Feature selection with the R package MXM

Feature (or variable) selection is the process of identifying the minimal set of features with the highest predictive performance on the target variable of interest. Numerous feature selection algorithms have been developed over the years, but only few have been implemented in R and made publicly available R as packages while offering few options. The R package MXM offers a variety of feature selection algorithms, and has unique features that make it advantageous over its competitors: a) it contains feature selection algorithms that can treat numerous types of target variables, including continuous, percentages, time to event (survival), binary, nominal, ordinal, clustered, counts, left censored, etc; b) it contains a variety of regression models that can be plugged into the feature selection algorithms (for example with time to event data the user can choose among Cox, Weibull, log logistic or exponential regression); c) it includes an algorithm for detecting multiple solutions (many sets of statistically equivalent features, plain speaking, two features can carry statistically equivalent information when substituting one with the other does not effect the inference or the conclusions); and d) it includes memory efficient algorithms for high volume data, data that cannot be loaded into R (In a 16GB RAM terminal for example, R cannot directly load data of 16GB size. By utilizing the proper package, we load the data and then perform feature selection.). In this paper, we qualitatively compare MXM with other relevant feature selection packages and discuss its advantages and disadvantages. Further, we provide a demonstration of MXM’s algorithms using real high-dimensional data from various applications.

This article is included in the gateway. Given a target (response or dependent) variable Y of n measurements and a set X of p features (predictor or independent variables) the problem of feature (or variable) selection (FS) is to identify the minimal set of features with the highest predictability a on the target variable (outcome) of interest. The natural question that arises, is why should researchers and practitioners perform FS. The answer to this is for a variety of reasons 1 , such as: a) many features may be expensive (and/or unnecessary) to measure, especially in the clinical and medical domains; b) FS may result in more accurate models (of higher predictability) by removing noise while treating the curse-of-dimensionality; c) the final produced parsimonious models are computationally cheaper and often easier to understand and interpret; d) future experiments can benefit from prior feature selection tasks and provide more insight into the problem of interest, its characteristics and structure. e) FS is indissolubly connected with causal inference that tries to identify the system's causal mechanism that generated the data.
R contains thousands of packages, but only a small portion of them are dedicated to the task of FS, yet offering limited or narrow capabilities. For example, some packages accept few or specific types of target variables (e.g. binary and multi-class only). This leaves many types of target variables, e.g. percentages, left censored, positive valued, matched case-control data, etc., untreated. The availability of regression models for some types of data is rather small. Count data is such an example, for which Poisson regression is the only model considered in nearly all R packages. Most algorithms including statistical tests offer limited statistical tests, e.g. likelihood ratio test only. Almost all available FS algorithms are devised for large sample sized data, thus they cannot be used in many biological settings where the number of observations rarely (or never in some cases) exceeds 100, but the number of features is in the order of tens of thousands. Finally, some packages are designed for high volume data b only.
In this paper we present MXM c 2 ; an R package that overcomes the above shortcomings. It contains many FS algorithms d , which can handle numerous and diverse types of target variables, while offering a pool of regression models to choose from and feed the FS algorithms. There is a plethora of statistical tests (likelihood-ratio, Wald, permutation based) and information criteria (BIC and eBIC) to plug into the FS algorithms. Algorithms that work with small and large sample sized data, algorithms that have been customized for high volume data, and an algorithm that returns multiple sets of statistically equivalent features are some of the key characteristics of MXM.
Over the next sections, a brief qualitative comparison of MXM with other packages available on CRAN and Bioconductor is presented, its (dis)advantages are discussed, its FS algorithms and related functions are mentioned. Finally a demonstration takes place, applying some FS algorithms available in MXM on real high dimensional data. a Predictive performance metrics include AUC, accuracy, mean squared error, mean absolute error, concordance index, F score, proportion of variance explained, etc. b In statistics and in the R packages the term "big data" is used to refer to such data. In the computer science terminology, big data are of much higher volume and require specific technology. For this reason we chose to use the term "high volume" instead of "big data".

