Calculate base_score based on input labels for mae. (#8107)

Fit an intercept as base score for abs loss.

src/common/stats.h

@@ -8,7 +8,8 @@
 #include <limits>
 #include <vector>
 
-#include "common.h"
+#include "common.h"  // AssertGPUSupport
+#include "xgboost/generic_parameters.h"
 #include "xgboost/linalg.h"
 
 namespace xgboost {
@@ -90,6 +91,44 @@ float WeightedQuantile(double alpha, Iter begin, Iter end, WeightIter weights) {
   idx = std::min(idx, static_cast<size_t>(n - 1));
   return val(idx);
 }
+
+namespace cuda {
+float Median(Context const* ctx, linalg::TensorView<float const, 2> t,
+             common::OptionalWeights weights);
+#if !defined(XGBOOST_USE_CUDA)
+inline float Median(Context const*, linalg::TensorView<float const, 2>, common::OptionalWeights) {
+  AssertGPUSupport();
+  return 0;
+}
+#endif  // !defined(XGBOOST_USE_CUDA)
+}  // namespace cuda
+
+inline float Median(Context const* ctx, linalg::Tensor<float, 2> const& t,
+                    HostDeviceVector<float> const& weights) {
+  if (!ctx->IsCPU()) {
+    weights.SetDevice(ctx->gpu_id);
+    auto opt_weights = OptionalWeights(weights.ConstDeviceSpan());
+    auto t_v = t.View(ctx->gpu_id);
+    return cuda::Median(ctx, t_v, opt_weights);
+  }
+
+  auto opt_weights = OptionalWeights(weights.ConstHostSpan());
+  auto t_v = t.HostView();
+  auto iter = common::MakeIndexTransformIter(
+      [&](size_t i) { return linalg::detail::Apply(t_v, linalg::UnravelIndex(i, t_v.Shape())); });
+  float q{0};
+  if (opt_weights.Empty()) {
+    q = common::Quantile(0.5, iter, iter + t_v.Size());
+  } else {
+    CHECK_NE(t_v.Shape(1), 0);
+    auto w_it = common::MakeIndexTransformIter([&](size_t i) {
+      auto sample_idx = i / t_v.Shape(1);
+      return opt_weights[sample_idx];
+    });
+    q = common::WeightedQuantile(0.5, iter, iter + t_v.Size(), w_it);
+  }
+  return q;
+}
 }  // namespace common
 }  // namespace xgboost
 #endif  // XGBOOST_COMMON_STATS_H_