BACKGROUND
in recent years, the success of gwas  makes it possible to detect genetic factors that influence the susceptibility to particular diseases in human populations  <cit> .
while most of gwas search for one single contributing locus at a time, they fail to identify the combinational effect  of genetic variants  associated with common complex diseases such as asthma, diabetes, and hypertension  <cit> .
it is well known that epistatic interactions, not individual variant, are critical in unravelling genetic causes of complex human diseases  <cit> .
however, the number of possible combinations of snps in a genome is enormous, which is infeasible to be evaluated exhaustively by experimental methods.
therefore, researchers resort to computational methods to detect epistatic interactions based on the genotyped data  <cit> .
recently, a number of statistical methods have been proposed to detect epistatic interactions.
among these methods, the most commonly used one is logistic regression   <cit> .
however, logistic regression may not be appropriate for epistasis due to its overfitting problem due to the fact that the number of parameters will be much larger than the available samples.
to avoid this shortcoming, ritchie et al.
proposed mdr   <cit> , which utilizes the ratio of the number of cases to the number of controls in cells of risk table to reduce the dimensionality to one and select snp combinations that have the highest prediction performance.
the process of labelling each cell of risk table as “high risk” or “low risk” is a process of estimating parameters, which may also result in the overfitting problems when the size of snp combinations is large.
furthermore, mdr selects the snp combinations purely by the prediction performance and thus, it may not find true causal factors.
park and hastie proposed the stepwise-penalized logistic regression  to overcome the drawbacks of logistic regression and mdr  <cit> .
stepplr makes some simple modifications for standard logistic regression .
for example, stepplr combines the lr criterion with a penalization of the l2-norm of the coefficients.
this modification makes stepplr more robust to high-order epistatic interactions.
despite its modifications, stepplr is time-consuming when estimating parameters, which is one essential limitation of regression methods.
beam is a bayesian marker partition model using markov chain monte carlo to reach an optimal marker partition and a new b statistic to check each marker or set of markers for significant associations  <cit> .
note that most statistical methods can not be applied to genome-wide analysis directly due to their computational complexity.
the alternative approaches to parametric statistical methods are machine learning methods including support vector machine   <cit>  and random forest  <cit> .
machine learning methods consider detecting epistatic interactions as a feature selection problem  <cit>  and try to find the best combination of snps with the highest prediction accuracy of disease status.
therefore, chen et al.
test three feature selection method: rfe , rfa , and ga  in  <cit>  and jiang et al.
perform a greedy search in  <cit> .
like mdr, machine learning methods select snps based on classification/prediction accuracy and can not find true causal factors for disease.
moreover, machine learning-based methods tend to introduce many false positives because using more snps tends to produce higher classification accuracies.
in this paper, we propose a new and fast markov blanket method, fepi-mb , to detect epistatic interactions.
the markov blanket is a minimal set of variables, which can completely shield the target variable from all other variables.
as shown in figure  <dig>  genome-wide association studies try to identify the k-way interaction among disease snps: snp <dig>  snp <dig> …,snpk and exclude all other unrelated normal snps .
thus, the markov blanket learning method is suitable for detection of epistatic interactions in genome-wide case-control studies, e.g., to identify a minimal set of snps which may cause the disease and require further experiments.
meanwhile the detected minimal set of causal snps can shield the disease from all other normal snps to decrease the false positive rate and reduce the cost of future validation experiments.
furthermore, markov blanket method performs a heuristic search by calculating the association between variables to avoid the time-consuming training process as in svm and random forest.
some markov blanket methods take a divide-and-conquer approach that breaks the problem of identifying markov blanket of variable t ) into two subproblems: first, identifying parents and children of t ) and, second, identifying the parents of the children of t .
the goal of epistatic interactions detection is to identify causal interacting genes or snps for some certain diseases and therefore it is a special application of markov blanket method because we only need to detect the parents of the target variable t .
our new markov blanket method makes some simplifications to adapt to this special condition.
we apply the fepi-mb algorithm to simulated datasets based on four disease models and a real dataset  dataset).
we demonstrate that the proposed method significantly outperforms other commonly-used methods and is capable of finding snps strongly associated with diseases.
comparing to other markov blanket learning methods, our method is faster and can still achieve a better performance.
