R/gappyPair.R

In kebabs: Kernel-Based Analysis Of Biological Sequences

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#' @rdname gappyPairKernel
#' @title Gappy Pair Kernel
#'
#' @description Create a gappy pair kernel object and the kernel matrix
#'
#' @param k length of the substrings (also called kmers) which are considered
#' in pairs by this kernel. This parameter together with parameter m (see below)
#' defines the size of the feature space, i.e. the total number of features
#' considered in this kernel is (|A|^(2*k))*(m+1), with |A| as the size
#' of the alphabet (4 for DNA and RNA sequences and 21 for amino acid
#' sequences). Sequences with a total number of characters shorter than
#' 2 * k + m will be accepted but not all possible patterns of the feature space
#' can be taken into account. When multiple kernels with different k and/or m
#' values should be generated, e.g. for model selection an integer vector can be
#' specified instead of a single numeric values. In this case a list of kernel
#' objects  with the individual values from the integer vector of parameter k is
#' generated as result. The processing effort for this kernel is highly
#' dependent on the value of k because of the additional factor 2 in the
#' exponent for the feature space size) and only small values of k will allow
#' efficient processing. Default=1
#'
#' @param m maximal number of irrelevant positions between a pair of kmers. The
#' value of m must be an integer value larger than 0. For example a value of m=2
#' means that zero, one or two irrelevant positions between kmer pairs are
#' considered as valid features. (A value of 0 corresponds to the spectrum
#' kernel with a kmer length of 2*k and is not allowed for the gappy pair
#' kernel). When an integer vector is specified a list of kernels is generated
#' as described above for parameter k. If multiple values are specified both
#' for parameter k and parameter m one kernel object is created for each of the
#' combinations of k and m. Default=1
#'
#' @param r exponent which must be > 0 (see details section  in
#' \link{spectrumKernel}). Default=1
#'
#' @param annSpec boolean that indicates whether sequence annotation should
#' be taken into account (details see on help page for
#' \code{\link{annotationMetadata}}). Annotation information is only
#' evaluated for the kmer positions of the kmer pair but not for the irrelevant
#' positions in between. For the annotation specific gappy pair kernel the
#' total number of features increases to (|A|^(2*k))*(|a|^(2*k)*(m+1) with
#' |A| as the size of the sequence alphabet and |a| as the size of the
#' annotation alphabet. Default=FALSE
#'
#' @param distWeight a numeric distance weight vector or a distance weighting
#' function (details see on help page for \code{\link{gaussWeight}}).
#' Default=NULL
#'
#' @param normalized generated data from this kernel will be normalized
#' (details see below). Default=TRUE
#'
#' @param exact use exact character set for the evaluation (details see below).
#' Default=TRUE
#'
#' @param ignoreLower ignore lower case characters in the sequence. If the
#' parameter is not set lower case characters are treated like uppercase.
#' Default=TRUE
#'
#' @param presence if this parameter is set only the presence of a kmers will
#' be considered, otherwise the number of occurances of the kmer is used.
#' Default=FALSE
#'
#' @param revComplement if this parameter is set a kmer pair and its reverse
#' complement are treated as the same feature. Default=FALSE
#'
#' @param mixCoef mixing coefficients for the mixture variant of the gappy
#' pair kernel. A numeric vector of length k is expected for this parameter
#' with the unused components in the mixture set to 0. Default=numeric(0)
#'
#' @details
#' Creation of kernel object\cr\cr
#' The function 'gappyPairKernel' creates a kernel object for the gappy pair
#' kernel. This kernel object can then be used with a set of DNA-, RNA- or
#' AA-sequences to generate a kernel matrix or an explicit representation for
#' this kernel. The gappy pair kernel uses pairs of neighboring subsequences
#' of length k (kmers) with up to m irrelevant positions between the kmers. For
#' sequences shorter than 2*k the self similarity (i.e. the value on the main
#' diagonal in the square kernel matrix) is 0. The explicit representation
