348 lines
12 KiB
C++
348 lines
12 KiB
C++
/*!
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* Copyright 2019-2020 by Contributors
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* \file survival_util.h
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* \brief Utility functions, useful for implementing objective and metric functions for survival
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* analysis
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* \author Avinash Barnwal, Hyunsu Cho and Toby Hocking
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*/
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#ifndef XGBOOST_COMMON_SURVIVAL_UTIL_H_
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#define XGBOOST_COMMON_SURVIVAL_UTIL_H_
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/*
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* For the derivation of the loss, gradient, and hessian for the Accelerated Failure Time model,
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* refer to the paper "Survival regression with accelerated failure time model in XGBoost"
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* at https://arxiv.org/abs/2006.04920.
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*/
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#include <xgboost/parameter.h>
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#include <memory>
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#include <algorithm>
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#include <limits>
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#include "probability_distribution.h"
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DECLARE_FIELD_ENUM_CLASS(xgboost::common::ProbabilityDistributionType);
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namespace xgboost {
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namespace common {
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#ifndef __CUDACC__
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using std::log;
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using std::fmax;
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#endif // __CUDACC__
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enum class CensoringType : uint8_t {
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kUncensored, kRightCensored, kLeftCensored, kIntervalCensored
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};
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namespace aft {
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// Allowable range for gradient and hessian. Used for regularization
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constexpr double kMinGradient = -15.0;
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constexpr double kMaxGradient = 15.0;
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constexpr double kMinHessian = 1e-16; // Ensure that no data point gets zero hessian
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constexpr double kMaxHessian = 15.0;
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constexpr double kEps = 1e-12; // A denominator in a fraction should not be too small
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// Clip (limit) x to fit range [x_min, x_max].
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// If x < x_min, return x_min; if x > x_max, return x_max; if x_min <= x <= x_max, return x.
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// This function assumes x_min < x_max; behavior is undefined if this assumption does not hold.
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XGBOOST_DEVICE
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inline double Clip(double x, double x_min, double x_max) {
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if (x < x_min) {
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return x_min;
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}
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if (x > x_max) {
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return x_max;
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}
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return x;
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}
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template<typename Distribution>
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XGBOOST_DEVICE inline double
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GetLimitGradAtInfPred(CensoringType censor_type, bool sign, double sigma);
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template<typename Distribution>
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XGBOOST_DEVICE inline double
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GetLimitHessAtInfPred(CensoringType censor_type, bool sign, double sigma);
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} // namespace aft
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/*! \brief Parameter structure for AFT loss and metric */
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struct AFTParam : public XGBoostParameter<AFTParam> {
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/*! \brief Choice of probability distribution for the noise term in AFT */
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ProbabilityDistributionType aft_loss_distribution;
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/*! \brief Scaling factor to be applied to the distribution */
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float aft_loss_distribution_scale;
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DMLC_DECLARE_PARAMETER(AFTParam) {
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DMLC_DECLARE_FIELD(aft_loss_distribution)
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.set_default(ProbabilityDistributionType::kNormal)
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.add_enum("normal", ProbabilityDistributionType::kNormal)
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.add_enum("logistic", ProbabilityDistributionType::kLogistic)
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.add_enum("extreme", ProbabilityDistributionType::kExtreme)
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.describe("Choice of distribution for the noise term in "
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"Accelerated Failure Time model");
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DMLC_DECLARE_FIELD(aft_loss_distribution_scale)
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.set_default(1.0f)
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.describe("Scaling factor used to scale the distribution in "
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"Accelerated Failure Time model");
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}
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};
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/*! \brief The AFT loss function */
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template<typename Distribution>
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struct AFTLoss {
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XGBOOST_DEVICE inline static
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double Loss(double y_lower, double y_upper, double y_pred, double sigma) {
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const double log_y_lower = log(y_lower);
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const double log_y_upper = log(y_upper);
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double cost;
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if (y_lower == y_upper) { // uncensored
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const double z = (log_y_lower - y_pred) / sigma;
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const double pdf = Distribution::PDF(z);
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// Regularize the denominator with eps, to avoid INF or NAN
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cost = -log(fmax(pdf / (sigma * y_lower), aft::kEps));
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} else { // censored; now check what type of censorship we have
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double z_u, z_l, cdf_u, cdf_l;
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if (isinf(y_upper)) { // right-censored
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cdf_u = 1;
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} else { // left-censored or interval-censored
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z_u = (log_y_upper - y_pred) / sigma;
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cdf_u = Distribution::CDF(z_u);
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}
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if (y_lower <= 0.0) { // left-censored
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cdf_l = 0;
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} else { // right-censored or interval-censored
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z_l = (log_y_lower - y_pred) / sigma;
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cdf_l = Distribution::CDF(z_l);
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}
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// Regularize the denominator with eps, to avoid INF or NAN
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cost = -log(fmax(cdf_u - cdf_l, aft::kEps));
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}
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return cost;
