regression_stealer.py 文件源码

def logistic_grad(w, X, Y, alpha):
    """
    Implementation of the logistic loss gradient when Y is a multi-ary
    probability distribution.
    """

    n_classes = Y.shape[1]
    n_features = X.shape[1]
    fit_intercept = w.size == (n_classes * (n_features + 1))
    grad = np.zeros((n_classes, n_features + int(fit_intercept)))

    w = w.reshape(n_classes, -1)

    if fit_intercept:
        intercept = w[:, -1]
        w = w[:, :-1]
    else:
        intercept = 0

    z = safe_sparse_dot(X, w.T) + intercept

    # normalization factor
    denom = expit(z)
    denom = denom.sum(axis=1).reshape((denom.shape[0], -1))

    #
    # d/dwj log(denom)
    #       = 1/denom * d/dw expit(wj * x + b)
    #       = 1/denom * expit(wj * x + b) * expit(-(wj * x + b)) * x
    #
    # d/dwj -Y * log_logistic(z)
    #       = -Y * expit(-(wj * x + b)) * x
    #
    z0 = (np.reciprocal(denom) * expit(z) - Y) * expit(-z)

    grad[:, :n_features] = safe_sparse_dot(z0.T, X)
    grad[:, :n_features] += alpha * w

    if fit_intercept:
        grad[:, -1] = z0.sum(axis=0)

    return grad.ravel()