def plot_data(self):
# construct figure
fig, axs = plt.subplots(1, 3, figsize=(8, 3))
# create subplot with 2 panels
gs = gridspec.GridSpec(1, 3, width_ratios=[1, 2, 1])
ax1 = plt.subplot(gs[0])
ax1.axis('off')
ax2 = plt.subplot(gs[1])
ax3 = plt.subplot(gs[2])
ax3.axis('off')
if np.shape(self.x)[1] == 2:
ax2 = plt.subplot(gs[1], projection='3d')
ind0 = np.argwhere(self.y == +1)
ax2.scatter(self.x[ind0, 0],
self.x[ind0, 1],
self.y[ind0],
s=55,
color=self.colors[0],
edgecolor='k')
ind1 = np.argwhere(self.y == -1)
ax2.scatter(self.x[ind1, 0],
self.x[ind1, 1],
self.y[ind1],
s=55,
color=self.colors[1],
edgecolor='k')
def plot_subproblem_data(self):
C = len(np.unique(self.y))
# construct figure
fig = plt.figure(figsize=(9,2.5))
# create subplot with 2 panels
gs = gridspec.GridSpec(1, C)
# scatter points
for c in range(C):
# create subproblem data
y_temp = copy.deepcopy(self.y)
ind = np.argwhere(y_temp.astype(int) == (c))
ind = ind[:,0]
ind2 = np.argwhere(y_temp.astype(int) != (c))
ind2 = ind2[:,0]
y_temp[ind] = 1
y_temp[ind2] = -1
# create new axis to plot
ax = plt.subplot(gs[c])
xmin,xmax = self.scatter_pts(ax,self.x,y_temp)
# pretty up panel
title = 'class ' + str(c+1) + ' versus all'
ax.set_title(title,fontsize = 14)
def standard_normalizer(self, x):
# compute the mean and standard deviation of the input
x_means = np.nanmean(x, axis=1)[:, np.newaxis]
x_stds = np.nanstd(x, axis=1)[:, np.newaxis]
# check to make sure thta x_stds > small threshold, for those not
# divide by 1 instead of original standard deviation
ind = np.argwhere(x_stds < 10**(-2))
if len(ind) > 0:
ind = [v[0] for v in ind]
adjust = np.zeros((x_stds.shape))
adjust[ind] = 1.0
x_stds += adjust
# fill in any nan values with means
ind = np.argwhere(np.isnan(x) == True)
for i in ind:
x[i[0], i[1]] = x_means[i[0]]
# create standard normalizer function
normalizer = lambda data: (data - x_means) / x_stds
# create inverse standard normalizer
inverse_normalizer = lambda data: data * x_stds + x_means
# return normalizer
return normalizer, inverse_normalizer
def plot_classif(self, id_1, id_2, labels):
# create figure for plotting
fig = plt.figure(figsize=(5, 5))
# setup colors / labels for plot
red_patch = mpatches.Patch(color='red', label=labels[0])
blue_patch = mpatches.Patch(color='blue', label=labels[1])
plt.legend(handles=[red_patch, blue_patch])
plt.legend(handles=[red_patch, blue_patch], loc=2)
# scatter plot data
ind = np.argwhere(self.y == -1)
ind = [v[1] for v in ind]
plt.scatter(self.x_orig[id_1, ind],
self.x_orig[id_2, ind],
color='r',
s=30) #plotting the data
ind = np.argwhere(self.y == +1)
ind = [v[1] for v in ind]
plt.scatter(self.x_orig[id_1, ind],
self.x_orig[id_2, ind],
color='b',
s=30) #plotting the data
plt.show()
def plot_all(X, y, w0,w1,w2):
# custom colors for plotting points
# red = [1, 0, 0.4]
# blue = [0, 0.4, 1]
# green = [0.4, 1, 0]
# yellow = [1, 0.4, 0]
# scatter plot points
fig = plt.figure(figsize=(4, 4))
ind = np.argwhere(y == 0)
ind = [s[0] for s in ind]
plt.scatter(X[ind,1], X[ind,2], color='blue', edgecolor='k', s=25)
ind = np.argwhere(y == 1)
ind = [s[0] for s in ind]
plt.scatter(X[ind,1], X[ind,2], color='red', edgecolor='k', s=25)
ind = np.argwhere(y == 2)
ind = [s[0] for s in ind]
plt.scatter(X[ind,1], X[ind,2], color='green', edgecolor='k', s=25)
plt.grid('off')
