Bring back BART to V4 and make it more general (#4914)

* frowardporting from unreleased v3 plus generalization

* aesarize

* improve docstrings

* small fix docstring and variable names

* fix format variable importance

* fix broadcasting issue and other minor fixes

* add test and fix pylint

* fix float32

* sample splitting variables non-uniformly

* remove xfail

* add back xfail on windows

* add back xfail on windows and for float32

* fix test

* clean rnd

* add size argument and check for NoDistribution

* stop updating split_prior after tuning

* clean code and small speed-up

* clean code and small speed-up

* revert xfail

* add tests

* fix number of chains

* revert test

* clean code, refactor and small speed-up

* test random

* test random

* add missing data test

Author: aloctavodia

Diff for: pymc3/distributions/bart.py

@@ -14,271 +14,127 @@
 
 import numpy as np
 
-from pandas import DataFrame, Series
+from aesara.tensor.random.op import RandomVariable, default_shape_from_params
 
 from pymc3.distributions.distribution import NoDistribution
-from pymc3.distributions.tree import LeafNode, SplitNode, Tree
 
 __all__ = ["BART"]
 
 
-class BaseBART(NoDistribution):
-    def __init__(self, X, Y, m=200, alpha=0.25, split_prior=None, *args, **kwargs):
-
-        self.X, self.Y, self.missing_data = self.preprocess_XY(X, Y)
-
-        super().__init__(shape=X.shape[0], dtype="float64", initval=0, *args, **kwargs)
-
-        if self.X.ndim != 2:
-            raise ValueError("The design matrix X must have two dimensions")
-
-        if self.Y.ndim != 1:
-            raise ValueError("The response matrix Y must have one dimension")
-        if self.X.shape[0] != self.Y.shape[0]:
-            raise ValueError(
-                "The design matrix X and the response matrix Y must have the same number of elements"
-            )
-        if not isinstance(m, int):
-            raise ValueError("The number of trees m type must be int")
-        if m < 1:
-            raise ValueError("The number of trees m must be greater than zero")
-
-        if alpha <= 0 or 1 <= alpha:
-            raise ValueError(
-                "The value for the alpha parameter for the tree structure "
-                "must be in the interval (0, 1)"
-            )
-
-        self.num_observations = X.shape[0]
-        self.num_variates = X.shape[1]
-        self.available_predictors = list(range(self.num_variates))
-        self.ssv = SampleSplittingVariable(split_prior, self.num_variates)
-        self.m = m
-        self.alpha = alpha
-        self.trees = self.init_list_of_trees()
-        self.all_trees = []
-        self.mean = fast_mean()
-        self.prior_prob_leaf_node = compute_prior_probability(alpha)
-
-    def preprocess_XY(self, X, Y):
-        if isinstance(Y, (Series, DataFrame)):
-            Y = Y.to_numpy()
-        if isinstance(X, (Series, DataFrame)):
-            X = X.to_numpy()
-        missing_data = np.any(np.isnan(X))
-        X = np.random.normal(X, np.std(X, 0) / 100)
-        return X, Y, missing_data
-
-    def init_list_of_trees(self):
-        initial_value_leaf_nodes = self.Y.mean() / self.m
-        initial_idx_data_points_leaf_nodes = np.array(range(self.num_observations), dtype="int32")
-        list_of_trees = []
-        for i in range(self.m):
-            new_tree = Tree.init_tree(
-                tree_id=i,
-                leaf_node_value=initial_value_leaf_nodes,
-                idx_data_points=initial_idx_data_points_leaf_nodes,
-            )
-            list_of_trees.append(new_tree)
-        # Diff trick to speed computation of residuals. From Section 3.1 of Kapelner, A and Bleich, J.
-        # bartMachine: A Powerful Tool for Machine Learning in R. ArXiv e-prints, 2013
-        # The sum_trees_output will contain the sum of the predicted output for all trees.
-        # When R_j is needed we subtract the current predicted output for tree T_j.
-        self.sum_trees_output = np.full_like(self.Y, self.Y.mean())
-
-        return list_of_trees
-
-    def __iter__(self):
-        return iter(self.trees)
-
-    def __repr_latex(self):
-        raise NotImplementedError
-
-    def get_available_splitting_rules(self, idx_data_points_split_node, idx_split_variable):
-        x_j = self.X[idx_data_points_split_node, idx_split_variable]
-        if self.missing_data:
-            x_j = x_j[~np.isnan(x_j)]
-        values = np.unique(x_j)
-        # The last value is never available as it would leave the right subtree empty.
