962 lines
32 KiB
Cython
962 lines
32 KiB
Cython
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# Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>
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# Fabian Pedregosa <fabian.pedregosa@inria.fr>
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# Olivier Grisel <olivier.grisel@ensta.org>
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# Alexis Mignon <alexis.mignon@gmail.com>
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# Manoj Kumar <manojkumarsivaraj334@gmail.com>
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#
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# License: BSD 3 clause
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from libc.math cimport fabs
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import numpy as np
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from cython cimport floating
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import warnings
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from ..exceptions import ConvergenceWarning
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from ..utils._cython_blas cimport (
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_axpy, _dot, _asum, _gemv, _nrm2, _copy, _scal
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)
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from ..utils._cython_blas cimport ColMajor, Trans, NoTrans
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from ..utils._typedefs cimport uint32_t
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from ..utils._random cimport our_rand_r
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# The following two functions are shamelessly copied from the tree code.
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cdef enum:
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# Max value for our rand_r replacement (near the bottom).
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# We don't use RAND_MAX because it's different across platforms and
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# particularly tiny on Windows/MSVC.
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# It corresponds to the maximum representable value for
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# 32-bit signed integers (i.e. 2^31 - 1).
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RAND_R_MAX = 2147483647
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cdef inline uint32_t rand_int(uint32_t end, uint32_t* random_state) noexcept nogil:
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"""Generate a random integer in [0; end)."""
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return our_rand_r(random_state) % end
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cdef inline floating fmax(floating x, floating y) noexcept nogil:
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if x > y:
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return x
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return y
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cdef inline floating fsign(floating f) noexcept nogil:
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if f == 0:
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return 0
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elif f > 0:
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return 1.0
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else:
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return -1.0
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cdef floating abs_max(int n, const floating* a) noexcept nogil:
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"""np.max(np.abs(a))"""
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cdef int i
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cdef floating m = fabs(a[0])
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cdef floating d
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for i in range(1, n):
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d = fabs(a[i])
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if d > m:
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m = d
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return m
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cdef floating max(int n, floating* a) noexcept nogil:
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"""np.max(a)"""
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cdef int i
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cdef floating m = a[0]
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cdef floating d
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for i in range(1, n):
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d = a[i]
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if d > m:
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m = d
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return m
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cdef floating diff_abs_max(int n, const floating* a, floating* b) noexcept nogil:
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"""np.max(np.abs(a - b))"""
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cdef int i
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cdef floating m = fabs(a[0] - b[0])
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cdef floating d
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for i in range(1, n):
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d = fabs(a[i] - b[i])
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if d > m:
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m = d
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return m
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def enet_coordinate_descent(
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floating[::1] w,
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floating alpha,
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floating beta,
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const floating[::1, :] X,
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const floating[::1] y,
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unsigned int max_iter,
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floating tol,
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object rng,
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bint random=0,
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bint positive=0
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):
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"""Cython version of the coordinate descent algorithm
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for Elastic-Net regression
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We minimize
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(1/2) * norm(y - X w, 2)^2 + alpha norm(w, 1) + (beta/2) norm(w, 2)^2
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Returns
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-------
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w : ndarray of shape (n_features,)
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ElasticNet coefficients.
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gap : float
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Achieved dual gap.
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tol : float
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Equals input `tol` times `np.dot(y, y)`. The tolerance used for the dual gap.
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n_iter : int
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Number of coordinate descent iterations.
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"""
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if floating is float:
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dtype = np.float32
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else:
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dtype = np.float64
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# get the data information into easy vars
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cdef unsigned int n_samples = X.shape[0]
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cdef unsigned int n_features = X.shape[1]
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# compute norms of the columns of X
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cdef floating[::1] norm_cols_X = np.square(X).sum(axis=0)
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# initial value of the residuals
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cdef floating[::1] R = np.empty(n_samples, dtype=dtype)
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cdef floating[::1] XtA = np.empty(n_features, dtype=dtype)
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cdef floating tmp
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cdef floating w_ii
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cdef floating d_w_max
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cdef floating w_max
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cdef floating d_w_ii
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cdef floating gap = tol + 1.0
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cdef floating d_w_tol = tol
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cdef floating dual_norm_XtA
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cdef floating R_norm2
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cdef floating w_norm2
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cdef floating l1_norm
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cdef floating const
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cdef floating A_norm2
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cdef unsigned int ii
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cdef unsigned int n_iter = 0
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cdef unsigned int f_iter
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cdef uint32_t rand_r_state_seed = rng.randint(0, RAND_R_MAX)
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cdef uint32_t* rand_r_state = &rand_r_state_seed
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if alpha == 0 and beta == 0:
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warnings.warn("Coordinate descent with no regularization may lead to "
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"unexpected results and is discouraged.")
