Add Accelerated Failure Time loss for survival analysis task (#4763)

* [WIP] Add lower and upper bounds on the label for survival analysis

* Update test MetaInfo.SaveLoadBinary to account for extra two fields

* Don't clear qids_ for version 2 of MetaInfo

* Add SetInfo() and GetInfo() method for lower and upper bounds

* changes to aft

* Add parameter class for AFT; use enum's to represent distribution and event type

* Add AFT metric

* changes to neg grad to grad

* changes to binomial loss

* changes to overflow

* changes to eps

* changes to code refactoring

* changes to code refactoring

* changes to code refactoring

* Re-factor survival analysis

* Remove aft namespace

* Move function bodies out of AFTNormal and AFTLogistic, to reduce clutter

* Move function bodies out of AFTLoss, to reduce clutter

* Use smart pointer to store AFTDistribution and AFTLoss

* Rename AFTNoiseDistribution enum to AFTDistributionType for clarity

The enum class was not a distribution itself but a distribution type

* Add AFTDistribution::Create() method for convenience

* changes to extreme distribution

* changes to extreme distribution

* changes to extreme

* changes to extreme distribution

* changes to left censored

* deleted cout

* changes to x,mu and sd and code refactoring

* changes to print

* changes to hessian formula in censored and uncensored

* changes to variable names and pow

* changes to Logistic Pdf

* changes to parameter

* Expose lower and upper bound labels to R package

* Use example weights; normalize log likelihood metric

* changes to CHECK

* changes to logistic hessian to standard formula

* changes to logistic formula

* Comply with coding style guideline

* Revert back Rabit submodule

* Revert dmlc-core submodule

* Comply with coding style guideline (clang-tidy)

* Fix an error in AFTLoss::Gradient()

* Add missing files to amalgamation

* Address @RAMitchell's comment: minimize future change in MetaInfo interface

* Fix lint

* Fix compilation error on 32-bit target, when size_t == bst_uint

* Allocate sufficient memory to hold extra label info

* Use OpenMP to speed up

* Fix compilation on Windows

* Address reviewer's feedback

* Add unit tests for probability distributions

* Make Metric subclass of Configurable

* Address reviewer's feedback: Configure() AFT metric

* Add a dummy test for AFT metric configuration

* Complete AFT configuration test; remove debugging print

* Rename AFT parameters

* Clarify test comment

* Add a dummy test for AFT loss for uncensored case

* Fix a bug in AFT loss for uncensored labels

* Complete unit test for AFT loss metric

* Simplify unit tests for AFT metric

* Add unit test to verify aggregate output from AFT metric

* Use EXPECT_* instead of ASSERT_*, so that we run all unit tests

* Use aft_loss_param when serializing AFTObj

This is to be consistent with AFT metric

* Add unit tests for AFT Objective

* Fix OpenMP bug; clarify semantics for shared variables used in OpenMP loops

* Add comments

* Remove AFT prefix from probability distribution; put probability distribution in separate source file

* Add comments

* Define kPI and kEulerMascheroni in probability_distribution.h

* Add probability_distribution.cc to amalgamation

* Remove unnecessary diff

* Address reviewer's feedback: define variables where they're used

* Eliminate all INFs and NANs from AFT loss and gradient

* Add demo

* Add tutorial

* Fix lint

* Use 'survival:aft' to be consistent with 'survival:cox'

* Move sample data to demo/data

* Add visual demo with 1D toy data

* Add Python tests

Co-authored-by: Philip Cho <chohyu01@cs.washington.edu>

include/xgboost/data.h

@@ -39,7 +39,7 @@ enum class DataType : uint8_t {
 class MetaInfo {
  public:
   /*! \brief number of data fields in MetaInfo */
-  static constexpr uint64_t kNumField = 7;
+  static constexpr uint64_t kNumField = 9;
 
   /*! \brief number of rows in the data */
   uint64_t num_row_{0};
@@ -62,6 +62,14 @@ class MetaInfo {
    * can be used to specify initial prediction to boost from.
    */
   HostDeviceVector<bst_float> base_margin_;
+  /*!
+   * \brief lower bound of the label, to be used for survival analysis (censored regression)
+   */
+  HostDeviceVector<bst_float> labels_lower_bound_;
+  /*!
+   * \brief upper bound of the label, to be used for survival analysis (censored regression)
+   */
+  HostDeviceVector<bst_float> labels_upper_bound_;
 
   /*! \brief default constructor */
   MetaInfo()  = default;

include/xgboost/metric.h

@@ -8,6 +8,7 @@
 #define XGBOOST_METRIC_H_
 
 #include <dmlc/registry.h>
+#include <xgboost/model.h>
 #include <xgboost/generic_parameters.h>
 #include <xgboost/data.h>
 #include <xgboost/base.h>
@@ -23,7 +24,7 @@ namespace xgboost {
  * \brief interface of evaluation metric used to evaluate model performance.
  *  This has nothing to do with training, but merely act as evaluation purpose.
  */
-class Metric {
+class Metric : public Configurable {
  protected:
   GenericParameter const* tparam_;
 
@@ -34,6 +35,21 @@ class Metric {
    */
   virtual void Configure(
       const std::vector<std::pair<std::string, std::string> >& args) {}
+  /*!
+   * \brief Load configuration from JSON object
+   * By default, metric has no internal configuration;
+   * override this function to maintain internal configuration
+   * \param in JSON object containing the configuration
+   */
+  virtual void LoadConfig(Json const& in) {}
+  /*!
+   * \brief Save configuration to JSON object
+   * By default, metric has no internal configuration;
+   * override this function to maintain internal configuration
+   * \param out pointer to output JSON object
+   */
+  virtual void SaveConfig(Json* out) const {}
+
   /*!
    * \brief evaluate a specific metric
    * \param preds prediction