Initial support for quantile loss. (#8750)

- Add support for Python.
- Add objective.

tests/cpp/objective/test_quantile_obj.cc

@@ -0,0 +1,74 @@
+/**
+ * Copyright 2023 by XGBoost contributors
+ */
+#include <gtest/gtest.h>
+#include <xgboost/base.h>       // Args
+#include <xgboost/context.h>    // Context
+#include <xgboost/objective.h>  // ObjFunction
+#include <xgboost/span.h>       // Span
+
+#include <memory>               // std::unique_ptr
+#include <vector>               // std::vector
+
+#include "../helpers.h"         // CheckConfigReload,CreateEmptyGenericParam,DeclareUnifiedTest
+
+namespace xgboost {
+TEST(Objective, DeclareUnifiedTest(Quantile)) {
+  Context ctx = CreateEmptyGenericParam(GPUIDX);
+
+  {
+    Args args{{"quantile_alpha", "[0.6, 0.8]"}};
+    std::unique_ptr<ObjFunction> obj{ObjFunction::Create("reg:quantileerror", &ctx)};
+    obj->Configure(args);
+    CheckConfigReload(obj, "reg:quantileerror");
+  }
+
+  Args args{{"quantile_alpha", "0.6"}};
+  std::unique_ptr<ObjFunction> obj{ObjFunction::Create("reg:quantileerror", &ctx)};
+  obj->Configure(args);
+  CheckConfigReload(obj, "reg:quantileerror");
+
+  std::vector<float> predts{1.0f, 2.0f, 3.0f};
+  std::vector<float> labels{3.0f, 2.0f, 1.0f};
+  std::vector<float> weights{1.0f, 1.0f, 1.0f};
+  std::vector<float> grad{-0.6f, 0.4f, 0.4f};
+  std::vector<float> hess = weights;
+  CheckObjFunction(obj, predts, labels, weights, grad, hess);
+}
+
+TEST(Objective, DeclareUnifiedTest(QuantileIntercept)) {
+  Context ctx = CreateEmptyGenericParam(GPUIDX);
+  Args args{{"quantile_alpha", "[0.6, 0.8]"}};
+  std::unique_ptr<ObjFunction> obj{ObjFunction::Create("reg:quantileerror", &ctx)};
+  obj->Configure(args);
+
+  MetaInfo info;
+  info.num_row_ = 10;
+  info.labels.ModifyInplace([&](HostDeviceVector<float>* data, common::Span<std::size_t> shape) {
+    data->SetDevice(ctx.gpu_id);
+    data->Resize(info.num_row_);
+    shape[0] = info.num_row_;
+    shape[1] = 1;
+
+    auto& h_labels = data->HostVector();
+    for (std::size_t i = 0; i < info.num_row_; ++i) {
+      h_labels[i] = i;
+    }
+  });
+
+  linalg::Vector<float> base_scores;
+  obj->InitEstimation(info, &base_scores);
+  ASSERT_EQ(base_scores.Size(), 1) << "Vector is not yet supported.";
+  // mean([5.6, 7.8])
+  ASSERT_NEAR(base_scores(0), 6.7, kRtEps);
+
+  for (std::size_t i = 0; i < info.num_row_; ++i) {
+    info.weights_.HostVector().emplace_back(info.num_row_ - i - 1.0);
+  }
+
+  obj->InitEstimation(info, &base_scores);
+  ASSERT_EQ(base_scores.Size(), 1) << "Vector is not yet supported.";
+  // mean([3, 5])
+  ASSERT_NEAR(base_scores(0), 4.0, kRtEps);
+}
+}  // namespace xgboost