Add build_tree function which takes in a histogram and builds a tree on top of it. The function will be used in CentralTreeSumQuery and DistributedTreeSumQuery in a following CL.

For more details about `CentralTreeSumQuery` and `DistributedTreeSumQuery`, please refer to the implementation design section in the following design doc: https://docs.google.com/document/d/14LL94yZx3MdorCEOE0QZNhyIx7P_3voyrl4Nlt2HF7k/edit?resourcekey=0-X3xeTk6w-fkYFezl5fxmCQ#

PiperOrigin-RevId: 382199971

tensorflow_privacy/privacy/dp_query/tree_aggregation.py

@@ -13,10 +13,14 @@
 # limitations under the License.
 """Tree aggregation algorithm.
 
-This algorithm computes cumulative sums of noise based on tree aggregation. When
-using an appropriate noise function (e.g., Gaussian noise), it allows for
-efficient differentially private algorithms under continual observation, without
-prior subsampling or shuffling assumptions.
+`TreeAggregator` and `EfficientTreeAggregator` compute cumulative sums of noise
+based on tree aggregation. When using an appropriate noise function (e.g.,
+Gaussian noise), it allows for efficient differentially private algorithms under
+continual observation, without prior subsampling or shuffling assumptions.
+
+`build_tree` constructs a tree given the leaf nodes by recursively summing the
+children nodes to get the parent node. It allows for efficient range queries and
+other statistics such as quantiles on the leaf nodes.
 """
 
 import abc
@@ -440,3 +444,79 @@ class EfficientTreeAggregator():
         level_buffer_idx=new_level_buffer_idx,
         value_generator_state=value_generator_state)
     return cumsum, new_state
+
+
+@tf.function
+def build_tree_from_leaf(leaf_nodes: tf.Tensor, arity: int) -> tf.RaggedTensor:
+  """A function constructs a complete tree given all the leaf nodes.
+
+  The function takes a 1-D array representing the leaf nodes of a tree and the
+  tree's arity, and constructs a complete tree by recursively summing the
+  adjacent children to get the parent until reaching the root node. Because we
+  assume a complete tree, if the number of leaf nodes does not divide arity, the
+  leaf nodes will be padded with zeros.
+
+  Args:
+    leaf_nodes: A 1-D array storing the leaf nodes of the tree.
+    arity: A `int` for the branching factor of the tree, i.e. the number of
+      children for each internal node.
+
+  Returns:
+    `tf.RaggedTensor` representing the tree. For example, if
+    `leaf_nodes=tf.Tensor([1, 2, 3, 4])` and `arity=2`, then the returned value
+    should be `tree=tf.RaggedTensor([[10],[3,7],[1,2,3,4]])`. In this way,
+    `tree[layer][index]` can be used to access the node indexed by (layer,
+    index) in the tree,
+
+  Raises:
+    ValueError: if parameters don't meet expectations. There are two situations
+    where the error is raised: (1) the input tensor has length smaller than 1;
+    (2) The arity is less than 2.
+  """
+
+  if len(leaf_nodes) <= 0:
+    raise ValueError(
+        'The number of leaf nodes should at least be 1.'
+        f'However, an array of length {len(leaf_nodes)} is detected')
+
+  if arity <= 1:
+    raise ValueError('The branching factor should be at least 2.'
+                     f'However, a branching factor of {arity} is detected.')
+
+  def pad_zero(leaf_nodes, size):
+    paddings = [[0, size - len(leaf_nodes)]]
+    return tf.pad(leaf_nodes, paddings)
+
+  leaf_nodes_size = tf.constant(len(leaf_nodes), dtype=tf.float32)
+  num_layers = tf.math.ceil(
+      tf.math.log(leaf_nodes_size) /
+      tf.math.log(tf.constant(arity, dtype=tf.float32))) + 1
+  leaf_nodes = pad_zero(leaf_nodes, tf.math.pow(float(arity), num_layers - 1))
+
+  def _shrink_layer(layer: tf.Tensor, arity: int) -> tf.Tensor:
+    return tf.reduce_sum((tf.reshape(layer, (-1, arity))), 1)
+
+  # The following `tf.while_loop` constructs the tree from bottom up by
+  # iteratively applying `_shrink_layer` to each layer of the tree. The reason
+  # for the choice of TF1.0-style `tf.while_loop` is that @tf.function does not
+  # support auto-translation from python loop to tf loop when loop variables
+  # contain a `RaggedTensor` whose shape changes across iterations.
+
+  idx = tf.identity(num_layers)
+  loop_cond = lambda i, h: tf.less_equal(2.0, i)
+
+  def _loop_body(i, h):
+    return [
+        tf.add(i, -1.0),
+        tf.concat(([_shrink_layer(h[0], arity)], h), axis=0)
+    ]
+
+  _, tree = tf.while_loop(
+      loop_cond,
+      _loop_body, [idx, tf.RaggedTensor.from_tensor([leaf_nodes])],
+      shape_invariants=[
+          idx.get_shape(),
+          tf.RaggedTensorSpec(dtype=leaf_nodes.dtype, ragged_rank=1)
+      ])
+
+  return tree

tensorflow_privacy/privacy/dp_query/tree_aggregation_test.py

@@ -365,5 +365,39 @@ class GaussianNoiseGeneratorTest(tf.test.TestCase):
       self.assertAllEqual(gstate, gstate2)
 
 
+class BuildTreeTest(tf.test.TestCase, parameterized.TestCase):
+
+  @parameterized.product(
+      leaf_nodes_size=[1, 2, 3, 4, 5],
+      arity=[2, 3],
+      dtype=[tf.int32, tf.float32],
+  )
+  def test_build_tree_from_leaf(self, leaf_nodes_size, arity, dtype):
+    """Test whether `build_tree_from_leaf` will output the correct tree."""
+
+    leaf_nodes = tf.cast(tf.range(leaf_nodes_size), dtype)
+    depth = math.ceil(math.log(leaf_nodes_size, arity)) + 1
+
+    tree = tree_aggregation.build_tree_from_leaf(leaf_nodes, arity)
+
+    self.assertEqual(depth, tree.shape[0])
+
+    for layer in range(depth):
+      reverse_depth = tree.shape[0] - layer - 1
+      span_size = arity**reverse_depth
+      for idx in range(arity**layer):
+        left = idx * span_size
+        right = (idx + 1) * span_size
+        expected_value = sum(leaf_nodes[left:right])
+        self.assertEqual(tree[layer][idx], expected_value)
+
+  @parameterized.named_parameters(('negative_arity', [1], -1),
+                                  ('empty_hist', [], 2))
+  def test_value_error_raises(self, leaf_nodes, arity):
+    """Test whether `build_tree_from_leaf` will raise the correct error when the input is illegal."""
+    with self.assertRaises(ValueError):
+      tree_aggregation.build_tree_from_leaf(leaf_nodes, arity)
+
+
 if __name__ == '__main__':
   tf.test.main()