[MINOR] Simplify GLM functions and remove duplicate script from tests This patch makes some minor GLM script simplifications for better debuggability. Due to less intermediates this also improves performance for binomial/bernoulli distribution functions. Furthermore, our applications now directly refer to the existing algorithm script.
Project: http://git-wip-us.apache.org/repos/asf/systemml/repo Commit: http://git-wip-us.apache.org/repos/asf/systemml/commit/631079c4 Tree: http://git-wip-us.apache.org/repos/asf/systemml/tree/631079c4 Diff: http://git-wip-us.apache.org/repos/asf/systemml/diff/631079c4 Branch: refs/heads/master Commit: 631079c43c5530084e8551f92aee77b2bb1538b5 Parents: b27cbf2 Author: Matthias Boehm <[email protected]> Authored: Mon Sep 25 16:39:44 2017 -0700 Committer: Matthias Boehm <[email protected]> Committed: Mon Sep 25 16:39:44 2017 -0700 ---------------------------------------------------------------------- scripts/algorithms/GLM.dml | 66 +- .../test/integration/applications/GLMTest.java | 4 +- src/test/scripts/applications/glm/GLM.dml | 1169 ------------------ 3 files changed, 24 insertions(+), 1215 deletions(-) ---------------------------------------------------------------------- http://git-wip-us.apache.org/repos/asf/systemml/blob/631079c4/scripts/algorithms/GLM.dml ---------------------------------------------------------------------- diff --git a/scripts/algorithms/GLM.dml b/scripts/algorithms/GLM.dml index db911d6..eab1256 100644 --- a/scripts/algorithms/GLM.dml +++ b/scripts/algorithms/GLM.dml @@ -686,30 +686,18 @@ glm_dist = function (Matrix[double] linear_terms, Matrix[double] Y, # g_Y = y_residual / (var_function * link_gradient); # w = 1.0 / (var_function * link_gradient ^ 2); { - num_records = nrow (linear_terms); - zeros_r = matrix (0.0, rows = num_records, cols = 1); - ones_r = 1 + zeros_r; + zeros_r = matrix(0, nrow(linear_terms), 1); + ones_r = matrix(1, nrow(linear_terms), 1); g_Y = zeros_r; w = zeros_r; # Some constants one_over_sqrt_two_pi = 0.39894228040143267793994605993438; - ones_2 = matrix (1.0, rows = 1, cols = 2); - p_one_m_one = ones_2; - p_one_m_one [1, 2] = -1.0; - m_one_p_one = ones_2; - m_one_p_one [1, 1] = -1.0; - zero_one = ones_2; - zero_one [1, 1] = 0.0; - one_zero = ones_2; - one_zero [1, 2] = 0.0; - flip_pos = matrix (0, rows = 2, cols = 2); - flip_neg = flip_pos; - flip_pos [1, 2] = 1; - flip_pos [2, 1] = 1; - flip_neg [1, 2] = -1; - flip_neg [2, 1] = 1; + p_one_m_one = matrix("1 -1", 1, 2); + m_one_p_one = matrix("-1 1", 1, 2); + flip_pos = matrix("0 1 1 0", 2, 2); + flip_neg = matrix("0 -1 1 0", 2, 2); if (dist_type == 1 & link_type == 1) { # POWER DISTRIBUTION @@ -753,15 +741,13 @@ glm_dist = function (Matrix[double] linear_terms, Matrix[double] Y, w = rowSums (Y) * vec1 / link_power ^ 2; } } else { - is_LT_pos_infinite = (linear_terms == 1.0/0.0); - is_LT_neg_infinite = (linear_terms == -1.0/0.0); - is_LT_infinite = is_LT_pos_infinite %*% one_zero + is_LT_neg_infinite %*% zero_one; + is_LT_infinite = cbind(linear_terms==1.0/0.0, linear_terms==-1.0/0.0); finite_linear_terms = replace (target = linear_terms, pattern = 1.0/0.0, replacement = 0); finite_linear_terms = replace (target = finite_linear_terms, pattern = -1.0/0.0, replacement = 0); if (link_type == 2) { # Binomial.logit - Y_prob = exp (finite_linear_terms) %*% one_zero + ones_r %*% zero_one; - Y_prob = Y_prob / (rowSums (Y_prob) %*% ones_2); - Y_prob = Y_prob * ((1.0 - rowSums (is_LT_infinite)) %*% ones_2) + is_LT_infinite; + Y_prob = cbind(exp(finite_linear_terms), ones_r); + Y_prob = Y_prob / rowSums (Y_prob); + Y_prob = Y_prob * (1.0 - rowSums (is_LT_infinite)) + is_LT_infinite; g_Y = rowSums (Y * (Y_prob %*% flip_neg)); ### = y_residual; w = rowSums (Y * (Y_prob %*% flip_pos) * Y_prob); ### = y_variance; } else if (link_type == 3) { # Binomial.probit @@ -786,7 +772,7 @@ glm_dist = function (Matrix[double] linear_terms, Matrix[double] Y, w = the_exp_exp * the_exp * rowSums (Y) / the_exp_ratio; } else if (link_type == 5) { # Binomial.cauchit Y_prob = 0.5 + (atan (finite_linear_terms) %*% p_one_m_one) / 3.1415926535897932384626433832795; - Y_prob = Y_prob * ((1.0 - rowSums (is_LT_infinite)) %*% ones_2) + is_LT_infinite; + Y_prob = Y_prob * (1.0 - rowSums (is_LT_infinite)) + is_LT_infinite; y_residual = Y [, 1] * Y_prob [, 2] - Y [, 2] * Y_prob [, 1]; var_function = rowSums (Y) * Y_prob [, 1] * Y_prob [, 2]; link_gradient_normalized = (1 + linear_terms ^ 2) * 3.1415926535897932384626433832795; @@ -932,22 +918,16 @@ binomial_probability_two_column = return (Matrix[double] Y_prob, int isNaN) { isNaN = 0; - num_records = nrow (linear_terms); # Define some auxiliary matrices ones_2 = matrix (1.0, rows = 1, cols = 2); - p_one_m_one = ones_2; - p_one_m_one [1, 2] = -1.0; - m_one_p_one = ones_2; - m_one_p_one [1, 1] = -1.0; - zero_one = ones_2; - zero_one [1, 1] = 0.0; - one_zero = ones_2; - one_zero [1, 2] = 0.0; - - zeros_r = matrix (0.0, rows = num_records, cols = 1); - ones_r = 1.0 + zeros_r; + p_one_m_one = matrix("1 -1", 1, 2); + m_one_p_one = matrix("-1 1", 1, 2); + zero_one = matrix("0 1", 1, 2); + one_zero = matrix("1 0", 1, 2); + zeros_r = matrix(0, nrow(linear_terms), 1); + ones_r = matrix(1, nrow(linear_terms), 1); # Begin the function body @@ -963,14 +943,12 @@ binomial_probability_two_column = isNaN = 1; } } else { # Binomial.non_power - is_LT_pos_infinite = (linear_terms == 1.0/0.0); - is_LT_neg_infinite = (linear_terms == -1.0/0.0); - is_LT_infinite = is_LT_pos_infinite %*% one_zero + is_LT_neg_infinite %*% zero_one; + is_LT_infinite = cbind(linear_terms==1.0/0.0, linear_terms==-1.0/0.0); finite_linear_terms = replace (target = linear_terms, pattern = 1.0/0.0, replacement = 0); finite_linear_terms = replace (target = finite_linear_terms, pattern = -1.0/0.0, replacement = 0); if (link_type == 2) { # Binomial.logit - Y_prob = exp (finite_linear_terms) %*% one_zero + ones_r %*% zero_one; - Y_prob = Y_prob / (rowSums (Y_prob) %*% ones_2); + Y_prob = cbind(exp(finite_linear_terms), ones_r); + Y_prob = Y_prob / rowSums (Y_prob); } else if (link_type == 3) { # Binomial.probit lt_pos_neg = (finite_linear_terms >= 0) %*% p_one_m_one + ones_r %*% zero_one; t_gp = 1.0 / (1.0 + abs (finite_linear_terms) * 0.231641888); # 0.231641888 = 0.3275911 / sqrt (2.0) @@ -980,7 +958,7 @@ binomial_probability_two_column = + t_gp * (-1.453152027 + t_gp * 1.061405429)))); the_gauss_exp = exp (- (finite_linear_terms ^ 2) / 2.0); - Y_prob = lt_pos_neg + ((the_gauss_exp * pt_gp) %*% ones_2) * (0.5 - lt_pos_neg); + Y_prob = lt_pos_neg + (0.5 - lt_pos_neg) * the_gauss_exp * pt_gp; } else if (link_type == 4) { # Binomial.cloglog the_exp = exp (finite_linear_terms); the_exp_exp = exp (- the_exp); @@ -992,7 +970,7 @@ binomial_probability_two_column = } else { isNaN = 1; } - Y_prob = Y_prob * ((1.0 - rowSums (is_LT_infinite)) %*% ones_2) + is_LT_infinite; + Y_prob = Y_prob * (1.0 - rowSums (is_LT_infinite)) + is_LT_infinite; } } http://git-wip-us.apache.org/repos/asf/systemml/blob/631079c4/src/test/java/org/apache/sysml/test/integration/applications/GLMTest.java ---------------------------------------------------------------------- diff --git a/src/test/java/org/apache/sysml/test/integration/applications/GLMTest.java b/src/test/java/org/apache/sysml/test/integration/applications/GLMTest.java index 854bf63..99081aa 100644 --- a/src/test/java/org/apache/sysml/test/integration/applications/GLMTest.java +++ b/src/test/java/org/apache/sysml/test/integration/applications/GLMTest.java @@ -36,7 +36,6 @@ import org.apache.sysml.test.utils.TestUtils; public abstract class GLMTest extends AutomatedTestBase { - protected final static String TEST_DIR = "applications/glm/"; protected final static String TEST_NAME = "GLM"; protected String TEST_CLASS_DIR = TEST_DIR + GLMTest.class.getSimpleName() + "/"; @@ -309,7 +308,8 @@ public abstract class GLMTest extends AutomatedTestBase proArgs.add("B=" + output("betas_SYSTEMML")); programArgs = proArgs.toArray(new String[proArgs.size()]); - fullDMLScriptName = getScript(); + fullDMLScriptName = (scriptType==ScriptType.DML) ? + "scripts/algorithms/GLM.dml" : getScript(); rCmd = getRCmd(input("X.mtx"), input("Y.mtx"), String.format ("%d", distFamilyType), String.format ("%f", distParam), String.format ("%d", linkType), String.format ("%f", linkPower), "1" /*intercept*/, "0.000000000001" /*tolerance (espilon)*/, http://git-wip-us.apache.org/repos/asf/systemml/blob/631079c4/src/test/scripts/applications/glm/GLM.dml ---------------------------------------------------------------------- diff --git a/src/test/scripts/applications/glm/GLM.dml b/src/test/scripts/applications/glm/GLM.dml deleted file mode 100644 index 9dc311d..0000000 --- a/src/test/scripts/applications/glm/GLM.dml +++ /dev/null @@ -1,1169 +0,0 @@ -#------------------------------------------------------------- -# -# Licensed to the Apache Software Foundation (ASF) under one -# or more contributor license agreements. See the NOTICE file -# distributed with this work for additional information -# regarding copyright ownership. The ASF licenses this file -# to you under the Apache License, Version 2.0 (the -# "License"); you may not use this file except in compliance -# with the License. You may obtain a copy of the License at -# -# http://www.apache.org/licenses/LICENSE-2.0 -# -# Unless required by applicable law or agreed to in writing, -# software distributed under the License is distributed on an -# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY -# KIND, either express or implied. See the License for the -# specific language governing permissions and limitations -# under the License. -# -#------------------------------------------------------------- - -# -# THIS SCRIPT SOLVES GLM REGRESSION USING NEWTON/FISHER SCORING WITH TRUST REGIONS -# -# INPUT PARAMETERS: -# --------------------------------------------------------------------------------------------- -# NAME TYPE DEFAULT MEANING -# --------------------------------------------------------------------------------------------- -# X String --- Location to read the matrix X of feature vectors -# Y String --- Location to read response matrix Y with either 1 or 2 columns: -# if dfam = 2, Y is 1-column Bernoulli or 2-column Binomial (#pos, #neg) -# B String --- Location to store estimated regression parameters (the betas) -# fmt String "text" The betas matrix output format, such as "text" or "csv" -# O String " " Location to write the printed statistics; by default is standard output -# Log String " " Location to write per-iteration variables for log/debugging purposes -# dfam Int 1 Distribution family code: 1 = Power, 2 = Binomial -# vpow Double 0.0 Power for Variance defined as (mean)^power (ignored if dfam != 1): -# 0.0 = Gaussian, 1.0 = Poisson, 2.0 = Gamma, 3.0 = Inverse Gaussian -# link Int 0 Link function code: 0 = canonical (depends on distribution), -# 1 = Power, 2 = Logit, 3 = Probit, 4 = Cloglog, 5 = Cauchit -# lpow Double 1.0 Power for Link function defined as (mean)^power (ignored if link != 1): -# -2.0 = 1/mu^2, -1.0 = reciprocal, 0.0 = log, 0.5 = sqrt, 1.0 = identity -# yneg Double 0.0 Response value for Bernoulli "No" label, usually 0.0 or -1.0 -# icpt Int 0 Intercept presence, X columns shifting and rescaling: -# 0 = no intercept, no shifting, no rescaling; -# 1 = add intercept, but neither shift nor rescale X; -# 2 = add intercept, shift & rescale X columns to mean = 0, variance = 1 -# reg Double 0.0 Regularization parameter (lambda) for L2 regularization -# tol Double 0.000001 Tolerance (epsilon) -# disp Double 0.0 (Over-)dispersion value, or 0.0 to estimate it from data -# moi Int 200 Maximum number of outer (Newton / Fisher Scoring) iterations -# mii Int 0 Maximum number of inner (Conjugate Gradient) iterations, 0 = no maximum -# --------------------------------------------------------------------------------------------- -# OUTPUT: Matrix beta, whose size depends on icpt: -# icpt=0: ncol(X) x 1; icpt=1: (ncol(X) + 1) x 1; icpt=2: (ncol(X) + 1) x 2 -# -# In addition, some GLM statistics are provided in CSV format, one comma-separated name-value -# pair per each line, as follows: -# -# NAME MEANING -# ------------------------------------------------------------------------------------------- -# TERMINATION_CODE A positive integer indicating success/failure as follows: -# 1 = Converged successfully; 2 = Maximum number of iterations reached; -# 3 = Input (X, Y) out of range; 4 = Distribution/link is not supported -# BETA_MIN Smallest beta value (regression coefficient), excluding the intercept -# BETA_MIN_INDEX Column index for the smallest beta value -# BETA_MAX Largest beta value (regression coefficient), excluding the intercept -# BETA_MAX_INDEX Column index for the largest beta value -# INTERCEPT Intercept value, or NaN if there is no intercept (if icpt=0) -# DISPERSION Dispersion used to scale deviance, provided as "disp" input parameter -# or estimated (same as DISPERSION_EST) if the "disp" parameter is <= 0 -# DISPERSION_EST Dispersion estimated from the dataset -# DEVIANCE_UNSCALED Deviance from the saturated model, assuming dispersion == 1.0 -# DEVIANCE_SCALED Deviance from the saturated model, scaled by the DISPERSION value -# ------------------------------------------------------------------------------------------- -# -# The Log file, when requested, contains the following per-iteration variables in CSV format, -# each line containing triple (NAME, ITERATION, VALUE) with ITERATION = 0 for initial values: -# -# NAME MEANING -# ------------------------------------------------------------------------------------------- -# NUM_CG_ITERS Number of inner (Conj.Gradient) iterations in this outer iteration -# IS_TRUST_REACHED 1 = trust region boundary was reached, 0 = otherwise -# POINT_STEP_NORM L2-norm of iteration step from old point (i.e. "beta") to new point -# OBJECTIVE The loss function we minimize (i.e. negative partial log-likelihood) -# OBJ_DROP_REAL Reduction in the objective during this iteration, actual value -# OBJ_DROP_PRED Reduction in the objective predicted by a quadratic approximation -# OBJ_DROP_RATIO Actual-to-predicted reduction ratio, used to update the trust region -# GRADIENT_NORM L2-norm of the loss function gradient (NOTE: sometimes omitted) -# LINEAR_TERM_MIN The minimum value of X %*% beta, used to check for overflows -# LINEAR_TERM_MAX The maximum value of X %*% beta, used to check for overflows -# IS_POINT_UPDATED 1 = new point accepted; 0 = new point rejected, old point restored -# TRUST_DELTA Updated trust region size, the "delta" -# ------------------------------------------------------------------------------------------- -# -# Example with distribution = "Binomial.logit": -# hadoop jar SystemML.jar -f GLM_HOME/GLM.dml -nvargs dfam=2 link=2 yneg=-1.0 icpt=2 reg=0.001 -# tol=0.00000001 disp=1.0 moi=100 mii=10 X=INPUT_DIR/X Y=INPUT_DIR/Y B=OUTPUT_DIR/betas -# fmt=csv O=OUTPUT_DIR/stats Log=OUTPUT_DIR/log -# -# SOME OF THE SUPPORTED GLM DISTRIBUTION FAMILIES -# AND LINK FUNCTIONS: -# ----------------------------------------------- -# INPUT PARAMETERS: MEANING: Cano- -# dfam vpow link lpow Distribution.link nical? -# ----------------------------------------------- -# 1 0.0 1 -1.0 Gaussian.inverse -# 1 0.0 1 0.0 Gaussian.log -# 1 0.0 1 1.0 Gaussian.id Yes -# 1 1.0 1 0.0 Poisson.log Yes -# 1 1.0 1 0.5 Poisson.sqrt -# 1 1.0 1 1.0 Poisson.id -# 1 2.0 1 -1.0 Gamma.inverse Yes -# 1 2.0 1 0.0 Gamma.log -# 1 2.0 1 1.0 Gamma.id -# 1 3.0 1 -2.0 InvGaussian.1/mu^2 Yes -# 1 3.0 1 -1.0 InvGaussian.inverse -# 1 3.0 1 0.0 InvGaussian.log -# 1 3.0 1 1.0 InvGaussian.id -# 1 * 1 * AnyVariance.AnyLink -# ----------------------------------------------- -# 2 * 1 0.0 Binomial.log -# 2 * 1 0.5 Binomial.sqrt -# 2 * 2 * Binomial.logit Yes -# 2 * 3 * Binomial.probit -# 2 * 4 * Binomial.cloglog -# 2 * 5 * Binomial.cauchit -# ----------------------------------------------- - - -# Default values for input parameters - -fileX = $X; -fileY = $Y; -fileB = $B; -fileO = ifdef ($O, " "); -fileLog = ifdef ($Log, " "); -fmtB = ifdef ($fmt, "text"); - -distribution_type = ifdef ($dfam, 1); # $dfam = 1; -variance_as_power_of_the_mean = ifdef ($vpow, 0.0); # $vpow = 0.0; -link_type = ifdef ($link, 0); # $link = 0; -link_as_power_of_the_mean = ifdef ($lpow, 1.0); # $lpow = 1.0; -bernoulli_No_label = ifdef ($yneg, 0.0); # $yneg = 0.0; -intercept_status = ifdef ($icpt, 0); # $icpt = 0; -dispersion = ifdef ($disp, 0.0); # $disp = 0.0; -regularization = ifdef ($reg, 0.0); # $reg = 0.0; -eps = ifdef ($tol, 0.000001); # $tol = 0.000001; -max_iteration_IRLS = ifdef ($moi, 200); # $moi = 200; -max_iteration_CG = ifdef ($mii, 0); # $mii = 0; - -variance_as_power_of_the_mean = as.double (variance_as_power_of_the_mean); -link_as_power_of_the_mean = as.double (link_as_power_of_the_mean); -bernoulli_No_label = as.double (bernoulli_No_label); -dispersion = as.double (dispersion); -eps = as.double (eps); - - -# Default values for output statistics: - -termination_code = 0; -min_beta = 0.0 / 0.0; -i_min_beta = 0.0 / 0.0; -max_beta = 0.0 / 0.0; -i_max_beta = 0.0 / 0.0; -intercept_value = 0.0 / 0.0; -dispersion = 0.0 / 0.0; -estimated_dispersion = 0.0 / 0.0; -deviance_nodisp = 0.0 / 0.0; -deviance = 0.0 / 0.0; - -print("BEGIN GLM SCRIPT"); -print("Reading X..."); -X = read (fileX); -print("Reading Y..."); -Y = read (fileY); - -num_records = nrow (X); -num_features = ncol (X); -zeros_r = matrix (0, rows = num_records, cols = 1); -ones_r = 1 + zeros_r; - -# Introduce the intercept, shift and rescale the columns of X if needed - -if (intercept_status == 1 | intercept_status == 2) # add the intercept column -{ - X = cbind (X, ones_r); - num_features = ncol (X); -} - -scale_lambda = matrix (1, rows = num_features, cols = 1); -if (intercept_status == 1 | intercept_status == 2) -{ - scale_lambda [num_features, 1] = 0; -} - -if (intercept_status == 2) # scale-&-shift X columns to mean 0, variance 1 -{ # Important assumption: X [, num_features] = ones_r - avg_X_cols = t(colSums(X)) / num_records; - var_X_cols = (t(colSums (X ^ 2)) - num_records * (avg_X_cols ^ 2)) / (num_records - 1); - is_unsafe = (var_X_cols <= 0.0); - scale_X = 1.0 / sqrt (var_X_cols * (1 - is_unsafe) + is_unsafe); - scale_X [num_features, 1] = 1; - shift_X = - avg_X_cols * scale_X; - shift_X [num_features, 1] = 0; - rowSums_X_sq = (X ^ 2) %*% (scale_X ^ 2) + X %*% (2 * scale_X * shift_X) + sum (shift_X ^ 2); -} else { - scale_X = matrix (1, rows = num_features, cols = 1); - shift_X = matrix (0, rows = num_features, cols = 1); - rowSums_X_sq = rowSums (X ^ 2); -} - -# Henceforth we replace "X" with "X %*% (SHIFT/SCALE TRANSFORM)" and rowSums(X ^ 2) -# with "rowSums_X_sq" in order to preserve the sparsity of X under shift and scale. -# The transform is then associatively applied to the other side of the expression, -# and is rewritten via "scale_X" and "shift_X" as follows: -# -# ssX_A = (SHIFT/SCALE TRANSFORM) %*% A --- is rewritten as: -# ssX_A = diag (scale_X) %*% A; -# ssX_A [num_features, ] = ssX_A [num_features, ] + t(shift_X) %*% A; -# -# tssX_A = t(SHIFT/SCALE TRANSFORM) %*% A --- is rewritten as: -# tssX_A = diag (scale_X) %*% A + shift_X %*% A [num_features, ]; - -# Initialize other input-dependent parameters - -lambda = scale_lambda * regularization; -if (max_iteration_CG == 0) { - max_iteration_CG = num_features; -} - -# In Bernoulli case, convert one-column "Y" into two-column - -if (distribution_type == 2 & ncol(Y) == 1) -{ - is_Y_negative = (Y == bernoulli_No_label); - Y = cbind (1 - is_Y_negative, is_Y_negative); - count_Y_negative = sum (is_Y_negative); - if (count_Y_negative == 0) { - stop ("GLM Input Error: all Y-values encode Bernoulli YES-label, none encode NO-label"); - } - if (count_Y_negative == nrow(Y)) { - stop ("GLM Input Error: all Y-values encode Bernoulli NO-label, none encode YES-label"); - } -} - -# Set up the canonical link, if requested [Then we have: Var(mu) * (d link / d mu) = const] - -if (link_type == 0) -{ - if (distribution_type == 1) { - link_type = 1; - link_as_power_of_the_mean = 1.0 - variance_as_power_of_the_mean; - } else { if (distribution_type == 2) { - link_type = 2; -} } } - -# For power distributions and/or links, we use two constants, -# "variance as power of the mean" and "link_as_power_of_the_mean", -# to specify the variance and the link as arbitrary powers of the -# mean. However, the variance-powers of 1.0 (Poisson family) and -# 2.0 (Gamma family) have to be treated as special cases, because -# these values integrate into logarithms. The link-power of 0.0 -# is also special as it represents the logarithm link. - -num_response_columns = ncol (Y); - -is_supported = check_if_supported (num_response_columns, distribution_type, variance_as_power_of_the_mean, link_type, link_as_power_of_the_mean); -if (is_supported == 1) -{ - -##### INITIALIZE THE BETAS ##### - -[beta, saturated_log_l, isNaN] = - glm_initialize (X, Y, distribution_type, variance_as_power_of_the_mean, link_type, link_as_power_of_the_mean, intercept_status, max_iteration_CG); -if (isNaN == 0) -{ - -##### START OF THE MAIN PART ##### - -sum_X_sq = sum (rowSums_X_sq); -trust_delta = 0.5 * sqrt (num_features) / max (sqrt (rowSums_X_sq)); -### max_trust_delta = trust_delta * 10000.0; -log_l = 0.0; -deviance_nodisp = 0.0; -new_deviance_nodisp = 0.0; -isNaN_log_l = 2; -newbeta = beta; -g = matrix (0.0, rows = num_features, cols = 1); -g_norm = sqrt (sum ((g + lambda * beta) ^ 2)); -accept_new_beta = 1; -reached_trust_boundary = 0; -neg_log_l_change_predicted = 0.0; -i_IRLS = 0; - -print ("BEGIN IRLS ITERATIONS..."); - -ssX_newbeta = diag (scale_X) %*% newbeta; -ssX_newbeta [num_features, ] = ssX_newbeta [num_features, ] + t(shift_X) %*% newbeta; -all_linear_terms = X %*% ssX_newbeta; - -[new_log_l, isNaN_new_log_l] = glm_log_likelihood_part - (all_linear_terms, Y, distribution_type, variance_as_power_of_the_mean, link_type, link_as_power_of_the_mean); - -if (isNaN_new_log_l == 0) { - new_deviance_nodisp = 2.0 * (saturated_log_l - new_log_l); - new_log_l = new_log_l - 0.5 * sum (lambda * newbeta ^ 2); -} - -if (fileLog != " ") { - log_str = "POINT_STEP_NORM," + i_IRLS + "," + sqrt (sum (beta ^ 2)); - log_str = append (log_str, "OBJECTIVE," + i_IRLS + "," + (- new_log_l)); - log_str = append (log_str, "LINEAR_TERM_MIN," + i_IRLS + "," + min (all_linear_terms)); - log_str = append (log_str, "LINEAR_TERM_MAX," + i_IRLS + "," + max (all_linear_terms)); -} else { - log_str = " "; -} - -# set w to avoid 'Initialization of w depends on if-else/while execution' warnings -w = matrix (0.0, rows=1, cols=1); -while (termination_code == 0) -{ - accept_new_beta = 1; - - if (i_IRLS > 0) - { - if (isNaN_log_l == 0) { - accept_new_beta = 0; - } - -# Decide whether to accept a new iteration point and update the trust region -# See Alg. 4.1 on p. 69 of "Numerical Optimization" 2nd ed. by Nocedal and Wright - - rho = (- new_log_l + log_l) / neg_log_l_change_predicted; - if (rho < 0.25 | isNaN_new_log_l == 1) { - trust_delta = 0.25 * trust_delta; - } - if (rho > 0.75 & isNaN_new_log_l == 0 & reached_trust_boundary == 1) { - trust_delta = 2 * trust_delta; - -### if (trust_delta > max_trust_delta) { -### trust_delta = max_trust_delta; -### } - - } - if (rho > 0.1 & isNaN_new_log_l == 0) { - accept_new_beta = 1; - } - } - - if (fileLog != " ") { - log_str = append (log_str, "IS_POINT_UPDATED," + i_IRLS + "," + accept_new_beta); - log_str = append (log_str, "TRUST_DELTA," + i_IRLS + "," + trust_delta); - } - if (accept_new_beta == 1) - { - beta = newbeta; log_l = new_log_l; deviance_nodisp = new_deviance_nodisp; isNaN_log_l = isNaN_new_log_l; - - [g_Y, w] = glm_dist (all_linear_terms, Y, distribution_type, variance_as_power_of_the_mean, link_type, link_as_power_of_the_mean); - - # We introduced these variables to avoid roundoff errors: - # g_Y = y_residual / (y_var * link_grad); - # w = 1.0 / (y_var * link_grad * link_grad); - - gXY = - t(X) %*% g_Y; - g = diag (scale_X) %*% gXY + shift_X %*% gXY [num_features, ]; - g_norm = sqrt (sum ((g + lambda * beta) ^ 2)); - - if (fileLog != " ") { - log_str = append (log_str, "GRADIENT_NORM," + i_IRLS + "," + g_norm); - } - } - - [z, neg_log_l_change_predicted, num_CG_iters, reached_trust_boundary] = - get_CG_Steihaug_point (X, scale_X, shift_X, w, g, beta, lambda, trust_delta, max_iteration_CG); - - newbeta = beta + z; - - ssX_newbeta = diag (scale_X) %*% newbeta; - ssX_newbeta [num_features, ] = ssX_newbeta [num_features, ] + t(shift_X) %*% newbeta; - all_linear_terms = X %*% ssX_newbeta; - - [new_log_l, isNaN_new_log_l] = glm_log_likelihood_part - (all_linear_terms, Y, distribution_type, variance_as_power_of_the_mean, link_type, link_as_power_of_the_mean); - - if (isNaN_new_log_l == 0) { - new_deviance_nodisp = 2.0 * (saturated_log_l - new_log_l); - new_log_l = new_log_l - 0.5 * sum (lambda * newbeta ^ 2); - } - - log_l_change = new_log_l - log_l; # R's criterion for termination: |dev - devold|/(|dev| + 0.1) < eps - - if (reached_trust_boundary == 0 & isNaN_new_log_l == 0 & - (2.0 * abs (log_l_change) < eps * (deviance_nodisp + 0.1) | abs (log_l_change) < (abs (log_l) + abs (new_log_l)) * 0.00000000000001) ) - { - termination_code = 1; - } - rho = - log_l_change / neg_log_l_change_predicted; - z_norm = sqrt (sum (z * z)); - - [z_norm_m, z_norm_e] = round_to_print (z_norm); - [trust_delta_m, trust_delta_e] = round_to_print (trust_delta); - [rho_m, rho_e] = round_to_print (rho); - [new_log_l_m, new_log_l_e] = round_to_print (new_log_l); - [log_l_change_m, log_l_change_e] = round_to_print (log_l_change); - [g_norm_m, g_norm_e] = round_to_print (g_norm); - - i_IRLS = i_IRLS + 1; - print ("Iter #" + i_IRLS + " completed" - + ", ||z|| = " + z_norm_m + "E" + z_norm_e - + ", trust_delta = " + trust_delta_m + "E" + trust_delta_e - + ", reached = " + reached_trust_boundary - + ", ||g|| = " + g_norm_m + "E" + g_norm_e - + ", new_log_l = " + new_log_l_m + "E" + new_log_l_e - + ", log_l_change = " + log_l_change_m + "E" + log_l_change_e - + ", rho = " + rho_m + "E" + rho_e); - - if (fileLog != " ") { - log_str = append (log_str, "NUM_CG_ITERS," + i_IRLS + "," + num_CG_iters); - log_str = append (log_str, "IS_TRUST_REACHED," + i_IRLS + "," + reached_trust_boundary); - log_str = append (log_str, "POINT_STEP_NORM," + i_IRLS + "," + z_norm); - log_str = append (log_str, "OBJECTIVE," + i_IRLS + "," + (- new_log_l)); - log_str = append (log_str, "OBJ_DROP_REAL," + i_IRLS + "," + log_l_change); - log_str = append (log_str, "OBJ_DROP_PRED," + i_IRLS + "," + (- neg_log_l_change_predicted)); - log_str = append (log_str, "OBJ_DROP_RATIO," + i_IRLS + "," + rho); - log_str = append (log_str, "LINEAR_TERM_MIN," + i_IRLS + "," + min (all_linear_terms)); - log_str = append (log_str, "LINEAR_TERM_MAX," + i_IRLS + "," + max (all_linear_terms)); - } - - if (i_IRLS == max_iteration_IRLS) { - termination_code = 2; - } -} - -beta = newbeta; -log_l = new_log_l; -deviance_nodisp = new_deviance_nodisp; - -if (termination_code == 1) { - print ("Converged in " + i_IRLS + " steps."); -} else { - print ("Did not converge."); -} - -ssX_beta = diag (scale_X) %*% beta; -ssX_beta [num_features, ] = ssX_beta [num_features, ] + t(shift_X) %*% beta; -if (intercept_status == 2) { - beta_out = cbind (ssX_beta, beta); -} else { - beta_out = ssX_beta; -} - -write (beta_out, fileB, format=fmtB); - -if (intercept_status == 1 | intercept_status == 2) { - intercept_value = as.scalar (beta_out [num_features, 1]); - beta_noicept = beta_out [1 : (num_features - 1), 1]; -} else { - beta_noicept = beta_out [1 : num_features, 1]; -} -min_beta = min (beta_noicept); -max_beta = max (beta_noicept); -tmp_i_min_beta = rowIndexMin (t(beta_noicept)) -i_min_beta = as.scalar (tmp_i_min_beta [1, 1]); -tmp_i_max_beta = rowIndexMax (t(beta_noicept)) -i_max_beta = as.scalar (tmp_i_max_beta [1, 1]); - -##### OVER-DISPERSION PART ##### - -all_linear_terms = X %*% ssX_beta; -[g_Y, w] = glm_dist (all_linear_terms, Y, distribution_type, variance_as_power_of_the_mean, link_type, link_as_power_of_the_mean); - -pearson_residual_sq = g_Y ^ 2 / w; -pearson_residual_sq = replace (target = pearson_residual_sq, pattern = 0.0/0.0, replacement = 0); -# pearson_residual_sq = (y_residual ^ 2) / y_var; - -if (num_records > num_features) { - estimated_dispersion = sum (pearson_residual_sq) / (num_records - num_features); -} -if (dispersion <= 0.0) { - dispersion = estimated_dispersion; -} -deviance = deviance_nodisp / dispersion; - -if (fileLog != " ") { - write (log_str, fileLog); -} - -##### END OF THE MAIN PART ##### - -} else { print ("Input matrices are out of range. Terminating the DML."); termination_code = 3; } -} else { print ("Distribution/Link not supported. Terminating the DML."); termination_code = 4; } - -str = "TERMINATION_CODE," + termination_code; -str = append (str, "BETA_MIN," + min_beta); -str = append (str, "BETA_MIN_INDEX," + i_min_beta); -str = append (str, "BETA_MAX," + max_beta); -str = append (str, "BETA_MAX_INDEX," + i_max_beta); -str = append (str, "INTERCEPT," + intercept_value); -str = append (str, "DISPERSION," + dispersion); -str = append (str, "DISPERSION_EST," + estimated_dispersion); -str = append (str, "DEVIANCE_UNSCALED," + deviance_nodisp); -str = append (str, "DEVIANCE_SCALED," + deviance); - -if (fileO != " ") { - write (str, fileO); -} else { - print (str); -} - - - - -check_if_supported = - function (int ncol_y, int dist_type, double var_power, int link_type, double link_power) - return (int is_supported) -{ - is_supported = 0; - if (ncol_y == 1 & dist_type == 1 & link_type == 1) - { # POWER DISTRIBUTION - is_supported = 1; - if (var_power == 0.0 & link_power == -1.0) {print ("Gaussian.inverse"); } else { - if (var_power == 0.0 & link_power == 0.0) {print ("Gaussian.log"); } else { - if (var_power == 0.0 & link_power == 0.5) {print ("Gaussian.sqrt"); } else { - if (var_power == 0.0 & link_power == 1.0) {print ("Gaussian.id"); } else { - if (var_power == 0.0 ) {print ("Gaussian.power_nonlog"); } else { - if (var_power == 1.0 & link_power == -1.0) {print ("Poisson.inverse"); } else { - if (var_power == 1.0 & link_power == 0.0) {print ("Poisson.log"); } else { - if (var_power == 1.0 & link_power == 0.5) {print ("Poisson.sqrt"); } else { - if (var_power == 1.0 & link_power == 1.0) {print ("Poisson.id"); } else { - if (var_power == 1.0 ) {print ("Poisson.power_nonlog"); } else { - if (var_power == 2.0 & link_power == -1.0) {print ("Gamma.inverse"); } else { - if (var_power == 2.0 & link_power == 0.0) {print ("Gamma.log"); } else { - if (var_power == 2.0 & link_power == 0.5) {print ("Gamma.sqrt"); } else { - if (var_power == 2.0 & link_power == 1.0) {print ("Gamma.id"); } else { - if (var_power == 2.0 ) {print ("Gamma.power_nonlog"); } else { - if (var_power == 3.0 & link_power == -2.0) {print ("InvGaussian.1/mu^2"); } else { - if (var_power == 3.0 & link_power == -1.0) {print ("InvGaussian.inverse"); } else { - if (var_power == 3.0 & link_power == 0.0) {print ("InvGaussian.log"); } else { - if (var_power == 3.0 & link_power == 0.5) {print ("InvGaussian.sqrt"); } else { - if (var_power == 3.0 & link_power == 1.0) {print ("InvGaussian.id"); } else { - if (var_power == 3.0 ) {print ("InvGaussian.power_nonlog");}else{ - if ( link_power == 0.0) {print ("PowerDist.log"); } else { - print ("PowerDist.power_nonlog"); - } }}}}} }}}}} }}}}} }}}}} }} - if (ncol_y == 1 & dist_type == 2) - { - print ("Error: Bernoulli response matrix has not been converted into two-column format."); - } - if (ncol_y == 2 & dist_type == 2 & link_type >= 1 & link_type <= 5) - { # BINOMIAL/BERNOULLI DISTRIBUTION - is_supported = 1; - if (link_type == 1 & link_power == -1.0) {print ("Binomial.inverse"); } else { - if (link_type == 1 & link_power == 0.0) {print ("Binomial.log"); } else { - if (link_type == 1 & link_power == 0.5) {print ("Binomial.sqrt"); } else { - if (link_type == 1 & link_power == 1.0) {print ("Binomial.id"); } else { - if (link_type == 1) {print ("Binomial.power_nonlog"); } else { - if (link_type == 2) {print ("Binomial.logit"); } else { - if (link_type == 3) {print ("Binomial.probit"); } else { - if (link_type == 4) {print ("Binomial.cloglog"); } else { - if (link_type == 5) {print ("Binomial.cauchit"); } - } }}}}} }}} - if (is_supported == 0) { - print ("Response matrix with " + ncol_y + " columns, distribution family (" + dist_type + ", " + var_power - + ") and link family (" + link_type + ", " + link_power + ") are NOT supported together."); - } -} - -glm_initialize = function (Matrix[double] X, Matrix[double] Y, int dist_type, double var_power, int link_type, double link_power, int icept_status, int max_iter_CG) -return (Matrix[double] beta, double saturated_log_l, int isNaN) -{ - saturated_log_l = 0.0; - isNaN = 0; - y_corr = Y [, 1]; - if (dist_type == 2) { - n_corr = rowSums (Y); - is_n_zero = (n_corr == 0.0); - y_corr = Y [, 1] / (n_corr + is_n_zero) + (0.5 - Y [, 1]) * is_n_zero; - } - linear_terms = y_corr; - if (dist_type == 1 & link_type == 1) { # POWER DISTRIBUTION - if (link_power == 0.0) { - if (sum (y_corr < 0.0) == 0) { - is_zero_y_corr = (y_corr == 0.0); - linear_terms = log (y_corr + is_zero_y_corr) - is_zero_y_corr / (1.0 - is_zero_y_corr); - } else { isNaN = 1; } - } else { if (link_power == 1.0) { - linear_terms = y_corr; - } else { if (link_power == -1.0) { - linear_terms = 1.0 / y_corr; - } else { if (link_power == 0.5) { - if (sum (y_corr < 0.0) == 0) { - linear_terms = sqrt (y_corr); - } else { isNaN = 1; } - } else { if (link_power > 0.0) { - if (sum (y_corr < 0.0) == 0) { - is_zero_y_corr = (y_corr == 0.0); - linear_terms = (y_corr + is_zero_y_corr) ^ link_power - is_zero_y_corr; - } else { isNaN = 1; } - } else { - if (sum (y_corr <= 0.0) == 0) { - linear_terms = y_corr ^ link_power; - } else { isNaN = 1; } - }}}}} - } - if (dist_type == 2 & link_type >= 1 & link_type <= 5) - { # BINOMIAL/BERNOULLI DISTRIBUTION - if (link_type == 1 & link_power == 0.0) { # Binomial.log - if (sum (y_corr < 0.0) == 0) { - is_zero_y_corr = (y_corr == 0.0); - linear_terms = log (y_corr + is_zero_y_corr) - is_zero_y_corr / (1.0 - is_zero_y_corr); - } else { isNaN = 1; } - } else { if (link_type == 1 & link_power > 0.0) { # Binomial.power_nonlog pos - if (sum (y_corr < 0.0) == 0) { - is_zero_y_corr = (y_corr == 0.0); - linear_terms = (y_corr + is_zero_y_corr) ^ link_power - is_zero_y_corr; - } else { isNaN = 1; } - } else { if (link_type == 1) { # Binomial.power_nonlog neg - if (sum (y_corr <= 0.0) == 0) { - linear_terms = y_corr ^ link_power; - } else { isNaN = 1; } - } else { - is_zero_y_corr = (y_corr <= 0.0); - is_one_y_corr = (y_corr >= 