plt_logistic_loss.py

"""----------------------------------------------------------------
 logistic_loss plotting routines and support
"""

from matplotlib import cm
from lab_utils_common import sigmoid, dlblue, dlorange, np, plt, compute_cost_matrix

def compute_cost_logistic_sq_err(X, y, w, b):
    """
    compute sq error cost on logicist data (for negative example only, not used in practice)
    Args:
      X (ndarray): Shape (m,n) matrix of examples with multiple features
      w (ndarray): Shape (n)   parameters for prediction
      b (scalar):              parameter  for prediction
    Returns:
      cost (scalar): cost
    """
    m = X.shape[0]
    cost = 0.0
    for i in range(m):
        z_i = np.dot(X[i],w) + b
        f_wb_i = sigmoid(z_i)                 #add sigmoid to normal sq error cost for linear regression
        cost = cost + (f_wb_i - y[i])**2
    cost = cost / (2 * m)
    return np.squeeze(cost)

def plt_logistic_squared_error(X,y):
    """ plots logistic squared error for demonstration """
    wx, by = np.meshgrid(np.linspace(-6,12,50),
                         np.linspace(10, -20, 40))
    points = np.c_[wx.ravel(), by.ravel()]
    cost = np.zeros(points.shape[0])

    for i in range(points.shape[0]):
        w,b = points[i]
        cost[i] = compute_cost_logistic_sq_err(X.reshape(-1,1), y, w, b)
    cost = cost.reshape(wx.shape)

    fig = plt.figure()
    fig.canvas.toolbar_visible = False
    fig.canvas.header_visible = False
    fig.canvas.footer_visible = False
    ax = fig.add_subplot(1, 1, 1, projection='3d')
    ax.plot_surface(wx, by, cost, alpha=0.6,cmap=cm.jet,)

    ax.set_xlabel('w', fontsize=16)
    ax.set_ylabel('b', fontsize=16)
    ax.set_zlabel("Cost", rotation=90, fontsize=16)
    ax.set_title('"Logistic" Squared Error Cost vs (w, b)')
    ax.xaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
    ax.yaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
    ax.zaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))


def plt_logistic_cost(X,y):
    """ plots logistic cost """
    wx, by = np.meshgrid(np.linspace(-6,12,50),
                         np.linspace(0, -20, 40))
    points = np.c_[wx.ravel(), by.ravel()]
    cost = np.zeros(points.shape[0],dtype=np.longdouble)

    for i in range(points.shape[0]):
        w,b = points[i]
        cost[i] = compute_cost_matrix(X.reshape(-1,1), y, w, b, logistic=True, safe=True)
    cost = cost.reshape(wx.shape)

    fig = plt.figure(figsize=(9,5))
    fig.canvas.toolbar_visible = False
    fig.canvas.header_visible = False
    fig.canvas.footer_visible = False
    ax = fig.add_subplot(1, 2, 1, projection='3d')
    ax.plot_surface(wx, by, cost, alpha=0.6,cmap=cm.jet,)

    ax.set_xlabel('w', fontsize=16)
    ax.set_ylabel('b', fontsize=16)
    ax.set_zlabel("Cost", rotation=90, fontsize=16)
    ax.set_title('Logistic Cost vs (w, b)')
    ax.xaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
    ax.yaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
    ax.zaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))

    ax = fig.add_subplot(1, 2, 2, projection='3d')

    ax.plot_surface(wx, by, np.log(cost), alpha=0.6,cmap=cm.jet,)

    ax.set_xlabel('w', fontsize=16)
    ax.set_ylabel('b', fontsize=16)
    ax.set_zlabel('\nlog(Cost)', fontsize=16)
    ax.set_title('log(Logistic Cost) vs (w, b)')
    ax.xaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
    ax.yaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
    ax.zaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))

    plt.show()
    return cost


def soup_bowl():
    """ creates 3D quadratic error surface """
    #Create figure and plot with a 3D projection
    fig = plt.figure(figsize=(4,4))
    fig.canvas.toolbar_visible = False
    fig.canvas.header_visible = False
    fig.canvas.footer_visible = False

