GPU implementation of AFT survival objective and metric (#5714)
* Add interval accuracy * De-virtualize AFT functions * Lint * Refactor AFT metric using GPU-CPU reducer * Fix R build * Fix build on Windows * Fix copyright header * Clang-tidy * Fix crashing demo * Fix typos in comment; explain GPU ID * Remove unnecessary #include * Add C++ test for interval accuracy * Fix a bug in accuracy metric: use log pred * Refactor AFT objective using GPU-CPU Transform * Lint * Fix lint * Use Ninja to speed up build * Use time, not /usr/bin/time * Add cpu_build worker class, with concurrency = 1 * Use concurrency = 1 only for CUDA build * concurrency = 1 for clang-tidy * Address reviewer's feedback * Update link to AFT paper
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Philip Hyunsu Cho
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/*!
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* Copyright 2020 by Contributors
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* Copyright 2019-2020 by Contributors
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* \file probability_distribution.h
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* \brief Implementation of a few useful probability distributions
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* \author Avinash Barnwal and Hyunsu Cho
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@@ -8,85 +8,115 @@
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#ifndef XGBOOST_COMMON_PROBABILITY_DISTRIBUTION_H_
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#define XGBOOST_COMMON_PROBABILITY_DISTRIBUTION_H_
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#include <cmath>
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namespace xgboost {
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namespace common {
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namespace probability_constant {
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#ifndef __CUDACC__
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using std::exp;
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using std::sqrt;
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using std::isinf;
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using std::isnan;
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#endif // __CUDACC__
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/*! \brief Constant PI */
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const double kPI = 3.14159265358979323846;
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constexpr double kPI = 3.14159265358979323846;
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/*! \brief The Euler-Mascheroni_constant */
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const double kEulerMascheroni = 0.57721566490153286060651209008240243104215933593992;
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} // namespace probability_constant
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constexpr double kEulerMascheroni = 0.57721566490153286060651209008240243104215933593992;
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/*! \brief Enum encoding possible choices of probability distribution */
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enum class ProbabilityDistributionType : int {
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kNormal = 0, kLogistic = 1, kExtreme = 2
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};
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/*! \brief Interface for a probability distribution */
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class ProbabilityDistribution {
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public:
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/*!
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* \brief Evaluate Probability Density Function (PDF) at a particular point
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* \param z point at which to evaluate PDF
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* \return Value of PDF evaluated
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*/
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virtual double PDF(double z) = 0;
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/*!
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* \brief Evaluate Cumulative Distribution Function (CDF) at a particular point
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* \param z point at which to evaluate CDF
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* \return Value of CDF evaluated
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*/
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virtual double CDF(double z) = 0;
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/*!
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* \brief Evaluate first derivative of PDF at a particular point
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* \param z point at which to evaluate first derivative of PDF
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* \return Value of first derivative of PDF evaluated
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*/
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virtual double GradPDF(double z) = 0;
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/*!
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* \brief Evaluate second derivative of PDF at a particular point
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* \param z point at which to evaluate second derivative of PDF
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* \return Value of second derivative of PDF evaluated
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*/
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virtual double HessPDF(double z) = 0;
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struct NormalDistribution {
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XGBOOST_DEVICE static double PDF(double z) {
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return exp(-z * z / 2.0) / sqrt(2.0 * kPI);
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}
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/*!
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* \brief Factory function to instantiate a new probability distribution object
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* \param dist kind of probability distribution
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* \return Reference to the newly created probability distribution object
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*/
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static ProbabilityDistribution* Create(ProbabilityDistributionType dist);
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virtual ~ProbabilityDistribution() = default;
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XGBOOST_DEVICE static double CDF(double z) {
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return 0.5 * (1 + erf(z / sqrt(2.0)));
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}
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XGBOOST_DEVICE static double GradPDF(double z) {
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return -z * PDF(z);
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}
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XGBOOST_DEVICE static double HessPDF(double z) {
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return (z * z - 1.0) * PDF(z);
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}
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XGBOOST_DEVICE static ProbabilityDistributionType Type() {
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return ProbabilityDistributionType::kNormal;
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}
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};
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/*! \brief The (standard) normal distribution */
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class NormalDist : public ProbabilityDistribution {
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public:
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double PDF(double z) override;
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double CDF(double z) override;
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double GradPDF(double z) override;
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double HessPDF(double z) override;
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struct LogisticDistribution {
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XGBOOST_DEVICE static double PDF(double z) {
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const double w = exp(z);
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const double sqrt_denominator = 1 + w;
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if (isinf(w) || isinf(w * w)) {
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return 0.0;
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} else {
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return w / (sqrt_denominator * sqrt_denominator);
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}
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}
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XGBOOST_DEVICE static double CDF(double z) {
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const double w = exp(z);
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return isinf(w) ? 1.0 : (w / (1 + w));
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}
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XGBOOST_DEVICE static double GradPDF(double z) {
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const double w = exp(z);
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return isinf(w) ? 0.0 : (PDF(z) * (1 - w) / (1 + w));
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}
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XGBOOST_DEVICE static double HessPDF(double z) {
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const double w = exp(z);
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if (isinf(w) || isinf(w * w)) {
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return 0.0;
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} else {
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return PDF(z) * (w * w - 4 * w + 1) / ((1 + w) * (1 + w));
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}
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}
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XGBOOST_DEVICE static ProbabilityDistributionType Type() {
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return ProbabilityDistributionType::kLogistic;
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}
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};
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/*! \brief The (standard) logistic distribution */
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class LogisticDist : public ProbabilityDistribution {
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public:
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double PDF(double z) override;
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double CDF(double z) override;
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double GradPDF(double z) override;
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double HessPDF(double z) override;
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};
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struct ExtremeDistribution {
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XGBOOST_DEVICE static double PDF(double z) {
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const double w = exp(z);
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return isinf(w) ? 0.0 : (w * exp(-w));
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}
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/*! \brief The extreme distribution, also known as the Gumbel (minimum) distribution */
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class ExtremeDist : public ProbabilityDistribution {
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public:
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double PDF(double z) override;
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double CDF(double z) override;
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double GradPDF(double z) override;
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double HessPDF(double z) override;
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XGBOOST_DEVICE static double CDF(double z) {
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const double w = exp(z);
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return 1 - exp(-w);
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}
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XGBOOST_DEVICE static double GradPDF(double z) {
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const double w = exp(z);
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return isinf(w) ? 0.0 : ((1 - w) * PDF(z));
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}
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XGBOOST_DEVICE static double HessPDF(double z) {
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const double w = exp(z);
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if (isinf(w) || isinf(w * w)) {
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return 0.0;
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} else {
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return (w * w - 3 * w + 1) * PDF(z);
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}
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}
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XGBOOST_DEVICE static ProbabilityDistributionType Type() {
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return ProbabilityDistributionType::kExtreme;
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}
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};
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} // namespace common
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