The SES function implements the Statistically Equivalent Signature (SES) algorithm as presented in "Tsamardinos, Lagani and Pappas, HSCBB 2012"
http://www.mensxmachina.org/publications/discovering-multiple-equivalent-biomarker-signatures/The MMPC function mplements the MMPC algorithm as presented in "Tsamardinos, Brown and Aliferis. The max-min hill-climbing Bayesian network structure learning algorithm" http://www.dsl-lab.org/supplements/mmhc_paper/paper_online.pdf
For faster computations in the internal SES functions, install the suggested package gRbase. In addition, the output value "univ" along with the output value "hashObject" can speed up the computations of subesequent runs of SES and MMPC. The first run with a specific pair of hyper-parameters (threshold and max_k) the univariate associations tests and the conditional independence tests (test statistic and logarithm of their corresponding p-values) are stored and returned. In the next run(s) with different pair(s) of hyper-parameters you can use this information to save time. With a few thousands of variables you will see the difference, which can be up to 50%. For the non robust correlation based tests, the difference may not be significant though, because a Fortran code is used to extract the (unconditional) correlation coefficients.
The max_k option: the maximum size of the conditioning set to use in the conditioning independence test. Larger values provide more accurate results, at the cost of higher computational times. When the sample size is small (e.g., $<50$ observations)="" the="" max_k="" parameter="" should="" be="" $="" \leq="" 5$,="" otherwise="" conditional="" independence="" test="" may="" not="" able="" to="" provide="" reliable="" results.<="" p="">
If the dataset (predictor variables) contains missing (NA) values, they will automatically be replaced by the current variable (column) mean value with an appropriate warning to the user after the execution.
If the target is a single integer value or a string, it has to corresponds to the column number or to the name of the target feature in the dataset. In any other case the target is a variable that is not contained in the dataset.
If the current 'test' argument is defined as NULL or "auto" and the user_test argument is NULL then the algorithm automatically selects the best test based on the type of the data. Particularly:
- if the target is a factor, the multinomial or the binary logistic regression is used. If the target has two values only, binary logistic regression will be used.
- if target is a ordered factor, ordinal regression is used in the logistic test. Hence, if you want to use multinomial or ordinal logistic regression, make sure your target is factor.
- if target is a numerical vector and the dataset is a matrix or a data.frame with continuous variables, the Fisher conditional independence test is used. If the dataset is a data.frame and there are categorical variables, linear regression is used.
- if target is discrete numerical (counts), the poisson regression conditional independence test is used. If there are only two values, the binary logistic regression is to be used.
- if target is a Surv object, a Survival conditional independence test is used.
- if target is a matrix with at least 2 columns, the multivariate linear regression is used.
- if target is a 2 column matrix whose columns are the number of successes and the number of trials (first and second column respectively) the testIndBinom should be used.
Conditional independence test functions to be pass through the user_test argument should have the same signature of the included test. See testIndFisher
for an example.
For all the available conditional independence tests that are currently included on the package, please see CondIndTests
.
If two or more p-values are below the machine epsilon (.Machine$double.eps which is equal to 2.220446e-16), all of them are set to 0. To make the comparison or the ordering feasible we use the logarithm of the p-value. The max-min heuristic though, requires comparison and an ordering of the p-values. Hence, all conditional independence tests calculate the logarithm of the p-value.
If there are missing values in the dataset (predictor variables) columnwise imputation takes place. The median is used for the continuous variables and the mode for categorical variables. It is a naive and not so clever method. For this reason the user is encouraged to make sure his data contain no missing values.
If you have percentages, in the (0, 1) interval, they are automatically mapped into $R$ by using the logit transformation. If you set the test to testIndBeta
, beta regression is used. If you have compositional data, positive multivariate data where each vector sums to 1, with NO zeros, they are also mapped into the Euclidean space using the additive log-ratio (multivariate logit) transformation (Aitchison, 1986).
If you use testIndSpearman (argument "test"), the ranks of the data calculated and those are used in the caclulations. This speeds up the whole procedure.
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