diff --git a/src/common/quantile.cu b/src/common/quantile.cu
index 776752476054..2bf6070d5e89 100644
--- a/src/common/quantile.cu
+++ b/src/common/quantile.cu
@@ -634,12 +634,25 @@ void SketchContainer::MakeCuts(HistogramCuts* p_cuts, bool is_column_split) {
         });
     CHECK_EQ(num_columns_, d_in_columns_ptr.size() - 1);
     max_values.resize(d_in_columns_ptr.size() - 1);
+
+    // In some cases (e.g. column-wise data split), we may have empty columns, so we need to keep
+    // track of the unique keys (feature indices) after the thrust::reduce_by_key` call.
+    dh::caching_device_vector<size_t> d_max_keys(d_in_columns_ptr.size() - 1);
     dh::caching_device_vector<SketchEntry> d_max_values(d_in_columns_ptr.size() - 1);
-    thrust::reduce_by_key(thrust::cuda::par(alloc), key_it, key_it + in_cut_values.size(), val_it,
-                          thrust::make_discard_iterator(), d_max_values.begin(),
-                          thrust::equal_to<bst_feature_t>{},
-                          [] __device__(auto l, auto r) { return l.value > r.value ? l : r; });
-    dh::CopyDeviceSpanToVector(&max_values, dh::ToSpan(d_max_values));
+    auto new_end = thrust::reduce_by_key(
+        thrust::cuda::par(alloc), key_it, key_it + in_cut_values.size(), val_it, d_max_keys.begin(),
+        d_max_values.begin(), thrust::equal_to<bst_feature_t>{},
+        [] __device__(auto l, auto r) { return l.value > r.value ? l : r; });
+    d_max_keys.erase(new_end.first, d_max_keys.end());
+    d_max_values.erase(new_end.second, d_max_values.end());
+
+    // The device vector needs to be initialized explicitly since we may have some missing columns.
+    SketchEntry default_entry{};
+    dh::caching_device_vector<SketchEntry> d_max_results(d_in_columns_ptr.size() - 1,
+                                                         default_entry);
+    thrust::scatter(thrust::cuda::par(alloc), d_max_values.begin(), d_max_values.end(),
+                    d_max_keys.begin(), d_max_results.begin());
+    dh::CopyDeviceSpanToVector(&max_values, dh::ToSpan(d_max_results));
     auto max_it = MakeIndexTransformIter([&](auto i) {
       if (IsCat(h_feature_types, i)) {
         return max_values[i].value;
diff --git a/src/common/quantile.h b/src/common/quantile.h
index 48758b8dce1e..47db5f875af5 100644
--- a/src/common/quantile.h
+++ b/src/common/quantile.h
@@ -35,13 +35,13 @@ struct WQSummary {
   /*! \brief an entry in the sketch summary */
   struct Entry {
     /*! \brief minimum rank */
-    RType rmin;
+    RType rmin{};
     /*! \brief maximum rank */
-    RType rmax;
+    RType rmax{};
     /*! \brief maximum weight */
-    RType wmin;
+    RType wmin{};
     /*! \brief the value of data */
-    DType value;
+    DType value{};
     // constructor
     XGBOOST_DEVICE Entry() {}  // NOLINT
     // constructor
diff --git a/tests/cpp/common/test_quantile.cu b/tests/cpp/common/test_quantile.cu
index 57c9da7038c6..49353439f21a 100644
--- a/tests/cpp/common/test_quantile.cu
+++ b/tests/cpp/common/test_quantile.cu
@@ -339,6 +339,31 @@ TEST(GPUQuantile, MultiMerge) {
   });
 }
 
+TEST(GPUQuantile, MissingColumns) {
+  auto dmat = std::unique_ptr<DMatrix>{[=]() {
+    std::size_t constexpr kRows = 1000, kCols = 100;
+    auto sparsity = 0.5f;
+    std::vector<FeatureType> ft(kCols);
+    for (size_t i = 0; i < ft.size(); ++i) {
+      ft[i] = (i % 2 == 0) ? FeatureType::kNumerical : FeatureType::kCategorical;
+    }
+    auto dmat = RandomDataGenerator{kRows, kCols, sparsity}
+                    .Seed(0)
+                    .Lower(.0f)
+                    .Upper(1.0f)
+                    .Type(ft)
+                    .MaxCategory(13)
+                    .GenerateDMatrix();
+    return dmat->SliceCol(2, 1);
+  }()};
+  dmat->Info().data_split_mode = DataSplitMode::kRow;
+
+  auto ctx = MakeCUDACtx(0);
+  std::size_t constexpr kBins = 64;
+  HistogramCuts cuts = common::DeviceSketch(&ctx, dmat.get(), kBins);
+  ASSERT_TRUE(cuts.HasCategorical());
+}
+
 namespace {
 void TestAllReduceBasic() {
   auto const world = collective::GetWorldSize();
@@ -422,18 +447,14 @@ TEST_F(MGPUQuantileTest, AllReduceBasic) {
 }
 
 namespace {
-void TestColumnSplitBasic() {
+void TestColumnSplit(DMatrix* dmat) {
   auto const world = collective::GetWorldSize();
   auto const rank = collective::GetRank();
-  std::size_t constexpr kRows = 1000, kCols = 100, kBins = 64;
-
-  auto m = std::unique_ptr<DMatrix>{[=]() {
-    auto dmat = RandomDataGenerator{kRows, kCols, 0}.GenerateDMatrix();
-    return dmat->SliceCol(world, rank);
-  }()};
+  auto m = std::unique_ptr<DMatrix>{dmat->SliceCol(world, rank)};
 
   // Generate cuts for distributed environment.
   auto ctx = MakeCUDACtx(GPUIDX);
+  std::size_t constexpr kBins = 64;
   HistogramCuts distributed_cuts = common::DeviceSketch(&ctx, m.get(), kBins);
 
   // Generate cuts for single node environment
@@ -466,7 +487,26 @@ void TestColumnSplitBasic() {
 }  // anonymous namespace
 
 TEST_F(MGPUQuantileTest, ColumnSplitBasic) {
-  DoTest(TestColumnSplitBasic);
+  std::size_t constexpr kRows = 1000, kCols = 100;
+  auto dmat = RandomDataGenerator{kRows, kCols, 0}.GenerateDMatrix();
+  DoTest(TestColumnSplit, dmat.get());
+}
+
+TEST_F(MGPUQuantileTest, ColumnSplitCategorical) {
+  std::size_t constexpr kRows = 1000, kCols = 100;
+  auto sparsity = 0.5f;
+  std::vector<FeatureType> ft(kCols);
+  for (size_t i = 0; i < ft.size(); ++i) {
+    ft[i] = (i % 2 == 0) ? FeatureType::kNumerical : FeatureType::kCategorical;
+  }
+  auto dmat = RandomDataGenerator{kRows, kCols, sparsity}
+                  .Seed(0)
+                  .Lower(.0f)
+                  .Upper(1.0f)
+                  .Type(ft)
+                  .MaxCategory(13)
+                  .GenerateDMatrix();
+  DoTest(TestColumnSplit, dmat.get());
 }
 
 namespace {