .
the previous described methods require several parameters that we have tuned in order to obtain stable ranking results.
additionally, we combine several preprocessing techniques, expression measures and networks:
preprocessing
gene expression data was preprocessed using three different techniques: mas <dig>  rma and gcrma .
expression measure
we have computed three different expression measures: log <dig> ratio, the test statistic .
network
four different mouse networks were selected for diffusion: two versions of the functional association network obtained from string , a ppi network obtained from biogrid , and a ppi network obtained from i <dig> d .
all strategies were applied to these four networks.
the similarity network for the kernel ridge regression ranking was obtained using the laplacian exponential diffusion kernel , the regularized commute time kernel , and the regularized laplacian diffusion kernel , see equations -.
for the heat kernel diffusion ranking we have applied discrete approximation of the heat kernel rank approach  <cit> , see equation .
for the arnoldi diffusion ranking we have applied arnoldi approximation  <cit> , see equation .
finally, for the direct neighborhood ranking we have used the network directly to capture a neighborhood for a candidate gene, see equation .
methods and parameter setting
kernel ridge regression ranking, heat kernel diffusion ranking, and arnoldi diffusion ranking require a value for the diffusion rate α. we have chosen this parameter to be  <dig>  for all strategies.
kernel ridge regression ranking requires two parameters, λ, for which we have chosen five different values{10- <dig> ,10- <dig> , <dig> , <dig> ,102}, and nn, the maximum number of neighbors, for which we have chosen three values:  <dig>   <dig>  and  <dig>
heat kernel diffusion ranking requires one parameter, m, defining the number of iterations, i.e., the number of steps in the random walk through the network.
arnoldi diffusion ranking requires one parameter, m, defining the number of iterations for obtaining an approximation of the network diffusion using the arnoldi algorithm.
direct neighborhood ranking requires a weight, a, for which we chose a value of  <dig> , so that both the expression of the candidate itself and its average surrounding expression in the network were weighted equally.
as potential values for ε, we have chosen  <dig> ,  <dig>  and  <dig>  .
validation
the parameter settings were tuned to obtain stable ranking results for the benchmark data, indicated by the rank of the knockout gene.
we have computed roc curves and the corresponding auc values and counted the number of knockout genes ranked in the top10% for all ranking lists using all parameter settings.
a description of the parameter tuning procedure follows.
in this step, we used the string network  in all the presented strategies.
after the determination of the optimal parameters, we have explored alternative kernels in the kernel ridge regression ranking, different preference vectors in the heat kernel diffusion ranking, and distinct networks in all strategies using the determined parameter settings.
parameter tuning
table s1a  illustrates the ranking results obtained by applying the kernel ridge regression ranking using different values for λ and nn and the laplacian exponential diffusion kernel with α =  <dig>  using the string network .
based on the results presented we have chosen λ to be  <dig> and nn to be  <dig> since these values lead to the most stable ranking results in comparison to other values, considering the auc and the number of top ranked knockout genes.
table s1c  illustrates the ranking results obtained by applying the heat kernel diffusion ranking using distinct number of steps in the random walk through the string network .
these results clearly show that the method is able to generate a reliable ranking in a reduced number of steps, i.e.
m =  <dig>
table s1f  illustrates the ranking results obtained by applying the arnoldi diffusion ranking using distinct number of iterations in the arnoldi approximation and the string network .
the results clearly show that the method is able to produce a reliable ranking using only  <dig> iterations, as in the case of the heat kernel diffusion ranking, i.e.
m =  <dig>
table s1e  illustrates the ranking results obtained by applying the direct neighborhood ranking using the string network  and a =  <dig>  with distinct thresholds ε. results show a decrease in performance with the increase of ε, due to information loss , i.e.
ε =  <dig> .
the results are based on optimized parameter settings for all presented strategies using different string networks.
note that the results of the simple expression ranking do not depend on the network because they are only using differential expression levels to rank the candidate genes.
kernels in kernel ridge regression ranking
the kernel ridge regression ranking is based on a kernel matrix derived from the string network or the ppi network from biogrid or i <dig> d, as shown in equations -.
as discussed in the methods section, several kernel matrices are available in the literature.
in this study, we have assessed which of the three considered kernels performs best in our application.
table s1b  shows the results based on the laplacian exponential diffusion kernel, regularized laplacian kernel and regularized commute time kernel with different parameters.
it stands out that the laplacian exponential diffusion kernel with α =  <dig>  performs better than the other kernels.
thus, in our study, the laplacian exponential diffusion kernel with α =  <dig>  will be used as the kernel matrix in the kernel ridge regression ranking.
preference vector initialization in heat kernel diffusion ranking
francisco et al.
suggested initializing the preference vector p <dig> with binary values  <cit> : the seed genes known to be involved in the disease would be set to  <dig>  as all other genes in the vector would be set to  <dig>  in order to assess the contribution of the gene expression levels to the ranking, we have compared four different scenarios: first, only the candidate genes were initialized with  <dig> and the remaining genes with  <dig> , independent of their expression value.
second, we have only initialized the candidate genes with their differential expression levels obtained in the experiment and the remaining genes with  <dig>  third, we have filled the preference vector p <dig> with all the expression values available in the experiment.
fourth, we have initialized all genes that are differentially expressed in the experiment with  <dig>  all other genes with  <dig>  thus we have made no difference between genes that were highly or weakly differentially expressed.
table s1d  shows the result of these four scenarios for initializing the preference vector.
it can be seen that by using only binary values , the heat kernel diffusion ranking performs poorly .
however, using expression values instead of binary ones, the method performs better.
this shows that the contribution of expression levels coming from a disease or knockout related microarray experiment is significant.
furthermore, if all available expression values are added to the preference vector , the results were further improved against the ones obtained by initializing the preference vector with the expression levels of the candidate genes only .
however, if the expression values are replaced by binary ones , the results are slightly worse than considering differential expression values.
by considering all available expression values , the ranking obtained between  <dig> and  <dig> top 10% ranked knockout genes with an auc of between  <dig> % and  <dig> % for the log <dig> ratio or the test statistic as the expression measure, independent of the preprocessing technique.
in subsequent steps, we use all available expression data for initializing the preference vector in the heat kernel diffusion ranking.