RESULTS
simulated data generation
we first evaluate the proposed fepi-mb on simulated data sets, which are generated from three commonly used two-locus epistatic models  <cit>  and one three-locus epistatic model developed  <cit> .
table  <dig> lists the disease odds for these four epistatic models, where α is the baseline effect and θ is the genotypic effect.
assume that an individual has genotype ga at locus a and genotype gb at locus b in a two-locus epistatic model, then the disease odds are
where p is the probability that an individual has the disease given genotype  and  is the probability that an individual does not have the disease given genotype .
in model <dig> the odds of disease increase in a multiplicative mode both within and between two loci.
for example, an individual with aa at locus a has larger odds, which are  <dig> + θ times relative to those of an individual who is homozygous aa; the aa homozygote has further increased disease odds by  <dig>  we can also find similar effects on locus b. finally the odds of disease for each combination of genotypes at loci a and b can be obtained by the product of the two within-locus effects.
model <dig> demonstrates two-locus interaction multiplicative effects because at least one disease-associated allele must be present at each locus to increase the odds beyond the baseline level.
moreover the increment of the disease-associated allele at loci a or b can further increase the disease odds by the multiplicative factor  <dig> + θ. model <dig> specifies two-locus interaction threshold effects.
like model  <dig>  model <dig> also requires at least one copy of the disease-associated alleles at both loci a and b. however the increment of the disease-associated allele does not increase the risk further.
we call this as disease threshold effect.
it means that a single copy of the disease-associated allele at each locus is required to increase odds of disease and this is the disease threshold.
but after the disease threshold has already been met, having both copies of the disease-associated allele at either locus has no additional influence on disease odds.
there are three disease loci in model  <dig>  some certain genotype combinations can increase disease risk and there are almost no marginal effects for each disease locus.
model  <dig> is more complex than models  <dig>   <dig> and  <dig>  all these four models are non-additive models and they differ in the way that the number of disease-associated allele increases the odds of disease.
the prevalence of a disease is the proportion the total number of cases of the disease in the population and we assume that the disease prevalence is  <dig>  for all these four disease models  <cit> .
to generate data, we need to determine three parameters associated with each model: the marginal effect of each disease locus , the minor allele frequencies  of both disease loci, and the strength of linkage disequilibrium  between the unobserved disease locus and a genotyped locus  <cit> .
ld is a nonrandom association of alleles at different loci and is quantified by the squared correlation coefficient r <dig> calculated from allele frequencies  <cit> .
in this paper, we set λ equal to  <dig> ,  <dig> , and  <dig>  for models  <dig>   <dig>  and  <dig>  respectively.
for model  <dig>  we set θ =  <dig> arbitrarily because there are almost no marginal effects in model  <dig>  we let maf take four values  and let r <dig> take two values  for each model.
for each non-disease marker we randomly chose its maf from a uniform distribution in .
we first generate  <dig> small datasets and each dataset contains  <dig> markers genotyped for  <dig>  cases and  <dig>  controls based on each parameter setting for each model.
to test the scalability of fepi-mb, we also generate  <dig> large datasets and each dataset contains  <dig> markers genotyped for  <dig>  cases and  <dig>  controls using the same parameter setting for each model.
epistasis detection on simulated data
we compare the fepi-mb algorithm with three commonly-used methods: beam, svm and mdr on the four simulated disease models.
to measure the performance of each method, we use “power” as the criterion function.
power is calculated as the fraction of  <dig> simulated datasets in which disease associated markers are identified and demonstrate statistically significant associations  with the disease  <cit> .
