perf: Compute evaluation criteria for PLS, sPLS, PLS-DA, sPLS-DA,...

In mixOmicsTeam/mixOmics: Omics Data Integration Project

Compute evaluation criteria for PLS, sPLS, PLS-DA, sPLS-DA, MINT and DIABLO

Description

Function to evaluate the performance of the fitted PLS, sparse PLS, PLS-DA, sparse PLS-DA, MINT (mint.splsda) and DIABLO (block.splsda) models using various criteria.

Usage

perf(object, ...)

## S3 method for class 'mixo_pls'
perf(
  object,
  validation = c("Mfold", "loo"),
  folds,
  progressBar = FALSE,
  nrepeat = 1,
  BPPARAM = SerialParam(),
  seed = NULL,
  ...
)

## S3 method for class 'mixo_spls'
perf(
  object,
  validation = c("Mfold", "loo"),
  folds,
  progressBar = FALSE,
  nrepeat = 1,
  BPPARAM = SerialParam(),
  seed = NULL,
  ...
)

## S3 method for class 'mixo_plsda'
perf(
  object,
  dist = c("all", "max.dist", "centroids.dist", "mahalanobis.dist"),
  validation = c("Mfold", "loo"),
  folds = 10,
  nrepeat = 1,
  auc = FALSE,
  progressBar = FALSE,
  signif.threshold = 0.01,
  BPPARAM = SerialParam(),
  seed = NULL,
  ...
)

## S3 method for class 'mixo_splsda'
perf(
  object,
  dist = c("all", "max.dist", "centroids.dist", "mahalanobis.dist"),
  validation = c("Mfold", "loo"),
  folds = 10,
  nrepeat = 1,
  auc = FALSE,
  progressBar = FALSE,
  signif.threshold = 0.01,
  BPPARAM = SerialParam(),
  seed = NULL,
  ...
)

## S3 method for class 'sgccda'
perf(
  object,
  dist = c("all", "max.dist", "centroids.dist", "mahalanobis.dist"),
  validation = c("Mfold", "loo"),
  folds = 10,
  nrepeat = 1,
  auc = FALSE,
  progressBar = FALSE,
  signif.threshold = 0.01,
  BPPARAM = SerialParam(),
  seed = NULL,
  ...
)

## S3 method for class 'mint.pls'
perf(
  object,
  validation = c("Mfold", "loo"),
  folds = 10,
  progressBar = FALSE,
  ...
)

## S3 method for class 'mint.spls'
perf(
  object,
  validation = c("Mfold", "loo"),
  folds = 10,
  progressBar = FALSE,
  ...
)

## S3 method for class 'mint.plsda'
perf(
  object,
  dist = c("all", "max.dist", "centroids.dist", "mahalanobis.dist"),
  auc = FALSE,
  progressBar = FALSE,
  signif.threshold = 0.01,
  ...
)

## S3 method for class 'mint.splsda'
perf(
  object,
  dist = c("all", "max.dist", "centroids.dist", "mahalanobis.dist"),
  auc = FALSE,
  progressBar = FALSE,
  signif.threshold = 0.01,
  ...
)

Arguments

object	object of class inherited from "pls", "plsda", "spls", "splsda" or "mint.splsda". The function will retrieve some key parameters stored in that object.
...	not used
validation	character. What kind of (internal) validation to use, matching one of "Mfold" or "loo" (see below). Default is "Mfold".
folds	the folds in the Mfold cross-validation. See Details.
progressBar	by default set to FALSE to output the progress bar of the computation.
nrepeat	Number of times the Cross-Validation process is repeated. This is an important argument to ensure the estimation of the performance to be as accurate as possible.
BPPARAM	A BiocParallelParam object indicating the type of parallelisation. See examples in ?tune.spca.
seed	set a number here if you want the function to give reproducible outputs. Not recommended during exploratory analysis. Note if RNGseed is set in 'BPPARAM', this will be overwritten by 'seed'. Note 'seed' is not required or used in perf.mint.plsda as this method uses loo cross-validation
dist	only applies to an object inheriting from "plsda", "splsda" or "mint.splsda" to evaluate the classification performance of the model. Should be a subset of "max.dist", "centroids.dist", "mahalanobis.dist". Default is "all". See predict.
auc	if TRUE calculate the Area Under the Curve (AUC) performance of the model.
signif.threshold	numeric between 0 and 1 indicating the significance threshold required for improvement in error rate of the components. Default to 0.01.

Details

Procedure. The process of evaluating the performance of a fitted model object is similar for all PLS-derived methods; a cross-validation approach is used to fit the method of object on folds-1 subsets of the data and then to predict on the subset left out. Different measures of performance are available depending on the model. Parameters such as logratio, multilevel, keepX or keepY are retrieved from object.

