tmp-tests/test-lasso2011-3.R

In privefl/bigstatsr: Statistical Tools for Filebacked Big Matrices

Rcpp::sourceCpp('tmp-tests/lasso.cpp')

X2 <- matrix(0, 1000, 1000)
X2[] <- rnorm(length(X2))
n <- nrow(X2)
m <- ncol(X2)

require(glmnet)
X3 <- sweep(X2, 2, colMeans(X2), '-')
X <- sweep(X3, 2, sqrt(colSums(X3^2) / (n-1)), '/')

# parameters
h2 <- 0.8 # heritability
h2.lims <- c(0.7, 0.9)
M <- 100
K <- 0.3

# simulation
v <- 1
while (v < h2.lims[1] || v > h2.lims[2]) {
  set <- sample(m, size = M)
  effects <- rnorm(M, sd = sqrt(h2 / M))
  y.simu <- X[, set] %*% effects
  print(v <- var(y.simu))
}
y.simu <- y.simu + rnorm(n, sd = sqrt(1 - v))
y.simu <- y.simu - mean(y.simu)
norm.y <- sqrt(sum(y.simu^2))

# rescale to unit norm (not variance)
X <- X / sqrt(n-1)
print(colSums(X^2))

# sc <- sqrt(n * (n - 1))
sc <- 1
tol <- 1e-7
cp0 <- abs(crossprod(X, y.simu)) / sc
# sc <- 999
lseq <- function(from, to, N) {
  exp(seq(log(from), log(to), length.out = N))
}
lam <- lseq(max(cp0), max(cp0) / 1000, 100)
print(lam[1])
print(glmnet(X, y.simu)$lambda[1])
print(lam[1]) / print(glmnet(X, y.simu)$lambda[1])

soft_thr <- function(z, g) sign(z) * max(abs(z) - g, 0)
b <- integer(length(lam))

printf <- function(...) cat(sprintf(...))
CD_lasso <- function(mat, r, betas, lambda) {
  remains <- rep(TRUE, length(betas))
  conv <- FALSE

  while (!conv) { # CD # TODO: warm starts
    conv <- TRUE
    for (j in which(remains)) {
      # print(j)
      tmpB <- crossprodCpp(mat, j, r) / sc + betas[j]
      tmp <- soft_thr(tmpB, lambda) # TODO: combine conds
      if (abs(diff <- (tmp - betas[j])) > tol) {
        if (abs(tmp) > tol) {
          betas[j] <- tmp
          r <- updateR(r, mat, j, diff) # need absolute reupdating?
        } else {
          betas[j] <- 0
          remains[j] <- FALSE
        }
        conv <- FALSE
      }
    }
  }

  betas
}

time <- proc.time()
A_ind <- which(cp0 > (2 * lam[2] - lam[1]))
all_betas <- numeric(ncol(X))
cp <- cp0
r <- y.simu
for (i in 2:length(lam)) {
  printf("i = %d\n", i)
  eps_ind <- A_ind
  seq_strong_thr <- 2 * lam[i] - lam[i - 1]
  KKT_thr <- lam[i] * 1.02
  # strong_ind <- which(cp > (2 * lam[i] - lam[i - 1]))
  # if (i == 2) A_ind <- strong_ind
  # l <- length(A_ind)
  # A_ind <- sort(union(A_ind, strong_ind))
  # printf("Lengths: A: %d, S: %d, AuS: %s\n",
  #        l, length(strong_ind), length(A_ind))
  while (TRUE) {
    printf("Length of eps_ind: %d\n", length(eps_ind))
    mat <- X[, eps_ind, drop = FALSE]
    betas <- all_betas[eps_ind]
    betas <- CD_lasso(mat, r, betas, lam[i])
    all_betas[eps_ind] <- betas

    r <- y.simu - mat %*% betas # reupdating (due to possible floating errors)
    cp <- abs(crossprod(X, r)) / sc

    # step c
    print(length(bad_KKT_c <- which(cp > max(seq_strong_thr, KKT_thr))))
    if (length(bad_KKT_c)) {
      # Add these predictors
      # sorting by appearance? and avoing recopying the matrix
      eps_ind <- sort(union(eps_ind, bad_KKT_c))
      next
    }

    # step d
    print(length(bad_KKT_d <- which(cp > KKT_thr)))
    if (length(bad_KKT_d)) {
      # Add these predictors
      # sorting by appearance? and avoing recopying the matrix
      eps_ind <- sort(union(eps_ind, bad_KKT_d))
      next
    }

    A_ind <- sort(union(A_ind, eps_ind[betas != 0])) # really that?
    b[i] <- sum(betas != 0)
    break
  }
}
print(proc.time() - time)

plot(cp)
abline(h = lam[i], col = "red")

print(b)
print(system.time(mod <- glmnet(X, y.simu, lambda = lam / sqrt(1000))))
print(colSums(mod$beta != 0))

require(biglasso)
X.big <- as.big.matrix(X)
print(system.time(mod2 <- biglasso(X.big, y.simu, lambda = lam / sqrt(1000))))
print(all.equal(mod$beta, mod2$beta[-1, ]))