the beam software is downloaded from http://www.fas.harv-ard.edu/~junliu/beam and we set the threshold of the b statistic as  <dig>   <cit> .
for svm, we use libsvm with a rbf kernel to detect epistatic interactions and the same searching strategy as shown in  <cit> .
since mdr algorithm can not be applied to a large dataset directly, we first reduce the number of snps to  <dig> by relieff  <cit> , a commonly-used feature selection algorithm, and then mdr performs an exhaustive search for a snp set that can maximize cross-validation consistency and prediction accuracy.
for the large datasets containing  <dig> markers genotyped for  <dig>  cases and  <dig>  controls, we only compare the performance of fepi-mb, beam and svm because relieff  <cit>  in mdr can not work for large datasets of this scale.
we show the results on the simulated data in figures  <dig> and  <dig>  as can be seen, fepi-mb performs the best comparing to other three methods.
beam is the second best.
in most cases, the powers of mdr are much smaller than these of the fepi-mb and beam algorithms.
for the mdr algorithm, the poor performance may be due to the use of relieff to reduce snps from a very large dimensionality.
we try another comparison experiment based on the simulated data containing only  <dig> markers, which makes us be able to apply mdr to the simulated data directly.
the performance of mdr is still poor and this indicates that perhaps using the risk table as a predictor to detect epistatic interactions is not a good choice.
in some cases, svm can achieve a comparable or even better performance than fepi-mb and beam, however, at the cost of introducing more false positives.
figure  <dig> also demonstrates the scalability of fepi-mb on large datasets.
an important issue for epistatic interaction detection in genome-wide association studies is the number of available samples.
typically, the size of samples is limited and consequently, computational model behaves differently.
we explore the effect of the number of samples on the performance of beam and fepi-mb .
we generate synthetic datasets containing  <dig> markers genotyped for different number of cases and controls with r <dig> =  <dig> and maf= <dig> .
the result is shown in figure  <dig> and we find that fepi-mb can achieve a higher power than beam when the number of samples is the same in most cases.
on the other hand, fepi-mb needs fewer samples to reach the perfect power comparing to beam.
so we can conclude that fepi-mb is more sample-efficient than beam.
we also compare the performance of fepi-mb with interiambnpc based on the large dataset from model <dig> to show the time efficiency of fepi-mb.
among the three variants of iamb, interiambnpc can achieve the best performance  <cit> .
both fepi-mb and interiambnpc are written in matlab and all the experiments are run on an intel core  <dig> duo t <dig>  <dig>  ghz, 4gb ram and windows vista.
the results are shown in table  <dig>  as seen, fepi-mb runs more than ten times faster than interiambnpc.
epistasis detection on amd data
fepi-mb demonstrates its greater power, sample-efficiency, and time-efficiency on simulated data with the number of snps less than  <dig>  in practical problems, a typical gwas genotype dataset contains at least more than  <dig>  common snps.
fepi-mb can also be scalable to large-scale datasets in real genome-wide case-control studies.
we apply fepi-mb to an age-related macular degeneration  dataset, which contains  <dig>  snps genotyped with  <dig> cases and  <dig> controls  <cit> .
amd   <cit>  is a common genetic disease related to the progressive visual dysfunction in age over  <dig> in the developed country.
we use the same preprocessing method as in  <cit> .
after filtering, there are  <dig>  snps lying in  <dig> autosomal chromosomes remained.
the searching time of fepi-mb for amd-related snps on an intel core  <dig> duo t <dig>  <dig>  ghz, 4gb ram and windows vista is  <dig> s and fepi-mb detects two associated snps: rs <dig> and rs <dig>  which have a g <dig> test p-value of  <dig> *10- <dig>  the first snp, rs <dig>  is already found in  <cit>  with a significant association with amd.
the other snp detected by the fepi-mb algorithm is snp rs <dig>  which is intergenic between tfec and tes in chromosome 7q <dig>  <cit> .