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with nogil:
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# R = y - np.dot(X, w)
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_copy(n_samples, &y[0], 1, &R[0], 1)
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_gemv(ColMajor, NoTrans, n_samples, n_features, -1.0, &X[0, 0],
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n_samples, &w[0], 1, 1.0, &R[0], 1)
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# tol *= np.dot(y, y)
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tol *= _dot(n_samples, &y[0], 1, &y[0], 1)
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for n_iter in range(max_iter):
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w_max = 0.0
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d_w_max = 0.0
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for f_iter in range(n_features): # Loop over coordinates
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if random:
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ii = rand_int(n_features, rand_r_state)
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else:
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ii = f_iter
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if norm_cols_X[ii] == 0.0:
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continue
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w_ii = w[ii] # Store previous value
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if w_ii != 0.0:
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# R += w_ii * X[:,ii]
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_axpy(n_samples, w_ii, &X[0, ii], 1, &R[0], 1)
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# tmp = (X[:,ii]*R).sum()
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tmp = _dot(n_samples, &X[0, ii], 1, &R[0], 1)
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if positive and tmp < 0:
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w[ii] = 0.0
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else:
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w[ii] = (fsign(tmp) * fmax(fabs(tmp) - alpha, 0)
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/ (norm_cols_X[ii] + beta))
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if w[ii] != 0.0:
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# R -= w[ii] * X[:,ii] # Update residual
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_axpy(n_samples, -w[ii], &X[0, ii], 1, &R[0], 1)
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# update the maximum absolute coefficient update
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d_w_ii = fabs(w[ii] - w_ii)
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d_w_max = fmax(d_w_max, d_w_ii)
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w_max = fmax(w_max, fabs(w[ii]))
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if (
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w_max == 0.0
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or d_w_max / w_max < d_w_tol
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or n_iter == max_iter - 1
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):
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# the biggest coordinate update of this iteration was smaller
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# than the tolerance: check the duality gap as ultimate
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# stopping criterion
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# XtA = np.dot(X.T, R) - beta * w
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_copy(n_features, &w[0], 1, &XtA[0], 1)
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_gemv(ColMajor, Trans,
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n_samples, n_features, 1.0, &X[0, 0], n_samples,
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&R[0], 1,
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-beta, &XtA[0], 1)
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if positive:
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dual_norm_XtA = max(n_features, &XtA[0])
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else:
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dual_norm_XtA = abs_max(n_features, &XtA[0])
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# R_norm2 = np.dot(R, R)
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R_norm2 = _dot(n_samples, &R[0], 1, &R[0], 1)
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# w_norm2 = np.dot(w, w)
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w_norm2 = _dot(n_features, &w[0], 1, &w[0], 1)
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if (dual_norm_XtA > alpha):
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const = alpha / dual_norm_XtA
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A_norm2 = R_norm2 * (const ** 2)
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gap = 0.5 * (R_norm2 + A_norm2)
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else:
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const = 1.0
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gap = R_norm2
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l1_norm = _asum(n_features, &w[0], 1)
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# np.dot(R.T, y)
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gap += (alpha * l1_norm
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- const * _dot(n_samples, &R[0], 1, &y[0], 1)
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+ 0.5 * beta * (1 + const ** 2) * (w_norm2))
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if gap < tol:
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# return if we reached desired tolerance
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break
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else:
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# for/else, runs if for doesn't end with a `break`
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with gil:
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message = (
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"Objective did not converge. You might want to increase "
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"the number of iterations, check the scale of the "
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"features or consider increasing regularisation. "
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f"Duality gap: {gap:.3e}, tolerance: {tol:.3e}"
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)
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if alpha < np.finfo(np.float64).eps:
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message += (
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" Linear regression models with null weight for the "
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"l1 regularization term are more efficiently fitted "
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"using one of the solvers implemented in "
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"sklearn.linear_model.Ridge/RidgeCV instead."
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)
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warnings.warn(message, ConvergenceWarning)
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return np.asarray(w), gap, tol, n_iter + 1
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def sparse_enet_coordinate_descent(
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floating[::1] w,
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floating alpha,
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floating beta,
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const floating[::1] X_data,
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const int[::1] X_indices,
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const int[::1] X_indptr,
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const floating[::1] y,
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const floating[::1] sample_weight,
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const floating[::1] X_mean,
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unsigned int max_iter,
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floating tol,
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object rng,
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bint random=0,
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bint positive=0,
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):
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"""Cython version of the coordinate descent algorithm for Elastic-Net
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We minimize:
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1/2 * norm(y - Z w, 2)^2 + alpha * norm(w, 1) + (beta/2) * norm(w, 2)^2
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where Z = X - X_mean.
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With sample weights sw, this becomes
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1/2 * sum(sw * (y - Z w)^2, axis=0) + alpha * norm(w, 1)
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+ (beta/2) * norm(w, 2)^2
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and X_mean is the weighted average of X (per column).
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Returns
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-------
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w : ndarray of shape (n_features,)
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ElasticNet coefficients.
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gap : float
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Achieved dual gap.
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tol : float
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Equals input `tol` times `np.dot(y, y)`. The tolerance used for the dual gap.
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n_iter : int
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Number of coordinate descent iterations.
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"""
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# Notes for sample_weight:
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# For dense X, one centers X and y and then rescales them by sqrt(sample_weight).
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# Here, for sparse X, we get the sample_weight averaged center X_mean. We take care
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# that every calculation results as if we had rescaled y and X (and therefore also
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# X_mean) by sqrt(sample_weight) without actually calculating the square root.