# plot separator
s = np.linspace(0, 1, 100)
plt.plot(s, (-w0[0] - w0[1] * s) / w0[2], color='k', linewidth=2)
plt.plot(s, (-w1[0] - w1[1] * s) / w1[2], color='k', linewidth=2)
plt.plot(s, (-w2[0] - w2[1] * s) / w2[2], color='k', linewidth=2)
# clean up plot
plt.xlim([-0.1, 1.1])
plt.ylim([-0.1, 1.1])
plt.show()
def train(x,y,feature_transforms,**kwargs):
# get and run optimizer to solve two-class problem
N = np.shape(x)[0]
C = np.size(np.unique(y))
max_its = 100;
alpha_choice = 1;
cost_name = 'softmax';
normalize = 'standard'
w = 0.1*np.random.randn(N+1,1);
# switches for user choices
if 'max_its' in kwargs:
max_its = kwargs['max_its']
if 'alpha_choice' in kwargs:
alpha_choice = kwargs['alpha_choice']
if 'cost_name' in kwargs:
cost_name = kwargs['cost_name']
if 'w' in kwargs:
w = kwargs['w']
if 'normalize' in kwargs:
normalize = kwargs['normalize']
# loop over subproblems and solve
weight_histories = []
for c in range(0,C):
# prepare temporary C vs notC sub-probem labels
y_temp = copy.deepcopy(y)
ind = np.argwhere(y_temp.astype(int) == c)
ind = ind[:,1]
ind2 = np.argwhere(y_temp.astype(int) != c)
ind2 = ind2[:,1]
y_temp[0,ind] = 1
y_temp[0,ind2] = -1
# run on normalized data
run = basic_runner.Setup(x,y_temp,feature_transforms,cost_name,normalize = normalize)
run.fit(w=w,alpha_choice = alpha_choice,max_its = max_its)
# store each weight history
weight_histories.append(run.weight_history)
# combine each individual classifier weights into single weight
# matrix per step
R = len(weight_histories[0])
combined_weights = []
for r in range(R):
a = []
for c in range(C):
a.append(weight_histories[c][r])
a = np.array(a).T
a = a[0,:,:]
combined_weights.append(a)
# run combined weight matrices through fusion rule to calculate
# number of misclassifications per step
counter = basic_runner.Setup(x,y,feature_transforms,'multiclass_counter',normalize = normalize).cost_func
count_history = [counter(v) for v in combined_weights]
return combined_weights, count_history
def two_input_contour_plot(self, weight_history, x, y, **kwargs):
cost_name = 'softmax'
if 'cost_name' in kwargs:
cost_name = kwargs['cost_name']
# compute number of classes
C = np.shape(weight_history[0])[1]
##### construct figure with panels #####
# construct figure
fig = plt.figure(figsize=(10, 6))
# create figure with single plot for contour
gs = gridspec.GridSpec(2, 2)
### make contour right plot - as well as horizontal and vertical axes ###
for c in range(C):
# prepare temporary C vs notC sub-probem labels
y_temp = copy.deepcopy(y)
ind = np.argwhere(y_temp.astype(int) == c)
ind = ind[:, 1]
ind2 = np.argwhere(y_temp.astype(int) != c)
ind2 = ind2[:, 1]
y_temp[0, ind] = 1
y_temp[0, ind2] = -1
g = cost_lib.choose_cost(x, y_temp, cost_name)
# create panel
ax = plt.subplot(gs[c])
ax.set_aspect('equal')
# plot contour and path
w_hist = [
weight_history[v][:, c][:, np.newaxis]
for v in range(len(weight_history))
]
self.contour_plot_setup(c, C, g, ax, **kwargs) # draw contour plot
self.draw_weight_path(ax, w_hist,
**kwargs) # draw path on contour plot
# label axes
ax.set_xlabel(r'$w_0^{(' + str(c + 1) + ')}$', fontsize=15)
ax.set_ylabel(r'$w_1^{(' + str(c + 1) + ')}$',
fontsize=15,
labelpad=15,
rotation=0)
# remove whitespace from figure
#gs.update(wspace=0.005, hspace=0.15) # set the spacing between axes.