it is worth noting that several lines of evidence have previously shown the long arm of 7q harbors genes implicated in retinal disorders.
among which is mapping of a locus on 7q31-q <dig> for retinitis pigmentosa, another retinal disease  <cit> .
ocular abnormalities have been reported for an individual with terminal deletion of chromosome 7q  <cit> .
mutations in a gene located at 7q <dig> have been reported in families with autosomal dominant retinitis pigmentosa  <cit> .
more recently, next-generation sequencing revealed mutations in another gene located on chromosome 7q <dig> in patients with a form of retinopathy  <cit> .
the rs <dig> snp identified in our study does not locate in any of the previously reported implicated genes in retinal disorders.
therefore, it may shed light on discovering a new genetic factor, on chromosome 7q, contributing to the underlying mechanism of amd, a complex form of retinal degenerative disorder.
the real mechanism of interaction between rs <dig> and rs <dig> should be explored further by biological experiments.
CONCLUSIONS
while many computational methods were used for identification of epistatic interactions, most existing computational methods do not consider the complexity of genetic mechanisms causing common diseases and only focus on the selection of snp sets, which show the best classification capacity.
this will introduce many false positives inevitably.
furthermore, most existing methods cannot directly handle genome-wide scale problems.
in this paper, we introduce a new and fast markov blanket-based method, fepi-mb, to identify epistatic interactions.
we compared fepi-mb with three other methods, beam, svm and mdr, over both simulated datasets and a real dataset.
our results show that the fepi-mb algorithm outperforms other methods in terms of the power and sample-efficiency.
moreover, we compare fepi-mb with one of the best markov blanket learning method, interiambnpc.
the fepi-mb is more than ten times faster than interiambnpc.

 in recent years, the success of gwas makes it possible to detect genetic factors that influence the susceptibility to particular diseases in human populations. while most of gwas search for one single contributing locus at a time, they fail to identify the combinational effect of genetic variants associated with common complex diseases such as asthma, diabetes, and hypertension. it is well known that epistatic interactions, not individual variant, are critical in unravelling genetic causes of complex human diseases. however, the number of possible combinations of snps in a genome is enormous, which is infeasible to be evaluated exhaustively by experimental methods. therefore, researchers resort to computational methods to detect epistatic interactions based on the genotyped data. recently, a number of statistical methods have been proposed to detect epistatic interactions. among these methods, the most commonly used one is logistic regression. however, logistic regression may not be appropriate for epistasis due to its overfitting problem due to the fact that the number of parameters will be much larger than the available samples. to avoid this shortcoming, ritchie et al. proposed mdr, which utilizes the ratio of the number of cases to the number of controls in cells of risk table to reduce the dimensionality to one and select snp combinations that have the highest prediction performance. the process of labelling each cell of risk table as “high risk” or “low risk” is a process of estimating parameters, which may also result in the overfitting problems when the size of snp combinations is large. furthermore, mdr selects the snp combinations purely by the prediction performance and thus, it may not find true causal factors. park and hastie proposed the stepwise-penalized logistic regression to overcome the drawbacks of logistic regression and mdr. stepplr makes some simple modifications for standard logistic regression. for example, stepplr combines the lr criterion with a penalization of the l2-norm of the coefficients. this modification makes stepplr more robust to high-order epistatic interactions. despite its modifications, stepplr is time-consuming when estimating parameters, which is one essential limitation of regression methods. beam is a bayesian marker partition model using markov chain monte carlo to reach an optimal marker partition and a new b statistic to check each marker or set of markers for significant associations. note that most statistical methods can not be applied to genome-wide analysis directly due to their computational complexity. the alternative approaches to parametric statistical methods are machine learning methods including support vector machine and random forest. machine learning methods consider detecting epistatic interactions as a feature selection problem and try to find the best combination of snps with the highest prediction accuracy of disease status. therefore, chen et al. test three feature selection method: rfe, rfa, and ga in and jiang et al. perform a greedy search in. like mdr, machine learning methods