error reduction
results of the heat kernel diffusion ranking using rma preprocessed data have obtained an auc value of 91% and  <dig> % using the string networks v <dig>  and v <dig> , respectively, and the significant log <dig> ratio as expression measure.
this presents an error reduction of  <dig> % relative to the simple expression ranking for the string network v <dig>  and  <dig> % for the string network v <dig> .
regarding the number of knockout genes, the heat kernel diffusion ranking has ranked a maximum of  <dig> knockout genes in the top 10% for both string network releases using the test statistic as expression measure, independent of the preprocessing technique.
the simple expression ranking could rank at most  <dig> knockout genes in the top 10% for mas <dig> preprocessed data, which again presents an error reduction of 50% using the heat kernel diffusion ranking.
the kernel ridge regression ranking strategy could outperform the simple expression ranking only for rma using the significant log <dig> ratio as expression measure and string network v <dig> .
the corresponding error reduction was of 19% regarding the auc  and the number of knockout genes  relative to the simple expression ranking using mas <dig>  for string v <dig>  and all other settings the kernel ridge regression ranking could not outperform the simple expression ranking.
the arnoldi diffusion ranking strategy could outperform the simple expression ranking for rma preprocessed data using the significant log <dig> ratio or test statistic as expression measure and string v <dig>  or for gcrma preprocessed data using the log <dig> ratio as expression measure and string v <dig> .
the error could be reduced by  <dig> % in terms of the auc for string v <dig>   and by  <dig> % for string v <dig>  .
regarding the number of top ranked knockout genes, we could reduce the error for both networks by 25%  relative to the simple expression ranking.
for some other settings this strategy could outperform the simple expression ranking as well.
the direct neighborhood ranking strategy could outperform the simple expression ranking for rma preprocessed data using the significant log <dig> ratio or test statistic as expression measure and the string network v <dig> .
the error could be reduced by  <dig> % in terms of the auc  and by 31% in terms of the number of knockout genes  relative to the simple expression ranking using mas <dig> preprocessed data.
for some other settings this strategy could outperform the simple expression ranking as well.
however, for string v <dig>  the direct neighborhood ranking could not outperform the simple expression ranking.
as a consequence, the heat kernel diffusion ranking shows the largest error reduction relative to the simple expression ranking considering both the auc values and the number of top ranked knockout genes.
furthermore, these results were achieved independent of the preprocessing technique and for both string network releases.
analysis of dependency on expression levels
we have further analyzed the influence of the expression levels of the candidate genes in the performance of the four presented ranking strategies.
for this purpose, we have set the expression levels of the knockout genes to  <dig> and compared with the original results.
table s <dig> shows that none of the strategies achieves a comparable level of performance if the expression level of the knockout gene is set to  <dig>  therefore it is reasonable to assume that the performance of all four strategies in this study is highly dependent on integration of the expression levels of the knockout gene.
comparison of different networks: functional association networks vs. protein-protein interaction networks
as shown in the methods section, the mouse ppi network originated from biogrid contains substantially less information then both mouse string networks.
nevertheless, we have analyzed to what extent the gene prioritization methods depend on the choice of the network and how sparsity is influencing the results.
using the mouse ppi network obtained from the biogrid database, we could not obtain good quality ranking results for our benchmark.
out of the  <dig> data sets, only six could be used on the ppi network because the knockout genes of the other  <dig> data sets were absent from the ppi network .
for validating the performance of the strategies, we have used  <dig> candidate genes that were ranked for each data set.
however, using this ppi network, only 4- <dig> of the candidate genes were found in the network .
therefore, we could not perform a meaningful comparison between the functional association network from string and the ppi network from biogrid.
thus, we can draw the conclusion that a sparse network, like the biogrid mouse network, is not suitable for our application.
the mouse ppi network from the i <dig> d database is a higher-coverage ppi network .
however, like for the biogrid mouse network, the i <dig> d mouse network is missing knockout genes from the benchmark.
only  <dig> out of  <dig> data sets could be used on the ppi network because the others were incomplete .
for this reason we have extended the network by five additional nodes which are isolated from the other nodes in the networks, since the database does not provide information about interactions between these nodes and the others in the network.
table s <dig>  shows that by using the i <dig> d network the results coming from the heat kernel diffusion ranking and the arnoldi diffusion ranking were only slightly better than those obtained by the simple expression ranking, for the other ranking strategies the i <dig> d network performed worse in terms of the auc value and top ranked knockout genes.
comparing with the string network, our results have shown that a functional association network like the string network performs better in our application than a ppi network.
comparison of different expression measures and preprocessing techniques
in this study, we have evaluated not only different networks applied on the four presented strategies, but also different expression measures in combination with the preprocessing techniques applied by the strategies.
table  <dig> illustrates that in our application rma best results correlates with the significant log <dig> ratio as expression measure, gcrma with the log <dig> ratio, and mas <dig> with test statics.
in terms of the presented prioritization strategies, table  <dig> shows that the kernel ridge regression best results correlate with the significant log <dig> ratio as expression measure, and the heat kernel diffusion ranking with test statistic and significant log <dig> ratio.
these results show that there is no clear conclusion to draw in terms of identifying the best performing preprocessing technique or expression measure.
finding the best performing preprocessing technique is a challenge and has been widely discussed in the literature, such as  <cit> .
discussion
as we have introduced in this study, there are several methods in the literature to prioritize candidate genes.
among these approaches, there are methods requiring knowledge about disease-gene association, whereas others do not have this precondition.
however, these methods will be ineffective if no knowledge is available for a specific disease.
in our previous study, we introduced an approach to overcome this limitation by replacing this knowledge by disease-specific experimental data  <cit> .
the purpose of this study was to further improve the performance of the prioritization results and the determination of an appropriate neighborhood for network analysis which has been a major issue in our previous work.
we have extended our previous work extensively by suggesting four strategies to prioritize candidate genes based on distinct machine learning approaches to determine whether a gene is surrounded by highly differentially expressed genes in a network, by considering variations in parameter settings, usage of different kernel functions, preprocessing techniques and expression measurements.
all prioritization results coming from these different settings were benchmarked on  <dig> mouse knockout data sets computing auc values and the number of knockout genes ranked in the top 10%.
the performance was assessed against results obtained using a standard procedure in genetics that ranks candidate genes based solely on their differential expression levels  that was clearly outperformed by the here presented ranking strategies in terms of auc values and ranking positions of knockout genes .