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# We work with:
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# yw = sample_weight
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# R = sample_weight * residual
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# norm_cols_X = np.sum(sample_weight * (X - X_mean)**2, axis=0)
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# get the data information into easy vars
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cdef unsigned int n_samples = y.shape[0]
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cdef unsigned int n_features = w.shape[0]
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# compute norms of the columns of X
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cdef unsigned int ii
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cdef floating[:] norm_cols_X
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cdef unsigned int startptr = X_indptr[0]
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cdef unsigned int endptr
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# initial value of the residuals
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# R = y - Zw, weighted version R = sample_weight * (y - Zw)
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cdef floating[::1] R
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cdef floating[::1] XtA
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cdef const floating[::1] yw
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if floating is float:
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dtype = np.float32
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else:
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dtype = np.float64
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norm_cols_X = np.zeros(n_features, dtype=dtype)
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XtA = np.zeros(n_features, dtype=dtype)
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cdef floating tmp
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cdef floating w_ii
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cdef floating d_w_max
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cdef floating w_max
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cdef floating d_w_ii
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cdef floating X_mean_ii
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cdef floating R_sum = 0.0
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cdef floating R_norm2
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cdef floating w_norm2
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cdef floating A_norm2
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cdef floating l1_norm
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cdef floating normalize_sum
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cdef floating gap = tol + 1.0
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cdef floating d_w_tol = tol
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cdef floating dual_norm_XtA
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cdef unsigned int jj
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cdef unsigned int n_iter = 0
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cdef unsigned int f_iter
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cdef uint32_t rand_r_state_seed = rng.randint(0, RAND_R_MAX)
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cdef uint32_t* rand_r_state = &rand_r_state_seed
|
||
|
|
cdef bint center = False
|
||
|
|
cdef bint no_sample_weights = sample_weight is None
|
||
|
|
cdef int kk
|
||
|
|
|
||
|
|
if no_sample_weights:
|
||
|
|
yw = y
|
||
|
|
R = y.copy()
|
||
|
|
else:
|
||
|
|
yw = np.multiply(sample_weight, y)
|
||
|
|
R = yw.copy()
|
||
|
|
|
||
|
|
with nogil:
|
||
|
|
# center = (X_mean != 0).any()
|
||
|
|
for ii in range(n_features):
|
||
|
|
if X_mean[ii]:
|
||
|
|
center = True
|
||
|
|
break
|
||
|
|
|
||
|
|
for ii in range(n_features):
|
||
|
|
X_mean_ii = X_mean[ii]
|
||
|
|
endptr = X_indptr[ii + 1]
|
||
|
|
normalize_sum = 0.0
|
||
|
|
w_ii = w[ii]
|
||
|
|
|
||
|
|
if no_sample_weights:
|
||
|
|
for jj in range(startptr, endptr):
|
||
|
|
normalize_sum += (X_data[jj] - X_mean_ii) ** 2
|
||
|
|
R[X_indices[jj]] -= X_data[jj] * w_ii
|
||
|
|
norm_cols_X[ii] = normalize_sum + \
|
||
|
|
(n_samples - endptr + startptr) * X_mean_ii ** 2
|
||
|
|
if center:
|
||
|
|
for jj in range(n_samples):
|
||
|
|
R[jj] += X_mean_ii * w_ii
|
||
|
|
else:
|
||
|
|
for jj in range(startptr, endptr):
|
||
|
|
tmp = sample_weight[X_indices[jj]]
|
||
|
|
# second term will be subtracted by loop over range(n_samples)
|
||
|
|
normalize_sum += (tmp * (X_data[jj] - X_mean_ii) ** 2
|
||
|
|
- tmp * X_mean_ii ** 2)
|
||
|
|
R[X_indices[jj]] -= tmp * X_data[jj] * w_ii
|
||
|
|
if center:
|
||
|
|
for jj in range(n_samples):
|
||
|
|
normalize_sum += sample_weight[jj] * X_mean_ii ** 2
|
||
|
|
R[jj] += sample_weight[jj] * X_mean_ii * w_ii
|
||
|
|
norm_cols_X[ii] = normalize_sum
|
||
|
|
startptr = endptr
|
||
|
|
|
||
|
|
# tol *= np.dot(y, y)
|
||
|
|
# with sample weights: tol *= y @ (sw * y)
|
||
|
|
tol *= _dot(n_samples, &y[0], 1, &yw[0], 1)
|
||
|
|
|
||
|
|
for n_iter in range(max_iter):
|
