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Improved runtime of pure R grad.

This commit is contained in:
Daniel Kapla 2019-09-16 11:57:10 +02:00
parent 998f8d3568
commit 0b2b1b76e6
3 changed files with 15 additions and 15 deletions
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24
CVE_R/R/gradient.R
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@ -40,15 +40,15 @@ grad <- function(X, Y, V, h,
# Vectorized distance matrix `D`. # Vectorized distance matrix `D`.
vecD <- colSums(tcrossprod(Q, X_diff)^2) vecD <- colSums(tcrossprod(Q, X_diff)^2)
# Weight matrix `W` (dnorm ... gaussean density function) # Create Kernel matrix (aka. apply kernel to distances)
W <- matrix(1, n, n) # `exp(0) == 1` K <- matrix(1, n, n) # `exp(0) == 1`
W[lower] <- exp((-0.5 / h) * vecD^2) # Set lower tri. part K[lower] <- exp((-0.5 / h) * vecD^2) # Set lower tri. part
W[upper] <- t.default(W)[upper] # Mirror lower tri. to upper K[upper] <- t(K)[upper] # Mirror lower tri. to upper
W <- sweep(W, 2, colSums(W), FUN = `/`) # Col-Normalize
# Weighted `Y` momentums # Weighted `Y` momentums
y1 <- Y %*% W # Result is 1D -> transposition irrelevant colSumsK <- colSums(K)
y2 <- Y^2 %*% W y1 <- (K %*% Y) / colSumsK
y2 <- (K %*% Y^2) / colSumsK
# Per example loss `L(V, X_i)` # Per example loss `L(V, X_i)`
L <- y2 - y1^2 L <- y2 - y1^2
@ -59,11 +59,11 @@ grad <- function(X, Y, V, h,
loss <<- mean(L) loss <<- mean(L)
} }
# Vectorized Weights with forced symmetry # Compute scaling vector `vecS` for `X_diff`.
vecS <- (L[i] - (Y[j] - y1[i])^2) * W[lower] tmp <- kronecker(matrix(y1, n, 1), matrix(Y, 1, n), `-`)^2
vecS <- vecS + ((L[j] - (Y[i] - y1[j])^2) * W[upper]) tmp <- as.vector(L) - tmp
# Compute scaling of `X` row differences tmp <- tmp * K / colSumsK
vecS <- vecS * vecD vecS <- (tmp + t(tmp))[lower] * vecD
# The gradient. # The gradient.
# 1. The `crossprod(A, B)` is equivalent to `t(A) %*% B`, # 1. The `crossprod(A, B)` is equivalent to `t(A) %*% B`,

2
test.R
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@ -2,7 +2,7 @@
# path <- '~/Projects/CVE/tmp/logger.R.pdf' # path <- '~/Projects/CVE/tmp/logger.R.pdf'
library(CVE) library(CVE)
path <- '~/Projects/CVE/tmp/seeded_test.pdf' path <- '~/Projects/CVE/tmp/logger.C.pdf'
epochs <- 100 epochs <- 100
attempts <- 25 attempts <- 25

4
wip.R
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@ -55,11 +55,10 @@ grad2 <- function(X, Y, V, h, persistent = TRUE) {
# vecD <- rowSums((X_diff %*% Q)^2) # vecD <- rowSums((X_diff %*% Q)^2)
vecD <- colSums(tcrossprod(Q, X_diff)^2) vecD <- colSums(tcrossprod(Q, X_diff)^2)
# Weight matrix `W` (dnorm ... gaussean density function) # Create Kernel matrix (aka. apply kernel to distances)
K <- matrix(1, n, n) # `exp(0) == 1` K <- matrix(1, n, n) # `exp(0) == 1`
K[lower] <- exp((-0.5 / h) * vecD^2) # Set lower tri. part K[lower] <- exp((-0.5 / h) * vecD^2) # Set lower tri. part
K[upper] <- t(K)[upper] # Mirror lower tri. to upper K[upper] <- t(K)[upper] # Mirror lower tri. to upper
# W <- sweep(K, 2, colSums(K), FUN = `/`) # Col-Normalize
# Weighted `Y` momentums # Weighted `Y` momentums
colSumsK <- colSums(K) colSumsK <- colSums(K)
@ -68,6 +67,7 @@ grad2 <- function(X, Y, V, h, persistent = TRUE) {
# Per example loss `L(V, X_i)` # Per example loss `L(V, X_i)`
L <- y2 - y1^2 L <- y2 - y1^2
# Compute scaling vector `vecS` for `X_diff`.
tmp <- kronecker(matrix(y1, n, 1), matrix(Y, 1, n), `-`)^2 tmp <- kronecker(matrix(y1, n, 1), matrix(Y, 1, n), `-`)^2
tmp <- as.vector(L) - tmp tmp <- as.vector(L) - tmp
tmp <- tmp * K / colSumsK tmp <- tmp * K / colSumsK