1.0); - y_corr = y_corr * (1.0 - is_zero_y_corr) * (1.0 - is_one_y_corr) + 0.5 * (is_zero_y_corr + is_one_y_corr); - if (link_type == 2) { # Binomial.logit - linear_terms = log (y_corr / (1.0 - y_corr)) - + is_one_y_corr / (1.0 - is_one_y_corr) - is_zero_y_corr / (1.0 - is_zero_y_corr); - } else { if (link_type == 3) { # Binomial.probit - y_below_half = y_corr + (1.0 - 2.0 * y_corr) * (y_corr > 0.5); - t = sqrt (- 2.0 * log (y_below_half)); - approx_inv_Gauss_CDF = - t + (2.515517 + t * (0.802853 + t * 0.010328)) / (1.0 + t * (1.432788 + t * (0.189269 + t * 0.001308))); - linear_terms = approx_inv_Gauss_CDF * (1.0 - 2.0 * (y_corr > 0.5)) - + is_one_y_corr / (1.0 - is_one_y_corr) - is_zero_y_corr / (1.0 - is_zero_y_corr); - } else { if (link_type == 4) { # Binomial.cloglog - linear_terms = log (- log (1.0 - y_corr)) - - log (- log (0.5)) * (is_zero_y_corr + is_one_y_corr) - + is_one_y_corr / (1.0 - is_one_y_corr) - is_zero_y_corr / (1.0 - is_zero_y_corr); - } else { if (link_type == 5) { # Binomial.cauchit - linear_terms = tan ((y_corr - 0.5) * 3.1415926535897932384626433832795) - + is_one_y_corr / (1.0 - is_one_y_corr) - is_zero_y_corr / (1.0 - is_zero_y_corr); - }} }}}}} - } - - if (isNaN == 0) { - [saturated_log_l, isNaN] = - glm_log_likelihood_part (linear_terms, Y, dist_type, var_power, link_type, link_power); - } - - if ((dist_type == 1 & link_type == 1 & link_power == 0.0) | - (dist_type == 2 & link_type >= 2)) - { - desired_eta = 0.0; - } else { if (link_type == 1 & link_power == 0.0) { - desired_eta = log (0.5); - } else { if (link_type == 1) { - desired_eta = 0.5 ^ link_power; - } else { - desired_eta = 0.5; - }}} - - beta = matrix (0.0, rows = ncol(X), cols = 1); - - if (desired_eta != 0.0) { - if (icept_status == 1 | icept_status == 2) { - beta [nrow(beta), 1] = desired_eta; - } else { - # We want: avg (X %*% ssX_transform %*% beta) = desired_eta - # Note that "ssX_transform" is trivial here, hence ignored - - beta = straightenX (X, 0.000001, max_iter_CG); - beta = beta * desired_eta; -} } } - - -glm_dist = function (Matrix[double] linear_terms, Matrix[double] Y, - int dist_type, double var_power, int link_type, double link_power) - return (Matrix[double] g_Y, Matrix[double] w) - # ORIGINALLY we returned more meaningful vectors, namely: - # Matrix[double] y_residual : y - y_mean, i.e. y observed - y predicted - # Matrix[double] link_gradient : derivative of the link function - # Matrix[double] var_function : variance without dispersion, i.e. the V(mu) function - # BUT, this caused roundoff errors, so we had to compute "directly useful" vectors - # and skip over the "meaningful intermediaries". Now we output these two variables: - # g_Y = y_residual / (var_function * link_gradient); - # w = 1.0 / (var_function * link_gradient ^ 2); -{ - num_records = nrow (linear_terms); - zeros_r = matrix (0.0, rows = num_records, cols = 1); - ones_r = 1 + zeros_r; - g_Y = zeros_r; - w = zeros_r; - - # Some constants - - one_over_sqrt_two_pi = 0.39894228040143267793994605993438; - ones_2 = matrix (1.0, rows = 1, cols = 2); - p_one_m_one = ones_2; - p_one_m_one [1, 2] = -1.0; - m_one_p_one = ones_2; - m_one_p_one [1, 1] = -1.0; - zero_one = ones_2; - zero_one [1, 1] = 0.0; - one_zero = ones_2; - one_zero [1, 2] = 0.0; - flip_pos = matrix (0, rows = 2, cols = 2); - flip_neg = flip_pos; - flip_pos [1, 2] = 1; - flip_pos [2, 1] = 1; - flip_neg [1, 2] = -1; - flip_neg [2, 1] = 1; - - if (dist_type == 1 & link_type == 1) { # POWER DISTRIBUTION - y_mean = zeros_r; - if (link_power == 0.0) { - y_mean = exp (linear_terms); - y_mean_pow = y_mean ^ (1 - var_power); - w = y_mean_pow * y_mean; - g_Y = y_mean_pow * (Y - y_mean); - } else { if (link_power == 1.0) { - y_mean = linear_terms; - w = y_mean ^ (- var_power); - g_Y = w * (Y - y_mean); - } else { - y_mean = linear_terms ^ (1.0 / link_power); - c1 = (1 - var_power) / link_power - 1; - c2 = (2 - var_power) / link_power - 2; - g_Y = (linear_terms ^ c1) * (Y - y_mean) / link_power; - w = (linear_terms ^ c2) / (link_power ^ 2); - } }} - if (dist_type == 2 & link_type >= 1 & link_type <= 5) - { # BINOMIAL/BERNOULLI DISTRIBUTION - if (link_type == 1) { # BINOMIAL.POWER LINKS - if (link_power == 0.0) { # Binomial.log - vec1 = 1 / (exp (- linear_terms) - 1); - g_Y = Y [, 1] - Y [, 2] * vec1; - w = rowSums (Y) * vec1; - } else { # Binomial.nonlog - vec1 = zeros_r; - if (link_power == 0.5) { - vec1 = 1 / (1 - linear_terms ^ 2); - } else { if (sum (linear_terms < 0.0) == 0) { - vec1 = linear_terms ^ (- 2 + 1 / link_power) / (1 - linear_terms ^ (1 / link_power)); - } else {isNaN = 1;}} - # We want a "zero-protected" version of - # vec2 = Y [, 1] / linear_terms; - is_y_0 = ((Y [, 1]) == 0.0); - vec2 = (Y [, 1] + is_y_0) / (linear_terms * (1 - is_y_0) + is_y_0) - is_y_0; - g_Y = (vec2 - Y [, 2] * vec1 * linear_terms) / link_power; - w = rowSums (Y) * vec1 / link_power ^ 2; - } - } else { - is_LT_pos_infinite = (linear_terms == (1.0/0.0)); - is_LT_neg_infinite = (linear_terms == (-1.0/0.0)); - is_LT_infinite = is_LT_pos_infinite %*% one_zero + is_LT_neg_infinite %*% zero_one; - finite_linear_terms = replace (target = linear_terms, pattern = 1.0/0.0, replacement = 0); - finite_linear_terms = replace (target = finite_linear_terms, pattern = -1.0/0.0, replacement = 0); - if (link_type == 2) { # Binomial.logit - Y_prob = exp (finite_linear_terms) %*% one_zero + ones_r %*% zero_one; - Y_prob = Y_prob / (rowSums (Y_prob) %*% ones_2); - Y_prob = Y_prob * ((1.0 - rowSums (is_LT_infinite)) %*% ones_2) + is_LT_infinite; - g_Y = rowSums (Y * (Y_prob %*% flip_neg)); ### = y_residual; - w = rowSums (Y * (Y_prob %*% flip_pos) * Y_prob); ### = y_variance; - } else { if (link_type == 3) { # Binomial.probit - is_lt_pos = (linear_terms >= 0.0); - t_gp = 1.0 / (1.0 + abs (finite_linear_terms) * 0.231641888); # 0.231641888 = 0.3275911 / sqrt (2.0) - pt_gp = t_gp * ( 0.254829592 - + t_gp * (-0.284496736 # "Handbook of Mathematical Functions", ed. by M. Abramowitz and I.A. Stegun, - + t_gp * ( 1.421413741 # U.S. Nat-l Bureau of Standards, 10th print (Dec 1972), Sec. 7.1.26, p. 299 - + t_gp * (-1.453152027 - + t_gp * 1.061405429)))); - the_gauss_exp = exp (- (linear_terms ^ 2) / 2.0); - vec1 = 0.25 * pt_gp * (2 - the_gauss_exp * pt_gp); - vec2 = Y [, 1] - rowSums (Y) * is_lt_pos + the_gauss_exp * pt_gp * rowSums (Y) * (is_lt_pos - 0.5); - w = the_gauss_exp * (one_over_sqrt_two_pi ^ 2) * rowSums (Y) / vec1; - g_Y = one_over_sqrt_two_pi * vec2 / vec1; - } else { if (link_type == 4) { # Binomial.cloglog - the_exp = exp (linear_terms) - the_exp_exp = exp (- the_exp); - is_too_small = ((10000000 + the_exp) == 10000000); - the_exp_ratio = (1 - is_too_small) * (1 - the_exp_exp) / (the_exp + is_too_small) + is_too_small * (1 - the_exp / 2); - g_Y = (rowSums (Y) * the_exp_exp - Y [, 2]) / the_exp_ratio; - w = the_exp_exp * the_exp * rowSums (Y) / the_exp_ratio; - } else { if (link_type == 5) { # Binomial.cauchit - Y_prob = 0.5 + (atan (finite_linear_terms) %*% p_one_m_one) / 3.1415926535897932384626433832795; - Y_prob = Y_prob * ((1.0 - rowSums (is_LT_infinite)) %*% ones_2) + is_LT_infinite; - y_residual = Y [, 1] * Y_prob [, 2] - Y [, 2] * Y_prob [, 1]; - var_function = rowSums (Y) * Y_prob [, 1] * Y_prob [, 2]; - link_gradient_normalized = (1 + linear_terms ^ 2) * 3.1415926535897932384626433832795; - g_Y = rowSums (Y) * y_residual / (var_function * link_gradient_normalized); - w = (rowSums (Y) ^ 2) / (var_function * link_gradient_normalized ^ 2); - }}}} - } - } -} - - -glm_log_likelihood_part = function (Matrix[double] linear_terms, Matrix[double] Y, - int dist_type, double var_power, int link_type, double link_power) - return (double log_l, int isNaN) -{ - isNaN = 0; - log_l = 0.0; - num_records = nrow (Y); - zeros_r = matrix (0.0, rows = num_records, cols = 1); - - if (dist_type == 1 & link_type == 1) - { # POWER DISTRIBUTION - b_cumulant = zeros_r; - natural_parameters = zeros_r; - is_natural_parameter_log_zero = zeros_r; - if (var_power == 1.0 & link_power == 0.0) { # Poisson.log - b_cumulant = exp (linear_terms); - is_natural_parameter_log_zero = (linear_terms == -1.0/0.0); - natural_parameters = replace (target = linear_terms, pattern = -1.0/0.0, replacement = 0); - } else { if (var_power == 1.0 & link_power == 1.0) { # Poisson.id - if (sum (linear_terms < 0.0) == 0) { - b_cumulant = linear_terms; - is_natural_parameter_log_zero = (linear_terms == 0.0); - natural_parameters = log (linear_terms + is_natural_parameter_log_zero); - } else {isNaN = 1;} - } else { if (var_power == 1.0 & link_power == 0.5) { # Poisson.sqrt - if (sum (linear_terms < 0.0) == 0) { - b_cumulant = linear_terms ^ 2; - is_natural_parameter_log_zero = (linear_terms == 0.0); - natural_parameters = 2.0 * log (linear_terms + is_natural_parameter_log_zero); - } else {isNaN = 1;} - } else { if (var_power == 1.0 & link_power > 0.0) { # Poisson.power_nonlog, pos - if (sum (linear_terms < 0.0) == 0) { - is_natural_parameter_log_zero = (linear_terms == 0.0); - b_cumulant = (linear_terms + is_natural_parameter_log_zero) ^ (1.0 / link_power) - is_natural_parameter_log_zero; - natural_parameters = log (linear_terms + is_natural_parameter_log_zero) / link_power; - } else {isNaN = 1;} - } else { if (var_power == 1.0) { # Poisson.power_nonlog, neg - if (sum (linear_terms <= 0.0) == 0) { - b_cumulant = linear_terms ^ (1.0 / link_power); - natural_parameters = log (linear_terms) / link_power; - } else {isNaN = 1;} - } else { if (var_power == 2.0 & link_power == -1.0) { # Gamma.inverse - if (sum (linear_terms <= 0.0) == 0) { - b_cumulant = - log (linear_terms); - natural_parameters = - linear_terms; - } else {isNaN = 1;} - } else { if (var_power == 2.0 & link_power == 1.0) { # Gamma.id - if (sum (linear_terms <= 0.0) == 0) { - b_cumulant = log (linear_terms); - natural_parameters = - 1.0 / linear_terms; - } else {isNaN = 1;} - } else { if (var_power == 2.0 & link_power == 0.0) { # Gamma.log - b_cumulant = linear_terms; - natural_parameters = - exp (- linear_terms); - } else { if (var_power == 2.0) { # Gamma.power_nonlog - if (sum (linear_terms <= 0.0) == 0) { - b_cumulant = log (linear_terms) / link_power; - natural_parameters = - linear_terms ^ (- 1.0 / link_power); - } else {isNaN = 1;} - } else { if (link_power == 0.0) { # PowerDist.log - natural_parameters = exp (linear_terms * (1.0 - var_power)) / (1.0 - var_power); - b_cumulant = exp (linear_terms * (2.0 - var_power)) / (2.0 - var_power); - } else { # PowerDist.power_nonlog - if (-2 * link_power == 1.0 - var_power) { - natural_parameters = 1.0 / (linear_terms ^ 2) / (1.0 - var_power); - } else { if (-1 * link_power == 1.0 - var_power) { - natural_parameters = 1.0 / linear_terms / (1.0 - var_power); - } else { if ( link_power == 1.0 - var_power) { - natural_parameters = linear_terms / (1.0 - var_power); - } else { if ( 2 * link_power == 1.0 - var_power) { - natural_parameters = linear_terms ^ 2 / (1.0 - var_power); - } else { - if (sum (linear_terms <= 0.0) == 0) { - power = (1.0 - var_power) / link_power; - natural_parameters = (linear_terms ^ power) / (1.0 - var_power); - } else {isNaN = 1;} - }}}} - if (-2 * link_power == 2.0 - var_power) { - b_cumulant = 1.0 / (linear_terms ^ 2) / (2.0 - var_power); - } else { if (-1 * link_power == 2.0 - var_power) { - b_cumulant = 1.0 / linear_terms / (2.0 - var_power); - } else { if ( link_power == 2.0 - var_power) { - b_cumulant = linear_terms / (2.0 - var_power); - } else { if ( 2 * link_power == 2.0 - var_power) { - b_cumulant = linear_terms ^ 2 / (2.0 - var_power); - } else { - if (sum (linear_terms <= 0.0) == 0) { - power = (2.0 - var_power) / link_power; - b_cumulant = (linear_terms ^ power) / (2.0 - var_power); - } else {isNaN = 1;} - }}}} - }}}}} }}}}} - if (sum (is_natural_parameter_log_zero * abs (Y)) > 0.0) { - log_l = -1.0 / 0.0; - isNaN = 1; - } - if (isNaN == 0) - { - log_l = sum (Y * natural_parameters - b_cumulant); - if (log_l != log_l | (log_l == log_l + 1.0 & log_l == log_l * 2.0)) { - log_l = -1.0 / 0.0; - isNaN = 1; - } } } - - if (dist_type == 2 & link_type >= 1 & link_type <= 5) - { # BINOMIAL/BERNOULLI DISTRIBUTION - - [Y_prob, isNaN] = binomial_probability_two_column (linear_terms, link_type, link_power); - - if (isNaN == 0) { - does_prob_contradict = (Y_prob <= 0.0); - if (sum (does_prob_contradict * abs (Y)) == 0.0) { - log_l = sum (Y * log (Y_prob * (1 - does_prob_contradict) + does_prob_contradict)); - if (log_l != log_l | (log_l == log_l + 1.0 & log_l == log_l * 2.0)) { - isNaN = 1; - } - } else { - log_l = -1.0 / 0.0; - isNaN = 1; - } } } - - if (isNaN == 1) { - log_l = - 1.0 / 0.0; - } -} - - - -binomial_probability_two_column = - function (Matrix[double] linear_terms, int link_type, double link_power) - return (Matrix[double] Y_prob, int isNaN) -{ - isNaN = 0; - num_records = nrow (linear_terms); - - # Define some auxiliary matrices - - ones_2 = matrix (1.0, rows = 1, cols = 2); - p_one_m_one = ones_2; - p_one_m_one [1, 2] = -1.0; - m_one_p_one = ones_2; - m_one_p_one [1, 1] = -1.0; - zero_one = ones_2; - zero_one [1, 1] = 0.0; - one_zero = ones_2; - one_zero [1, 2] = 0.0; - - zeros_r = matrix (0.0, rows = num_records, cols = 1); - ones_r = 1.0 + zeros_r; - - # Begin the function body - - Y_prob = zeros_r %*% ones_2; - if (link_type == 1) { # Binomial.power - if (link_power == 0.0) { # Binomial.log - Y_prob = exp (linear_terms) %*% p_one_m_one + ones_r %*% zero_one; - } else { if (link_power == 0.5) { # Binomial.sqrt - Y_prob = (linear_terms ^ 2) %*% p_one_m_one + ones_r %*% zero_one; - } else { # Binomial.power_nonlog - if (sum (linear_terms < 0.0) == 0) { - Y_prob = (linear_terms ^ (1.0 / link_power)) %*% p_one_m_one + ones_r %*% zero_one; - } else {isNaN = 1;} - }} - } else { # Binomial.non_power - is_LT_pos_infinite = (linear_terms == (1.0/0.0)); - is_LT_neg_infinite = (linear_terms == (-1.0/0.0)); - is_LT_infinite = is_LT_pos_infinite %*% one_zero + is_LT_neg_infinite %*% zero_one; - finite_linear_terms = replace (target = linear_terms, pattern = 1.0/0.0, replacement = 0); - finite_linear_terms = replace (target = finite_linear_terms, pattern = -1.0/0.0, replacement = 0); - if (link_type == 2) { # Binomial.logit - Y_prob = exp (finite_linear_terms) %*% one_zero + ones_r %*% zero_one; - Y_prob = Y_prob / (rowSums (Y_prob) %*% ones_2); - } else { if (link_type == 3) { # Binomial.probit - lt_pos_neg = (finite_linear_terms >= 0.0) %*% p_one_m_one + ones_r %*% zero_one; - t_gp = 1.0 / (1.0 + abs (finite_linear_terms) * 0.231641888); # 0.231641888 = 0.3275911 / sqrt (2.0) - pt_gp = t_gp * ( 0.254829592 - + t_gp * (-0.284496736 # "Handbook of Mathematical Functions", ed. by M. Abramowitz and I.A. Stegun, - + t_gp * ( 1.421413741 # U.S. Nat-l Bureau of Standards, 10th print (Dec 1972), Sec. 7.1.26, p. 299 - + t_gp * (-1.453152027 - + t_gp * 1.061405429)))); - the_gauss_exp = exp (- (finite_linear_terms ^ 2) / 2.0); - Y_prob = lt_pos_neg + ((the_gauss_exp * pt_gp) %*% ones_2) * (0.5 - lt_pos_neg); - } else { if (link_type == 4) { # Binomial.cloglog - the_exp = exp (finite_linear_terms); - the_exp_exp = exp (- the_exp); - is_too_small = ((10000000 + the_exp) == 10000000); - Y_prob [, 1] = (1 - is_too_small) * (1 - the_exp_exp) + is_too_small * the_exp * (1 - the_exp / 2); - Y_prob [, 2] = the_exp_exp; - } else { if (link_type == 5) { # Binomial.cauchit - Y_prob = 0.5 + (atan (finite_linear_terms) %*% p_one_m_one) / 3.1415926535897932384626433832795; - } else { - isNaN = 1; - }}}} - Y_prob = Y_prob * ((1.0 - rowSums (is_LT_infinite)) %*% ones_2) + is_LT_infinite; -} } - - -# THE CG-STEIHAUG PROCEDURE SCRIPT - -# Apply Conjugate Gradient - Steihaug algorithm in order to approximately minimize -# 0.5 z^T (X^T diag(w) X + diag (lambda)) z + (g + lambda * beta)^T z -# under constraint: ||z|| <= trust_delta. -# See Alg. 7.2 on p. 171 of "Numerical Optimization" 2nd ed. by Nocedal and Wright -# IN THE ABOVE, "X" IS UNDERSTOOD TO BE "X %*% (SHIFT/SCALE TRANSFORM)"; this transform -# is given separately because sparse "X" may become dense after applying the transform. -# -get_CG_Steihaug_point = - function (Matrix[double] X, Matrix[double] scale_X, Matrix[double] shift_X, Matrix[double] w, - Matrix[double] g, Matrix[double] beta, Matrix[double] lambda, double trust_delta, int max_iter_CG) - return (Matrix[double] z, double neg_log_l_change, int i_CG, int reached_trust_boundary) -{ - trust_delta_sq = trust_delta ^ 2; - size_CG = nrow (g); - z = matrix (0.0, rows = size_CG, cols = 1); - neg_log_l_change = 0.0; - reached_trust_boundary = 0; - g_reg = g + lambda * beta; - r_CG = g_reg; - p_CG = -r_CG; - rr_CG = sum(r_CG * r_CG); - eps_CG = rr_CG * min (0.25, sqrt (rr_CG)); - converged_CG = 0; - if (rr_CG < eps_CG) { - converged_CG = 1; - } - - max_iteration_CG = max_iter_CG; - if (max_iteration_CG <= 0) { - max_iteration_CG = size_CG; - } - i_CG = 0; - while (converged_CG == 0) - { - i_CG = i_CG + 1; - ssX_p_CG = diag (scale_X) %*% p_CG; - ssX_p_CG [size_CG, ] = ssX_p_CG [size_CG, ] + t(shift_X) %*% p_CG; - temp_CG = t(X) %*% (w * (X %*% ssX_p_CG)); - q_CG = (lambda * p_CG) + diag (scale_X) %*% temp_CG + shift_X %*% temp_CG [size_CG, ]; - pq_CG = sum (p_CG * q_CG); - if (pq_CG <= 0) { - pp_CG = sum (p_CG * p_CG); - if (pp_CG > 0) { - [z, neg_log_l_change] = - get_trust_boundary_point (g_reg, z, p_CG, q_CG, r_CG, pp_CG, pq_CG, trust_delta_sq); - reached_trust_boundary = 1; - } else { - neg_log_l_change = 0.5 * sum (z * (r_CG + g_reg)); - } - converged_CG = 1; - } - if (converged_CG == 0) { - alpha_CG = rr_CG / pq_CG; - new_z = z + alpha_CG * p_CG; - if (sum(new_z * new_z) >= trust_delta_sq) { - pp_CG = sum (p_CG * p_CG); - [z, neg_log_l_change] = - get_trust_boundary_point (g_reg, z, p_CG, q_CG, r_CG, pp_CG, pq_CG, trust_delta_sq); - reached_trust_boundary = 1; - converged_CG = 1; - } - if (converged_CG == 0) { - z = new_z; - old_rr_CG = rr_CG; - r_CG = r_CG + alpha_CG * q_CG; - rr_CG = sum(r_CG * r_CG); - if (i_CG == max_iteration_CG | rr_CG < eps_CG) { - neg_log_l_change = 0.5 * sum (z * (r_CG + g_reg)); - reached_trust_boundary = 0; - converged_CG = 1; - } - if (converged_CG == 0) { - p_CG = -r_CG + (rr_CG / old_rr_CG) * p_CG; -} } } } } - - -# An auxiliary function used twice inside the CG-STEIHAUG loop: -get_trust_boundary_point = - function (Matrix[double] g, Matrix[double] z, Matrix[double] p, - Matrix[double] q, Matrix[double] r, double pp, double pq, - double trust_delta_sq) - return (Matrix[double] new_z, double f_change) -{ - zz = sum (z * z); pz = sum (p * z); - sq_root_d = sqrt (pz * pz - pp * (zz - trust_delta_sq)); - tau_1 = (- pz + sq_root_d) / pp; - tau_2 = (- pz - sq_root_d) / pp; - zq = sum (z * q); gp = sum (g * p); - f_extra = 0.5 * sum (z * (r + g)); - f_change_1 = f_extra + (0.5 * tau_1 * pq + zq + gp) * tau_1; - f_change_2 = f_extra + (0.5 * tau_2 * pq + zq + gp) * tau_2; - if (f_change_1 < f_change_2) { - new_z = z + (tau_1 * p); - f_change = f_change_1; - } - else { - new_z = z + (tau_2 * p); - f_change = f_change_2; - } -} - - -# Computes vector w such that ||X %*% w - 1|| -> MIN given avg(X %*% w) = 1 -# We find z_LS such that ||X %*% z_LS - 1|| -> MIN unconditionally, then scale -# it to compute w = c * z_LS such that sum(X %*% w) = nrow(X). -straightenX = - function (Matrix[double] X, double eps, int max_iter_CG) - return (Matrix[double] w) -{ - w_X = t(colSums(X)); - lambda_LS = 0.000001 * sum(X ^ 2) / ncol(X); - eps_LS = eps * nrow(X); - - # BEGIN LEAST SQUARES - - r_LS = - w_X; - z_LS = matrix (0.0, rows = ncol(X), cols = 1); - p_LS = - r_LS; - norm_r2_LS = sum (r_LS ^ 2); - i_LS = 0; - while (i_LS < max_iter_CG & i_LS < ncol(X) & norm_r2_LS >= eps_LS) - { - q_LS = t(X) %*% X %*% p_LS; - q_LS = q_LS + lambda_LS * p_LS; - alpha_LS = norm_r2_LS / sum (p_LS * q_LS); - z_LS = z_LS + alpha_LS * p_LS; - old_norm_r2_LS = norm_r2_LS; - r_LS = r_LS + alpha_LS * q_LS; - norm_r2_LS = sum (r_LS ^ 2); - p_LS = -r_LS + (norm_r2_LS / old_norm_r2_LS) * p_LS; - i_LS = i_LS + 1; - } - - # END LEAST SQUARES - - w = (nrow(X) / sum (w_X * z_LS)) * z_LS; -} - - -round_to_print = function (double x_to_truncate) -return (double mantissa, int eee) -{ - mantissa = 1.0; - eee = 0; - positive_infinity = 1.0 / 0.0; - x = abs (x_to_truncate); - if (x != x / 2.0) { - log_ten = log (10.0); - d_eee = round (log (x) / log_ten - 0.5); - mantissa = round (x * exp (log_ten * (4.0 - d_eee))) / 10000; - if (mantissa == 10.0) { - mantissa = 1.0; - d_eee = d_eee + 1; - } - if (x_to_truncate < 0.0) { - mantissa = - mantissa; - } - eee = 0; - pow_two = 1; - res_eee = abs (d_eee); - while (res_eee != 0.0) { - new_res_eee = round (res_eee / 2.0 - 0.3); - if (new_res_eee * 2.0 < res_eee) { - eee = eee + pow_two; - } - res_eee = new_res_eee; - pow_two = 2 * pow_two; - } - if (d_eee < 0.0) { - eee = - eee; - } - } else { mantissa = x_to_truncate; } -}