select snps based on classification/prediction accuracy and can not find true causal factors for disease. moreover, machine learning-based methods tend to introduce many false positives because using more snps tends to produce higher classification accuracies. in this paper, we propose a new and fast markov blanket method, fepi-mb, to detect epistatic interactions. the markov blanket is a minimal set of variables, which can completely shield the target variable from all other variables. as shown in figure genome-wide association studies try to identify the k-way interaction among disease snps: snp snp …,snpk and exclude all other unrelated normal snps. thus, the markov blanket learning method is suitable for detection of epistatic interactions in genome-wide case-control studies, e.g., to identify a minimal set of snps which may cause the disease and require further experiments. meanwhile the detected minimal set of causal snps can shield the disease from all other normal snps to decrease the false positive rate and reduce the cost of future validation experiments. furthermore, markov blanket method performs a heuristic search by calculating the association between variables to avoid the time-consuming training process as in svm and random forest. some markov blanket methods take a divide-and-conquer approach that breaks the problem of identifying markov blanket of variable t ) into two subproblems: first, identifying parents and children of t ) and, second, identifying the parents of the children of t. the goal of epistatic interactions detection is to identify causal interacting genes or snps for some certain diseases and therefore it is a special application of markov blanket method because we only need to detect the parents of the target variable t. our new markov blanket method makes some simplifications to adapt to this special condition. we apply the fepi-mb algorithm to simulated datasets based on four disease models and a real dataset dataset). we demonstrate that the proposed method significantly outperforms other commonly-used methods and is capable of finding snps strongly associated with diseases. comparing to other markov blanket learning methods, our method is faster and can still achieve a better performance.  simulated data generation we first evaluate the proposed fepi-mb on simulated data sets, which are generated from three commonly used two-locus epistatic models and one three-locus epistatic model developed. table lists the disease odds for these four epistatic models, where α is the baseline effect and θ is the genotypic effect. assume that an individual has genotype ga at locus a and genotype gb at locus b in a two-locus epistatic model, then the disease odds are where p is the probability that an individual has the disease given genotype and is the probability that an individual does not have the disease given genotype. in model the odds of disease increase in a multiplicative mode both within and between two loci. for example, an individual with aa at locus a has larger odds, which are + θ times relative to those of an individual who is homozygous aa; the aa homozygote has further increased disease odds by we can also find similar effects on locus b. finally the odds of disease for each combination of genotypes at loci a and b can be obtained by the product of the two within-locus effects. model demonstrates two-locus interaction multiplicative effects because at least one disease-associated allele must be present at each locus to increase the odds beyond the baseline level. moreover the increment of the disease-associated allele at loci a or b can further increase the disease odds by the multiplicative factor + θ. model specifies two-locus interaction threshold effects. like model model also requires at least one copy of the disease-associated alleles at both loci a and b. however the increment of the disease-associated allele does not increase the risk further. we call this as disease threshold effect. it means that a single copy of the disease-associated allele at each locus is required to increase odds of disease and this is the disease threshold. but after the disease threshold has already been met, having both copies of the disease-associated allele at either locus has no additional influence on disease odds. there are three disease loci in model some certain genotype combinations can increase disease risk and there are almost no marginal effects for each disease locus. model is more complex than models and all these four models are non-additive models and they differ in the way that the number of disease-associated allele increases the odds of disease. the prevalence of a disease is the proportion the total number of cases of the disease in the population and we assume that the disease prevalence is for all these four disease models. to generate data, we need to determine three parameters associated with each model: the marginal effect of each disease locus, the minor allele frequencies of both disease loci, and the strength of linkage disequilibrium between the unobserved disease