127 lines
4.1 KiB
R
127 lines
4.1 KiB
R
#' Simple implementation of the CVE method. 'Simple' means that this method is
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#' a classic GD method unsing no further tricks.
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#'
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#' @keywords internal
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#' @export
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cve_sgd <- function(X, Y, k,
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nObs = sqrt(nrow(X)),
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h = NULL,
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tau = 0.01,
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tol = 1e-3,
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epochs = 50L,
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batch.size = 16L,
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attempts = 10L
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) {
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# Set `grad` functions environment to enable if to find this environments
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# local variabels, needed to enable the manipulation of this local variables
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# from within `grad`.
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environment(grad) <- environment()
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# Setup histories.
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loss.history <- matrix(NA, epochs, attempts)
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error.history <- matrix(NA, epochs, attempts)
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# Get dimensions.
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n <- nrow(X) # Number of samples.
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p <- ncol(X) # Data dimensions
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q <- p - k # Complement dimension of the SDR space.
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# Save initial learning rate `tau`.
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tau.init <- tau
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# Addapt tolearance for break condition.
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tol <- sqrt(2 * q) * tol
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# Estaimate bandwidth if not given.
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if (missing(h) | !is.numeric(h)) {
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h <- estimate.bandwidth(X, k, nObs)
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}
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# Compute persistent data.
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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(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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# Identity matrix.
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I_p <- diag(1, p)
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# Init a list of data indices (shuffled for batching).
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indices <- seq(n)
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# Init tracking of current best (according multiple attempts).
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V.best <- NULL
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loss.best <- Inf
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# Start loop for multiple attempts.
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for (attempt in 1:attempts) {
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# Reset learning rate `tau`.
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tau <- tau.init
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# Sample a `(p, q)` dimensional matrix from the stiefel manifold as
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# optimization start value.
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V <- rStiefl(p, q)
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# Keep track of last `V` for computing error after an epoch.
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V.last <- V
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# Repeat `epochs` times
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for (epoch in 1:epochs) {
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# Shuffle batches
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batch.shuffle <- sample(indices)
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# Make a step for each batch.
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for (start in seq(1, n, batch.size)) {
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# Select batch data indices.
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batch <- batch.shuffle[start:(start + batch.size - 1)]
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# Remove `NA`'s (when `n` isn't a multiple of `batch.size`).
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batch <- batch[!is.na(batch)]
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# Compute batch gradient.
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loss <- NULL
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G <- grad(X[batch, ], Y[batch], V, h, loss.out = TRUE)
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# Cayley transform matrix.
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A <- (G %*% t(V)) - (V %*% t(G))
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# Apply learning rate `tau`.
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A.tau <- tau * A
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# Parallet transport (on Stiefl manifold) into direction of `G`.
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V <- solve(I_p + A.tau) %*% ((I_p - A.tau) %*% V)
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}
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# Compute actuall loss after finishing optimization.
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loss <- grad(X, Y, V, h, loss.only = TRUE, persistent = TRUE)
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# And the error for the history.
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error <- norm(V.last %*% t(V.last) - V %*% t(V), type = "F")
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V.last <- V
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# Finaly write history.
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loss.history[epoch, attempt] <- loss
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error.history[epoch, attempt] <- error
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# Check break condition.
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if (error < tol) {
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break()
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}
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}
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# After each attempt, check if last attempt reached a better result.
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if (loss < loss.best) {
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loss.best <- loss
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V.best <- V
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}
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}
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return(list(
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loss.history = loss.history,
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error.history = error.history,
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loss = loss.best,
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V = V.best,
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B = null(V.best),
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h = h
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))
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}
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