74 lines
2.5 KiB
R
74 lines
2.5 KiB
R
#' Compute get gradient of `L(V)` given a dataset `X`.
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#'
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#' @param X Data matrix.
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#' @param Y Responce.
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#' @param V Position to compute the gradient at, aka point on Stiefl manifold.
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#' @param h Bandwidth
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#' @param loss.out Iff \code{TRUE} loss will be written to parent environment.
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#' @param loss.only Boolean to only compute the loss, of \code{TRUE} a single
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#' value loss is returned and \code{envir} is ignored.
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#' @param persistent Determines if data indices and dependent calculations shall
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#' be reused from the parent environment. ATTENTION: Do NOT set this flag, only
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#' intended for internal usage by carefully aligned functions!
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#' @keywords internal
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#' @export
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grad <- function(X, Y, V, h,
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loss.out = FALSE,
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loss.only = FALSE,
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persistent = FALSE) {
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# Get number of samples and dimension.
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n <- nrow(X)
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p <- ncol(X)
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if (!persistent) {
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# Compute lookup indexes for symmetrie, lower/upper
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# triangular parts and vectorization.
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pair.index <- elem.pairs(seq(n))
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i <- pair.index[, 1] # `i` indices of `(i, j)` pairs
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j <- pair.index[, 2] # `j` indices of `(i, j)` pairs
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# Matrix of vectorized indices. (vec(index) -> seq)
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index <- matrix(seq(n * n), n, n)
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lower <- index[lower.tri(index)]
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upper <- t.default(index)[lower]
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# Create all pairewise differences of rows of `X`.
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X_diff <- X[i, , drop = F] - X[j, , drop = F]
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}
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# Projection matrix onto `span(V)`
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Q <- diag(1, p) - tcrossprod(V, V)
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# Vectorized distance matrix `D`.
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vecD <- rowSums((X_diff %*% Q)^2)
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# Weight matrix `W` (dnorm ... gaussean density function)
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W <- matrix(1, n, n) # `exp(0) == 1`
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W[lower] <- exp((-0.5 / h) * vecD^2) # Set lower tri. part
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W[upper] <- t.default(W)[upper] # Mirror lower tri. to upper
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W <- sweep(W, 2, colSums(W), FUN = `/`) # Col-Normalize
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# Weighted `Y` momentums
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y1 <- Y %*% W # Result is 1D -> transposition irrelevant
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y2 <- Y^2 %*% W
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# Per example loss `L(V, X_i)`
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L <- y2 - y1^2
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if (loss.only) {
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return(mean(L))
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}
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if (loss.out) {
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loss <<- mean(L)
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}
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# Vectorized Weights with forced symmetry
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vecS <- (L[i] - (Y[j] - y1[i])^2) * W[lower]
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vecS <- vecS + ((L[j] - (Y[i] - y1[j])^2) * W[upper])
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# Compute scaling of `X` row differences
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vecS <- vecS * vecD
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# The gradient.
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G <- crossprod(X_diff, sweep(X_diff %*% V, 1, vecS, `*`))
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G <- (-2 / (n * h^2)) * G
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return(G)
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}
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