locus and a genotyped locus. ld is a nonrandom association of alleles at different loci and is quantified by the squared correlation coefficient r calculated from allele frequencies. in this paper, we set λ equal to,, and for models and respectively. for model we set θ = arbitrarily because there are almost no marginal effects in model we let maf take four values and let r take two values for each model. for each non-disease marker we randomly chose its maf from a uniform distribution in. we first generate small datasets and each dataset contains markers genotyped for cases and controls based on each parameter setting for each model. to test the scalability of fepi-mb, we also generate large datasets and each dataset contains markers genotyped for cases and controls using the same parameter setting for each model. epistasis detection on simulated data we compare the fepi-mb algorithm with three commonly-used methods: beam, svm and mdr on the four simulated disease models. to measure the performance of each method, we use “power” as the criterion function. power is calculated as the fraction of simulated datasets in which disease associated markers are identified and demonstrate statistically significant associations with the disease. the beam software is downloaded from http://www.fas.harv-ard.edu/~junliu/beam and we set the threshold of the b statistic as. for svm, we use libsvm with a rbf kernel to detect epistatic interactions and the same searching strategy as shown in. since mdr algorithm can not be applied to a large dataset directly, we first reduce the number of snps to by relieff, a commonly-used feature selection algorithm, and then mdr performs an exhaustive search for a snp set that can maximize cross-validation consistency and prediction accuracy. for the large datasets containing markers genotyped for cases and controls, we only compare the performance of fepi-mb, beam and svm because relieff in mdr can not work for large datasets of this scale. we show the results on the simulated data in figures and as can be seen, fepi-mb performs the best comparing to other three methods. beam is the second best. in most cases, the powers of mdr are much smaller than these of the fepi-mb and beam algorithms. for the mdr algorithm, the poor performance may be due to the use of relieff to reduce snps from a very large dimensionality. we try another comparison experiment based on the simulated data containing only markers, which makes us be able to apply mdr to the simulated data directly. the performance of mdr is still poor and this indicates that perhaps using the risk table as a predictor to detect epistatic interactions is not a good choice. in some cases, svm can achieve a comparable or even better performance than fepi-mb and beam, however, at the cost of introducing more false positives. figure also demonstrates the scalability of fepi-mb on large datasets. an important issue for epistatic interaction detection in genome-wide association studies is the number of available samples. typically, the size of samples is limited and consequently, computational model behaves differently. we explore the effect of the number of samples on the performance of beam and fepi-mb. we generate synthetic datasets containing markers genotyped for different number of cases and controls with r = and maf=. the result is shown in figure and we find that fepi-mb can achieve a higher power than beam when the number of samples is the same in most cases. on the other hand, fepi-mb needs fewer samples to reach the perfect power comparing to beam. so we can conclude that fepi-mb is more sample-efficient than beam. we also compare the performance of fepi-mb with interiambnpc based on the large dataset from model to show the time efficiency of fepi-mb. among the three variants of iamb, interiambnpc can achieve the best performance. both fepi-mb and interiambnpc are written in matlab and all the experiments are run on an intel core duo t ghz, 4gb ram and windows vista. the results are shown in table as seen, fepi-mb runs more than ten times faster than interiambnpc. epistasis detection on amd data fepi-mb demonstrates its greater power, sample-efficiency, and time-efficiency on simulated data with the number of snps less than in practical problems, a typical gwas genotype dataset contains at least more than common snps. fepi-mb can also be scalable to large-scale datasets in real genome-wide case-control studies. we apply fepi-mb to an age-related macular degeneration dataset, which contains snps genotyped with cases and controls. amd is a common genetic disease related to the progressive visual dysfunction in age over in the developed country. we use the same preprocessing method as in. after filtering, there are snps lying in autosomal chromosomes remained. the searching time of fepi-mb for amd-related snps on an intel core duo t ghz, 4gb ram and windows vista is s and fepi-mb detects two associated snps: rs and rs which have a g test p-value of *10- the first snp, rs is already found in with a significant association with amd. the other snp