||
|
|
|
||
|
|
w_max = 0.0
|
||
|
|
d_w_max = 0.0
|
||
|
|
|
||
|
|
for f_iter in range(n_features): # Loop over coordinates
|
||
|
|
if random:
|
||
|
|
ii = rand_int(n_features, rand_r_state)
|
||
|
|
else:
|
||
|
|
ii = f_iter
|
||
|
|
|
||
|
|
if norm_cols_X[ii] == 0.0:
|
||
|
|
continue
|
||
|
|
|
||
|
|
startptr = X_indptr[ii]
|
||
|
|
endptr = X_indptr[ii + 1]
|
||
|
|
w_ii = w[ii] # Store previous value
|
||
|
|
X_mean_ii = X_mean[ii]
|
||
|
|
|
||
|
|
if w_ii != 0.0:
|
||
|
|
# R += w_ii * X[:,ii]
|
||
|
|
if no_sample_weights:
|
||
|
|
for jj in range(startptr, endptr):
|
||
|
|
R[X_indices[jj]] += X_data[jj] * w_ii
|
||
|
|
if center:
|
||
|
|
for jj in range(n_samples):
|
||
|
|
R[jj] -= X_mean_ii * w_ii
|
||
|
|
else:
|
||
|
|
for jj in range(startptr, endptr):
|
||
|
|
tmp = sample_weight[X_indices[jj]]
|
||
|
|
R[X_indices[jj]] += tmp * X_data[jj] * w_ii
|
||
|
|
if center:
|
||
|
|
for jj in range(n_samples):
|
||
|
|
R[jj] -= sample_weight[jj] * X_mean_ii * w_ii
|
||
|
|
|
||
|
|
# tmp = (X[:,ii] * R).sum()
|
||
|
|
tmp = 0.0
|
||
|
|
for jj in range(startptr, endptr):
|
||
|
|
tmp += R[X_indices[jj]] * X_data[jj]
|
||
|
|
|
||
|
|
if center:
|
||
|
|
R_sum = 0.0
|
||
|
|
for jj in range(n_samples):
|
||
|
|
R_sum += R[jj]
|
||
|
|
tmp -= R_sum * X_mean_ii
|
||
|
|
|
||
|
|
if positive and tmp < 0.0:
|
||
|
|
w[ii] = 0.0
|
||
|
|
else:
|
||
|
|
w[ii] = fsign(tmp) * fmax(fabs(tmp) - alpha, 0) \
|
||
|
|
/ (norm_cols_X[ii] + beta)
|
||
|
|
|
||
|
|
if w[ii] != 0.0:
|
||
|
|
# R -= w[ii] * X[:,ii] # Update residual
|
||
|
|
if no_sample_weights:
|
||
|
|
for jj in range(startptr, endptr):
|
||
|
|
R[X_indices[jj]] -= X_data[jj] * w[ii]
|
||
|
|
if center:
|
||
|
|
for jj in range(n_samples):
|
||
|
|
R[jj] += X_mean_ii * w[ii]
|
||
|
|
else:
|
||
|
|
for jj in range(startptr, endptr):
|
||
|
|
tmp = sample_weight[X_indices[jj]]
|
||
|
|
R[X_indices[jj]] -= tmp * X_data[jj] * w[ii]
|
||
|
|
if center:
|
||
|
|
for jj in range(n_samples):
|
||
|
|
R[jj] += sample_weight[jj] * X_mean_ii * w[ii]
|
||
|
|
|
||
|
|
# update the maximum absolute coefficient update
|
||
|
|
d_w_ii = fabs(w[ii] - w_ii)
|
||
|
|
d_w_max = fmax(d_w_max, d_w_ii)
|
||
|
|
|
||
|
|
w_max = fmax(w_max, fabs(w[ii]))
|
||
|
|
|
||
|
|
if w_max == 0.0 or d_w_max / w_max < d_w_tol or n_iter == max_iter - 1:
|
||
|
|
# the biggest coordinate update of this iteration was smaller than
|
||
|
|
# the tolerance: check the duality gap as ultimate stopping
|
||
|
|
# criterion
|
||
|
|
|
||
|
|
# sparse X.T / dense R dot product
|
||
|
|
if center:
|
||
|
|
R_sum = 0.0
|
||
|
|
for jj in range(n_samples):
|
||
|
|
R_sum += R[jj]
|
||
|
|
|
||
|
|
# XtA = X.T @ R - beta * w
|
||
|
|
for ii in range(n_features):
|
||
|
|
XtA[ii] = 0.0
|
||
|
|
for kk in range(X_indptr[ii], X_indptr[ii + 1]):
|
||
|
|
XtA[ii] += X_data[kk] * R[X_indices[kk]]
|
||
|
|
|
||
|
|
if center:
|
||
|
|
XtA[ii] -= X_mean[ii] * R_sum
|
||
|
|
XtA[ii] -= beta * w[ii]
|
||
|
|
|
||
|
|
if positive:
|
||
|
|
dual_norm_XtA = max(n_features, &XtA[0])
|
||
|
|
else:
|
||
|
|
dual_norm_XtA = abs_max(n_features, &XtA[0])
|
||
|
|
|
||
|
|
# R_norm2 = np.dot(R, R)
|
||
|
|
if no_sample_weights:
|
||
|
|
R_norm2 = _dot(n_samples, &R[0], 1, &R[0], 1)
|
||
|
|
else:
|
||
|
|
R_norm2 = 0.0
|
||
|
|
for jj in range(n_samples):
|
||
|
|
# R is already multiplied by sample_weight
|
||
|
|
if sample_weight[jj] != 0:
|
||
|
|
R_norm2 += (R[jj] ** 2) / sample_weight[jj]
|
||
|
|
|
||
|
|
# w_norm2 = np.dot(w, w)
|
||
|
|
w_norm2 = _dot(n_features, &w[0], 1, &w[0], 1)
|
||
|
|
if (dual_norm_XtA > alpha):
|
||
|
|
const = alpha / dual_norm_XtA
|
||
|
|
A_norm2 = R_norm2 * const**2
|
||
|
|
gap = 0.5 * (R_norm2 + A_norm2)
|
||
|
|
else:
|
||
|
|
const = 1.0
|
||
|
|
gap = R_norm2
|
||
|
|
|
||
|
|
l1_norm = _asum(n_features, &w[0], 1)
|
||
|
|
|
||
|
|
gap += (alpha * l1_norm - const * _dot(
|
||
|
|
n_samples,
|
||
|
|
&R[0], 1,
|
||
|
|
&y[0], 1
|
||
|
|
)
|
||
|
|
+ 0.5 * beta * (1 + const ** 2) * w_norm2)
|
||
|
|
|
||
|
|
if gap < tol:
|
||
|
|
# return if we reached desired tolerance
|
||
|
|
break
|
||
|
|
|
||
|
|
else:
|
||
|
|
# for/else, runs if for doesn't end with a `break`
|
||
|
|
with gil:
|
||
|
|
warnings.warn("Objective did not converge. You might want to "
|
||
|
|
"increase the number of iterations. Duality "
|
||
|
|
"gap: {}, tolerance: {}".format(gap, tol),
|
||
|
|
ConvergenceWarning)
|
||
|
|
|
||
|
|
return np.asarray(w), gap, tol, n_iter + 1
|
||
|
|
|
||
|
|
|
||
|
|
def enet_coordinate_descent_gram(
|
||
|
|
floating[::1] w,
|
||
|
|
floating alpha,
|
||
|
|
floating beta,
|
||
|
|
const floating[:, ::1] Q,
|
||
|
|
const floating[::1] q,
|
||
|
|
const floating[:] y,
|
||
|
|
unsigned int max_iter,
|
||
|
|
floating tol,
|
||
|
|
object rng,
|
||
|
|
bint random=0,
|
||
|
|
bint positive=0
|
||
|
|
):
|
||
|
|
"""Cython version of the coordinate descent algorithm
|
||
|
|
for Elastic-Net regression
|
||
|
|
|
||
|
|
We minimize
|
||
|
|
|
||
|
|
(1/2) * w^T Q w - q^T w + alpha norm(w, 1) + (beta/2) * norm(w, 2)^2
|
||
|
|
|
||
|
|
which amount to the Elastic-Net problem when:
|
||
|
|
Q = X^T X (Gram matrix)
|
||
|
|
q = X^T y
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
w : ndarray of shape (n_features,)
|
||
|
|
ElasticNet coefficients.
