ma.mmpc: Feature selection algorithm for identifying minimal feature subsets with multiple datasets
ma.ses(target, dataset, ina, statistic = FALSE, max_k = 3, threshold = 0.05,
test = NULL, ini = NULL, user_test = NULL, hash = FALSE, hashObject = NULL,
robust = FALSE, ncores = 1)
ma.mmpc(target, dataset, ina, statistic = FALSE, max_k = 3, threshold = 0.05,
test = NULL, ini = NULL, user_test = NULL, hash = FALSE, hashObject = NULL,
robust = FALSE, ncores = 1, backward = FALSE)CondIndTests.
Important: the generated hashObjects should be used only when the same dataset is re-analyzed, possibly with different values of max_k and threshold.
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.
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 use testIndSpearman (argument "test"), the ranks of the data calculated and those are used in the caclulations. This speeds up the whole procedure.
Currently only the testIndFisher and testIndSpearman tests are supported for use in the algorithm.
If the argument statistic is set to FALSE, the p-values from the hypothesis test of each dataset are combined via Fisher's meta-analytic approach, that is $ T=-2\sum_{i=1}^k\log{p_i} $ and $ T~\chi^2_{2k} $. If statistic is TRUE, the test statistics are combined as $ T = \frac{{\sum_{i=1}^kt_i/se(t_i)}}{\sum_{i=1}^k 1/se(t_i)}$ and $T~N(0,1)$.
I. Tsamardinos, V. Lagani and D. Pappas (2012). Discovering multiple, equivalent biomarker signatures. In proceedings of the 7th conference of the Hellenic Society for Computational Biology & Bioinformatics - HSCBB12.
Tsamardinos, Brown and Aliferis (2006). The max-min hill-climbing Bayesian network structure learning algorithm. Machine learning, 65(1), 31-78.
SES, CondIndTests, cv.ses
set.seed(123)
require(hash)
#simulate a dataset with continuous data
dataset <- matrix(runif(1000 * 100, 1, 100), ncol = 100)
#define a simulated class variable
target <- 3 * dataset[, 10] + 2 * dataset[, 20] + 3 * dataset[, 30] + rnorm(1000, 0, 5)
#define some simulated equivalences
dataset[, 15] <- dataset[, 10] + rnorm(1000, 0, 2)
dataset[, 10] <- dataset[ , 10] + rnorm(1000, 0, 2)
dataset[, 25] <- dataset[, 20] + rnorm(1000, 0, 2)
dataset[, 23] <- dataset[, 20] + rnorm(1000, 0, 2)
require("hash", quietly = TRUE)
#run the SES algorithm
a1 <- SES(target , dataset, max_k = 5, threshold = 0.05, test = "testIndFisher",
hash = TRUE, hashObject = NULL)
ina <- rbinom(1000, 2, 0.5) + 1
a2 <- ma.ses(target , dataset, ina = ina, max_k = 5, threshold = 0.05, test = "testIndFisher",
hash = TRUE, hashObject = NULL)
a3 <- ma.mmpc(target , dataset, ina = ina, max_k = 5, threshold = 0.05, test = "testIndFisher",
hash = TRUE, hashObject = NULL)
#get the generated signatures
a1@signatures
a2@signatures
a3@selectedVars
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