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}
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XGBOOST_DEVICE inline static
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double Gradient(double y_lower, double y_upper, double y_pred, double sigma) {
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const double log_y_lower = log(y_lower);
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const double log_y_upper = log(y_upper);
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double numerator, denominator, gradient; // numerator and denominator of gradient
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CensoringType censor_type;
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bool z_sign; // sign of z-score
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if (y_lower == y_upper) { // uncensored
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const double z = (log_y_lower - y_pred) / sigma;
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const double pdf = Distribution::PDF(z);
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const double grad_pdf = Distribution::GradPDF(z);
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censor_type = CensoringType::kUncensored;
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numerator = grad_pdf;
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denominator = sigma * pdf;
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z_sign = (z > 0);
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} else { // censored; now check what type of censorship we have
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double z_u = 0.0, z_l = 0.0, pdf_u, pdf_l, cdf_u, cdf_l;
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censor_type = CensoringType::kIntervalCensored;
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if (isinf(y_upper)) { // right-censored
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pdf_u = 0;
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cdf_u = 1;
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censor_type = CensoringType::kRightCensored;
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} else { // interval-censored or left-censored
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z_u = (log_y_upper - y_pred) / sigma;
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pdf_u = Distribution::PDF(z_u);
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cdf_u = Distribution::CDF(z_u);
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}
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if (y_lower <= 0.0) { // left-censored
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pdf_l = 0;
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cdf_l = 0;
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censor_type = CensoringType::kLeftCensored;
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} else { // interval-censored or right-censored
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z_l = (log_y_lower - y_pred) / sigma;
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pdf_l = Distribution::PDF(z_l);
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cdf_l = Distribution::CDF(z_l);
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}
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z_sign = (z_u > 0 || z_l > 0);
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numerator = pdf_u - pdf_l;
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denominator = sigma * (cdf_u - cdf_l);
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}
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gradient = numerator / denominator;
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if (denominator < aft::kEps && (isnan(gradient) || isinf(gradient))) {
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gradient = aft::GetLimitGradAtInfPred<Distribution>(censor_type, z_sign, sigma);
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}
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return aft::Clip(gradient, aft::kMinGradient, aft::kMaxGradient);
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}
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XGBOOST_DEVICE inline static
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double Hessian(double y_lower, double y_upper, double y_pred, double sigma) {
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const double log_y_lower = log(y_lower);
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const double log_y_upper = log(y_upper);
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double numerator, denominator, hessian; // numerator and denominator of hessian
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CensoringType censor_type;
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bool z_sign; // sign of z-score
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if (y_lower == y_upper) { // uncensored
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const double z = (log_y_lower - y_pred) / sigma;
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const double pdf = Distribution::PDF(z);
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const double grad_pdf = Distribution::GradPDF(z);
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const double hess_pdf = Distribution::HessPDF(z);
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censor_type = CensoringType::kUncensored;
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numerator = -(pdf * hess_pdf - grad_pdf * grad_pdf);
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denominator = sigma * sigma * pdf * pdf;
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z_sign = (z > 0);
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} else { // censored; now check what type of censorship we have
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double z_u = 0.0, z_l = 0.0, grad_pdf_u, grad_pdf_l, pdf_u, pdf_l, cdf_u, cdf_l;
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censor_type = CensoringType::kIntervalCensored;
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if (isinf(y_upper)) { // right-censored
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pdf_u = 0;
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cdf_u = 1;
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grad_pdf_u = 0;
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censor_type = CensoringType::kRightCensored;
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} else { // interval-censored or left-censored
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z_u = (log_y_upper - y_pred) / sigma;
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pdf_u = Distribution::PDF(z_u);
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cdf_u = Distribution::CDF(z_u);
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grad_pdf_u = Distribution::GradPDF(z_u);
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}
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if (y_lower <= 0.0) { // left-censored
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pdf_l = 0;
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cdf_l = 0;
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grad_pdf_l = 0;
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censor_type = CensoringType::kLeftCensored;
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} else { // interval-censored or right-censored
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z_l = (log_y_lower - y_pred) / sigma;
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pdf_l = Distribution::PDF(z_l);
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cdf_l = Distribution::CDF(z_l);
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grad_pdf_l = Distribution::GradPDF(z_l);
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}
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const double cdf_diff = cdf_u - cdf_l;
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const double pdf_diff = pdf_u - pdf_l;
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const double grad_diff = grad_pdf_u - grad_pdf_l;
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const double sqrt_denominator = sigma * cdf_diff;
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z_sign = (z_u > 0 || z_l > 0);
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numerator = -(cdf_diff * grad_diff - pdf_diff * pdf_diff);
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denominator = sqrt_denominator * sqrt_denominator;
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}
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hessian = numerator / denominator;
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if (denominator < aft::kEps && (isnan(hessian) || isinf(hessian))) {
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hessian = aft::GetLimitHessAtInfPred<Distribution>(censor_type, z_sign, sigma);
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}
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return aft::Clip(hessian, aft::kMinHessian, aft::kMaxHessian);
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}
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};
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namespace aft {
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template <>
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XGBOOST_DEVICE inline double
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GetLimitGradAtInfPred<NormalDistribution>(CensoringType censor_type, bool sign, double sigma) {
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// Remove unused parameter compiler warning.