The R package MXM MXM versus other R packages
When searching for FS packages on CRAN and Bioconductor repositories using the keywords "feature selection", "variable selection", "selection", "screening" and "LASSO" e , we detected 184 R packages until the 7th of May 2018 f . Table 1 shows the frequency of the target variable types those packages accept g , while Figure 1 shows the frequency of R packages whose FS algorithms can treat at least k types of target variables, for k = 1, 2, . . . , 8, of those presented in Table 1. Table 2 presents the frequency of pairwise types of target variables offered in R packages and Table 3 contains information on packages allowing for less frequent regression models. Most packages offer FS algorithms that are oriented towards specific types of target variables, methodology and regression models, offering at most 3-4 options. Out of these 184 packages, 65 (35.32%) offer LASSO type FS algorithms, while 19 (10.32%) address the problem of FS from the Bayesian perspective. Only 2 (1.08%) R packages treat the case of FS with multiple datasets h while only 4 (2.17%) packages are devised for high volume data.       15 both in predictive performance and computational efficiency. FBED 5 was compared to LASSO for the task of binary classification with sparse data exhibiting performance similar to that of LASSO. As for gOMP, our experiments have showed very promising results, achieving similar or better performance, while enjoying higher computational efficiency than LASSO 6 .

Advantages and disadvantages of MXM's FS algorithms
The main advantage of MXM is that all FS algorithms accept numerous and diverse types of target variables. MMPC, SES and FBED treat all types of target variables presented in Table 4, while gOMP handles fewer types i .
MXM is the only R package that offers many different regression models to be employed by the FS algorithms, even for the same type of response variable, such as Poisson, quasi Poisson, negative binomial and zero inflated Poisson regression for count data. For repeated measurements, the user has the option of using GLMM or the GEE methodology (the latter with more options in the correlation structure) and for time-toevent data, Cox, Weibull and exponential regression models are the available options.
A range of statistical tests and methodologies to select the features is offered. Instead of the usual log-likelihood ratio test, the user has the option to use the Wald test or produce a p-value based on permutations. The latter is useful and advised when the sample size is small, emphasizing the need for use of MMPC and SES, both of which are designed for small sample sized datasets. FBED on the other hand, appart from the log-likelihood ratio test offers the possibility of using information criteria, such as BIC 16 and eBIC 17 .
No p-values correction (e.g. Benjamini and Hochberg 18 ,) is applied. Specifically MMPC (and SES essentially) has been proved to control the False Discovery Rate 19 . However, we allow for permutation-based p-values when performing MMPC and SES. FBED addresses this issue either by removing the non-significant variables or by using information criteria such as the extended BIC 17 . Borboudakis and Tsamardinos 5 have conducted experiments showing that FBED reduces the percentage of falsely selected features. gOMP on the other hand relies on correlations and does not select the candidate feature using p-values.
Statistically Equivalent Signatures (SES) 2,20 builds upon the ideas of MMPC and returns multiple (statistically equivalent) sets of predictor variables, making it one of the few FS algorithms suggested in the literature, and available in CRAN, with this trait 21 . demonstrated that multiple, equivalent prognostic signatures for breast cancer can be extracted just by analyzing the same dataset with a different partition in training and test sets, showing the existence of several genes which are practically interchangeable in terms of predictive power. SES along with MMPC are two among the few algorithms, available on CRAN , that can be used to perform FS with multiple datasets in a meta-analytic way, following 22 . MXM contains FS algorithms for small sample sized data (MMPC, MMMB, and SES) j and for large sample sized data (FBED, gOMP). FBED and gOMP have been adopted for high volume data, going beyond the limits of R. The importance of these customizations can be appreciated by the fact that nowadays large scale datasets are more frequent than before. Since classical FS algorithms cannot handle such data, modifications must be made, in an algorithm level, in a memory efficient manner, in a computer architecture level, and/or in any other way. MXM is using the efficient memory handling R package bigmemory 23 .