#fig.subplots_adjust(left=0, right=1, bottom=0, top=1) # remove whitespace
fig.subplots_adjust(wspace=0.001, hspace=0.001)
# plot
plt.show()
def animate(k):
# clear panels
ax1.cla()
ax2.cla()
ax3.cla()
# print rendering update
if np.mod(k+1,25) == 0:
print ('rendering animation frame ' + str(k+1) + ' of ' + str(num_frames))
if k == num_frames - 1:
print ('animation rendering complete!')
time.sleep(1.5)
clear_output()
# scatter data
ind0 = np.argwhere(self.y == +1)
ind0 = [e[1] for e in ind0]
ind1 = np.argwhere(self.y == -1)
ind1 = [e[1] for e in ind1]
for ax in [ax1,ax2,ax3]:
ax.scatter(self.x[0,ind0],self.x[1,ind0],s = pt_size, color = self.colors[0], edgecolor = 'k',antialiased=True)
ax.scatter(self.x[0,ind1],self.x[1,ind1],s = pt_size, color = self.colors[1], edgecolor = 'k',antialiased=True)
if k == 0:
ax1.set_title(str(0) + ' units fit to data',fontsize = 14,color = 'w')
ax1.set_title(str(0) + ' units fit to data',fontsize = 14,color = 'w')
ax1.set_title(str(0) + ' units fit to data',fontsize = 14,color = 'w')
ax1.set_xlim([xmin1,xmax1])
ax1.set_ylim([xmin2,xmax2])
ax2.set_xlim([xmin1,xmax1])
ax2.set_ylim([xmin2,xmax2])
ax3.set_xlim([xmin1,xmax1])
ax3.set_ylim([xmin2,xmax2])
# plot fit
if k > 0:
# get current run
a1 = inds1[k-1]
a2 = inds2[k-1]
a3 = inds3[k-1]
run1 = runs1[a1]
a1 = len(run1.w_init) - 1
run2 = runs2[a2]
model3 = runs3.models[a3]
steps = runs3.best_steps[:a3+1]
# plot models to data
self.draw_fit(ax1,run1,a1)
self.draw_fit(ax2,run2,a2 + 1)
self.draw_boosting_fit(ax3,steps,a3)
return artist,
def animate(k):
# clear panels
ax.cla()
# print rendering update
if np.mod(k + 1, 25) == 0:
print('rendering animation frame ' + str(k + 1) + ' of ' +
str(num_frames))
if k == num_frames - 1:
print('animation rendering complete!')
time.sleep(1.5)
clear_output()
#### scatter data ####
# plot points in 2d and 3d
ind0 = np.argwhere(self.y == +1)
ind0 = [e[1] for e in ind0]
ax.scatter(self.x[0, ind0],
self.x[1, ind0],
s=55,
color=self.colors[0],
edgecolor='k')
ind1 = np.argwhere(self.y == -1)
ind1 = [e[1] for e in ind1]
ax.scatter(self.x[0, ind1],
self.x[1, ind1],
s=55,
color=self.colors[1],
edgecolor='k')
# plot boundary
if k > 0:
# get current run for cost function history plot
a = inds[k - 1]
model = run.models[a]
steps = run.best_steps[:a + 1]
# pluck out current weights
self.draw_boosting_fit(ax, steps, a)
# cleanup panel
ax.set_yticklabels([])
ax.set_xticklabels([])
ax.set_xticks([])
ax.set_yticks([])
ax.set_xlabel(r'$x_1$', fontsize=15)
ax.set_ylabel(r'$x_2$', fontsize=15, rotation=0, labelpad=20)
return artist,
def animate(k):
# clear panels
ax1.cla()
ax2.cla()
# print rendering update
if np.mod(k+1,25) == 0:
print ('rendering animation frame ' + str(k+1) + ' of ' + str(num_frames))
if k == num_frames - 1:
print ('animation rendering complete!')