we have used three distinct random walk based strategies plus one naïve strategy without network diffusion but a direct neighborhood analysis.
the random walk strategies all base on the exponential diffusion kernel, although the methodology is distinct: the kernel ridge regression ranking computes the  kernel to solve a regression problem, the heat kernel diffusion ranking computes an iterative diffusion with only  <dig> steps over the network and combines it with expression data coming from the experiment which is the heat kernel rank, and the arnoldi diffusion ranking combines an approximation of the kernel with expression data.
it has to be noted that the convergence in the heat kernel diffusion ranking and in the arnoldi diffusion ranking has been measured in terms of ranking results and not in terms of kernel assimilation which makes it not comparable to the kernel matrix computation resulting from the kernel ridge regression ranking.
although we have considered and benchmarked many variables occurring in our ranking strategies, there are still a few that influence the performance of our prioritization strategies.
first, the quality and coverage of the network around the actual disease gene will be a strict bottleneck as we already analyzed in  <cit> .
for example, an isolated gene with no edges in the network can not be effectively prioritized by our methods.
we have used the string network based on the assumption that a network, integrating multiple heterogeneous data sources, is more complete and robust and therefore less prone to the problems caused by sparsity.
further, we must note that extending the data sources from version  <dig> to  <dig> has resulted in a larger network with good coverage.
errors in the network might cause both false negatives and false positives.
continuing improvements in the quality of protein association networks are expected to contribute to increased effectiveness of the proposed method which could be demonstrated by comparing the two releases string v <dig>  and string v <dig> .
in the latter release the performance could be increased further from 91% to  <dig> % using the heat kernel diffusion ranking, although the performances obtained by using both releases are not as significant as by using the kernel ridge regression ranking and direct neighborhood ranking.
the performance for the kernel ridge regression ranking and direct neighborhood ranking using the string network v <dig>  was better than using the string network v <dig> .
by updating the string network from version  <dig>  to  <dig> , the error was increased by approx.
30%-50%, dependent of the setting.
worsening in the performance using the updated version of the string network in the direct neighborhood ranking could be explained by the fact that we could observe more neighbors for the candidate genes so that a few highly differentially expressed genes lost their influence in comparison to version  <dig>  in which fewer neighbors were detected.
for the kernel ridge regression ranking, however, the similarity matrices of both string releases differ substantially from each other and cannot be compared directly since there is only a small overlap between both string networks.
to evaluate to what extent the coverage of the interaction network influences our method, we have further applied  <dig> distinct ppi networks of different coverage.
using the biogrid network, results have shown that this network was too sparse for our application because most of the knockout genes from the data sets and candidate genes to be ranked in the underlying study were absent from the network .
using the i <dig> d network, results have shown that we could slightly outperform our baseline, the simple expression ranking.
nevertheless, the string network is more densely connected and contains more genes , which led to a better performance for the ranking results.
like in the biogrid network, some knockout genes were also absent from the i <dig> d network.
therefore we extended the network by these nodes, but with no interaction between them and the other nodes in the network.
our results have shown that some of the isolated genes could be ranked highly  despite their missing interactions because the ranking strategies also consider the candidate genes' expression levels.
as long as an isolated gene has a large differential expression level, it can be ranked highly.
however, this is not a guarantee to detect this gene among the top ranked genes because a highly differentially expressed neighborhood will still dominate.
therefore an isolated gene cannot be reliably prioritized by our ranking strategies.
nevertheless, the ranking strategies using the string network have performed better than using the i <dig> d network, probably because of the difference in coverage.
one may argue that it is not appropriate to compare a ppi network with a functional association network because the latter is including associations apart from physical interactions, but we are seeking for a suitable and high-coverage interaction network for our application that leads to reliable ranking results of candidate genes, regardless of the nature of the associations.
in the literature, several databases can be found to construct an interaction network that can be categorized in terms of types and scope of data sources, types of interactions, or range of details on protein interactions  <cit> .
comprehensive protein interaction databases, such as biogrid  <cit> , dip  <cit> , bind  <cit> , intact  <cit> , mint  <cit> , i <dig> d  <cit> , irefindex  <cit>  or string  <cit>  collect physical interactions or functional associations between proteins, integrating distinct information sources about protein interactions coming from high-throughput experimental data, structural data, manual curation, or functional predictions.
specialized protein interaction databases, such as mips  <cit>  or hprd  <cit>  collect  curated interactions from yeast or human, respectively.
for this study, the biogrid database was used to represent a  ppi network containing only high-throughput experimental data, the i <dig> d database was used to represent a high-coverage ppi network integrating different information sources, and string was used to represent a high-coverage functional association network combining associations and physical interactions coming from distinct data sources.
in nitsch et al.
we adopted the hypothesis from köhler et al.
that global network-similarity measures capture relationships between disease proteins better than algorithms based on direct interactions  <cit> .
the latter was considered in the direct neighborhood ranking strategy which performed worse than the heat kernel diffusion ranking leading to a global diffusion measure.
since we have proposed the direct neighborhood ranking as a naïve method for comparison purposes, we have already expected not to outperform the other three random walk based strategies because of its systematic bias favoring highly connected genes in the network .
second, the integration of expression data proved to have a significant influence on the performance of the prioritization strategies which is supported by the results using the mouse knockout experiments data.
by using mouse knockout data sets, we could guarantee to use disease relevant tissue which is an important issue in identifying disease related genes .
we have further analyzed the dependency of the ranking performance on the preprocessing of expression data.
in the literature there are many controversial discussions about the performance of these, including mas <dig>  rma, and gcrma, and the community cannot harmonize .
for this reason we have applied mas <dig>  rma, and gcrma on the benchmark data sets leading to different ranking results, as we would have expected.
in the results section we have claimed that we could not draw a clear conclusion in terms of identifying the best performing preprocessing technique or expression measure.
nevertheless, the best results were achieved using rma preprocessed data in comparison to the other preprocessing techniques.
however, in other applications alternative techniques might perform better.
the same matters for finding an appropriate expression measure.
in the literature there are many measures, from which we have chosen the log <dig> ratio, the significant log <dig> ratio, and test statistic derived from cybert.