Finally, many utility functions are available, such as constructing a model from the object an algorithm returned, construct a regression model, long verbose output with useful information, etc. Using hash objects, the computational cost of MMPC and SES is significantly reduced. Further, communication between the input and outputs of the algorithms is possible. The univariate associations computed by MMPC can be supplied to SES and FBED, and vice versa, and save computational time.
i For this long list of available target variables and regression models, expanding Table 4, see Guide on performing FS with the R package MXM.
j The Wald and log-likelihood ratio tests are asymptotic tests. In addition, the fitted regression models require large sample size. With small sample sizes, the fitted regression models must not contain many predictor variables in order not to estimate many parameters.
To address these issues both MMPC and SES perform conditional independence tests using subsets of selected variables, thus reducing the number of estimated parameters.
Not all MXM's FS algorithms and all regression models used are computationally efficient. The (algorithmic) order of complexity of the FS algortihms is comparable to state-of-art FS algorithms, but the nature of the other algorithms is such that many regression models must be fit increasing the computational burden. In addition, R itself does not allow for further speed improvement. For example, MMPC can be slow for many regression models, such as negative binomial or ordinal regression for which we rely on implementations in other R packages. gOMP, on the other hand, is the most efficient algorithm available in MXM k gOMP superseded the LASSO implementation in the package glmnet 24 in both time and performance., because it is residual based and few regression models are fit. With clustered/longitudinal data, SES (and MMPC) were shown to scale to tens of thousands and be dramatically faster than LASSO 14 . Computational efficiency is also programming language-dependent. Most of the algorithms are currently written in R and we are constantly working towards transferring them to C++ so as to decrease the computational cost significantly.
It is impossible to cover all cases of target variables; we have no algorithms for time series, and do not treat multi-state time-to-event target variables for example, yet we regularly search for R packages that treat other types of target variables and link them to MXM l . All algorithms are limited to linear or generalised linear relationships, and we plan to address this issue in the future. The gOMP algorithm does not accept all types of target variables and works only with continuous predictor variables. This is a limitation of the algorithm, but we plan to address this in the future as well.
Cross-validation functions currently exist only for MMPC, SES and gOMP, but performance metrics are not available for all target variables. When the target variable is binary AUC, accuracy or the F score can be utilised, when the target takes continuous values, the mean squared error, the mean absolute error or the proportion of variance explained can be used, whereas with survival target variables the concordance index can be computed. Left censored data, is an example of target variable whose predictive performance estimation is not offered. A last drawback is that currently MXM does not offer graphical visualization of the algorithms and of the final produced models.
Which FS algorithm from MXM to use and when In terms of sample size, FBED and gOMP are generally advised for large-sample-sized datasets, whereas MMPC and SES are designed mainly for small-sample-sized datasets m . In the case of a large sample size and few features, FSR or BSR are also suggested. In terms of number of features, gOMP is the only algorithm that scales up when the number of features is in the order of the hundreds of thousands. gOMP is also suitable for high volume data that contain a high number of features, really large sample sizes or both. FBED has been customized to handle high volume data as well, but with large sample sizes and only a few thousand features. If the user is interested in discovering more than one set of features, SES is suitable for returning multiple solutions, which are statistically equivalent. With multiple datasets n , both MMPC and SES are currently the only two algorithms that can handle some cases (both the target variable and the set of features are continuous). As for the availability of the target variable, MMPC, SES and FBED handle all types of target variables available in MXM, listed in Table 4, while gOMP accepts fewer types of target variables. Regarding the type of features, gOMP currently works with continuous features only, whereas all other algorithms accept both continuous and categorical features. All this information is presented in Table 5.