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(void) sigma;
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switch (censor_type) {
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case CensoringType::kUncensored:
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return sign ? kMinGradient : kMaxGradient;
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case CensoringType::kRightCensored:
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return sign ? kMinGradient : 0.0;
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case CensoringType::kLeftCensored:
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return sign ? 0.0 : kMaxGradient;
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case CensoringType::kIntervalCensored:
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return sign ? kMinGradient : kMaxGradient;
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}
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return std::numeric_limits<double>::quiet_NaN();
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}
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template <>
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XGBOOST_DEVICE inline double
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GetLimitHessAtInfPred<NormalDistribution>(CensoringType censor_type, bool sign, double sigma) {
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switch (censor_type) {
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case CensoringType::kUncensored:
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return 1.0 / (sigma * sigma);
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case CensoringType::kRightCensored:
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return sign ? (1.0 / (sigma * sigma)) : kMinHessian;
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case CensoringType::kLeftCensored:
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return sign ? kMinHessian : (1.0 / (sigma * sigma));
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case CensoringType::kIntervalCensored:
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return 1.0 / (sigma * sigma);
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}
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return std::numeric_limits<double>::quiet_NaN();
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}
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template <>
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XGBOOST_DEVICE inline double
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GetLimitGradAtInfPred<LogisticDistribution>(CensoringType censor_type, bool sign, double sigma) {
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switch (censor_type) {
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case CensoringType::kUncensored:
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return sign ? (-1.0 / sigma) : (1.0 / sigma);
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case CensoringType::kRightCensored:
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return sign ? (-1.0 / sigma) : 0.0;
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case CensoringType::kLeftCensored:
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return sign ? 0.0 : (1.0 / sigma);
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case CensoringType::kIntervalCensored:
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return sign ? (-1.0 / sigma) : (1.0 / sigma);
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}
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return std::numeric_limits<double>::quiet_NaN();
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}
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template <>
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XGBOOST_DEVICE inline double
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GetLimitHessAtInfPred<LogisticDistribution>(CensoringType censor_type, bool sign, double sigma) {
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// Remove unused parameter compiler warning.
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(void) sign;
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(void) sigma;
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switch (censor_type) {
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case CensoringType::kUncensored:
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case CensoringType::kRightCensored:
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case CensoringType::kLeftCensored:
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case CensoringType::kIntervalCensored:
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return kMinHessian;
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}
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return std::numeric_limits<double>::quiet_NaN();
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}
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template <>
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XGBOOST_DEVICE inline double
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GetLimitGradAtInfPred<ExtremeDistribution>(CensoringType censor_type, bool sign, double sigma) {
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switch (censor_type) {
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case CensoringType::kUncensored:
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return sign ? kMinGradient : (1.0 / sigma);
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case CensoringType::kRightCensored:
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return sign ? kMinGradient : 0.0;
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case CensoringType::kLeftCensored:
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return sign ? 0.0 : (1.0 / sigma);
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case CensoringType::kIntervalCensored:
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return sign ? kMinGradient : (1.0 / sigma);
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}
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return std::numeric_limits<double>::quiet_NaN();
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}
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template <>
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XGBOOST_DEVICE inline double
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GetLimitHessAtInfPred<ExtremeDistribution>(CensoringType censor_type, bool sign, double sigma) {
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// Remove unused parameter compiler warning.
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(void) sigma;
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switch (censor_type) {
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case CensoringType::kUncensored:
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case CensoringType::kRightCensored:
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return sign ? kMaxHessian : kMinHessian;
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case CensoringType::kLeftCensored:
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return kMinHessian;
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case CensoringType::kIntervalCensored:
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return sign ? kMaxHessian : kMinHessian;
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}
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return std::numeric_limits<double>::quiet_NaN();
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}
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} // namespace aft
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} // namespace common
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} // namespace xgboost
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#endif // XGBOOST_COMMON_SURVIVAL_UTIL_H_
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