|
||
|
|
gap : float
|
||
|
|
Achieved dual gap.
|
||
|
|
tol : float
|
||
|
|
Equals input `tol` times `np.dot(y, y)`. The tolerance used for the dual gap.
|
||
|
|
n_iter : int
|
||
|
|
Number of coordinate descent iterations.
|
||
|
|
"""
|
||
|
|
|
||
|
|
if floating is float:
|
||
|
|
dtype = np.float32
|
||
|
|
else:
|
||
|
|
dtype = np.float64
|
||
|
|
|
||
|
|
# get the data information into easy vars
|
||
|
|
cdef unsigned int n_features = Q.shape[0]
|
||
|
|
|
||
|
|
# initial value "Q w" which will be kept of up to date in the iterations
|
||
|
|
cdef floating[:] H = np.dot(Q, w)
|
||
|
|
|
||
|
|
cdef floating[:] XtA = np.zeros(n_features, dtype=dtype)
|
||
|
|
cdef floating tmp
|
||
|
|
cdef floating w_ii
|
||
|
|
cdef floating d_w_max
|
||
|
|
cdef floating w_max
|
||
|
|
cdef floating d_w_ii
|
||
|
|
cdef floating q_dot_w
|
||
|
|
cdef floating w_norm2
|
||
|
|
cdef floating gap = tol + 1.0
|
||
|
|
cdef floating d_w_tol = tol
|
||
|
|
cdef floating dual_norm_XtA
|
||
|
|
cdef unsigned int ii
|
||
|
|
cdef unsigned int n_iter = 0
|
||
|
|
cdef unsigned int f_iter
|
||
|
|
cdef uint32_t rand_r_state_seed = rng.randint(0, RAND_R_MAX)
|
||
|
|
cdef uint32_t* rand_r_state = &rand_r_state_seed
|
||
|
|
|
||
|
|
cdef floating y_norm2 = np.dot(y, y)
|
||
|
|
cdef floating* w_ptr = &w[0]
|
||
|
|
cdef const floating* Q_ptr = &Q[0, 0]
|
||
|
|
cdef const floating* q_ptr = &q[0]
|
||
|
|
cdef floating* H_ptr = &H[0]
|
||
|
|
cdef floating* XtA_ptr = &XtA[0]
|
||
|
|
tol = tol * y_norm2
|
||
|
|
|
||
|
|
if alpha == 0:
|
||
|
|
warnings.warn(
|
||
|
|
"Coordinate descent without L1 regularization may "
|
||
|
|
"lead to unexpected results and is discouraged. "
|
||
|
|
"Set l1_ratio > 0 to add L1 regularization."