#' contains only zeros for such a sample. Dependent on the learning task it
#' might make sense to remove such sequences from the data set as they do not
#' contribute to the model but still influence performance values.\cr\cr
#' For values different from 1 (=default value) parameter \code{r}
#' leads to a transfomation of similarities by taking each element of the
#' similarity matrix to the power of r. If \code{normalized=TRUE}, the feature
#' vectors are scaled to the unit sphere before computing the similarity value
#' for the kernel matrix. For two samples with the feature vectors \code{x}
#' and \code{y} the similarity is computed as:
#' \deqn{s=\frac{\vec{x}^T\vec{y}}{\|\vec{x}\|\|\vec{y}\|}}{s=(x^T y)/(|x| |y|)}
#' For an explicit representation generated with the feature map of a
#' normalized kernel the rows are normalized by dividing them through their
#' Euclidean norm. For parameter \code{exact=TRUE} the sequence characters
#' are interpreted according to an exact character set. If the flag is not
#' set ambigous characters from the IUPAC characterset are also evaluated.
#'
#' The annotation specific variant (for details see
#' \link{annotationMetadata}) and the position dependent variants (for
#' details see \link{positionMetadata}) either in the form of a position
#' specific or a distance weighted kernel are supported for the gappy
#' pair kernel. The generation of an explicit representation is not possible
#' for the position dependent variants of this kernel.\cr\cr
#' Creation of kernel matrix\cr\cr
#' The kernel matrix is created with the function \code{\link{getKernelMatrix}}
#' or via a direct call with the kernel object as shown in the examples below.
#'
#' @return
#' gappyPairKernel: upon successful completion, the function returns a kernel
#' object of class \code{\linkS4class{GappyPairKernel}}.
#'
#' @seealso \code{\link{getKernelMatrix}}, \code{\link{getExRep}},
#' \code{\link{kernelParameters-method}}, \code{\link{spectrumKernel}},
#' \code{\link{mismatchKernel}}, \code{\link{motifKernel}},
#' \code{\linkS4class{GappyPairKernel}}
#' @examples
#'
#' ## instead of user provided sequences in XStringSet format
#' ## for this example a set of DNA sequences is created
#' ## RNA- or AA-sequences can be used as well with the gappy pair kernel
#' dnaseqs <- DNAStringSet(c("AGACTTAAGGGACCTGGTCACCACGCTCGGTGAGGGGGACGGGGTGT",
#'                           "ATAAAGGTTGCAGACATCATGTCCTTTTTGTCCCTAATTATTTCAGC",
#'                           "CAGGAATCAGCACAGGCAGGGGCACGGCATCCCAAGACATCTGGGCC",
#'                           "GGACATATACCCACCGTTACGTGTCATACAGGATAGTTCCACTGCCC",
#'                           "ATAAAGGTTGCAGACATCATGTCCTTTTTGTCCCTAATTATTTCAGC"))
#' names(dnaseqs) <- paste("S", 1:length(dnaseqs), sep="")
#'
#' ## create the kernel object for dimer pairs with up to ten irrelevant
#' ## position between the kmers of the pair without normalization
#' gappy <- gappyPairKernel(k=2, m=10, normalized=FALSE)
#' ## show details of kernel object
#' gappy
#'
#' ## generate the kernel matrix with the kernel object
#' km <- gappy(dnaseqs)
#' dim(km)
#' km[1:5,1:5]
#'
#' ## alternative way to generate the kernel matrix
#' km <- getKernelMatrix(gappy, dnaseqs)
#' km[1:5,1:5]
#'
#' \dontrun{
#' ## plot heatmap of the kernel matrix
#' heatmap(km, symm=TRUE)
#' }
#' @author Johannes Palme <kebabs@@bioinf.jku.at>
#' @references
#' \url{http://www.bioinf.jku.at/software/kebabs}\cr\cr
#' (Mahrenholz, 2011) -- C.C. Mahrenholz, I.G. Abfalter, U. Bodenhofer, R. Volkmer
#' and S. Hochreiter. Complex networks govern coiled-coil oligomerizations -
#' predicting and profiling by means of a machine learning approach.\cr
#' (Bodenhofer, 2009) -- U. Bodenhofer, K. Schwarzbauer, M. Ionescu and
#' S. Hochreiter. Modelling position specificity in sequence kernels by fuzzy
#' equivalence relations. \cr\cr
#' (Kuksa, 2008) -- P. Kuksa, P.-H. Huang and V. Pavlovic. Fast Protein Homology
#' and Fold Detection with Sparse Spatial Sample Kernels\cr\cr
#' J. Palme, S. Hochreiter, and U. Bodenhofer (2015) KeBABS: an R package
#' for kernel-based analysis of biological sequences.
#' \emph{Bioinformatics}, 31(15):2574-2576, 2015.
#' DOI: \href{http://dx.doi.org/10.1093/bioinformatics/btv176}{10.1093/bioinformatics/btv176}.
#' @keywords kernel
#' @keywords gappy pair
#' @keywords methods
#' @export