by analyzing their performance in our application, we could not claim one measure to be outperforming another, however, the significant log <dig> ratio led to the most stable results over the majority of the settings.
the quality of the experimental data has also an important impact on the performance of the prioritization strategies.
by using expression data that was either incomplete or of poor quality, the prioritization strategies could not lead to reliable results.
the sensitivity of the different scoring strategies or the underlying networks to this effect may vary .
this issue may come up when applying the presented method to real genetic disorders in human.
in our previous study, we could already detect four known disease genes in human using public available expression data of good quality  <cit> .
therefore, the bottleneck of our method is again the sparseness and quality of experimental data.
third, the choice of appropriate parameters for the presented strategies has a large influence on the performance.
therefore we had several parameters and settings to optimize.
by using the optimal parameters and settings, we have obtained stable and robust results for the prioritization problem.
all presented strategies have outperformed our baseline, the simple expression ranking - as we have expected - for certain settings.
the heat kernel diffusion ranking has shown the largest error reduction relative to the simple expression ranking in terms of auc values and number of top ranked knockout genes, independent of the preprocessing technique and for both string network releases.
our results show that the simple expression ranking is performing well for mas <dig> preprocessed data.
however, the heat kernel diffusion ranking on rma preprocessed data could achieve and error reduction of  <dig> % for the string network v <dig>  and  <dig> % for the string network v <dig> .
fourth, the fact that a disease related gene may have only a weakly differentially expressed neighborhood negatively affects the prioritization methods.
in this case, our hypothesis of observing a strongly differentially expressed neighborhood for disease related genes can fail.
by introducing a better experimental design that can trigger a disease pathway more reliably in which the effect is more focused around the disease gene, would overcome this limitation because in our approach we do not consider pathways but only neighbors that are surrounding a gene in the network.
in this case the simple expression ranking can perform better as long as the disease gene is highly differentially expressed since this naïve method does not depend on expressed pathways or neighborhoods.
fifth, a systematic bias using a biological network favoring highly connected genes can be observed in our method which leads to sensitivity to skewed degree distributions.
this bias is clearly a limitation of our method and can be addressed through proper randomization.
by randomizing signals across the network, the bias caused by the higher connectivity  can be removed since highly connected nodes will have a higher baseline signal across the randomizations.
we are currently investigating this issue.
CONCLUSIONS
in this study, we have extended extensively our previous work by applying machine learning approaches based on random walk models to determine whether a gene's neighborhood is highly differentially expressed.
we have explored three different random walk based strategies plus one naïve strategy based on a direct neighborhood analysis.
these four network-based prioritization strategies for scoring candidate genes based on their differentially expressed neighborhood were benchmarked on  <dig> publicly available knockout experiments in mice.
performance was assessed against results obtained using a standard procedure in genetics that ranks candidate genes based solely on their differential expression levels .
results showed that our strategies could outperform this standard procedure and that the best results were obtained using the heat kernel diffusion ranking leading to an average ranking position of  <dig> out of  <dig> genes, an auc value of  <dig> % and an error reduction of  <dig> % relative to the standard procedure approach which ranked the knockout gene in average at position  <dig> with an auc value of  <dig> %.
thus, we could identify promising candidate genes using network-based machine learning approaches even if no knowledge is available about the disease or phenotype.

 discovering novel disease genes is still challenging for constitutional genetic diseases for which no prior knowledge - such as known disease genes or disease-related pathways - is available. performing genetic studies frequently result in large lists of candidate genes of which only few can be followed up for further investigation. gene prioritization establishes the ranking of candidate genes based on their relevance with respect to a biological process of interest, from which the most promising genes can be selected for further analysis. several computational methods for prioritizing candidate genes have been proposed, such as endeavour, genewanderer, or prioritizer that rank candidate genes based on associations between known disease genes and candidate genes using different data sources and methodology. lage et al. developed a phenome-interactome network that integrates phenotypic literature information from omim with a cross species protein-protein interaction network. chen et al. applied link based strategies widely used in social and web network analyses to prioritize disease candidate genes based on ppi networks. subramanian et al. developed a computational method, gene set enrichment analysis, that determines whether an a priori defined set of genes shows statistically significant concordant differences between two biological states, i.e. whether the genes are differentially expressed or not. similarly, liu et al. developed a network-based approach, gene network enrichment analysis for the identification of transcriptionally altered biological processes between disease and normal states. it analyzes gene expression microarray and protein-protein interaction data to identify the affected regions in a protein-protein interaction network. beside these methods, others can be found in the literature that prioritize candidate genes for human diseases. among these, several were implemented as web-based applications that can be freely accessed. in a previous study we have reviewed distinct web-based and freely accessible gene prioritization tools for human diseases. the aforementioned methods usually rank candidate genes by matching their information across multiple data sources against a profile derived from a set of genes, keywords, pathways, or biological processes already known to be associated with the phenotype. however, often only little is known about the molecular basis of the phenotype, such as no known disease genes and limited knowledge about the biological cascades involved, and only few or no keywords are known which can be used either to retrieve genes or to perform text mining. to overcome this limitation, we proposed in a previous study a computational method to identify the most promising candidates within a region for which limited or no prior knowledge is available regarding a phenotype of interest by using experimental data on differential gene expression between affected and healthy individuals. using a network-based approach, we assessed the relevance of a candidate gene by considering the level of differential expression in its neighborhood under the assumption that strong candidates tend to be surrounded by differentially expressed neighbors. for several genetic diseases, however, there is no guarantee that the expression levels of the disease gene itself is affected, rather, genes''downstream'' of the disease gene are those whose expression will be affected. therefore, we consider the differential expression data at the network levels instead of gene levels. mapping expression patterns on a network, we then expect to observe a disrupted expression module around the disease gene, while other candidate genes should not be part of such a disrupted expression module. this approach is less biased than assessing relevant candidate genes by performing text mining, finding associations between known disease genes and candidate genes, or detecting disease relevant pathways. we define a notion of a soft neighborhood where each gene is given a contributing weight, which decreases with the distance from the candidate gene in the network. to account for multiple paths between genes, we defined a notion of distance using the laplacian exponential diffusion kernel. finally, we scored candidates by aggregating the differential expression of their neighbors weighted as a function of distance. to further improve prioritization results we have extended our previous work in this study by applying four different strategies to prioritize candidate genes based on network analysis of differential