103 lines
3.2 KiB
R
103 lines
3.2 KiB
R
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ising_conditional_fit <- function(X, Y, ..., callback = NULL) {
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# get and check dimensions
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n <- if (is.null(nrow(Y))) length(Y) else nrow(Y)
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p <- ncol(X)
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q <- if (is.null(ncol(Y))) attr(Y, "p") else ncol(Y)
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# check dimensions
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stopifnot(nrow(X) == n)
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### Initial value estimate
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# SVD of the predictor covariance estimate `Sigma = U_Sigma D_Sigma U_Sigma'`
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SigmaSVD <- La.svd(cov(X), min(p, q), 0)
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# Estimate `pi` as the single and two way effect means (approx conditional
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# probabilities through the marginal probability estimate)
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pi <- mean.mvbinary(Y, twoway = TRUE)
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# convert conditional probabilities into natural parameters (log-odds)
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theta <- ising_theta_from_cond_prob(pi)
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# convert natural parameters `theta` to square matrix form `Theta`
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Theta <- matrix(NA, q, q)
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Theta[lower.tri(diag(q), diag = TRUE)] <- theta
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Theta[upper.tri(diag(q))] <- t(Theta)[upper.tri(diag(q))]
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Theta <- (0.5 + diag(0.5, q, q)) * Theta
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# SVD of `Theta`
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ThetaSVD <- La.svd(Theta, min(p, q), 0)
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# Finally, initial `alpha` parameter estimate
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# `alpha_0 = U_Sigma D_Sigma^-1/2 D_Theta^1/2 U_Theta'`
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alpha <- with(list(S = SigmaSVD, T = ThetaSVD), {
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S$u %*% diag(sqrt(T$d[seq_len(min(p, q))] / S$d[seq_len(min(p, q))])) %*% t(T$u)
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})
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### Optimize log-likelihood for `alpha`
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tensorPredictors::NAGD(
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fun.loss = function(alpha) -ising_conditional_log_likelihood(alpha, X, Y),
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fun.grad = function(alpha) -ising_conditional_score(alpha, X, Y),
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params = alpha,
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...,
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callback = callback
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)
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}
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n <- 1000
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p <- 7
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q <- 9
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alpha.true <- matrix(rnorm(p * q), p)
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X <- matrix(runif(n * p), n)
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theta <- function(alpha, x) {
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Theta <- crossprod(crossprod(x, alpha))
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diag(Theta) <- 0.5 * diag(Theta)
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2 * Theta[lower.tri(diag(ncol(alpha)), diag = TRUE)]
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}
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# sample Y ~ P( . | X = x) for x in X
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Y <- apply(X, 1, function(x) ising_sample(1, theta(alpha.true, x)))
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attr(Y, "p") <- as.integer(q)
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alpha.est <- ising_conditional_fit(X, Y,
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callback = function(iter, alpha) {
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cat(sprintf(
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"%4d - diff: %12.4f - ll: %12.4f\n",
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iter,
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min(norm(alpha - alpha.true, "F"), norm(alpha + alpha.true, "F")),
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ising_conditional_log_likelihood(alpha, X, Y)
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))
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})
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##
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par(mfrow = c(3, 3), mar = c(2, 2, 1, 1))
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for (i in 1:9) {
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tensorPredictors::matrixImage(
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flip(vech.inv(theta(alpha.true, X[i, ]))),
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main = paste(round(range(theta(alpha.true, X[i, ])), 3), collapse = " ")
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)
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}
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par(mfrow = c(3, 3), mar = c(2, 2, 1, 1))
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for (i in 1:9) {
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P <- flip(vech.inv(ising_cond_probs(theta(alpha.true, X[i, ]))))
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tensorPredictors::matrixImage(
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round(P, 5), P < .Machine$double.eps | 1 < P + .Machine$double.eps
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)
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}
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par(mfrow = c(3, 3), mar = c(2, 2, 1, 1))
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for (i in 1:3) {
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tensorPredictors::matrixImage(
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alpha.true
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)
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tensorPredictors::matrixImage(
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flip(vech.inv(theta(alpha.true, X[i, ]))),
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main = paste(round(range(theta(alpha.true, X[i, ])), 3), collapse = " ")
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)
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P <- flip(vech.inv(ising_cond_probs(theta(alpha.true, X[i, ]))))
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tensorPredictors::matrixImage(
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round(P, 5), P < .Machine$double.eps | 1 < P + .Machine$double.eps
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)
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}
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