gappyPairKernel <- function(k=1, m=1, r=1, annSpec=FALSE, distWeight=numeric(0),
                      normalized=TRUE, exact=TRUE, ignoreLower=TRUE,
                      presence=FALSE, revComplement=FALSE, mixCoef=numeric(0))
{
    ## check data independent kernel parameters and create closure

    if (!is.numeric(k) || any(k < 1))
        stop("'k' must be larger than 0\n")

    if (!is.numeric(m) || any(m < 1))
        stop("'m' must be larger than 0 or use spectrum kernel\n")

    if (any(m > 30))
        stop("'m' must be between 1 and 30\n")

    if (!isSingleNumber(r) || r <= 0)
        stop("'r' must be a number greater than 0\n")

    if (!isTRUEorFALSE(normalized))
        stop("'normalized' must be TRUE or FALSE\n")

    if (!isTRUEorFALSE(exact))
        stop("'exact' must be TRUE or FALSE\n")

    if (!isTRUEorFALSE(ignoreLower))
        stop("'ignoreLower' must be TRUE or FALSE\n")

    if (!isTRUEorFALSE(presence))
        stop("'presence' must be TRUE or FALSE\n")

    if (!isTRUEorFALSE(revComplement))
        stop("'revComplement' must be TRUE or FALSE\n")

    if (!isTRUEorFALSE(annSpec))
        stop("'annSpec' must be TRUE or FALSE\n")

    if (length(distWeight) > 0)
    {
        if (!(is.numeric(distWeight) || is.function(distWeight)))
            stop("'distWeight' must be a numeric vector or a function\n")
    
        if (is.function(distWeight))
        {
            func <- deparse(distWeight)[2]
            index <- grep("(", strsplit(func, split="")[[1]], fixed=TRUE,
                          value=FALSE)
        
            if (length(index) < 1)
                stop("Missing parentheses in 'distWeight'\n")
        }
    }

    if (presence && length(distWeight) > 0)
    {
        stop("'presence' can only be used with the position independent\n",
             "       gappy pair kernel\n")
    }

    if (length(mixCoef) > 0)
    {
        if (!is.numeric(mixCoef) ||
            length(mixCoef) != k)
            stop("'mixCoef' must be a numeric vector of length k\n")

        if (any(mixCoef < 0))
            stop("mixing coefficients must be non-negative\n")
    }

    if (length(k) == 1 && length(m) == 1)
    {
        ## define function for kernel matrix processing
        rval<- function(x, y = NULL, selx = NULL, sely = NULL, self=NULL)
        {
            return(gappyPairProcessing(x=x, y=y, selx=selx, sely=sely, k=k,
                        m=m, r=r, annSpec=annSpec, distWeight=distWeight,
                        normalized=normalized, exact=exact,
                        ignoreLower=ignoreLower, presence=presence,
                        revComplement=revComplement, mixCoef=mixCoef,
                        self=self))
        }

        return(new("GappyPairKernel", .Data=rval, .userDefKernel=FALSE,
                   k=k, m=m, r=r, normalized=normalized, annSpec=annSpec,
                   distWeight=distWeight, exact=exact,
                   ignoreLower=ignoreLower, presence=presence,
                   revComplement=revComplement, mixCoef=mixCoef))
    }
    else
    {
        kmPairs <- as.matrix(expand.grid(m,k))
        colnames(kmPairs) <- NULL