detected by the fepi-mb algorithm is snp rs which is intergenic between tfec and tes in chromosome 7q. it is worth noting that several lines of evidence have previously shown the long arm of 7q harbors genes implicated in retinal disorders. among which is mapping of a locus on 7q31-q for retinitis pigmentosa, another retinal disease. ocular abnormalities have been reported for an individual with terminal deletion of chromosome 7q. mutations in a gene located at 7q have been reported in families with autosomal dominant retinitis pigmentosa. more recently, next-generation sequencing revealed mutations in another gene located on chromosome 7q in patients with a form of retinopathy. the rs snp identified in our study does not locate in any of the previously reported implicated genes in retinal disorders. therefore, it may shed light on discovering a new genetic factor, on chromosome 7q, contributing to the underlying mechanism of amd, a complex form of retinal degenerative disorder. the real mechanism of interaction between rs and rs should be explored further by biological experiments.  while many computational methods were used for identification of epistatic interactions, most existing computational methods do not consider the complexity of genetic mechanisms causing common diseases and only focus on the selection of snp sets, which show the best classification capacity. this will introduce many false positives inevitably. furthermore, most existing methods cannot directly handle genome-wide scale problems. in this paper, we introduce a new and fast markov blanket-based method, fepi-mb, to identify epistatic interactions. we compared fepi-mb with three other methods, beam, svm and mdr, over both simulated datasets and a real dataset. our results show that the fepi-mb algorithm outperforms other methods in terms of the power and sample-efficiency. moreover, we compare fepi-mb with one of the best markov blanket learning method, interiambnpc. the fepi-mb is more than ten times faster than interiambnpc. 
most computational methods to detect epistatic interactions are predictor-based methods and can not find true causal factor elements. we propose a new and fast markov blanket-based method, fepi-mb, for epistatic interactions detection. learning of markov blankets can be used to detect epistatic interactions by a heuristic search for a minimal set of snps, which may cause the disease. fepi-mb algorithm outperforms other computational methods for detection of epistatic interactions in terms of both the power and sample-efficiency. the markov blanket is a minimal set of variables that can completely shield the target variable from all other variables. moreover, compared to other markov blanket learning methods, fepi-mb is more time-efficient and achieves a better performance. experimental results on both simulated data sets and a real data set demonstrate that fepi-mb significantly outperforms other existing methods and is capable of finding snps that have a strong association with common diseases. however, the difficulties of detecting epistatic interaction arose from the large number of genetic factors and the enormous size of possible combinations of genetic factors. with the availability of genotyped data from genome-wide association studies, it is now possible to computationally unravel epistasis related to the susceptibility to common complex human diseases such as asthma, diabetes, and hypertension.
 the interactions among genetic factors related to diseases are called epistasis. with the availability of genotyped data from genome-wide association studies, it is now possible to computationally unravel epistasis related to the susceptibility to common complex human diseases such as asthma, diabetes, and hypertension. however, the difficulties of detecting epistatic interaction arose from the large number of genetic factors and the enormous size of possible combinations of genetic factors. most computational methods to detect epistatic interactions are predictor-based methods and can not find true causal factor elements. moreover, they are both time-consuming and sample-consuming.  we propose a new and fast markov blanket-based method, fepi-mb, for epistatic interactions detection. the markov blanket is a minimal set of variables that can completely shield the target variable from all other variables. learning of markov blankets can be used to detect epistatic interactions by a heuristic search for a minimal set of snps, which may cause the disease. experimental results on both simulated data sets and a real data set demonstrate that fepi-mb significantly outperforms other existing methods and is capable of finding snps that have a strong association with common diseases.  fepi-mb algorithm outperforms other computational methods for detection of epistatic interactions in terms of both the power and sample-efficiency. moreover, compared to other markov blanket learning methods, fepi-mb is more time-efficient and achieves a better performance. 9th international workshop on data mining in bioinformatics washington, dc, usa 