time.sleep(1.5)
clear_output()
#### scatter data ####
# plot points in 2d and 3d
ind0 = np.argwhere(self.y == +1)
ind0 = [e[1] for e in ind0]
ax1.scatter(self.x[0,ind0],self.x[1,ind0],s = 55, color = self.colors[0], edgecolor = 'k')
ind1 = np.argwhere(self.y == -1)
ind1 = [e[1] for e in ind1]
ax1.scatter(self.x[0,ind1],self.x[1,ind1],s = 55, color = self.colors[1], edgecolor = 'k')
# plot boundary
if k > 0:
# get current run for cost function history plot
a = inds[k-1]
run = runs[a]
# pluck out current weights
self.draw_fit(ax1,run,a)
# cost function value
ax2.plot(np.arange(1,num_elements + 1),cost_evals,color = 'k',linewidth = 2.5,zorder = 1)
ax2.scatter(a + 1,cost_evals[a],color = self.colors[0],s = 70,edgecolor = 'w',linewidth = 1.5,zorder = 3)
# cleanup panels
ax1.set_yticklabels([])
ax1.set_xticklabels([])
ax1.set_xticks([])
ax1.set_yticks([])
ax1.set_xlabel(r'$x_1$',fontsize = 15)
ax1.set_ylabel(r'$x_2$',fontsize = 15,rotation = 0,labelpad = 20)
ax2.set_xlabel('number of units',fontsize = 12)
ax2.set_title('cost function plot',fontsize = 14)
ax2.set_xlim([minxc,maxxc])
ax2.set_ylim([ymin,ymax])
return artist,
def ZCA_sphere(x,**kwargs):
'''
A function for producing the ZCA sphereing on an input dataset X.
'''
# Step 1: mean-center the data
x_means = np.mean(x,axis = 1)[:,np.newaxis]
x_centered = x - x_means
# Step 2: compute pca transform on mean-centered data
d,V = PCA(x_centered,**kwargs)
# Step 3: divide off standard deviation of each (transformed) input,
# which are equal to the returned eigenvalues in 'd'.
stds = (d[:,np.newaxis])**(0.5)
# check to make sure thta x_stds > small threshold, for those not
# divide by 1 instead of original standard deviation
ind = np.argwhere(stds < 10**(-2))
if len(ind) > 0:
ind = [v[0] for v in ind]
adjust = np.zeros((stds.shape))
adjust[ind] = 1.0
stds += adjust
pca_sphered_x = np.dot(V.T,x - x_means)/stds
# Step 3: divide off standard deviation of each (transformed) input,
# which are equal to the returned eigenvalues in 'd'.
# Then rotate back to original orientation of space
stds = (d[:,np.newaxis])**(0.5)
normalizer = lambda data: np.dot(V,np.dot(V.T,data - x_means)/stds)
return normalizer
def PCA_sphereing(self, x, **kwargs):
# Step 1: mean-center the data
x_means = np.mean(x, axis=1)[:, np.newaxis]
x_centered = x - x_means
# Step 2: compute pca transform on mean-centered data
d, V = self.PCA(x_centered, **kwargs)
# Step 3: divide off standard deviation of each (transformed) input,
# which are equal to the returned eigenvalues in 'd'.
stds = (d[:, np.newaxis])**(0.5)
# check to make sure thta x_stds > small threshold, for those not
# divide by 1 instead of original standard deviation
ind = np.argwhere(stds < 10**(-2))
if len(ind) > 0:
ind = [v[0] for v in ind]
adjust = np.zeros((stds.shape))
adjust[ind] = 1.0
stds += adjust
normalizer = lambda data: np.dot(V.T, data - x_means) / stds
# create inverse normalizer
inverse_normalizer = lambda data: np.dot(V, data * stds) + x_means
# return normalizer
return normalizer, inverse_normalizer
def plot_data(self,ax,special_class,special_size):
# scatter points in both panels
class_nums = np.unique(self.y)
C = len(class_nums)
for c in range(C):
ind = np.argwhere(self.y == class_nums[c])
ind = [v[1] for v in ind]
s = 80
if class_nums[c] == special_class:
s = special_size
ax.scatter(self.x[0,ind],self.x[1,ind],s = s,color = self.color_opts[c],edgecolor = 'k',linewidth = 1.5)
# control viewing limits
minx = min(self.x[0,:])
maxx = max(self.x[0,:])
gapx = (maxx - minx)*0.1
minx -= gapx
maxx += gapx
miny = min(self.x[1,:])
maxy = max(self.x[1,:])
gapy = (maxy - miny)*0.1
miny -= gapy
maxy += gapy
ax.set_xlim([minx,maxx])
ax.set_ylim([miny,maxy])
#ax.axis('equal')
ax.axis('off')
def animate_weightings(self,csvname,**kwargs):
self.x,self.y,special_class = self.load_data(csvname)
self.color_opts = np.array([[1,0,0.4], [ 0, 0.4, 1],[0, 1, 0.5],[1, 0.7, 0.5],[0.7, 0.6, 0.5]])