        ## return list of kernel objects
        kernels <- mapply(gappyPairKernel, k=kmPairs[,2], m=kmPairs[,1],
                          MoreArgs=list(r=r, annSpec=annSpec,
                          distWeight=distWeight, normalized=normalized,
                          exact=exact, ignoreLower=ignoreLower,
                          presence=presence, revComplement=revComplement,
                          mixCoef=mixCoef))
        return(kernels)
    }
}

gappyPairProcessing <- function(x, y, selx, sely, k, m, r, annSpec, distWeight,
                                normalized, exact, ignoreLower, presence,
                                revComplement, mixCoef, self=NULL)
{
    if (!is.null(self))
    {
        ## retrieval of kernel parameters
        return(list(k=self@k, m=self@m, r=self@r,
                    normalized=self@normalized,
                    annSpec=self@annSpec,
                    exact=self@exact,
                    ignoreLower=self@ignoreLower,
                    presence=self@presence,
                    distWeight=self@distWeight,
                    revComplement=self@revComplement,
                    mixCoef=self@mixCoef))
    }

    if (missing(x) || is.null(x))
    {
        stop(paste("'x' must be a",
                   paste(kebabsInfo@allowedSeqClasses, collapse=", "), "\n"))
    }

    if (length(x) < 1)
        stop("sequence info is missing\n")

    if (missing(y))
        y <- NULL

    if (missing(selx) || is.null(selx))
        selx <- integer(0)

    if (missing(sely) || is.null(sely))
        sely <- integer(0)

    if (class(x) %in% c("DNAString", "RNAString", "AAString"))
    {
        x <- switch(class(x),
                    "DNAString" = DNAStringSet(x),
                    "RNAString" = RNAStringSet(x),
                    "AAString"  = AAStringSet(x)
                    )
    }

    if (!(class(x) %in% kebabsInfo@allowedSeqSetClasses))
    {
        stop(paste("'x' must be a",
                   paste(kebabsInfo@allowedSeqClasses, collapse=", "), "\n"))
    }

    if (length(selx) > 0)
    {
        if (!is.numeric(selx) || length(selx) > length(x))
            stop("'selx' must be an integer vector with indices into 'x'\n")

        selx <- as.integer(selx)
    }
    else
        selx <- 1L:length(x)

    selxC <- selx - 1L
    symmetric <- TRUE

    if (length(k) > 1 || length(m) > 1 || length(r) > 1)
    {
        stop("multiple values for kernel parameter are only allowed\n",
             "        in model selection\n")
    }

    if (!is.null(y))
    {
        symmetric <- FALSE

        if (class(y) %in% c("DNAString", "RNAString", "AAString"))
        {
            y <- switch(class(y),
                        "DNAString" = DNAStringSet(y),
                        "RNAString" = RNAStringSet(y),
                        "AAString"  = AAStringSet(y)
                        )
        }

        if (!(class(y) %in% kebabsInfo@allowedSeqSetClasses))
        {
            stop(paste("'y' must be a",
                    paste(kebabsInfo@allowedSeqClasses, collapse=", "), "\n"))
        }

        if (class(x) != class(y))
            stop("'x' and 'y' must be of matching classes\n")

        if (length(sely) > 0)
        {
            if (!is.numeric(sely) || length(sely) > length(y))
                stop("'sely' must be an integer vector with indices into 'y'\n")

            sely <- as.integer(sely)
        }
        else
            sely <- 1L:length(y)

        selyC <- sely - 1L
    }
    else
    {
        sely <- integer(0)
        selyC <- sely
    }

    bioCharset <- getBioCharset(x, exact)

    if (annSpec)
    {
        ## limit k to 64 bit feature space
        if (names(bioCharset[[1]]) %in% c("AAexact", "AAiupac") && k > 2)
            stop("'k' must be smaller than or equal to 2\n")
        else if (names(bioCharset[[1]]) %in% c("DNAexact", "RNAexact") && k > 4)
            stop("for exact charset 'k' must be smaller than or equal to 4\n")
        else if (k > 4)
            stop("for iupac charset 'k' must be smaller than or equal to 4\n")
    }
    else
    {
        ## limit k to 64 bit feature space
        if (names(bioCharset[[1]]) %in% c("AAexact", "AAiupac") && k > 6)
            stop("'k' must be smaller than or equal to 6\n")
        else if (names(bioCharset[[1]]) %in% c("DNAexact", "RNAexact") && 
                 k > 10)
            stop("for exact charset 'k' must be smaller than or equal to 10\n")
        else if (names(bioCharset[[1]]) %in% c("DNAiupac", "RNAiupac") &&
                 k > 7)
            stop("for iupac charset 'k' must be smaller than or equal to 7\n")
    }