|
||
|
|
)
|
||
|
|
|
||
|
|
with nogil:
|
||
|
|
for n_iter in range(max_iter):
|
||
|
|
w_max = 0.0
|
||
|
|
d_w_max = 0.0
|
||
|
|
for f_iter in range(n_features): # Loop over coordinates
|
||
|
|
if random:
|
||
|
|
ii = rand_int(n_features, rand_r_state)
|
||
|
|
else:
|
||
|
|
ii = f_iter
|
||
|
|
|
||
|
|
if Q[ii, ii] == 0.0:
|
||
|
|
continue
|
||
|
|
|
||
|
|
w_ii = w[ii] # Store previous value
|
||
|
|
|
||
|
|
if w_ii != 0.0:
|
||
|
|
# H -= w_ii * Q[ii]
|
||
|
|
_axpy(n_features, -w_ii, Q_ptr + ii * n_features, 1,
|
||
|
|
H_ptr, 1)
|
||
|
|
|
||
|
|
tmp = q[ii] - H[ii]
|
||
|
|
|
||
|
|
if positive and tmp < 0:
|
||
|
|
w[ii] = 0.0
|
||
|
|
else:
|
||
|
|
w[ii] = fsign(tmp) * fmax(fabs(tmp) - alpha, 0) \
|
||
|
|
/ (Q[ii, ii] + beta)
|
||
|
|
|
||
|
|
if w[ii] != 0.0:
|
||
|
|
# H += w[ii] * Q[ii] # Update H = X.T X w
|
||
|
|
_axpy(n_features, w[ii], Q_ptr + ii * n_features, 1,
|
||
|
|
H_ptr, 1)
|
||
|
|
|
||
|
|
# update the maximum absolute coefficient update
|
||
|
|
d_w_ii = fabs(w[ii] - w_ii)
|
||
|
|
if d_w_ii > d_w_max:
|
||
|
|
d_w_max = d_w_ii
|
||
|
|
|
||
|
|
if fabs(w[ii]) > w_max:
|
||
|
|
w_max = fabs(w[ii])
|
||
|
|
|
||
|
|
if w_max == 0.0 or d_w_max / w_max < d_w_tol or n_iter == max_iter - 1:
|
||
|
|
# the biggest coordinate update of this iteration was smaller than
|
||
|
|
# the tolerance: check the duality gap as ultimate stopping
|
||
|
|
# criterion
|
||
|
|
|
||
|
|
# q_dot_w = np.dot(w, q)
|
||
|
|
q_dot_w = _dot(n_features, w_ptr, 1, q_ptr, 1)
|
||
|
|
|
||
|
|
for ii in range(n_features):
|
||
|
|
XtA[ii] = q[ii] - H[ii] - beta * w[ii]
|
||
|
|
if positive:
|
||
|
|
dual_norm_XtA = max(n_features, XtA_ptr)
|
||
|
|
else:
|
||
|
|
dual_norm_XtA = abs_max(n_features, XtA_ptr)
|
||
|
|
|
||
|
|
# temp = np.sum(w * H)
|
||
|
|
tmp = 0.0
|
||
|
|
for ii in range(n_features):
|
||
|
|
tmp += w[ii] * H[ii]
|
||
|
|
R_norm2 = y_norm2 + tmp - 2.0 * q_dot_w
|
||
|
|
|
||
|
|
# w_norm2 = np.dot(w, w)
|
||
|
|
w_norm2 = _dot(n_features, &w[0], 1, &w[0], 1)
|
||
|
|
|
||
|
|
if (dual_norm_XtA > alpha):
|
||
|
|
const = alpha / dual_norm_XtA
|
||
|
|
A_norm2 = R_norm2 * (const ** 2)
|
||
|
|
gap = 0.5 * (R_norm2 + A_norm2)
|
||
|
|
else:
|
||
|
|
const = 1.0
|
||
|
|
gap = R_norm2
|
||
|
|
|
||
|
|
# The call to asum is equivalent to the L1 norm of w
|
||
|
|
gap += (
|
||
|
|
alpha * _asum(n_features, &w[0], 1)
|
||
|
|
- const * y_norm2
|
||
|
|
+ const * q_dot_w
|
||
|
|
+ 0.5 * beta * (1 + const ** 2) * w_norm2
|
||
|
|
)
|
||
|
|
|
||
|
|
if gap < tol:
|
||
|
|
# return if we reached desired tolerance
|
||
|
|
break
|
||
|
|
|
||
|
|
else:
|
||
|
|
# for/else, runs if for doesn't end with a `break`
|
||
|
|
with gil:
|
||
|
|
warnings.warn("Objective did not converge. You might want to "
|
||
|
|
"increase the number of iterations. Duality "
|
||
|
|
"gap: {}, tolerance: {}".format(gap, tol),
|
||
|
|
ConvergenceWarning)
|
||
|
|
|
||
|
|
return np.asarray(w), gap, tol, n_iter + 1
|
||
|
|
|
||
|
|
|
||
|
|
def enet_coordinate_descent_multi_task(
|
||
|
|
const floating[::1, :] W,
|
||
|
|
floating l1_reg,
|
||
|
|
floating l2_reg,
|
||
|
|
const floating[::1, :] X,
|
||
|
|
const floating[::1, :] Y,
|
||
|
|
unsigned int max_iter,
|
||
|
|
floating tol,
|
||
|
|
object rng,
|
||
|
|
bint random=0
|
||
|
|
):
|
||
|
|
"""Cython version of the coordinate descent algorithm
|
||
|
|
for Elastic-Net mult-task regression
|
||
|
|
|
||
|
|
We minimize
|
||
|
|
|
||
|
|
0.5 * norm(Y - X W.T, 2)^2 + l1_reg ||W.T||_21 + 0.5 * l2_reg norm(W.T, 2)^2
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
W : ndarray of shape (n_tasks, n_features)
|
||
|
|
ElasticNet coefficients.
|
||
|
|
gap : float
|
||
|
|
Achieved dual gap.
|
||
|
|
tol : float
|
||
|
|
Equals input `tol` times `np.dot(y, y)`. The tolerance used for the dual gap.
|
||
|
|
n_iter : int
|
||
|
|
Number of coordinate descent iterations.
