[MT-TREE] Support prediction cache and model slicing. (#8968)

- Fix prediction range.
- Support prediction cache in mt-hist.
- Support model slicing.
- Make the booster a Python iterable by defining `__iter__`.
- Cleanup removed/deprecated parameters.
- A new field in the output model `iteration_indptr` for pointing to the ranges of trees for each iteration.

tests/cpp/predictor/test_gpu_predictor.cu

@@ -1,5 +1,5 @@
-/*!
- * Copyright 2017-2022 XGBoost contributors
+/**
+ * Copyright 2017-2023, XGBoost contributors
  */
 #include <gtest/gtest.h>
 #include <xgboost/c_api.h>
@@ -155,7 +155,7 @@ TEST(GPUPredictor, ShapStump) {
 
   std::vector<std::unique_ptr<RegTree>> trees;
   trees.push_back(std::unique_ptr<RegTree>(new RegTree));
-  model.CommitModel(std::move(trees), 0);
+  model.CommitModelGroup(std::move(trees), 0);
 
   auto gpu_lparam = CreateEmptyGenericParam(0);
   std::unique_ptr<Predictor> gpu_predictor = std::unique_ptr<Predictor>(
@@ -183,7 +183,7 @@ TEST(GPUPredictor, Shap) {
   std::vector<std::unique_ptr<RegTree>> trees;
   trees.push_back(std::unique_ptr<RegTree>(new RegTree));
   trees[0]->ExpandNode(0, 0, 0.5, true, 1.0, -1.0, 1.0, 0.0, 5.0, 2.0, 3.0);
-  model.CommitModel(std::move(trees), 0);
+  model.CommitModelGroup(std::move(trees), 0);
 
   auto gpu_lparam = CreateEmptyGenericParam(0);
   auto cpu_lparam = CreateEmptyGenericParam(-1);

tests/cpp/predictor/test_predictor.cc

@@ -209,7 +209,7 @@ void GBTreeModelForTest(gbm::GBTreeModel *model, uint32_t split_ind,
   p_tree->ExpandCategorical(0, split_ind, split_cats, true, 1.5f,
                             left_weight, right_weight,
                             3.0f, 2.2f, 7.0f, 9.0f);
-  model->CommitModel(std::move(trees), 0);
+  model->CommitModelGroup(std::move(trees), 0);
 }
 
 void TestCategoricalPrediction(std::string name) {
@@ -445,7 +445,7 @@ void TestVectorLeafPrediction(Context const *ctx) {
   ASSERT_TRUE(mparam.IsVectorLeaf());
 
   gbm::GBTreeModel model{&mparam, ctx};
-  model.CommitModel(std::move(trees), 0);
+  model.CommitModelGroup(std::move(trees), 0);
 
   auto run_test = [&](float expected, HostDeviceVector<float> *p_data) {
     {

tests/cpp/predictor/test_predictor.h

@@ -14,6 +14,23 @@
 #include "../helpers.h"
 
 namespace xgboost {
+inline gbm::GBTreeModel CreateTestModel(LearnerModelParam const* param, Context const* ctx,
+                                        size_t n_classes = 1) {
+  gbm::GBTreeModel model(param, ctx);
+
+  for (size_t i = 0; i < n_classes; ++i) {
+    std::vector<std::unique_ptr<RegTree>> trees;
+    trees.push_back(std::unique_ptr<RegTree>(new RegTree));
+    if (i == 0) {
+      (*trees.back())[0].SetLeaf(1.5f);
+      (*trees.back()).Stat(0).sum_hess = 1.0f;
+    }
+    model.CommitModelGroup(std::move(trees), i);
+  }
+
+  return model;
+}
+
 template <typename Page>
 void TestPredictionFromGradientIndex(std::string name, size_t rows, size_t cols,
                                      std::shared_ptr<DMatrix> p_hist) {