ENH More efficient B.dot and B.T.dot in Cox datafit (#168)

Author: Badr-MOUFAD

skglm/datafits/single_task.py

@@ -561,19 +561,24 @@ class Cox(BaseDatafit):
 
     Attributes
     ----------
-    B : array-like, shape (n_samples, n_samples)
-        Matrix where every ``(i, j)`` entry (row, column) equals ``1``
-        if ``tm[j] >= tm[i]`` and ``0`` otherwise. This matrix is initialized
-        using the ``.initialize`` method.
+    T_indices : array-like, shape (n_samples,)
+        Indices of observations with the same occurrence times stacked horizontally as
+        ``[group_1, group_2, ...]`` in ascending order. It is initialized
+        with the ``.initialize`` method (or ``initialize_sparse`` for sparse ``X``).
 
-    H_indices : array-like, shape (n_samples,)
-        Indices of observations with the same occurrence times stacked horizontally
-        as ``[group_1, group_2, ...]``. This array is initialized
-        when calling ``.initialize`` method when ``use_efron=True``.
+    T_indptr : array-like, (np.unique(tm) + 1,)
+        Array where two consecutive elements delimit a group of
+        observations having the same occurrence times.
 
-    H_indptr : array-like, (np.unique(tm) + 1,)
-        Array where two consecutive elements delimits a group of observations
-        having the same occurrence times.
+    H_indices : array-like, shape (n_samples,)
+        Indices of uncensored observations with the same occurrence times stacked
+        horizontally as ``[group_1, group_2, ...]`` in ascending order.
+        It is initialized when calling the ``.initialize`` method
+        (or ``initialize_sparse`` for sparse ``X``) when ``use_efron=True``.
+
+    H_indptr : array-like, shape (np.unique(tm[s != 0]) + 1,)
+        Array where two consecutive elements delimits a group of uncensored
+        observations having the same occurrence time.
     """
 
     def __init__(self, use_efron=False):
@@ -582,9 +587,8 @@ def __init__(self, use_efron=False):
     def get_spec(self):
         return (
             ('use_efron', bool_),
-            ('B', float64[:, ::1]),
-            ('H_indptr', int64[:]),
-            ('H_indices', int64[:]),
+            ('T_indptr', int64[:]), ('T_indices', int64[:]),
+            ('H_indptr', int64[:]), ('H_indices', int64[:]),
         )
 
     def params_to_dict(self):
@@ -597,7 +601,7 @@ def value(self, y, w, Xw):
 
         # compute inside log term
         exp_Xw = np.exp(Xw)
-        B_exp_Xw = self.B @ exp_Xw
+        B_exp_Xw = self._B_dot_vec(exp_Xw)
         if self.use_efron:
             B_exp_Xw -= self._A_dot_vec(exp_Xw)
 
@@ -614,12 +618,12 @@ def raw_grad(self, y, Xw):
         n_samples = Xw.shape[0]
 
         exp_Xw = np.exp(Xw)
-        B_exp_Xw = self.B @ exp_Xw
+        B_exp_Xw = self._B_dot_vec(exp_Xw)
         if self.use_efron:
             B_exp_Xw -= self._A_dot_vec(exp_Xw)
 
         s_over_B_exp_Xw = s / B_exp_Xw
-        out = -s + exp_Xw * (self.B.T @ (s_over_B_exp_Xw))
+        out = -s + exp_Xw * self._B_T_dot_vec(s_over_B_exp_Xw)
         if self.use_efron:
             out -= exp_Xw * self._AT_dot_vec(s_over_B_exp_Xw)
 
@@ -635,12 +639,12 @@ def raw_hessian(self, y, Xw):
         n_samples = Xw.shape[0]
 
         exp_Xw = np.exp(Xw)
-        B_exp_Xw = self.B @ exp_Xw
+        B_exp_Xw = self._B_dot_vec(exp_Xw)
         if self.use_efron:
             B_exp_Xw -= self._A_dot_vec(exp_Xw)
 
         s_over_B_exp_Xw = s / B_exp_Xw
-        out = exp_Xw * (self.B.T @ (s_over_B_exp_Xw))
+        out = exp_Xw * self._B_T_dot_vec(s_over_B_exp_Xw)
         if self.use_efron:
             out -= exp_Xw * self._AT_dot_vec(s_over_B_exp_Xw)
 