expression using distinct machine learning approaches to determine whether a gene is surrounded by highly differentially expressed genes in a functional association or protein-protein interaction network. here, we have mainly focused on further performance improvement and determination of an appropriate neighborhood for network propagation of differential expression analysis by considering and benchmarking many variables occurring here in the presented ranking strategies. we have further compared our prioritization results with a standard procedure in genetics that ranks candidate genes based solely on their differential expression levels. first, we propose an alternative to our previous idea of defining a notion of distance using the laplacian exponential diffusion kernel. instead of aggregating the differential expression of neighbors weighted as a function of distance, we have smoothed a candidate gene's differential expression levels through kernel ridge regression. we name this strategy kernel ridge regression ranking. second, we have applied the heat kernel diffusion ranking, introduced by chung and yau, to our problem of disease candidate gene prioritization. third, we have carried out network diffusion by applying the arnoldi algorithm based on a kyrlov space method as presented in. we name this strategy arnoldi diffusion ranking. fourth, we have ranked the candidate genes by combining their differential expression levels with the average of the differential expression levels among their direct neighbors in a functional association or protein-protein interaction network, which we name direct neighborhood ranking. this straightforward approach for scoring candidates is presented here for comparison purposes as a naïve strategy for network analysis of differential expression. we have benchmarked these four strategies on publicly available data sets originated from affymetrix chips on which mice with knockout genes were tested against controls. the raw cel files were downloaded from geo. for each data set we have computed the differential expression levels for each gene in our network based on the expression in the knockout experiment versus the expression in the control. since we were seeking for a suitable interaction network for our application, we have considered two different types of networks: functional association networks and protein-protein interaction networks. as a functional association network, we have used two different string releases, which include associations and physical interactions coming from heterogeneous databases. as ppi networks, we have used biogrid and i d. by using different networks in our ranking strategies, we evaluated their suitability as an interaction network for our application, and to what extent performance is influenced by the characteristics of the underlying network. in the field of cancer, some methods for network analysis are available for gene expression towards identification of expression signatures or of dysregulated subnetworks as biomarkers. however, the task we address is that of prioritization of disease causing genes in constitutional genetic disorders using expression data. that problem is different from that of signature identification in cancer because it focuses on the ranking of candidate genes instead of the identification of subnetworks. there is no established method to tackle the specific problem of candidate gene prioritization in constitutional disorders from expression data.  in this section, we have evaluated the gene prioritization results obtained using each of the presented strategies, focusing on performance improvement. we aim to assess whether machine learning approaches based on random walks can outperform a standard procedure in genetics, the simple expression ranking. the previous described methods require several parameters that we have tuned in order to obtain stable ranking results. additionally, we combine several preprocessing techniques, expression measures and networks: preprocessing gene expression data was preprocessed using three different techniques: mas rma and gcrma. expression measure we have computed three different expression measures: log ratio, the test statistic. network four different mouse networks were selected for diffusion: two versions of the functional association network obtained from string, a ppi network obtained from biogrid, and a ppi network obtained from i d. all strategies were applied to these four networks. the similarity network for the kernel ridge regression ranking was obtained using the laplacian exponential diffusion kernel, the regularized commute time kernel, and the regularized laplacian diffusion kernel, see equations -. for the heat kernel diffusion ranking we have applied discrete approximation of the heat kernel rank approach, see equation. for the arnoldi diffusion ranking we have applied arnoldi approximation, see equation. finally, for the direct neighborhood ranking we have used the network directly to capture a neighborhood for a candidate gene, see equation. methods and parameter setting kernel ridge regression ranking, heat kernel diffusion ranking, and arnoldi diffusion ranking require a value for the diffusion rate α. we have chosen this parameter to be for all strategies. kernel ridge regression ranking requires two parameters, λ, for which we have chosen five different values{10-,10-,,,102}, and nn, the maximum number of neighbors, for which we have chosen three values: and heat kernel diffusion ranking requires one parameter, m, defining the number of iterations, i.e., the number of steps in the random walk through the network. arnoldi diffusion ranking requires one parameter, m, defining the number of iterations for obtaining an approximation of the network diffusion using the arnoldi algorithm. direct neighborhood ranking requires a weight, a, for which we chose a value of, so that both the expression of the candidate itself and its average surrounding expression in the network were weighted equally. as potential values for ε, we have chosen, and. validation the parameter settings were tuned to obtain stable ranking results for the benchmark data, indicated by the rank of the knockout gene. we have computed roc curves and the corresponding auc values and counted the number of knockout genes ranked in the top10% for all ranking lists using all parameter settings. a description of the parameter tuning procedure follows. in this step, we used the string network in all the presented strategies. after the determination of the optimal parameters, we have explored alternative kernels in the kernel ridge regression ranking, different preference vectors in the heat kernel diffusion ranking, and distinct networks in all strategies using the determined parameter settings. parameter tuning table s1a illustrates the ranking results obtained by applying the kernel ridge regression ranking using different values for λ and nn and the laplacian exponential diffusion kernel with α = using the string network. based on the results presented we have chosen λ to be and nn to be since these values lead to the most stable ranking results in comparison to other values, considering the auc and the number of top ranked knockout genes. table s1c illustrates the ranking results obtained by applying the heat kernel diffusion ranking using distinct number of steps in the random walk through the string network. these results clearly show that the method is able to generate a reliable ranking in a reduced number of steps, i.e. m = table s1f illustrates the ranking results obtained by applying the arnoldi diffusion ranking using distinct number of iterations in the arnoldi approximation and the string network. the results clearly show that the method is able to produce a reliable ranking using only iterations, as in the case of the heat kernel diffusion ranking, i.e. m = table s1e illustrates the ranking results obtained by applying the direct neighborhood ranking using the string network and a = with distinct thresholds ε. results show a decrease in performance with the increase of ε, due to information loss, i.e. ε =. the results are based on optimized parameter settings for all presented strategies using different string networks. note that the results of the simple expression ranking do not depend on the network because they are only using differential expression levels to rank the candidate genes. kernels in kernel ridge regression ranking the kernel ridge regression ranking is based on a kernel matrix derived from the string network or the ppi network from biogrid or i d, as shown in equations -. as discussed in the methods section, several kernel matrices are available in the literature. in this study, we have assessed which of the three considered kernels performs best in our application. table s1b shows the results based on the laplacian exponential diffusion kernel, regularized laplacian kernel and regularized commute time kernel with different parameters. it stands out that the laplacian exponential diffusion