|
||
|
|
"""
|
||
|
|
|
||
|
|
if floating is float:
|
||
|
|
dtype = np.float32
|
||
|
|
else:
|
||
|
|
dtype = np.float64
|
||
|
|
|
||
|
|
# get the data information into easy vars
|
||
|
|
cdef unsigned int n_samples = X.shape[0]
|
||
|
|
cdef unsigned int n_features = X.shape[1]
|
||
|
|
cdef unsigned int n_tasks = Y.shape[1]
|
||
|
|
|
||
|
|
# to store XtA
|
||
|
|
cdef floating[:, ::1] XtA = np.zeros((n_features, n_tasks), dtype=dtype)
|
||
|
|
cdef floating XtA_axis1norm
|
||
|
|
cdef floating dual_norm_XtA
|
||
|
|
|
||
|
|
# initial value of the residuals
|
||
|
|
cdef floating[::1, :] R = np.zeros((n_samples, n_tasks), dtype=dtype, order='F')
|
||
|
|
|
||
|
|
cdef floating[::1] norm_cols_X = np.zeros(n_features, dtype=dtype)
|
||
|
|
cdef floating[::1] tmp = np.zeros(n_tasks, dtype=dtype)
|
||
|
|
cdef floating[::1] w_ii = np.zeros(n_tasks, dtype=dtype)
|
||
|
|
cdef floating d_w_max
|
||
|
|
cdef floating w_max
|
||
|
|
cdef floating d_w_ii
|
||
|
|
cdef floating nn
|
||
|
|
cdef floating W_ii_abs_max
|
||
|
|
cdef floating gap = tol + 1.0
|
||
|
|
cdef floating d_w_tol = tol
|
||
|
|
cdef floating R_norm
|
||
|
|
cdef floating w_norm
|
||
|
|
cdef floating ry_sum
|
||
|
|
cdef floating l21_norm
|
||
|
|
cdef unsigned int ii
|
||
|
|
cdef unsigned int jj
|
||
|
|
cdef unsigned int n_iter = 0
|
||
|
|
cdef unsigned int f_iter
|
||
|
|
cdef uint32_t rand_r_state_seed = rng.randint(0, RAND_R_MAX)
|
||
|
|
cdef uint32_t* rand_r_state = &rand_r_state_seed
|
||
|
|
|
||
|
|
cdef const floating* X_ptr = &X[0, 0]
|
||
|
|
cdef const floating* Y_ptr = &Y[0, 0]
|
||
|
|
|
||
|
|
if l1_reg == 0:
|
||
|
|
warnings.warn(
|
||
|
|
"Coordinate descent with l1_reg=0 may lead to unexpected"
|
||
|
|
" results and is discouraged."
|
||
|
|
)
|
||
|
|
|
||
|
|
with nogil:
|
||
|
|
# norm_cols_X = (np.asarray(X) ** 2).sum(axis=0)
|
||
|
|
for ii in range(n_features):
|
||
|
|
norm_cols_X[ii] = _nrm2(n_samples, X_ptr + ii * n_samples, 1) ** 2
|
||
|
|
|
||
|
|
# R = Y - np.dot(X, W.T)
|
||
|
|
_copy(n_samples * n_tasks, Y_ptr, 1, &R[0, 0], 1)
|
||
|
|
for ii in range(n_features):
|
||
|
|
for jj in range(n_tasks):
|
||
|
|
if W[jj, ii] != 0:
|
||
|
|
_axpy(n_samples, -W[jj, ii], X_ptr + ii * n_samples, 1,
|
||
|
|
&R[0, jj], 1)
|
||
|
|
|
||
|
|
# tol = tol * linalg.norm(Y, ord='fro') ** 2
|
||
|
|
tol = tol * _nrm2(n_samples * n_tasks, Y_ptr, 1) ** 2
|
||
|
|
|
||
|
|
for n_iter in range(max_iter):
|
||
|
|
w_max = 0.0
|
||
|
|
d_w_max = 0.0
|
||
|
|
for f_iter in range(n_features): # Loop over coordinates
|
||
|
|
if random:
|
||
|
|
ii = rand_int(n_features, rand_r_state)
|
||
|
|
else:
|
||
|
|
ii = f_iter
|
||
|
|
|
||
|
|
if norm_cols_X[ii] == 0.0:
|
||
|
|
continue
|
||
|
|
|
||
|
|
# w_ii = W[:, ii] # Store previous value
|
||
|
|
_copy(n_tasks, &W[0, ii], 1, &w_ii[0], 1)
|
||
|
|
|
||
|
|
# Using Numpy:
|
||
|
|
# R += np.dot(X[:, ii][:, None], w_ii[None, :]) # rank 1 update
|
||
|
|
# Using Blas Level2:
|
||
|
|
# _ger(RowMajor, n_samples, n_tasks, 1.0,
|
||
|
|
# &X[0, ii], 1,
|
||
|
|
# &w_ii[0], 1, &R[0, 0], n_tasks)
|
||
|
|
# Using Blas Level1 and for loop to avoid slower threads
|
||
|
|
# for such small vectors
|
||
|
|
for jj in range(n_tasks):
|
||
|
|
if w_ii[jj] != 0:
|
||
|
|
_axpy(n_samples, w_ii[jj], X_ptr + ii * n_samples, 1,
|
||
|
|
&R[0, jj], 1)
|
||
|
|
|
||
|
|
# Using numpy:
|
||
|
|
# tmp = np.dot(X[:, ii][None, :], R).ravel()
|
||
|
|
# Using BLAS Level 2:
|
||
|
|
# _gemv(RowMajor, Trans, n_samples, n_tasks, 1.0, &R[0, 0],
|
||
|
|
# n_tasks, &X[0, ii], 1, 0.0, &tmp[0], 1)
|
||