@@ -654,38 +658,53 @@ def initialize(self, X, y):
         """Initialize the datafit attributes."""
         tm, s = y
 
-        tm_as_col = tm.reshape((-1, 1))
-        self.B = (tm >= tm_as_col).astype(X.dtype)
+        self.T_indices = np.argsort(tm)
+        self.T_indptr = self._get_indptr(tm, self.T_indices)
 
         if self.use_efron:
-            H_indices = np.argsort(tm)
             # filter out censored data
-            H_indices = H_indices[s[H_indices] != 0]
-            n_uncensored_samples = H_indices.shape[0]
-
-            # build H_indptr
-            H_indptr = [0]
-            count = 1
-            for i in range(1, n_uncensored_samples):
-                if tm[H_indices[i-1]] == tm[H_indices[i]]:
-                    count += 1
-                else:
-                    H_indptr.append(count + H_indptr[-1])
-                    count = 1
-            H_indptr.append(n_uncensored_samples)
-            H_indptr = np.asarray(H_indptr, dtype=np.int64)
-
-            # save in instance
-            self.H_indptr = H_indptr
-            self.H_indices = H_indices
+            self.H_indices = self.T_indices[s[self.T_indices] != 0]
+            self.H_indptr = self._get_indptr(tm, self.H_indices)
 
     def initialize_sparse(self, X_data, X_indptr, X_indices, y):
         """Initialize the datafit attributes in sparse dataset case."""
-        # initialize_sparse and initialize have the same implementation
+        # `initialize_sparse` and `initialize` have the same implementation
         # small hack to avoid repetitive code: pass in X_data as only its dtype is used
         self.initialize(X_data, y)
 
+    def _B_dot_vec(self, vec):
+        # compute `B @ vec` in O(n) instead of O(n^2)
+        out = np.zeros_like(vec)
+        n_T = self.T_indptr.shape[0] - 1
+        cum_sum = 0.
+
+        # reverse loop to avoid starting from cum_sum and subtracting vec coordinates
+        # subtracting big numbers results in 'cancellation errors' and hence erroneous
+        # results. Ref. J Nocedal, "Numerical optimization", page 615
+        for idx in range(n_T - 1, -1, -1):
+            current_T_idx = self.T_indices[self.T_indptr[idx]: self.T_indptr[idx+1]]
+
+            cum_sum += np.sum(vec[current_T_idx])
+            out[current_T_idx] = cum_sum
+
+        return out
+
+    def _B_T_dot_vec(self, vec):
+        # compute `B.T @ vec` in O(n) instead of O(n^2)
+        out = np.zeros_like(vec)
+        n_T = self.T_indptr.shape[0] - 1
+        cum_sum = 0.
+
+        for idx in range(n_T):
+            current_T_idx = self.T_indices[self.T_indptr[idx]: self.T_indptr[idx+1]]
+
+            cum_sum += np.sum(vec[current_T_idx])
+            out[current_T_idx] = cum_sum
+
+        return out
+
     def _A_dot_vec(self, vec):
+        # compute `A @ vec` in O(n) instead of O(n^2)
         out = np.zeros_like(vec)
         n_H = self.H_indptr.shape[0] - 1
 
@@ -700,6 +719,7 @@ def _A_dot_vec(self, vec):
         return out
 
     def _AT_dot_vec(self, vec):
+        # compute `A.T @ vec` in O(n) instead of O(n^2)
         out = np.zeros_like(vec)
         n_H = self.H_indptr.shape[0] - 1
 
@@ -712,3 +732,21 @@ def _AT_dot_vec(self, vec):
             out[current_H_idx] = weighted_sum_vec_H * np.ones(size_current_H)
 
         return out
+
+    def _get_indptr(self, vals, indices):
+        # given `indices = argsort(vals)`
+        # build and array `indptr` where two consecutive elements
+        # delimit indices with the same val
+        n_indices = indices.shape[0]
+
+        indptr = [0]
+        count = 1
+        for i in range(n_indices - 1):
+            if vals[indices[i]] == vals[indices[i+1]]:
+                count += 1
+            else:
+                indptr.append(count + indptr[-1])
+                count = 1
+        indptr.append(n_indices)
+
+        return np.asarray(indptr, dtype=np.int64)