kernel with α = performs better than the other kernels. thus, in our study, the laplacian exponential diffusion kernel with α = will be used as the kernel matrix in the kernel ridge regression ranking. preference vector initialization in heat kernel diffusion ranking francisco et al. suggested initializing the preference vector p with binary values: the seed genes known to be involved in the disease would be set to as all other genes in the vector would be set to in order to assess the contribution of the gene expression levels to the ranking, we have compared four different scenarios: first, only the candidate genes were initialized with and the remaining genes with, independent of their expression value. second, we have only initialized the candidate genes with their differential expression levels obtained in the experiment and the remaining genes with third, we have filled the preference vector p with all the expression values available in the experiment. fourth, we have initialized all genes that are differentially expressed in the experiment with all other genes with thus we have made no difference between genes that were highly or weakly differentially expressed. table s1d shows the result of these four scenarios for initializing the preference vector. it can be seen that by using only binary values, the heat kernel diffusion ranking performs poorly. however, using expression values instead of binary ones, the method performs better. this shows that the contribution of expression levels coming from a disease or knockout related microarray experiment is significant. furthermore, if all available expression values are added to the preference vector, the results were further improved against the ones obtained by initializing the preference vector with the expression levels of the candidate genes only. however, if the expression values are replaced by binary ones, the results are slightly worse than considering differential expression values. by considering all available expression values, the ranking obtained between and top 10% ranked knockout genes with an auc of between % and % for the log ratio or the test statistic as the expression measure, independent of the preprocessing technique. in subsequent steps, we use all available expression data for initializing the preference vector in the heat kernel diffusion ranking. error reduction results of the heat kernel diffusion ranking using rma preprocessed data have obtained an auc value of 91% and % using the string networks v and v, respectively, and the significant log ratio as expression measure. this presents an error reduction of % relative to the simple expression ranking for the string network v and % for the string network v. regarding the number of knockout genes, the heat kernel diffusion ranking has ranked a maximum of knockout genes in the top 10% for both string network releases using the test statistic as expression measure, independent of the preprocessing technique. the simple expression ranking could rank at most knockout genes in the top 10% for mas preprocessed data, which again presents an error reduction of 50% using the heat kernel diffusion ranking. the kernel ridge regression ranking strategy could outperform the simple expression ranking only for rma using the significant log ratio as expression measure and string network v. the corresponding error reduction was of 19% regarding the auc and the number of knockout genes relative to the simple expression ranking using mas for string v and all other settings the kernel ridge regression ranking could not outperform the simple expression ranking. the arnoldi diffusion ranking strategy could outperform the simple expression ranking for rma preprocessed data using the significant log ratio or test statistic as expression measure and string v or for gcrma preprocessed data using the log ratio as expression measure and string v. the error could be reduced by % in terms of the auc for string v and by % for string v. regarding the number of top ranked knockout genes, we could reduce the error for both networks by 25% relative to the simple expression ranking. for some other settings this strategy could outperform the simple expression ranking as well. the direct neighborhood ranking strategy could outperform the simple expression ranking for rma preprocessed data using the significant log ratio or test statistic as expression measure and the string network v. the error could be reduced by % in terms of the auc and by 31% in terms of the number of knockout genes relative to the simple expression ranking using mas preprocessed data. for some other settings this strategy could outperform the simple expression ranking as well. however, for string v the direct neighborhood ranking could not outperform the simple expression ranking. as a consequence, the heat kernel diffusion ranking shows the largest error reduction relative to the simple expression ranking considering both the auc values and the number of top ranked knockout genes. furthermore, these results were achieved independent of the preprocessing technique and for both string network releases. analysis of dependency on expression levels we have further analyzed the influence of the expression levels of the candidate genes in the performance of the four presented ranking strategies. for this purpose, we have set the expression levels of the knockout genes to and compared with the original results. table s shows that none of the strategies achieves a comparable level of performance if the expression level of the knockout gene is set to therefore it is reasonable to assume that the performance of all four strategies in this study is highly dependent on integration of the expression levels of the knockout gene. comparison of different networks: functional association networks vs. protein-protein interaction networks as shown in the methods section, the mouse ppi network originated from biogrid contains substantially less information then both mouse string networks. nevertheless, we have analyzed to what extent the gene prioritization methods depend on the choice of the network and how sparsity is influencing the results. using the mouse ppi network obtained from the biogrid database, we could not obtain good quality ranking results for our benchmark. out of the data sets, only six could be used on the ppi network because the knockout genes of the other data sets were absent from the ppi network. for validating the performance of the strategies, we have used candidate genes that were ranked for each data set. however, using this ppi network, only 4- of the candidate genes were found in the network. therefore, we could not perform a meaningful comparison between the functional association network from string and the ppi network from biogrid. thus, we can draw the conclusion that a sparse network, like the biogrid mouse network, is not suitable for our application. the mouse ppi network from the i d database is a higher-coverage ppi network. however, like for the biogrid mouse network, the i d mouse network is missing knockout genes from the benchmark. only out of data sets could be used on the ppi network because the others were incomplete. for this reason we have extended the network by five additional nodes which are isolated from the other nodes in the networks, since the database does not provide information about interactions between these nodes and the others in the network. table s shows that by using the i d network the results coming from the heat kernel diffusion ranking and the arnoldi diffusion ranking were only slightly better than those obtained by the simple expression ranking, for the other ranking strategies the i d network performed worse in terms of the auc value and top ranked knockout genes. comparing with the string network, our results have shown that a functional association network like the string network performs better in our application than a ppi network. comparison of different expression measures and preprocessing techniques in this study, we have evaluated not only different networks applied on the four presented strategies, but also different expression measures in combination with the preprocessing techniques applied by the strategies. table illustrates that in our application rma best results correlates with the significant log ratio as expression measure, gcrma with the log ratio, and mas with test statics. in terms of the presented prioritization strategies, table shows that the kernel ridge regression best results correlate with the significant log ratio as expression measure, and the heat kernel diffusion ranking with test statistic and significant log ratio. these results show that there is no clear conclusion to draw in terms of identifying the best performing preprocessing technique or expression measure. finding the best performing preprocessing technique is a challenge and has been widely discussed in the literature, such as. discussion as we have introduced in this study, there are several methods in the literature to