# pick out user-defined arguments
num_slides = 2
if 'num_slides' in kwargs:
num_slides = kwargs['num_slides']
# make range for plot
base_size = 100
size_range = np.linspace(base_size, 20*base_size, num_slides)
weight_range = np.linspace(1,10,num_slides)
# generate figure to plot onto
fig = plt.figure(figsize=(5,5))
artist = fig
ax = plt.subplot(111)
# animation sub-function
ind1 = np.argwhere(self.y == special_class)
ind1 = [v[1] for v in ind1]
# run animator
max_its = 5
w = 0.1*np.random.randn(3,1)
g = bits.softmax
def animate(k):
ax.cla()
# print rendering update
if np.mod(k+1,25) == 0:
print ('rendering animation frame ' + str(k+1) + ' of ' + str(num_slides))
if k == num_slides - 1:
print ('animation rendering complete!')
time.sleep(1.5)
clear_output()
# define beta
special_size = size_range[k]
special_weight = weight_range[k]
beta = np.ones((1,self.y.size))
beta[:,ind1] = special_weight
# run optimizer
w_hist,g_hist = bits.newtons_method(g,w,self.x,self.y,beta,max_its)
w_best = w_hist[-1]
self.model = lambda data: bits.model(data,w_best)
# scatter plot all data
self.plot_data(ax,special_class,special_size)
# draw decision boundary
self.draw_decision_boundary(ax)
return artist,
anim = animation.FuncAnimation(fig, animate ,frames=num_slides, interval=num_slides, blit=True)
return(anim)
def pad_tensor(self, tensor, kernel_size):
odd_nums = np.array([int(2 * n + 1) for n in range(100)])
pad_val = np.argwhere(odd_nums == kernel_size)[0][0]
tensor_padded = np.zeros(
(np.shape(tensor)[0], np.shape(tensor)[1] + 2 * pad_val,
np.shape(tensor)[2] + 2 * pad_val))
tensor_padded[:, pad_val:-pad_val, pad_val:-pad_val] = tensor
return tensor_padded
def measureED(x, y, yerr, tpeak, fwhm, num_fwhm=10):
'''
Measure the equivalent duration of a flare in a smoothed light
curve. FINDflare typically doesnt identify the entire flare, so
integrate num_fwhm/2*fwhm away from the peak. As long as the light
curve is flat away from the flare, the region around the flare should
not significantly contribute.
Parameters
----------
x : numpy array
time values from the entire light curve
y : numpy array
flux values from the entire light curve
yerr : numpy array
error in the flux values
tpeak : float
Peak time of the flare detection
fwhm : float
Full-width half maximum of the flare
num_fwhm : float, optional
Size of the integration window in units of fwhm
Returns
-------
ED - Equivalent duration of the flare
ED_err - The uncertainty in the equivalent duration
'''
try:
width = fwhm * num_fwhm
istart = np.argwhere(x > tpeak - width / 2)[0]
ipeak = np.argwhere(x > tpeak)[0]
istop = np.argwhere(x > tpeak + width / 2)[0]
dx = np.diff(x)
x = x[:-1]
y = y[:-1]
yerr = yerr[:-1]
mask = (x > x[istart]) & (x < x[istop])
ED = np.trapz(y[mask], x[mask])
ED_err = np.sqrt(np.sum((dx[mask] * yerr[mask])**2))
except IndexError:
return -1, -1
return ED, ED_err
def d_x_d_t_numpy_batchs(y, x, t, rrpc, delta_t):
alpha = 1 - ((x * x) + (y * y))**0.5
cast = (t / delta_t).astype(int)
tensor_temp = 1 + cast
tensor_temp = tensor_temp % len(rrpc)
specific_rrpc_values = rrpc[tensor_temp]
omega = np.zeros_like(x).astype(float)
zero_indexes = np.argwhere(specific_rrpc_values == 0)[:, 0]
non_zero_indexes = np.argwhere(specific_rrpc_values != 0)[:, 0]
omega[zero_indexes] = (2.0 * math.pi / 1e-3)
omega[non_zero_indexes] = (2.0 * math.pi /
specific_rrpc_values[non_zero_indexes])
f_x = alpha * x - omega * y
return f_x
def make_matrix_full_row_rank(x, min_ev=1e-8):
"""Return a matrix with full row rank such that
x.T @ x = new_x.T @ new_x
"""
u, s, vh = np.linalg.svd(x, full_matrices=False)
s_nonzero = np.argwhere(s > min_ev)[:,0]
new_x = np.diag(s[s_nonzero]) @ vh[s_nonzero, :]
return new_x
def plot_data_and_subproblem_separators(self):
# determine plotting ranges
minx = min(min(self.x[:, 0]), min(self.x[:, 1]))
maxx = max(max(self.x[:, 0]), max(self.x[:, 1]))