    ## limit m to 64 bit feature space
    if (nchar(bioCharset[[1]])^(2*k) * (m+1) > (2^64 - 1))
        stop("feature space exceeds maximum range\n")

    if (!is.null(y))
        seqLength <- c(width(x)[selx], width(y)[sely])
    else
        seqLength <- width(x)[selx]

    maxSeqLength <- max(seqLength)
    posSpec <- FALSE
    offsetX <- integer(0)
    offsetY <- integer(0)

    if (length(distWeight) > 0)
    {
        offsetX <- mcols(x)[["offset"]]

        if (!is.null(offsetX))
        {
            if (!is.integer(offsetX))
                stop("position metadata of 'x' must be an integer vector\n")

            maxDist <- max(width(x[selx]) - offsetX[selx]) -
                       min(-offsetX[selx] + 1)
        }
        else
        {
            offsetX <- integer(0)
            maxDist <- maxSeqLength - 1
        }

        if (!is.null(y))
        {
            offsetY <- mcols(y)[["offset"]]

            if (!is.null(offsetY))
            {
                if (!is.integer(offsetY))
                    stop("position metadata of 'y' must be an integer vector\n")

                if (length(offsetX) > 0)
                {
                    maxDist <- max(c(width(x)[selx] - offsetX[selx],
                                     width(y)[sely] - offsetY[sely])) -
                               min(c(-offsetX[selx] + 1, -offsetY[sely] + 1))
                }
                else
                {
                    maxDist <- max(c(width(x)[selx],
                                     width(y)[sely] - offsetY[sely])) -
                               min(c(1, -offsetY[sely] + 1))
                }
            }
            else
            {
                offsetY <- integer(0)

                if (length(offsetX) > 0)
                {
                    maxDist <- max(c(width(x)[selx] - offsetX[selx],
                                     width(y)[sely])) -
                               min(c(-offsetX[selx] + 1, 1))
                }
                else
                    maxDist <- max(c(width(x)[selx], width(y)[sely])) - 1
            }
        }

        if (is.function(distWeight))
        {
            if (length(mixCoef) == 0)
                min2K <- 2 * k
            else
                min2K <- 2
            
            ## precompute distance weight vector
            ## terminate on stop and warning
            ## assuming that all distances are partially overlapping
            distWeight <- tryCatch(distWeight(0:(maxDist - min2K + 1)),
                                   warning=function(w) {stop(w)},
                                   error=function(e) {stop(e)})

            if (!(is.vector(distWeight, mode="numeric") &&
                  length(distWeight) == (maxDist - min2K + 2)))
            {
                stop("distWeight function did not return a numeric vector\n",
                     "       of correct length\n")
            }

            ## limit to values larger than .Machine$double.eps
            ## for non-monotonic decreasing functions search from end
            if (length(mixCoef) == 0)
            {
                for (i in (maxDist - min2K + 2):1)
                {
                    if (distWeight[i] > .Machine$double.eps)
                        break
                }

                distWeight <- distWeight[1:i]
            }
        }

        if (length(distWeight) == 0)
            stop("only zero values for distance weights\n")

        if (isTRUE(all.equal(distWeight, c(1, rep(0, length(distWeight)-1)))))
        {
            posSpec <- TRUE
            distWeight <- numeric(0)
        }
    }

    annCharset <- NULL
    annX <- NULL
    annY <- NULL

    if (annSpec)
    {
        annCharset <- metadata(x)$annotationCharset

        if (is.null(annCharset))
            stop("missing annotation characterset metadata in 'x'\n")

        if (length(annCharset) > 1)
            stop("annotation character set must be one character string\n")

        if (nchar(annCharset[1]) < 2)
        {
            stop("at least two annotation characters needed in annotation\n",
                 "        character set\n")
        }

        annX <- mcols(x)[["annotation"]]

        if (!is.null(y))
            annY <- mcols(y)[["annotation"]]

        if (is.null(annX) || (!is.null(y) && is.null(annY)))
            stop("missing annotation information in 'x' and/or 'y'\n")

        if (!is.character(annX))
            stop("annotation metadata of 'x' must be a character vector\n")

        if (!is.null(y) && !is.character(annY))
            stop("annotation metadata of 'y' must be a character vector\n")
    }

    isXStringSet <- inherits(x, "XStringSet")
    unmapped <- is(x, "DNAStringSet") || is(x, "RNAStringSet")