Implementation
MXM is an R package that makes use of (depends or imports) other packages that offer regression models or utility functions.
k Based on our experiments 6 . l Currently, with little effort, one should be able to plug-in their own regression model into some of the algorithms. We plan to expand this possibility for all algorithms. m To the best of our knowledge there are not many FS algorithms dealing with small sample sized data.
n Instead of having one dataset only to analyze one might have multiple datasets from different sources. We do not combine all datasets into a larger one, neither perform FS for each dataset separately. Each step of the MMPC and SES algorithms is performed simultaneously to all datasets.
• MASS: for negative binomial regression, ordinal regression and robust (MM type) regression.
• survival: for survival regression and Tobit regression.
• Rfast: for computational efficiency. MMPC and SES have been implemented in such a way that the user has the option to store the results (p-values and test statistic values) from a single run in a hash object. In subsequent runs, with different hyperparameters this can lead to significant amounts of computational savings because it avoids performing tests that have been already been performed. These two algorithms give the user an extra advantage. They can search for the subset of feature(s) that rendered one more specific feature(s) independent of the target variable by using the function certificate.of.exclusion.
FBED, SES and MMPC are three algorithms that share common grounds. The list with the results of the univariate associations (test statistic and logged p-value) can be calculated from either algorithm and be passed onto any of them. When one is interested in running many algorithms, this can reduce the computational cost significantly. Note also that the univariate associations in MMPC and SES can be calculated in parallel, with multi-core machines. More FS related functions can be found in MXM's reference manual and vignettes section available on CRAN.

Operation
MXM is distributed as part of the CRAN R package repository and is compatible with Mac OS X, Windows, Solaris and Linux operating systems. Once the package is installed and loaded > install.packages("MXM") > library(MXM) it is ready to be used without internet connection. The system requirements are documented on MXM's webpage on CRAN.

Use cases
We will now demonstrate some FS algorithms available in MXM, using real datasets. Specifically we will show the relevant commands and describe part of their output. With user-friendliness taken into consideration, extra attention has been put in keeping the functions within the MXM package as consistent as the nature of the algorithms allows for, in terms of syntax, required input objects and parameter arguments. Table 6 contains a list of the current FS algorithms, but we will demonstrate some of them here. In all cases, the arguments "target", "dataset" and "test" refer to the target variable, set of features and type of regression model to be used. o We plan to implement this more efficiently in the future The first column of $res denotes the selected features, i.e. the 28th and the 6th feature were selected. The second and third columns refer to the feature(s)'s associated test statistic and p-value. The $info informs the user on the value of K used, the number of selected features and the number of tests (or regression models) performed. p Censoring occurs when partial information about some observations is available. It might be the case that some individuals will experience the event after completion of the study. Or when an individual is not part of the study for anymore, for a reason other than the occurrence of the event of interest. In a study about cancer, for example, some patients may die of another cause, e.g. another disease or car accident for example. The survival times of those patients has been recorded, but offer limited information.
q The logarithm of the p-values is computed and return in order to avoid small p-values (less than the machine epsilon 10 −16 ) being rounded to 0. This is a crucial and key element of the algorithms because they rely on the correct ordering of the p-values.
The above output was produced using Cox regression. If we used Weibull regression instead (test = "testIndWR"), the output would be slightly different. Only one feature (the 28th) was selected, and FBED performed 75 tests (based upon 75 fitted regression models). The element res presented below is one of the elements of the returned output. The first column shows the selected variables in order of inclusion and the second column is the deviance of each regression model. Longitudinal data The next dataset we will use is NCBI Gene Expression Omnibus accession number GSE9105 28 , which contains 22,283 features about skeletal muscles from 12 normal, healthy glucose-tolerant individuals exposed to acute physiological hyperinsulinemia, measured at 3 distinct time points. Following 14 , we will also use SES and not FBED because the sample size is small. The grouping variable that identifies the subject along with the time points is necessary in our case. If the data were clustered data, i.e. families, where no time is involved, the argument "reps" would not be provided. The user has the option to use GLMM 29 or GEE 30 . The output of SES (and of MMPC) is long and verbose, and thus we present the first 10 set of equivalent signatures. The first row is the set of selected features, and every other row is an equivalent set. In this example, the last four columns are the same and only the first changes. This means, that the feature 2683 has 9 statistically equivalent features, (2, 7, 10, ...).