Parameters. If validation = "Mfold", M-fold cross-validation is performed. folds specifies the number of folds to generate. The folds also can be supplied as a list of vectors containing the indexes defining each fold as produced by split. When using validation = "Mfold", make sure that you repeat the process several times (as the results will be highly dependent on the random splits and the sample size).

If validation = "loo", leave-one-out cross-validation is performed (in that case, there is no need to repeat the process).

Measures of performance. For fitted PLS and sPLS regression models, perf estimates the mean squared error of prediction (MSEP), R^2, and Q^2 to assess the predictive perfity of the model using M-fold or leave-one-out cross-validation. Note that only the classic, regression and invariant modes can be applied. For sPLS, the MSEP, R^2, and Q^2 criteria are averaged across all folds. Note that for PLS and sPLS objects, perf is performed on the pre-processed data after log ratio transform and multilevel analysis, if any.

Sparse methods. The sPLS, sPLS-DA and sgccda functions are run on several and different subsets of data (the cross-folds) and will certainly lead to different subset of selected features. Those are summarised in the output features$stable (see output Value below) to assess how often the variables are selected across all folds. Note that for PLS-DA and sPLS-DA objects, perf is performed on the original data, i.e. before the pre-processing step of the log ratio transform and multilevel analysis, if any. In addition for these methods, the classification error rate is averaged across all folds.

The mint.sPLS-DA function estimates errors based on Leave-one-group-out cross validation (where each levels of object$study is left out (and predicted) once) and provides study-specific outputs (study.specific.error) as well as global outputs (global.error). Note the mint perf methods do not use seed or BPPARAM arguments.

AUROC. For PLS-DA, sPLS-DA, mint.PLS-DA, mint.sPLS-DA, and block.splsda methods: if auc=TRUE, Area Under the Curve (AUC) values are calculated from the predicted scores obtained from the predict function applied to the internal test sets in the cross-validation process, either for all samples or for study-specific samples (for mint models). Therefore we minimise the risk of overfitting. For block.splsda model, the calculated AUC is simply the blocks-combined AUC for each component calculated using auroc.sgccda. See auroc for more details. Our multivariate supervised methods already use a prediction threshold based on distances (see predict) that optimally determine class membership of the samples tested. As such AUC and ROC are not needed to estimate the performance of the model. We provide those outputs as complementary performance measures. See more details in our mixOmics article.

Prediction distances. See details from ?predict, and also our supplemental material in the mixOmics article.

Repeats of the CV-folds. Repeated cross-validation implies that the whole CV process is repeated a number of times (nrepeat) to reduce variability across the different subset partitions. In the case of Leave-One-Out CV (validation = 'loo'), each sample is left out once (folds = N is set internally) and therefore nrepeat is by default 1.

BER is appropriate in case of an unbalanced number of samples per class as it calculates the average proportion of wrongly classified samples in each class, weighted by the number of samples in each class. BER is less biased towards majority classes during the performance assessment.

For sgccda objects, we provide weighted measures (e.g. error rate) in which the weights are simply the correlation of the derived components of a given block with the outcome variable Y.

More details about the PLS modes in ?pls.

Value

For PLS and sPLS models, perf produces a list with the following components for every repeat:

MSEP	Mean Square Error Prediction for each Y variable, only applies to object inherited from "pls", and "spls". Only available when in regression (s)PLS.
RMSEP	Root Mean Square Error Prediction for each Y variable, only applies to object inherited from "pls", and "spls". Only available when in regression (s)PLS.
R2	a matrix of R^2 values of the Y-variables for models with 1, \ldots ,ncomp components, only applies to object inherited from "pls", and "spls". Only available when in regression (s)PLS.
Q2	if Y contains one variable, a vector of Q^2 values else a list with a matrix of Q^2 values for each Y-variable. Note that in the specific case of an sPLS model, it is better to have a look at the Q2.total criterion, only applies to object inherited from "pls", and "spls". Only available when in regression (s)PLS.
Q2.total	a vector of Q^2-total values for models with 1, \ldots ,ncomp components, only applies to object inherited from "pls", and "spls". Available in both (s)PLS modes.
RSS	Residual Sum of Squares across all selected features and the components.
PRESS	Predicted Residual Error Sum of Squares across all selected features and the components.
features	a list of features selected across the folds ($stable.X and $stable.Y) for the keepX and keepY parameters from the input object. Note, this will be NULL if using standard (non-sparse) PLS.
cor.tpred, cor.upred	Correlation between the predicted and actual components for X (t) and Y (u)
RSS.tpred, RSS.upred	Residual Sum of Squares between the predicted and actual components for X (t) and Y (u)
error.rate	For PLS-DA and sPLS-DA models, perf produces a matrix of classification error rate estimation. The dimensions correspond to the components in the model and to the prediction method used, respectively. Note that error rates reported in any component include the performance of the model in earlier components for the specified keepX parameters (e.g. error rate reported for component 3 for keepX = 20 already includes the fitted model on components 1 and 2 for keepX = 20). For more advanced usage of the perf function, see www.mixomics.org/methods/spls-da/ and consider using the predict function.
auc	Averaged AUC values over the nrepeat