prioritize candidate genes. among these approaches, there are methods requiring knowledge about disease-gene association, whereas others do not have this precondition. however, these methods will be ineffective if no knowledge is available for a specific disease. in our previous study, we introduced an approach to overcome this limitation by replacing this knowledge by disease-specific experimental data. the purpose of this study was to further improve the performance of the prioritization results and the determination of an appropriate neighborhood for network analysis which has been a major issue in our previous work. we have extended our previous work extensively by suggesting four strategies to prioritize candidate genes based on distinct machine learning approaches to determine whether a gene is surrounded by highly differentially expressed genes in a network, by considering variations in parameter settings, usage of different kernel functions, preprocessing techniques and expression measurements. all prioritization results coming from these different settings were benchmarked on mouse knockout data sets computing auc values and the number of knockout genes ranked in the top 10%. the performance was assessed against results obtained using a standard procedure in genetics that ranks candidate genes based solely on their differential expression levels that was clearly outperformed by the here presented ranking strategies in terms of auc values and ranking positions of knockout genes. we have used three distinct random walk based strategies plus one naïve strategy without network diffusion but a direct neighborhood analysis. the random walk strategies all base on the exponential diffusion kernel, although the methodology is distinct: the kernel ridge regression ranking computes the kernel to solve a regression problem, the heat kernel diffusion ranking computes an iterative diffusion with only steps over the network and combines it with expression data coming from the experiment which is the heat kernel rank, and the arnoldi diffusion ranking combines an approximation of the kernel with expression data. it has to be noted that the convergence in the heat kernel diffusion ranking and in the arnoldi diffusion ranking has been measured in terms of ranking results and not in terms of kernel assimilation which makes it not comparable to the kernel matrix computation resulting from the kernel ridge regression ranking. although we have considered and benchmarked many variables occurring in our ranking strategies, there are still a few that influence the performance of our prioritization strategies. first, the quality and coverage of the network around the actual disease gene will be a strict bottleneck as we already analyzed in. for example, an isolated gene with no edges in the network can not be effectively prioritized by our methods. we have used the string network based on the assumption that a network, integrating multiple heterogeneous data sources, is more complete and robust and therefore less prone to the problems caused by sparsity. further, we must note that extending the data sources from version to has resulted in a larger network with good coverage. errors in the network might cause both false negatives and false positives. continuing improvements in the quality of protein association networks are expected to contribute to increased effectiveness of the proposed method which could be demonstrated by comparing the two releases string v and string v. in the latter release the performance could be increased further from 91% to % using the heat kernel diffusion ranking, although the performances obtained by using both releases are not as significant as by using the kernel ridge regression ranking and direct neighborhood ranking. the performance for the kernel ridge regression ranking and direct neighborhood ranking using the string network v was better than using the string network v. by updating the string network from version to, the error was increased by approx. 30%-50%, dependent of the setting. worsening in the performance using the updated version of the string network in the direct neighborhood ranking could be explained by the fact that we could observe more neighbors for the candidate genes so that a few highly differentially expressed genes lost their influence in comparison to version in which fewer neighbors were detected. for the kernel ridge regression ranking, however, the similarity matrices of both string releases differ substantially from each other and cannot be compared directly since there is only a small overlap between both string networks. to evaluate to what extent the coverage of the interaction network influences our method, we have further applied distinct ppi networks of different coverage. using the biogrid network, results have shown that this network was too sparse for our application because most of the knockout genes from the data sets and candidate genes to be ranked in the underlying study were absent from the network. using the i d network, results have shown that we could slightly outperform our baseline, the simple expression ranking. nevertheless, the string network is more densely connected and contains more genes, which led to a better performance for the ranking results. like in the biogrid network, some knockout genes were also absent from the i d network. therefore we extended the network by these nodes, but with no interaction between them and the other nodes in the network. our results have shown that some of the isolated genes could be ranked highly despite their missing interactions because the ranking strategies also consider the candidate genes' expression levels. as long as an isolated gene has a large differential expression level, it can be ranked highly. however, this is not a guarantee to detect this gene among the top ranked genes because a highly differentially expressed neighborhood will still dominate. therefore an isolated gene cannot be reliably prioritized by our ranking strategies. nevertheless, the ranking strategies using the string network have performed better than using the i d network, probably because of the difference in coverage. one may argue that it is not appropriate to compare a ppi network with a functional association network because the latter is including associations apart from physical interactions, but we are seeking for a suitable and high-coverage interaction network for our application that leads to reliable ranking results of candidate genes, regardless of the nature of the associations. in the literature, several databases can be found to construct an interaction network that can be categorized in terms of types and scope of data sources, types of interactions, or range of details on protein interactions. comprehensive protein interaction databases, such as biogrid, dip, bind, intact, mint, i d, irefindex or string collect physical interactions or functional associations between proteins, integrating distinct information sources about protein interactions coming from high-throughput experimental data, structural data, manual curation, or functional predictions. specialized protein interaction databases, such as mips or hprd collect curated interactions from yeast or human, respectively. for this study, the biogrid database was used to represent a ppi network containing only high-throughput experimental data, the i d database was used to represent a high-coverage ppi network integrating different information sources, and string was used to represent a high-coverage functional association network combining associations and physical interactions coming from distinct data sources. in nitsch et al. we adopted the hypothesis from köhler et al. that global network-similarity measures capture relationships between disease proteins better than algorithms based on direct interactions. the latter was considered in the direct neighborhood ranking strategy which performed worse than the heat kernel diffusion ranking leading to a global diffusion measure. since we have proposed the direct neighborhood ranking as a naïve method for comparison purposes, we have already expected not to outperform the other three random walk based strategies because of its systematic bias favoring highly connected genes in the network. second, the integration of expression data proved to have a significant influence on the performance of the prioritization strategies which is supported by the results using the mouse knockout experiments data. by using mouse knockout data sets, we could guarantee to use disease relevant tissue which is an important issue in identifying disease related genes. we have further analyzed the dependency of the ranking performance on the preprocessing of expression data. in the literature there are many controversial discussions about the performance of these, including mas rma, and gcrma, and the community cannot harmonize. for this reason we have applied mas rma, and gcrma on the benchmark data sets leading to different ranking results, as