Count data
The final example is on discrete valued target variable (count data) for which Poisson and quasi-Poisson regression models will be employed by the gOMP algorithm. The dataset with GEO accession number GSE47774 32 contains RNA-seq data with 256 samples and 43,919 features. We selected the first feature to be the target variable and all the rest are the features.
We ran gOMP using Poisson (test="testIndPois") and quasi Poisson (test="testIndQPois") regression models, but we changed the stopping value to tol=12. Due to over-dispersion (variance > mean), quasi Poisson is more appropriate r than Poisson regression that assumes that the mean and the variance are equal. When Poisson was used, 107 features were selected; since the wrong model was used, many false positive features were included, while with the quasi Poisson regression only 10 features were selected. r Negative binomial regression, test="testIndNB" is another alternative option. More recently 34 , applied MMPC in order to identify the features that provide novel information about steady-state plasma glucose (SSPG, a measure of peripheral insulin resistance) and are thus most useful for prediction 35 . used gOMP and identified the viscoelastic properties of the arterial tree as an important contributor to the circulating bubble production after a dive. Finally 36 , applied SES and gOMP were applied in the field of fisheries for identifying the genetic SNP loci that are associated with certain phenotypes of the gilthead seabream (Sparus aurata). Measurements from multiple cultured seabream families were taken, and since the data were correlated and GLMM was applied. The study led to a catalogue of genetic markers that set the ground for understanding growth and other traits of interest in Gilthead seabream, in order to maximize the aquaculture yield.

Summary
We presented the R package MXM and some of its feature selection algorithms. We discussed its advantages and disadvantages and compared it, at a high level, with other competing R packages. We then demonstrated, using real high-dimensional data with a diversity of types of target variables, four FS algorithms, including different regression models in some cases.
The package is constantly being updated with new functions and improvements being added and algorithms being transferred to C++ to decrease the computational cost. Computational efficiency was mentioned as one of MXM' disadvantage which we are trying to address. However, computational efficiency is one aspect, and flexibility another. Towards flexibility we plan to add of more regression models, more functionalities, options and graphical visualizations.

Data availability
• The first dataset we used (survival target variable) is available from Computational Cancer Biology.
• The second dataset we used (unmatched case control target variable) is available from GEO.
• The third dataset we used (longitudinal data) is available from GEO.
• The fourth dataset we used (continuous target variable) is available from GEO.
• The fifth dataset we used (count data) is available from GEO.

Thodoris Kypraios
School of Mathematical Sciences, University of Nottingham, Nottingham, UK I am satisfied with the authors' response to my comments and the paper now looks in better shape in conjunction with replying to Huitong's comments.
No competing interests were disclosed.

