def mk_cost_lines(self, firsttime=False):
''' makes vertical cost lines'''
if not firsttime:
for artist in self.cost_items:
artist.remove()
self.cost_items = []
cstr = f"cost = (1/{self.m})*("
ctot = 0
label = 'cost for point'
addedbreak = False
for p in zip(self.x_train, self.y_train):
f_wb_p = sigmoid(self.w * p[0] + self.b)
c_p = compute_cost_matrix(p[0].reshape(-1, 1),
p[1],
np.array(self.w),
self.b,
logistic=True,
lambda_=0,
safe=True)
c_p_txt = c_p
a = self.ax.vlines(p[0],
p[1],
f_wb_p,
lw=3,
color=dlc["dlpurple"],
ls='dotted',
label=label)
label = '' #just one
cxy = [p[0], p[1] + (f_wb_p - p[1]) / 2]
b = self.ax.annotate(f'{c_p_txt:0.1f}',
xy=cxy,
xycoords='data',
color=dlc["dlpurple"],
xytext=(5, 0),
textcoords='offset points')
cstr += f"{c_p_txt:0.1f} +"
if len(cstr) > 38 and addedbreak is False:
cstr += "\n"
addedbreak = True
ctot += c_p
self.cost_items.extend((a, b))
ctot = ctot / (len(self.x_train))
cstr = cstr[:-1] + f") = {ctot:0.2f}"
## todo.. figure out how to get this textbox to extend to the width of the subplot
c = self.ax.text(0.05,
0.02,
cstr,
transform=self.ax.transAxes,
color=dlc["dlpurple"])
self.cost_items.append(c)
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 draw_logistic_lines(self, firsttime=False):
if not firsttime:
self.aline[0].remove()
self.bline[0].remove()
self.alegend.remove()
xlim = self.ax.get_xlim()
x_hat = np.linspace(*xlim, 30)
y_hat = sigmoid(np.dot(x_hat.reshape(-1, 1), self.w) + self.b)
self.aline = self.ax.plot(x_hat,
y_hat,
color=dlc["dlblue"],
label="y = sigmoid(z)")
f_wb = np.dot(x_hat.reshape(-1, 1), self.w) + self.b
self.bline = self.ax.plot(
x_hat,
f_wb,
color=dlc["dlorange"],
lw=1,
label=f"z = {np.squeeze(self.w):0.2f}x+({self.b:0.2f})")
self.alegend = self.ax.legend(loc='upper left')
def plt_prob(ax, w_out, b_out):
""" plots a decision boundary but include shading to indicate the probability """
#setup useful ranges and common linspaces
x0_space = np.linspace(0, 4, 100)
x1_space = np.linspace(0, 4, 100)
# get probability for x0,x1 ranges
tmp_x0, tmp_x1 = np.meshgrid(x0_space, x1_space)
z = np.zeros_like(tmp_x0)
for i in range(tmp_x0.shape[0]):
for j in range(tmp_x1.shape[1]):
z[i, j] = sigmoid(
np.dot(w_out, np.array([tmp_x0[i, j], tmp_x1[i, j]])) + b_out)
cmap = plt.get_cmap('Blues')
new_cmap = truncate_colormap(cmap, 0.0, 0.5)
pcm = ax.pcolormesh(tmp_x0,
tmp_x1,
z,
norm=cm.colors.Normalize(vmin=0, vmax=1),
cmap=new_cmap,
shading='nearest',
alpha=0.9)
ax.figure.colorbar(pcm, ax=ax)
def calc_logistic(self, event):
if self.bthresh.get_status()[0]:
self.remove_thresh()
for it in [1, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096]:
self.w, self.b, _ = gradient_descent(self.x.reshape(-1, 1),
self.y.reshape(-1, 1),
self.w.reshape(-1, 1),
self.b,
0.1,
it,
logistic=True,
lambda_=0,
verbose=False)
self.aline[0].remove()
self.bline[0].remove()
self.alegend.remove()
xlim = self.ax[0].get_xlim()
x_hat = np.linspace(*xlim, 30)
y_hat = sigmoid(np.matmul(x_hat.reshape(-1, 1), self.w) + self.b)
self.aline = self.ax[0].plot(x_hat,
y_hat,
color=dlblue,
label="y = sigmoid(z)")
f_wb = np.matmul(x_hat.reshape(-1, 1), self.w) + self.b
self.bline = self.ax[0].plot(
x_hat,
f_wb,
color=dlorange,
lw=1,
label=f"z = {np.squeeze(self.w):0.2f}x+({self.b:0.2f})")
self.alegend = self.ax[0].legend(loc='lower right')
time.sleep(0.3)
self.fig.canvas.draw()
if self.bthresh.get_status()[0]:
self.draw_thresh()
self.fig.canvas.draw()
def __init__(self, x, y, w, b, logistic=True):
self.logistic = logistic
pos = y == 1
neg = y == 0
fig, ax = plt.subplots(1, 1, figsize=(8, 4))
fig.canvas.toolbar_visible = False
fig.canvas.header_visible = False
fig.canvas.footer_visible = False
plt.subplots_adjust(bottom=0.25)
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(-0.05, 1.1)
xlim = ax.get_xlim()
ax.set_xlim(xlim[0], xlim[1] * 2)
ax.set_ylabel('y')
ax.set_xlabel('Tumor Size')
self.alegend = ax.legend(loc='lower right')
if self.logistic:
ax.set_title("Example of Logistic Regression on Categorical Data")
else:
ax.set_title("Example of Linear Regression on Categorical Data")
ax.text(0.65,
0.8,
"[Click to add data points]",
size=10,
transform=ax.transAxes)
axcalc = plt.axes([0.1, 0.05, 0.38, 0.075]) #l,b,w,h
axthresh = plt.axes([0.5, 0.05, 0.38, 0.075]) #l,b,w,h
self.tlist = []
self.fig = fig
self.ax = [ax, axcalc, axthresh]
self.x = x
self.y = y
self.w = copy.deepcopy(w)
self.b = b
f_wb = np.matmul(self.x.reshape(-1, 1), self.w) + self.b
if self.logistic:
self.aline = self.ax[0].plot(self.x, sigmoid(f_wb), color=dlblue)
self.bline = self.ax[0].plot(self.x, f_wb, color=dlorange, lw=1)
else:
self.aline = self.ax[0].plot(self.x, sigmoid(f_wb), color=dlblue)
self.cid = fig.canvas.mpl_connect('button_press_event', self.add_data)
if self.logistic:
self.bcalc = Button(axcalc,
'Run Logistic Regression (click)',
color=dlblue)
self.bcalc.on_clicked(self.calc_logistic)
else:
self.bcalc = Button(axcalc,
'Run Linear Regression (click)',
color=dlblue)
self.bcalc.on_clicked(self.calc_linear)
self.bthresh = CheckButtons(
axthresh, ('Toggle 0.5 threshold (after regression)', ))
self.bthresh.on_clicked(self.thresh)
self.resize_sq(self.bthresh)