gapx = (maxx - minx) * 0.1
minx -= gapx
maxx += gapx
# initialize figure, plot data, and dress up panels with axes labels etc.
num_classes = np.size(np.unique(self.y))
##### setup figure to plot #####
# initialize figure
fig = plt.figure(figsize=(9, 5))
gs = gridspec.GridSpec(2, num_classes)
# create subplots for each sub-problem
r = np.linspace(minx, maxx, 400)
for a in range(0, num_classes):
# setup current axis
ax = plt.subplot(gs[a], aspect='equal')
# get current weights
w = self.W[a]
# color current class
ax.scatter(self.x[:, 0], self.x[:, 1], s=30, color='0.75')
t = np.argwhere(self.y == a)
t = t[:, 0]
ax.scatter(self.x[t, 0],
self.x[t, 1],
s=50,
color=self.colors[a],
edgecolor='k',
linewidth=1.5)
# draw subproblem separator
z = -w[0] / w[2] - w[1] / w[2] * r
ax.plot(r, z, linewidth=2, color=self.colors[a], zorder=3)
ax.plot(r, z, linewidth=2.75, color='k', zorder=2)
# dress panel correctly
ax.set_xlim(minx, maxx)
ax.set_ylim(minx, maxx)
ax.axis('off')
# plot final panel with all data and separators
ax4 = plt.subplot(gs[num_classes + 1], aspect='equal')
self.plot_data(ax4)
self.plot_all_separators(ax4)
# dress panel
ax4.set_xlim(minx, maxx)
ax4.set_ylim(minx, maxx)
ax4.axis('off')
plt.show()
def plot_data(self,ax):
# initialize figure, plot data, and dress up panels with axes labels etc.
num_classes = np.size(np.unique(self.y))
# color current class
for a in range(0,num_classes):
t = np.argwhere(self.y == a+1)
t = t[:,0]
ax.scatter(self.x[t,0],self.x[t,1], s = 50,color = self.colors[a],edgecolor = 'k',linewidth = 1.5)
def naive_fitting_demo(self, **kwargs):
##### setup figure to plot #####
# initialize figure
fig = plt.figure(figsize=(8, 4))
artist = fig
# create subplot with 2 panels
gs = gridspec.GridSpec(2, 1, height_ratios=[1, 1])
ax1 = plt.subplot(gs[0], aspect='equal')
ax2 = plt.subplot(gs[1], aspect='equal')
#### plot data in both panels ####
self.scatter_pts(ax1)
self.scatter_pts(ax2)
#### fit line to data and plot ####
# make plotting range
xmin = copy.deepcopy(min(self.x))
xmax = copy.deepcopy(max(self.x))
xgap = (xmax - xmin) * 0.4
xmin -= xgap
xmax += xgap
# produce fit
x_fit = np.linspace(xmin, xmax, 300)
w = self.w_hist[-1]
y_fit = w[0] + x_fit * w[1]
# plot linear fit
ax2.plot(x_fit, y_fit, color='lime', linewidth=1.5)
# plot sign version of linear fit
f = np.sign(y_fit)
bot_ind = np.argwhere(f == -1)
bot_ind = [s[0] for s in bot_ind]
bot_in = x_fit[bot_ind]
bot_out = f[bot_ind]
ax2.plot(bot_in, bot_out, color='r', linewidth=1.5, linestyle='--')
top_ind = np.argwhere(f == +1)
top_ind = [s[0] for s in top_ind]
top_in = x_fit[top_ind]
top_out = f[top_ind]
ax2.plot(top_in, top_out, color='r', linewidth=1.5, linestyle='--')
def counting_cost(self,w):
# compute predicted labels
y_hat = np.sign(self.model(self.x,w))
# compare to true labels
ind = np.argwhere(self.y != y_hat)
ind = [v[1] for v in ind]