Competing Interests:
I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard. expertise to confirm that it is of an acceptable scientific standard. The manuscript introduces a new R package, MXM, that offers a variety of feature selection algorithms in regression models. The new package presents relevant contribution to the toolbox of feature selection algorithms by covering more types of target variables than most existing packages, accommodating data with small or big sample sizes, and providing additional functionalities and utility features. The manuscript also demonstrates the usage of several functions in the package by analyzing real data.
Regarding the presentation of the manuscript, I share the same concern with reviewer Thodoris that the acronyms in the paper come with poor explanation. Although several of the acronyms are explained in Table 4 and Table 6, most of appearances of these acronyms have no reference to these tables or explanations. This makes the paper unnecessarily hard to read.
Secondly, I think the demonstration of the usage of the package could be more informative with more interpretations. For example, how can we interpret the p-values, adjusted R-squares, and deviance in the results of the model fittings? High level descriptions of the algorithms behind the demonstrated functions could also help the reader better understand the results.
Below are comments to specific places in the manuscript: The 3rd paragraph in Introduction mentions that statistical tests (likelihood ratio, Wald, permutation based) can be plugged into the feature selection algorithms that work with small sample sized data. The aforementioned tests traditionally rely on large sample theory. I wonder what adjustments are needed to accommodate small sample sizes? Tables 1, 2, and Figure 1 shows statistics of target variable types supported by a number of R packages. What algorithm was used to identify the types of target variables accepted by an R package? What does "multiple datasets" mean as in "Only 2 (1.08%) R packages teat the case of FS with multiple datasets ..." (last sentence of Paragraph 1 on Page 5)? I find the last paragraph on Page 5 particularly uneasy to read due to the acronyms used without explanation. Some of these are later explained in Table 6 while a couple are not (e.g., MMHC). I think it would be helpful to make a comprehensive table explaining the algorithm acronyms used in this paper, and refer to the table here.
In the last paragraph on Page 5, there are multiple places that compare algorithms in terms of "(predictive) performance". I think it would be more informative to clarify what performance metrics we are looking at.
In Paragraph 5 on Page 6, the manuscript states that "SES ... returns multiple (statistically In Paragraph 5 on Page 6, the manuscript states that "SES ... returns multiple (statistically equivalent) sets of predictor variables ...". What does statistically equivalent mean? What does the package name, MXM, stand for? The second last paragraph on Page 6 is a bit confusing to me. The paragraph starts with pointing out computational efficiency as a disadvantage of MXM. However, this is followed by explaining why gOMP is efficient, and pointing out that SES and MMPC scales better and run faster than LASSO package. These seem like advantages in computational efficiency. In Paragraph 2 of "FS-related functions" section: for MMPC and SES, storing the results from one run and passing it to subsequent runs can lead to significant computational savings. Are there savings because the trained models serve as good starting points in the subsequent runs? On Page 9 in the output of MXM::fbed.reg, there are p-values associated with each selected variable. How can we interpret these p-values? It seems that these p-values are not adjusted for the extra degrees of freedom from feature selection. Below are some minor suggestions/typo fixes: In Abstract -"The R package MXM is such an example, which offers ...": It's unclear to me what "such an example" refers to. It's clearer to state "The R package MXM offers ..." directly. Second paragraph in Introduction: "For example, packages that accept few or specific types of target variables." → "For example, some packages accept few or specific types of target variables." (make it a complete sentence.) In "MXM versus other R packages" section: "... can treat at least one type of target variable, ..." → "... can treat at least k types of target variables, for k = 1, 2, ..., 8, ..." In the last paragraph on Page 5, does "BN" refer to Bayesian network (which also appears in the same paragraph)?
In Paragraph 5 on Page 6 -"... making it one one of the few FS algorithms ...": remove the extra "one". In Paragraph 6 on Page6 -"MXM is using an efficient memory handling R package.": please cite the package. Last Paragraph on Page 7: "generalised" → "generalized" to be consistent with other places in the paper. First paragraph in Section "Use cases": the argument "test" refers to the type of regression model to be used. Why not name the argument something like "model type"? Some of the citations are not easily distinguishable from footnotes. e.g., citation 21 for Rfast on Page 8 and footnote 7 are both superscripts. Paragraph 2 on Page 11: "gOMP on the other has ..." → "gOMP on the other hand ...". First paragraph on Page 12 -"YouTube video streaming applications applications": duplicate "applications".

Is the rationale for developing the new software tool clearly explained? Yes
Is the description of the software tool technically sound? Yes

Are sufficient details of the code, methods and analysis (if applicable) provided to allow replication of the software development and its use by others? Partly
Is sufficient information provided to allow interpretation of the expected output datasets and any results generated using the tool?

Partly Partly
Are the conclusions about the tool and its performance adequately supported by the findings presented in the article? Yes No competing interests were disclosed. Competing Interests: Reviewer Expertise: statistical machine learning, feature selection, high dimensional data, graphical models, time series analysis, clinical trial design I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above.
Author Response 12 Jul 2019 , University of Crete, Greece