|
|
# Using BLAS Level 1 (faster for small vectors like here):
|
||
|
|
for jj in range(n_tasks):
|
||
|
|
tmp[jj] = _dot(n_samples, X_ptr + ii * n_samples, 1,
|
||
|
|
&R[0, jj], 1)
|
||
|
|
|
||
|
|
# nn = sqrt(np.sum(tmp ** 2))
|
||
|
|
nn = _nrm2(n_tasks, &tmp[0], 1)
|
||
|
|
|
||
|
|
# W[:, ii] = tmp * fmax(1. - l1_reg / nn, 0) / (norm_cols_X[ii] + l2_reg)
|
||
|
|
_copy(n_tasks, &tmp[0], 1, &W[0, ii], 1)
|
||
|
|
_scal(n_tasks, fmax(1. - l1_reg / nn, 0) / (norm_cols_X[ii] + l2_reg),
|
||
|
|
&W[0, ii], 1)
|
||
|
|
|
||
|
|
# Using numpy:
|
||
|
|
# R -= np.dot(X[:, ii][:, None], W[:, ii][None, :])
|
||
|
|
# Using BLAS Level 2:
|
||
|
|
# Update residual : rank 1 update
|
||
|
|
# _ger(RowMajor, n_samples, n_tasks, -1.0,
|
||
|
|
# &X[0, ii], 1, &W[0, ii], 1,
|
||
|
|
# &R[0, 0], n_tasks)
|
||
|
|
# Using BLAS Level 1 (faster for small vectors like here):
|
||
|
|
for jj in range(n_tasks):
|
||
|
|
if W[jj, ii] != 0:
|
||
|
|
_axpy(n_samples, -W[jj, ii], X_ptr + ii * n_samples, 1,
|
||
|
|
&R[0, jj], 1)
|
||
|
|
|
||
|
|
# update the maximum absolute coefficient update
|
||
|
|
d_w_ii = diff_abs_max(n_tasks, &W[0, ii], &w_ii[0])
|
||
|
|
|
||
|
|
if d_w_ii > d_w_max:
|
||
|
|
d_w_max = d_w_ii
|
||
|
|
|
||
|
|
W_ii_abs_max = abs_max(n_tasks, &W[0, ii])
|
||
|
|
if W_ii_abs_max > w_max:
|
||
|
|
w_max = W_ii_abs_max
|
||
|
|
|
||
|
|
if w_max == 0.0 or d_w_max / w_max < d_w_tol or n_iter == max_iter - 1:
|
||
|
|
# the biggest coordinate update of this iteration was smaller than
|
||
|
|
# the tolerance: check the duality gap as ultimate stopping
|
||
|
|
# criterion
|
||
|
|
|
||
|
|
# XtA = np.dot(X.T, R) - l2_reg * W.T
|
||
|
|
for ii in range(n_features):
|
||
|
|
for jj in range(n_tasks):
|
||
|
|
XtA[ii, jj] = _dot(
|
||
|
|
n_samples, X_ptr + ii * n_samples, 1, &R[0, jj], 1
|
||
|
|
) - l2_reg * W[jj, ii]
|
||
|
|
|
||
|
|
# dual_norm_XtA = np.max(np.sqrt(np.sum(XtA ** 2, axis=1)))
|
||
|
|
dual_norm_XtA = 0.0
|
||
|
|
for ii in range(n_features):
|
||
|
|
# np.sqrt(np.sum(XtA ** 2, axis=1))
|
||
|
|
XtA_axis1norm = _nrm2(n_tasks, &XtA[ii, 0], 1)
|
||
|
|
if XtA_axis1norm > dual_norm_XtA:
|
||
|
|
dual_norm_XtA = XtA_axis1norm
|
||
|
|
|
||
|
|
# TODO: use squared L2 norm directly
|
||
|
|
# R_norm = linalg.norm(R, ord='fro')
|
||
|
|
# w_norm = linalg.norm(W, ord='fro')
|
||
|
|
R_norm = _nrm2(n_samples * n_tasks, &R[0, 0], 1)
|
||
|
|
w_norm = _nrm2(n_features * n_tasks, &W[0, 0], 1)
|
||
|
|
if (dual_norm_XtA > l1_reg):
|
||
|
|
const = l1_reg / dual_norm_XtA
|
||
|
|
A_norm = R_norm * const
|
||
|
|
gap = 0.5 * (R_norm ** 2 + A_norm ** 2)
|
||
|
|
else:
|
||
|
|
const = 1.0
|
||
|
|
gap = R_norm ** 2
|
||
|
|
|
||
|
|
# ry_sum = np.sum(R * y)
|
||
|
|
ry_sum = _dot(n_samples * n_tasks, &R[0, 0], 1, &Y[0, 0], 1)
|
||
|
|
|
||
|
|
# l21_norm = np.sqrt(np.sum(W ** 2, axis=0)).sum()
|
||
|
|
l21_norm = 0.0
|
||
|
|
for ii in range(n_features):
|
||
|
|
l21_norm += _nrm2(n_tasks, &W[0, ii], 1)
|
||
|
|
|
||
|
|
gap += (
|
||
|
|
l1_reg * l21_norm
|
||
|
|
- const * ry_sum
|
||
|
|
+ 0.5 * l2_reg * (1 + const ** 2) * (w_norm ** 2)
|
||
|
|
)
|
||
|
|
|
||
|
|
if gap < tol:
|
||
|
|
# return if we reached desired tolerance
|
||
|
|
break
|
||
|
|
else:
|
||
|
|
# for/else, runs if for doesn't end with a `break`
|
||
|
|
with gil:
|
||
|
|
warnings.warn("Objective did not converge. You might want to "
|
||
|
|
"increase the number of iterations. Duality "
|
||
|
|
"gap: {}, tolerance: {}".format(gap, tol),
|
||
|
|
ConvergenceWarning)
|
||
|
|
|
||
|
|
return np.asarray(W), gap, tol, n_iter + 1
|