cost = np.sum(len(ind))
return cost
def scatter_2d_classification_data(self, ax, scatter, **kwargs):
### from above
ax.set_xlabel(r'$x_1$', fontsize=15)
ax.set_ylabel(r'$x_2$', fontsize=15, rotation=0, labelpad=20)
ax.xaxis.set_major_formatter(FormatStrFormatter('%.1f'))
ax.yaxis.set_major_formatter(FormatStrFormatter('%.1f'))
# plot points in 2d and 3d
C = len(np.unique(self.y))
if C == 2:
ind0 = np.argwhere(self.y == +1)
ind0 = [v[0] for v in ind0]
ind1 = np.argwhere(self.y == -1)
ind1 = [v[0] for v in ind1]
if scatter == 'on':
ax.scatter(self.x[ind0, 0],
self.x[ind0, 1],
s=55,
color=self.colors[0],
edgecolor='k')
ax.scatter(self.x[ind1, 0],
self.x[ind1, 1],
s=55,
color=self.colors[1],
edgecolor='k')
else:
ax.scatter(self.x[ind0, 0],
self.x[ind0, 1],
s=55,
color=self.colors[0]) #, edgecolor = 'k')
ax.scatter(self.x[ind1, 0],
self.x[ind1, 1],
s=55,
color=self.colors[1]) #, edgecolor = 'k')
else:
for c in range(C):
ind0 = np.argwhere(self.y == c)
ax.scatter(self.x[ind0, 0],
self.x[ind0, 1],
s=55,
color=self.colors[c],
edgecolor='k')
def surface_plot(self,g,ax,wmax,view):
##### Produce cost function surface #####
r = np.linspace(-wmax,wmax,300)
# create grid from plotting range
w1_vals,w2_vals = np.meshgrid(r,r)
w1_vals.shape = (len(r)**2,1)
w2_vals.shape = (len(r)**2,1)
w_ = np.concatenate((w1_vals,w2_vals),axis = 1)
g_vals = []
for i in range(len(r)**2):
g_vals.append(g(w_[i,:]))
g_vals = np.asarray(g_vals)
w1_vals.shape = (np.size(r),np.size(r))
w2_vals.shape = (np.size(r),np.size(r))
### is this a counting cost? if so re-calculate ###
levels = np.unique(g_vals)
if np.size(levels) < 30:
# plot each level of the counting cost
levels = np.unique(g_vals)
for u in levels:
# make copy of cost and nan out all non level entries
z = g_vals.copy()
ind = np.argwhere(z != u)
ind = [v[0] for v in ind]
z[ind] = np.nan
# plot the current level
z.shape = (len(r),len(r))
ax.plot_surface(w1_vals,w2_vals,z,alpha = 1,color = '#696969',zorder = 0,shade = True,linewidth=0)
else: # smooth cost function, plot usual
# reshape and plot the surface, as well as where the zero-plane is
g_vals.shape = (np.size(r),np.size(r))
# plot cost surface
ax.plot_surface(w1_vals,w2_vals,g_vals,alpha = 1,color = 'w',rstride=25, cstride=25,linewidth=1,edgecolor = 'k',zorder = 2)
### clean up panel ###
ax.xaxis.pane.fill = False
ax.yaxis.pane.fill = False
ax.zaxis.pane.fill = False
ax.xaxis.pane.set_edgecolor('white')
ax.yaxis.pane.set_edgecolor('white')
ax.zaxis.pane.set_edgecolor('white')
ax.xaxis._axinfo["grid"]['color'] = (1,1,1,0)
ax.yaxis._axinfo["grid"]['color'] = (1,1,1,0)
ax.zaxis._axinfo["grid"]['color'] = (1,1,1,0)
ax.view_init(view[0],view[1])
def load_data(self,csvname):
data = np.loadtxt(csvname,delimiter = ',')
self.data = data
x = data[0:2,:]
y = data[-1,:][np.newaxis,:]
# remove points from one class for illustrative purposes
ind0 = np.argwhere(y == -1)
