linreg_map

def linreg_map(X, t, alpha, beta, max_iter=100, tol=1e-4, display=False):
    if display:
        print('%9s %15s' % ('iteration', 'f'))

    n, d = X.shape
    F = lambda w, xi: (alpha * np.sum(xi + (X.dot(w) - t) ** 2 / xi) + n * beta * w.dot(w)) / 2.
    delta = 1e-8

    w = np.ones(d)
    xi = np.ones(n)
    f = F(w, xi)
    if display:
        print('%9d %15.11f' % (0, f))

    for iteration in xrange(1, max_iter + 1):
        A = alpha * ((X).T / xi).dot(X) + n * beta * np.identity(d)
        b = alpha * np.sum(X.T * t / xi, axis=1)
        w = solve(A, b)

        xi = np.abs(X.dot(w) - t)
        xi[xi < delta] = delta
        f_ = f
        f = F(w, xi)

        if display:
            print('%9d %15.11f' % (iteration, f))
        if (np.abs(f_ - f) < tol):
            break
    return w.reshape((-1, 1))