For mint.splsda models, perf produces the following outputs:

study.specific.error	A list that gives BER, overall error rate and error rate per class, for each study
global.error	A list that gives BER, overall error rate and error rate per class for all samples
predict	A list of length ncomp that produces the predicted values of each sample for each class
class	A list which gives the predicted class of each sample for each dist and each of the ncomp components. Directly obtained from the predict output.
auc	AUC values
auc.study	AUC values for each study in mint models

For sgccda models, perf produces the following outputs:

error.rate	Prediction error rate for each block of object$X and each dist
error.rate.per.class	Prediction error rate for each block of object$X, each dist and each class
predict	Predicted values of each sample for each class, each block and each component
class	Predicted class of each sample for each block, each dist, each component and each nrepeat
features	a list of features selected across the folds ($stable.X and $stable.Y) for the keepX and keepY parameters from the input object.
AveragedPredict.class	if more than one block, returns the average predicted class over the blocks (averaged of the Predict output and prediction using the max.dist distance)
AveragedPredict.error.rate	if more than one block, returns the average predicted error rate over the blocks (using the AveragedPredict.class output)
WeightedPredict.class	if more than one block, returns the weighted predicted class over the blocks (weighted average of the Predict output and prediction using the max.dist distance). See details for more info on weights.
WeightedPredict.error.rate	if more than one block, returns the weighted average predicted error rate over the blocks (using the WeightedPredict.class output.)
MajorityVote	if more than one block, returns the majority class over the blocks. NA for a sample means that there is no consensus on the predicted class for this particular sample over the blocks.
MajorityVote.error.rate	if more than one block, returns the error rate of the MajorityVote output
WeightedVote	if more than one block, returns the weighted majority class over the blocks. NA for a sample means that there is no consensus on the predicted class for this particular sample over the blocks.
WeightedVote.error.rate	if more than one block, returns the error rate of the WeightedVote output
weights	Returns the weights of each block used for the weighted predictions, for each nrepeat and each fold
choice.ncomp	For supervised models; returns the optimal number of components for the model for each prediction distance using one-sided t-tests that test for a significant difference in the mean error rate (gain in prediction) when components are added to the model. See more details in Rohart et al 2017 Suppl. For more than one block, an optimal ncomp is returned for each prediction framework.

Author(s)

Ignacio González, Amrit Singh, Kim-Anh Lê Cao, Benoit Gautier, Florian Rohart, Al J Abadi

References

Singh A., Shannon C., Gautier B., Rohart F., Vacher M., Tebbutt S. and Lê Cao K.A. (2019), DIABLO: an integrative approach for identifying key molecular drivers from multi-omics assays, Bioinformatics, Volume 35, Issue 17, 1 September 2019, Pages 3055–3062.

mixOmics article:

Rohart F, Gautier B, Singh A, Lê Cao K-A. mixOmics: an R package for 'omics feature selection and multiple data integration. PLoS Comput Biol 13(11): e1005752

MINT:

Rohart F, Eslami A, Matigian, N, Bougeard S, Lê Cao K-A (2017). MINT: A multivariate integrative approach to identify a reproducible biomarker signature across multiple experiments and platforms. BMC Bioinformatics 18:128.

PLS and PLS citeria for PLS regression: Tenenhaus, M. (1998). La regression PLS: theorie et pratique. Paris: Editions Technic.

Chavent, Marie and Patouille, Brigitte (2003). Calcul des coefficients de regression et du PRESS en regression PLS1. Modulad n, 30 1-11. (this is the formula we use to calculate the Q2 in perf.pls and perf.spls)

Mevik, B.-H., Cederkvist, H. R. (2004). Mean Squared Error of Prediction (MSEP) Estimates for Principal Component Regression (PCR) and Partial Least Squares Regression (PLSR). Journal of Chemometrics 18(9), 422-429.

sparse PLS regression mode:

Lê Cao, K. A., Rossouw D., Robert-Granie, C. and Besse, P. (2008). A sparse PLS for variable selection when integrating Omics data. Statistical Applications in Genetics and Molecular Biology 7, article 35.

