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 __init__(self, regularize=False):
self.regularize = regularize
self.lambda_ = 0
fig = plt.figure(figsize=(8, 6))
fig.canvas.toolbar_visible = False
fig.canvas.header_visible = False
fig.canvas.footer_visible = False
fig.set_facecolor('#ffffff') #white
gs = GridSpec(5, 3, figure=fig)
ax0 = fig.add_subplot(gs[0:3, :])
ax1 = fig.add_subplot(gs[-2, :])
ax2 = fig.add_subplot(gs[-1, :])
ax1.set_axis_off()
ax2.set_axis_off()
self.ax = [ax0, ax1, ax2]
self.fig = fig
self.axfitdata = plt.axes([0.26, 0.124, 0.12, 0.1]) #lx,by,w,h
self.bfitdata = Button(self.axfitdata, 'fit data', color=dlc['dlblue'])
self.bfitdata.label.set_fontsize(12)
self.bfitdata.on_clicked(self.fitdata_clicked)
#clear data is a future enhancement
#self.axclrdata = plt.axes([0.26,0.06,0.12,0.05 ]) #lx,by,w,h
#self.bclrdata = Button(self.axclrdata , 'clear data', color='white')
#self.bclrdata.label.set_fontsize(12)
#self.bclrdata.on_clicked(self.clrdata_clicked)
self.cid = fig.canvas.mpl_connect('button_press_event', self.add_data)
self.typebut = button_manager(fig, [0.4, 0.07, 0.15, 0.15],
["Regression", "Categorical"],
[False, True], self.toggle_type)
self.fig.text(0.1, 0.02 + 0.21, "Degree", fontsize=12)
self.degrbut = button_manager(
fig, [0.1, 0.02, 0.15, 0.2], ['1', '2', '3', '4', '5', '6'],
[True, False, False, False, False, False], self.update_equation)
if self.regularize:
self.fig.text(0.6, 0.02 + 0.21, r"lambda($\lambda$)", fontsize=12)
self.lambut = button_manager(
fig, [0.6, 0.02, 0.15, 0.2],
['0.0', '0.2', '0.4', '0.6', '0.8', '1'],
[True, False, False, False, False, False], self.updt_lambda)
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 __init__(self, x_train, y_train, w_range, b_range):
# setup figure
fig = plt.figure(figsize=(10, 6))
fig.canvas.toolbar_visible = False
fig.canvas.header_visible = False
fig.canvas.footer_visible = False
fig.set_facecolor('#ffffff') #white
gs = GridSpec(2, 2, figure=fig)
ax0 = fig.add_subplot(gs[0, 0])
ax1 = fig.add_subplot(gs[0, 1])
ax2 = fig.add_subplot(gs[1, 0], projection='3d')
ax3 = fig.add_subplot(gs[1, 1])
pos = ax3.get_position().get_points() ##[[lb_x,lb_y], [rt_x, rt_y]]
h = 0.05
width = 0.2
axcalc = plt.axes([pos[1, 0] - width, pos[1, 1] - h, width,
h]) #lx,by,w,h
ax = np.array([ax0, ax1, ax2, ax3, axcalc])
self.fig = fig
self.ax = ax
self.x_train = x_train
self.y_train = y_train
self.w = 0. #initial point, non-array
self.b = 0.
# initialize subplots
self.dplot = data_plot(ax[0], x_train, y_train, self.w, self.b)
self.con_plot = contour_and_surface_plot(ax[1], ax[2], x_train,
y_train, w_range, b_range,
self.w, self.b)
self.cplot = cost_plot(ax[3])
# setup events
self.cid = fig.canvas.mpl_connect('button_press_event',
self.click_contour)
self.bcalc = Button(axcalc,
'Run Gradient Descent \nfrom current w,b (click)',
color=dlc["dlorange"])
self.bcalc.on_clicked(self.calc_logistic)