-        return values[:-1]
-
-    def grow_tree(self, tree, index_leaf_node):
-        current_node = tree.get_node(index_leaf_node)
-
-        index_selected_predictor = self.ssv.rvs()
-        selected_predictor = self.available_predictors[index_selected_predictor]
-        available_splitting_rules = self.get_available_splitting_rules(
-            current_node.idx_data_points, selected_predictor
-        )
-        # This can be unsuccessful when there are not available splitting rules
-        if available_splitting_rules.size == 0:
-            return False, None
-
-        index_selected_splitting_rule = discrete_uniform_sampler(len(available_splitting_rules))
-        selected_splitting_rule = available_splitting_rules[index_selected_splitting_rule]
-        new_split_node = SplitNode(
-            index=index_leaf_node,
-            idx_split_variable=selected_predictor,
-            split_value=selected_splitting_rule,
-        )
-
-        left_node_idx_data_points, right_node_idx_data_points = self.get_new_idx_data_points(
-            new_split_node, current_node.idx_data_points
-        )
-
-        left_node_value = self.draw_leaf_value(left_node_idx_data_points)
-        right_node_value = self.draw_leaf_value(right_node_idx_data_points)
-
-        new_left_node = LeafNode(
-            index=current_node.get_idx_left_child(),
-            value=left_node_value,
-            idx_data_points=left_node_idx_data_points,
-        )
-        new_right_node = LeafNode(
-            index=current_node.get_idx_right_child(),
-            value=right_node_value,
-            idx_data_points=right_node_idx_data_points,
-        )
-        tree.grow_tree(index_leaf_node, new_split_node, new_left_node, new_right_node)
-
-        return True, index_selected_predictor
-
-    def get_new_idx_data_points(self, current_split_node, idx_data_points):
-        idx_split_variable = current_split_node.idx_split_variable
-        split_value = current_split_node.split_value
-
-        left_idx = self.X[idx_data_points, idx_split_variable] <= split_value
-        left_node_idx_data_points = idx_data_points[left_idx]
-        right_node_idx_data_points = idx_data_points[~left_idx]
-
-        return left_node_idx_data_points, right_node_idx_data_points
-
-    def get_residuals(self):
-        """Compute the residuals."""
-        R_j = self.Y - self.sum_trees_output
-        return R_j
-
-    def get_residuals_loo(self, tree):
-        """Compute the residuals without leaving the passed tree out."""
-        R_j = self.Y - (self.sum_trees_output - tree.predict_output(self.num_observations))
-        return R_j
-
-    def draw_leaf_value(self, idx_data_points):
-        """Draw the residual mean."""
-        R_j = self.get_residuals()[idx_data_points]
-        draw = self.mean(R_j)
-        return draw
-
-    def predict(self, X_new):
-        """Compute out of sample predictions evaluated at X_new"""
-        trees = self.all_trees
-        num_observations = X_new.shape[0]
-        pred = np.zeros((len(trees), num_observations))
-        np.random.randint(len(trees))
-        for draw, trees_to_sum in enumerate(trees):
-            new_Y = np.zeros(num_observations)
-            for tree in trees_to_sum:
-                new_Y += [tree.predict_out_of_sample(x) for x in X_new]
-            pred[draw] = new_Y
-        return pred
-
-
-def compute_prior_probability(alpha):
+class BARTRV(RandomVariable):
     """
-    Calculate the probability of the node being a LeafNode (1 - p(being SplitNode)).
-    Taken from equation 19 in [Rockova2018].
-
-    Parameters
-    ----------
-    alpha : float
-
-    Returns
-    -------
-    list with probabilities for leaf nodes
-
-    References
-    ----------
-    .. [Rockova2018] Veronika Rockova, Enakshi Saha (2018). On the theory of BART.
-    arXiv, `link <https://arxiv.org/abs/1810.00787>`__
+    Base class for BART
     """
-    prior_leaf_prob = [0]
-    depth = 1
-    while prior_leaf_prob[-1] < 1:
-        prior_leaf_prob.append(1 - alpha ** depth)
-        depth += 1
-    return prior_leaf_prob
-
-
-def fast_mean():
-    """If available use Numba to speed up the computation of the mean."""
-    try:
-        from numba import jit
-    except ImportError:
-        return np.mean
-
-    @jit
-    def mean(a):
-        count = a.shape[0]
-        suma = 0
-        for i in range(count):
-            suma += a[i]
-        return suma / count
-
-    return mean
 