we would have expected. in the results section we have claimed that we could not draw a clear conclusion in terms of identifying the best performing preprocessing technique or expression measure. nevertheless, the best results were achieved using rma preprocessed data in comparison to the other preprocessing techniques. however, in other applications alternative techniques might perform better. the same matters for finding an appropriate expression measure. in the literature there are many measures, from which we have chosen the log ratio, the significant log ratio, and test statistic derived from cybert. by analyzing their performance in our application, we could not claim one measure to be outperforming another, however, the significant log ratio led to the most stable results over the majority of the settings. the quality of the experimental data has also an important impact on the performance of the prioritization strategies. by using expression data that was either incomplete or of poor quality, the prioritization strategies could not lead to reliable results. the sensitivity of the different scoring strategies or the underlying networks to this effect may vary. this issue may come up when applying the presented method to real genetic disorders in human. in our previous study, we could already detect four known disease genes in human using public available expression data of good quality. therefore, the bottleneck of our method is again the sparseness and quality of experimental data. third, the choice of appropriate parameters for the presented strategies has a large influence on the performance. therefore we had several parameters and settings to optimize. by using the optimal parameters and settings, we have obtained stable and robust results for the prioritization problem. all presented strategies have outperformed our baseline, the simple expression ranking - as we have expected - for certain settings. the heat kernel diffusion ranking has shown the largest error reduction relative to the simple expression ranking in terms of auc values and number of top ranked knockout genes, independent of the preprocessing technique and for both string network releases. our results show that the simple expression ranking is performing well for mas preprocessed data. however, the heat kernel diffusion ranking on rma preprocessed data could achieve and error reduction of % for the string network v and % for the string network v. fourth, the fact that a disease related gene may have only a weakly differentially expressed neighborhood negatively affects the prioritization methods. in this case, our hypothesis of observing a strongly differentially expressed neighborhood for disease related genes can fail. by introducing a better experimental design that can trigger a disease pathway more reliably in which the effect is more focused around the disease gene, would overcome this limitation because in our approach we do not consider pathways but only neighbors that are surrounding a gene in the network. in this case the simple expression ranking can perform better as long as the disease gene is highly differentially expressed since this naïve method does not depend on expressed pathways or neighborhoods. fifth, a systematic bias using a biological network favoring highly connected genes can be observed in our method which leads to sensitivity to skewed degree distributions. this bias is clearly a limitation of our method and can be addressed through proper randomization. by randomizing signals across the network, the bias caused by the higher connectivity can be removed since highly connected nodes will have a higher baseline signal across the randomizations. we are currently investigating this issue.  in this study, we have extended extensively our previous work by applying machine learning approaches based on random walk models to determine whether a gene's neighborhood is highly differentially expressed. we have explored three different random walk based strategies plus one naïve strategy based on a direct neighborhood analysis. these four network-based prioritization strategies for scoring candidate genes based on their differentially expressed neighborhood were benchmarked on publicly available knockout experiments in mice. performance was assessed against results obtained using a standard procedure in genetics that ranks candidate genes based solely on their differential expression levels. results showed that our strategies could outperform this standard procedure and that the best results were obtained using the heat kernel diffusion ranking leading to an average ranking position of out of genes, an auc value of % and an error reduction of % relative to the standard procedure approach which ranked the knockout gene in average at position with an auc value of %. thus, we could identify promising candidate genes using network-based machine learning approaches even if no knowledge is available about the disease or phenotype. 
our results showed that our four strategies could outperform this standard procedure and that the best results were obtained using the heat kernel diffusion ranking leading to an average ranking position of out of genes, an auc value of % and an error reduction of % relative to the standard procedure approach which ranked the knockout gene on average at position with an auc value of %. performing genetic studies frequently results in large lists of candidate genes of which only few can be followed up for further investigation. we have benchmarked these strategies on publicly available knockout experiments in mice, and performance was assessed against results obtained using a standard procedure in genetics that ranks candidate genes based solely on their differential expression levels. we have proposed three strategies scoring disease candidate genes relying on network-based machine learning approaches, such as kernel ridge regression, heat kernel, and arnoldi kernel approximation. we have recently developed a computational method for constitutional genetic disorders that identifies the most promising candidate genes by replacing prior knowledge by experimental data of differential gene expression between affected and healthy individuals. to improve the performance of our prioritization strategy, we have extended our previous work by applying different machine learning approaches that identify promising candidate genes by determining whether a gene is surrounded by highly differentially expressed genes in a functional association or protein-protein interaction network. in this study we could identify promising candidate genes using network based machine learning approaches even if no knowledge is available about the disease or phenotype. for comparison purposes, a local measure based on the expression of the direct neighbors is also computed. discovering novel disease genes is still challenging for diseases for which no prior knowledge - such as known disease genes or disease-related pathways - is available.
 discovering novel disease genes is still challenging for diseases for which no prior knowledge - such as known disease genes or disease-related pathways - is available. performing genetic studies frequently results in large lists of candidate genes of which only few can be followed up for further investigation. we have recently developed a computational method for constitutional genetic disorders that identifies the most promising candidate genes by replacing prior knowledge by experimental data of differential gene expression between affected and healthy individuals. to improve the performance of our prioritization strategy, we have extended our previous work by applying different machine learning approaches that identify promising candidate genes by determining whether a gene is surrounded by highly differentially expressed genes in a functional association or protein-protein interaction network.  we have proposed three strategies scoring disease candidate genes relying on network-based machine learning approaches, such as kernel ridge regression, heat kernel, and arnoldi kernel approximation. for comparison purposes, a local measure based on the expression of the direct neighbors is also computed. we have benchmarked these strategies on publicly available knockout experiments in mice, and performance was assessed against results obtained using a standard procedure in genetics that ranks candidate genes based solely on their differential expression levels. our results showed that our four strategies could outperform this standard procedure and that the best results were obtained using the heat kernel diffusion ranking leading to an average ranking position of out of genes, an auc value of % and an error reduction of % relative to the standard procedure approach which ranked the knockout gene on average at position with an auc value of %.  in this study we could identify promising candidate genes using network based machine learning approaches even if no knowledge is available about the disease or phenotype. 