    if (length(mixCoef) == 0)
    {
        res <- .Call("gappyPairKernelMatrixC", x, y, selxC, selyC,
                     as.integer(length(selxC)), as.integer(length(selyC)),
                     as.logical(isXStringSet), as.logical(symmetric),
                     offsetX, offsetY, annCharset, annX, annY,
                     as.integer(bioCharset[[2]]), as.logical(ignoreLower),
                     as.logical(unmapped), as.integer(maxSeqLength),
                     as.integer(k), as.integer(m), as.logical(posSpec),
                     distWeight, as.logical(normalized), as.logical(presence),
                     as.logical(revComplement))
    }
    else
    {
        currK <- 0
        distWeightCurr <- distWeight

        if (is.null(y))
            res <- matrix(0, length(selxC), length(selxC))
        else
            res <- matrix(0, length(selxC), length(selyC))

        for (i in 1:k)
        {
            currK <- currK + 1

            if (mixCoef[i] != 0)
            {
                if (length(distWeight) > 0)
                {
                    distWeightCurr <- distWeight[1:(length(distWeight) -
                                                    2 * currK + 2)]

                    for (j in length(distWeightCurr):1)
                    {
                        if (distWeightCurr[j] > .Machine$double.eps)
                            break
                    }

                    distWeightCurr <- distWeightCurr[1:j]
                }

                res <- res + mixCoef[i] *
                .Call("gappyPairKernelMatrixC", x, y, selxC, selyC,
                      as.integer(length(selxC)), as.integer(length(selyC)),
                      as.logical(isXStringSet), as.logical(symmetric),
                      offsetX, offsetY, annCharset, annX, annY,
                      as.integer(bioCharset[[2]]), as.logical(ignoreLower),
                      as.logical(unmapped), as.integer(maxSeqLength),
                      as.integer(currK), as.integer(m), as.logical(posSpec),
                      distWeightCurr, as.logical(normalized),
                      as.logical(presence), as.logical(revComplement))
            }
        }
    }

    if (length(names(x)) > 0)
    {
        rownames(res) <- names(x)[selx]

        if (is.null(y))
            colnames(res) <- names(x)[selx]
    }

    if (length(names(y)) > 0)
        colnames(res) <- names(y)[sely]

    if (r != 1)
        return(as.KernelMatrix(res^r))
    else
        return(as.KernelMatrix(res))
}

getFeatureSpaceDimension.gappy <- function(kernel, x)
{
    ## if sequences are not available feature space dimension cannot be
    ## determined
    if (is(x, "KernelMatrix") || is(x, "ExplicitRepresentation"))
        return(-1)

    if (!(class(x) %in% kebabsInfo@allowedSeqSetClasses))
    {
        stop(paste("'x' must be a",
                   paste(kebabsInfo@allowedSeqClasses, collapse=", "), "\n"))
    }

    bioCharset <- getBioCharset(x, kernelParameters(kernel)$exact)
    numAlphaChars <- nchar(bioCharset[[1]])

    ## for IUPAC charactersets the characters - and + are not relevant for
    ## kernels
    if (bioCharset[[2]] %in% c(2,4))
        numAlphaChars <- numAlphaChars - 2

    dimFeatureSpace <- (kernelParameters(kernel)$m + 1) *
                       numAlphaChars ^ (2 * kernelParameters(kernel)$k)

    if (kernelParameters(kernel)$annSpec == TRUE)
    {
        numAnnotChars <- nchar(metadata(x)$annotationCharset)

        if (numAnnotChars == 0)
            stop("Missing annotation in 'x'\n")

        dimFeatureSpace <- dimFeatureSpace *
            numAnnotChars ^ (2 * kernelParameters(kernel)$k)
    }

    dimFeatureSpace
}

#' @rdname gappyPairKernel
#' @aliases
#' getFeatureSpaceDimension,GappyPairKernel-method
#'
#' @param kernel a sequence kernel object
#' @param x one or multiple biological sequences in the form of a
#' \code{\linkS4class{DNAStringSet}}, \code{\linkS4class{RNAStringSet}},
#' \code{\linkS4class{AAStringSet}} (or as \code{\linkS4class{BioVector}})
#' @return of getDimFeatureSpace:
#' dimension of the feature space as numeric value
#' @export
#'

setMethod("getFeatureSpaceDimension",
          signature=signature(kernel="GappyPairKernel"),
          getFeatureSpaceDimension.gappy)