Michail Tsagris
We are grateful to the reviewers for their on-the-spot comments which we have addressed.
The manuscript introduces a new R package, MXM, that offers a variety of feature selection algorithms in regression models. The new package presents relevant contribution to the toolbox of feature selection algorithms by covering more types of target variables than most existing packages, accommodating data with small or big sample sizes, and providing additional functionalities and utility features. The manuscript also demonstrates the usage of several functions in the package by analyzing real data.
Comment: Regarding the presentation of the manuscript, I share the same concern with reviewer Thodoris that the acronyms in the paper come with poor explanation. Although several of the acronyms are explained in Table 4 and  Figure 1 shows statistics of target variable types supported by a number of R packages. What algorithm was used to identify the types of target variables accepted by an R package? Reply: We did this manually. We searched on CRAN and went through all packages one by one. We did this process twice to make sure we did not omit any package. Bear in mind that this search was made a few months ago. Comment: What does "multiple datasets" mean as in " Reply: This comment was raised by the other reviewer as well. In the Abstract we have added a sentence inside parentheses briefly explain this. Also in Section "The MXM's FS algorithms and comparison with other FS algorithms" we have added one sentence when mention the SES algorithm (this is in magenta colour). This comment was also made by the first reviewer and we have answered this previously. Comment: What does the package name, MXM, stand for? Reply: We thank the reviewer for this comment. We added the meaning of this acronym in the 4rth footnote of page 2. It stands for Mens ex Machina. Comment: The second last paragraph on Page 6 is a bit confusing to me. The paragraph starts with pointing out computational efficiency as a disadvantage of MXM. However, this is followed by explaining why gOMP is efficient, and pointing out that SES and MMPC scales better and run faster than LASSO package. These seem like advantages in computational efficiency. Reply: We thank the reviewer for this clarification. Indeed the message is diluted. We have reworded this point, towards the end of page 5. Comment: In Paragraph 2 of "FS-related functions" section: for MMPC and SES, storing the results from one run and passing it to subsequent runs can lead to significant computational savings. Are there savings because the trained models serve as good starting points in the subsequent runs?
Reply: We have added a few sentences clarifying this point. All p-values are stored to avoid I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above.
Author Response 12 Jul 2019 , University of Crete, Greece

Michail Tsagris
We are grateful to the reviewers for their on-the-spot comments.
The paper is concerned with the method of feature selection using the R package MXM. The package appears to be fairly versatile in the sense that it can handle a huge variety of types of data. It can be very useful for applied researchers and, at the very least, it is another tool in the toolbox for the applied statistician.
Comment: I believe that the paper it will be a useful addition in the literature. However, I found difficult to read/understand in places. For example, is the MXM a package that only includes methodology that has been developed by the authors or does it include methods that have been developed by other researchers too? Either way is fine, but it would be helpful to clarify. Reply: We have added an extra column in Table 5 giving this information. Also, in Section "The MXM's FS algorithms and comparison with other FS algorithms" where we describe the algorithms we have added the relevant references. Comment: Another major issue for me is that the paper is flooded with acronyms that I believe most users will be unfamiliar with. It would improve the paper's presentation significantly, if there is some explanation (a couple of sentences per method would suffice) about each of them. Reply: We have added the explanation of all acronyms when the algorithm is first mentioned. Also in Section "The MXM's FS algorithms and comparison with other FS algorithms" we briefly mention how they work. Below are some more specific points to consider: Abstract Comment: It it not clear when one first reads what "b)it contains a variety of regression models to plug into the feature selection algorithms;" means. Reply: We have added a sentence inside parentheses giving some examples of target variables and appropriate regression models explaining this sentence. Comment: c), "equivalent" in what sense? Reply: We added a sentence inside parentheses explaining this sentence. Equivalent refers to the"information" a feature contains. If for example the information gain of a variable is not significant it could be attributed to another feature that contains the same information as this one. Think for example collinear variables, such as length of left hand and length of the right hand. Either hand can be used in a regression model. This phenomenon is prevalent, but also not highly examined, in bioinformatics where the selected genes may not be the ones expected by the biologists, only because some equivalent genes were selected. Only few feature selection algorithms return all equivalent features and SES is one of them. Comment: "it includes memory efficient algorithms for high volume data, data that cannot be loaded into R" -> "it includes memory efficient algorithms for high volume data that often cannot be loaded easily into R"?
Reply: We have added a sentence inside parentheses explaining this sentence. The term