+    name = "BART"
+    ndim_supp = 1
+    ndims_params = [2, 1, 0, 0, 0, 1]
+    dtype = "floatX"
+    _print_name = ("BART", "\\operatorname{BART}")
+    all_trees = None
+
+    def _shape_from_params(self, dist_params, rep_param_idx=1, param_shapes=None):
+        return default_shape_from_params(self.ndim_supp, dist_params, rep_param_idx, param_shapes)
+
+    @classmethod
+    def rng_fn(cls, rng=np.random.default_rng(), *args, **kwargs):
+        size = kwargs.pop("size", None)
+        X_new = kwargs.pop("X_new", None)
+        all_trees = cls.all_trees
+        if all_trees:
+
+            if size is None:
+                size = ()
+            elif isinstance(size, int):
+                size = [size]
+
+            flatten_size = 1
+            for s in size:
+                flatten_size *= s
+
+            idx = rng.randint(len(all_trees), size=flatten_size)
+
+            if X_new is None:
+                pred = np.zeros((flatten_size, all_trees[0][0].num_observations))
+                for ind, p in enumerate(pred):
+                    for tree in all_trees[idx[ind]]:
+                        p += tree.predict_output()
+            else:
+                pred = np.zeros((flatten_size, X_new.shape[0]))
+                for ind, p in enumerate(pred):
+                    for tree in all_trees[idx[ind]]:
+                        p += np.array([tree.predict_out_of_sample(x) for x in X_new])
+            return pred.reshape((*size, -1))
+        else:
+            return np.full_like(cls.Y, cls.Y.mean())
 
-def discrete_uniform_sampler(upper_value):
-    """Draw from the uniform distribution with bounds [0, upper_value)."""
-    return int(np.random.random() * upper_value)
-
-
-class SampleSplittingVariable:
-    def __init__(self, prior, num_variates):
-        self.prior = prior
-        self.num_variates = num_variates
-
-        if self.prior is not None:
-            self.prior = np.asarray(self.prior)
-            self.prior = self.prior / self.prior.sum()
-            if self.prior.size != self.num_variates:
-                raise ValueError(
-                    f"The size of split_prior ({self.prior.size}) should be the "
-                    f"same as the number of covariates ({self.num_variates})"
-                )
-            self.enu = list(enumerate(np.cumsum(self.prior)))
 
-    def rvs(self):
-        if self.prior is None:
-            return int(np.random.random() * self.num_variates)
-        else:
-            r = np.random.random()
-            for i, v in self.enu:
-                if r <= v:
-                    return i
+bart = BARTRV()
 
 
-class BART(BaseBART):
+class BART(NoDistribution):
     """
-    BART distribution.
+    Bayesian Additive Regression Tree distribution.
 
     Distribution representing a sum over trees
 
     Parameters
     ----------
     X : array-like
-        The design matrix.
+        The covariate matrix.
     Y : array-like
         The response vector.
     m : int
         Number of trees
     alpha : float
-        Control the prior probability over the depth of the trees. Must be in the interval (0, 1),
-        altought it is recomenned to be in the interval (0, 0.5].
+        Control the prior probability over the depth of the trees. Even when it can takes values in
+        the interval (0, 1), it is recommended to be in the interval (0, 0.5].
+    k : float
+        Scale parameter for the values of the leaf nodes. Defaults to 2. Recomended to be between 1
+        and 3.
     split_prior : array-like
-        Each element of split_prior should be in the [0, 1] interval and the elements should sum
-        to 1. Otherwise they will be normalized.
-        Defaults to None, all variable have the same a prior probability
+        Each element of split_prior should be in the [0, 1] interval and the elements should sum to
+        1. Otherwise they will be normalized.
+        Defaults to None, i.e. all covariates have the same prior probability to be selected.
     """
 
-    def __init__(self, X, Y, m=200, alpha=0.25, split_prior=None):
-        super().__init__(X, Y, m, alpha, split_prior)
+    def __new__(
+        cls,
+        name,
+        X,
+        Y,
+        m=50,
+        alpha=0.25,
+        k=2,
+        split_prior=None,
+        **kwargs,
+    ):
+
+        cls.all_trees = []
+
+        bart_op = type(
+            f"BART_{name}",
+            (BARTRV,),
+            dict(
+                name="BART",
+                all_trees=cls.all_trees,
+                inplace=False,
+                initval=Y.mean(),
+                X=X,
+                Y=Y,
+                m=m,
+                alpha=alpha,
+                k=k,
+                split_prior=split_prior,
+            ),
+        )()
+
+        NoDistribution.register(BARTRV)
+
+        cls.rv_op = bart_op
+        params = [X, Y, m, alpha, k]
+        return super().__new__(cls, name, *params, **kwargs)
+
+    @classmethod
+    def dist(cls, *params, **kwargs):
+        return super().dist(params, **kwargs)