One-sided t-tests (suppl material):

Rohart F, Mason EA, Matigian N, Mosbergen R, Korn O, Chen T, Butcher S, Patel J, Atkinson K, Khosrotehrani K, Fisk NM, Lê Cao K-A&, Wells CA& (2016). A Molecular Classification of Human Mesenchymal Stromal Cells. PeerJ 4:e1845.

See Also

predict, nipals, plot.perf, auroc and www.mixOmics.org for more details.

Examples

## validation for objects of class 'pls' (regression)
# ----------------------------------------
data(liver.toxicity)
X <- liver.toxicity$gene
Y <- liver.toxicity$clinic

# try tune the number of component to choose
# ---------------------
# first learn the full model
liver.pls <- pls(X, Y, ncomp = 5)

# with 5-fold cross validation: we use the same parameters as in model above
# but we perform cross validation to compute the MSEP, Q2 and R2 criteria
# ---------------------------
liver.val <- perf(liver.pls, validation = "Mfold", folds = 5)

# see available criteria
names(liver.val$measures)
# see values for all repeats
liver.val$measures$Q2.total$values
# see summary over repeats
liver.val$measures$Q2.total$summary
# Q2 total should decrease until it reaches a threshold
liver.val$measures$Q2.total

# ncomp = 2 is enough
plot(liver.val, criterion  = 'Q2.total')

## Not run: 

# have a look at the other criteria
# ----------------------
# R2
plot(liver.val, criterion  = 'R2')
## correlation of components (see docs)
plot(liver.val, criterion  = 'cor.tpred')

# MSEP
plot(liver.val, criterion  = 'MSEP')
## validation for objects of class 'spls' (regression)
# ----------------------------------------
ncomp = 7
# first, learn the model on the whole data set
model.spls = spls(X, Y, ncomp = ncomp, mode = 'regression',
                  keepX = c(rep(10, ncomp)), keepY = c(rep(4,ncomp)))


# with leave-one-out cross validation
model.spls.val <- perf(model.spls, validation = "Mfold", folds = 5, seed = 45 )

#Q2 total
model.spls.val$measures$Q2$summary

# R2: we can see how the performance degrades when ncomp increases
plot(model.spls.val, criterion="R2")

## validation for objects of class 'splsda' (classification)
# ----------------------------------------
data(srbct)
X <- srbct$gene
Y <- srbct$class

ncomp = 2

srbct.splsda <- splsda(X, Y, ncomp = ncomp, keepX = rep(10, ncomp))

# with Mfold
# ---------
error <- perf(srbct.splsda, validation = "Mfold", folds = 8,
dist = "all", auc = TRUE, seed = 45)
error
error$auc

plot(error)

# parallel code
library(BiocParallel)
error <- perf(srbct.splsda, validation = "Mfold", folds = 8,
dist = "all", auc = TRUE, BPPARAM = SnowParam(workers = 2), seed = 45)

# with 5 components and nrepeat=5, to get a $choice.ncomp
ncomp = 5
srbct.splsda <- splsda(X, Y, ncomp = ncomp, keepX = rep(10, ncomp))

error <- perf(srbct.splsda, validation = "Mfold", folds = 8,
dist = "all", nrepeat = 5, seed = 45)
error$choice.ncomp

plot(error)


## validation for objects of class 'mint.splsda' (classification)
# ----------------------------------------

data(stemcells)
res = mint.splsda(X = stemcells$gene, Y = stemcells$celltype, 
                  ncomp = 3, keepX = c(10, 5, 15),
                  study = stemcells$study)

out = perf(res, auc = TRUE)
out
plot(out)
out$auc
out$auc.study

## validation for objects of class 'sgccda' (classification)
# ----------------------------------------

data(nutrimouse)
Y = nutrimouse$diet
data = list(gene = nutrimouse$gene, lipid = nutrimouse$lipid)

nutrimouse.sgccda <- block.splsda(X=data,
Y = Y,
design = 'full',
keepX = list(gene=c(10,10), lipid=c(15,15)),
ncomp = 2,
scheme = "horst")

perf = perf(nutrimouse.sgccda)
perf
plot(perf)


# with 5 components and nrepeat=5 to get $choice.ncomp
nutrimouse.sgccda <- block.splsda(X=data,
Y = Y,
design = 'full',
keepX = list(gene=c(10,10), lipid=c(15,15)),
ncomp = 5,
scheme = "horst")

perf = perf(nutrimouse.sgccda, folds = 5, nrepeat = 5)
perf
plot(perf)
perf$choice.ncomp

## End(Not run)

mixOmicsTeam/mixOmics documentation built on Nov. 4, 2024, 8:56 a.m.