    #Plot configuration
    ax = fig.add_subplot(111, projection='3d')
    ax.xaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
    ax.yaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
    ax.zaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
    ax.zaxis.set_rotate_label(False)
    ax.view_init(15, -120)

    #Useful linearspaces to give values to the parameters w and b
    w = np.linspace(-20, 20, 100)
    b = np.linspace(-20, 20, 100)

    #Get the z value for a bowl-shaped cost function
    z=np.zeros((len(w), len(b)))
    j=0
    for x in w:
        i=0
        for y in b:
            z[i,j] = x**2 + y**2
            i+=1
        j+=1

    #Meshgrid used for plotting 3D functions
    W, B = np.meshgrid(w, b)

    #Create the 3D surface plot of the bowl-shaped cost function
    ax.plot_surface(W, B, z, cmap = "Spectral_r", alpha=0.7, antialiased=False)
    ax.plot_wireframe(W, B, z, color='k', alpha=0.1)
    ax.set_xlabel("$w$")
    ax.set_ylabel("$b$")
    ax.set_zlabel("Cost", rotation=90)
    ax.set_title("Squared Error Cost used in Linear Regression")

    plt.show()


def plt_simple_example(x, y):
    """ plots tumor data """
    pos = y == 1
    neg = y == 0

    fig,ax = plt.subplots(1,1,figsize=(5,3))
    fig.canvas.toolbar_visible = False
    fig.canvas.header_visible = False
    fig.canvas.footer_visible = False

    ax.scatter(x[pos], y[pos], marker='x', s=80, c = 'red', label="malignant")
    ax.scatter(x[neg], y[neg], marker='o', s=100, label="benign", facecolors='none', edgecolors=dlblue,lw=3)
    ax.set_ylim(-0.075,1.1)
    ax.set_ylabel('y')
    ax.set_xlabel('Tumor Size')
    ax.legend(loc='lower right')
    ax.set_title("Example of Logistic Regression on Categorical Data")


def plt_two_logistic_loss_curves():
    """ plots the logistic loss """
    fig,ax = plt.subplots(1,2,figsize=(6,3),sharey=True)
    fig.canvas.toolbar_visible = False
    fig.canvas.header_visible = False
    fig.canvas.footer_visible = False
    x = np.linspace(0.01,1-0.01,20)
    ax[0].plot(x,-np.log(x))
    #ax[0].set_title("y = 1")
    ax[0].text(0.5, 4.0, "y = 1", fontsize=12)
    ax[0].set_ylabel("loss")
    ax[0].set_xlabel(r"$f_{w,b}(x)$")
    ax[1].plot(x,-np.log(1-x))
    #ax[1].set_title("y = 0")
    ax[1].text(0.5, 4.0, "y = 0", fontsize=12)
    ax[1].set_xlabel(r"$f_{w,b}(x)$")
    ax[0].annotate("prediction \nmatches \ntarget ", xy= [1,0], xycoords='data',
                 xytext=[-10,30],textcoords='offset points', ha="right", va="center",
                   arrowprops={'arrowstyle': '->', 'color': dlorange, 'lw': 3},)
    ax[0].annotate("loss increases as prediction\n differs from target", xy= [0.1,-np.log(0.1)], xycoords='data',
                 xytext=[10,30],textcoords='offset points', ha="left", va="center",
                   arrowprops={'arrowstyle': '->', 'color': dlorange, 'lw': 3},)
    ax[1].annotate("prediction \nmatches \ntarget ", xy= [0,0], xycoords='data',
                 xytext=[10,30],textcoords='offset points', ha="left", va="center",
                   arrowprops={'arrowstyle': '->', 'color': dlorange, 'lw': 3},)
    ax[1].annotate("loss increases as prediction\n differs from target", xy= [0.9,-np.log(1-0.9)], xycoords='data',
                 xytext=[-10,30],textcoords='offset points', ha="right", va="center",
                   arrowprops={'arrowstyle': '->', 'color': dlorange, 'lw': 3},)
    plt.suptitle("Loss Curves for Two Categorical Target Values", fontsize=12)
    plt.tight_layout()
    plt.show()