ind0 = [v[1] for v in ind0]
ind1 = np.argwhere(y == +1)
ind1 = [v[1] for v in ind1]
ind0 = ind0[-5:]
inds = ind0 + ind1
x = x[:,inds]
y = y[:,inds]
special_class = -1
return x,y,special_class
def pred(self, xt, x1, ykdt, params):
kern_params, wnoise, mean_params = self.unpack_params(params,
fudge=self.fudge)
k, d, t = ykdt.shape
if self.mean:
mu = self.mean(self.xt, params)[None] # D x T ### TO BE CHANGED
yc = (ykdt - mu).reshape([self.k, -1])
else:
yc = ykdt.reshape([k, -1])
KXX = self.build_Kxx(xt, xt, params, prior=True)
# select points to condition on
val_inds = np.argwhere(np.isnan(yc[0]) == False).squeeze()
nval_inds = np.argwhere(np.isnan(yc[0]) == True).squeeze()
KXX = KXX[:, val_inds]
KXX = KXX[val_inds]
yc = yc[:, val_inds]
L = np.linalg.cholesky(KXX)
iL = inv(L)
Kinv = iL.T @ iL
KXx = self.build_Kxx(xt, x1, params, prior=False)
t0 = xt.shape[0]
t1 = x1.shape[0]
KXx = KXx.reshape([t0, d, t1, d]).reshape([t0 * d, -1])
noise = np.kron(np.diag(wnoise), np.eye(t0))
noise[nval_inds, nval_inds] = 0
KXx[:t0 * d, :t0 * d] += noise
KXx = KXx.reshape([t0, d, t1, d]).reshape([d * t0, -1])
KXx = KXx[val_inds]
Kxx = self.build_Kxx(x1, x1, params, prior=True)
mu_pred = KXx.T.dot(Kinv).dot(yc.T).T
cov_pred = Kxx - KXx.T.dot(Kinv).dot(KXx)
mu_pred = mu_pred.reshape([k, d, -1])
return mu_pred, np.sqrt(
np.diag(cov_pred).reshape([d, -1]) + self.fudge)
def inds_to_effect_change(leverage, desired_delta):
# Argsort sorts low to high.
# We are removing points, so multiply by -1.
sort_inds = np.argsort(leverage * np.sign(desired_delta))
deltas = -1 * np.cumsum(leverage[sort_inds])
change_sign_inds = np.argwhere(
np.sign(desired_delta) * (desired_delta - deltas) <= 0.)
if len(change_sign_inds) > 0:
first_ind_change_sign = np.min(change_sign_inds)
remove_inds = sort_inds[:(first_ind_change_sign + 1)]
return remove_inds
else:
return None
def generate_mixture_data(num_obs, true_centroids, true_probs, x_covs):
true_z = np.random.multinomial(1, true_probs, num_obs)
true_z_ind = np.full(num_obs, -1)
for row in np.argwhere(true_z):
true_z_ind[row[0]] = row[1]
x = np.array([
np.random.multivariate_normal(
mean=np.squeeze(true_centroids[true_z_ind[n], :]),
cov=np.squeeze(x_covs[n, :])) for n in range(num_obs)
])
return x, true_z, true_z_ind
def plot_subproblem_fits(self,weights,**kwargs):
C = len(np.unique(self.y))
# construct figure
fig = plt.figure(figsize=(9,2.5))
# create subplot with 2 panels
gs = gridspec.GridSpec(1, C)
# scatter points
for c in range(C):
# create subproblem data
y_temp = copy.deepcopy(self.y)
ind = np.argwhere(y_temp.astype(int) == (c))
ind = ind[:,0]
ind2 = np.argwhere(y_temp.astype(int) != (c))
ind2 = ind2[:,0]
y_temp[ind] = 1
y_temp[ind2] = -1
# create new axis to plot
ax = plt.subplot(gs[c])
xmin,xmax = self.scatter_pts(ax,self.x,y_temp)
# create fit
s = np.linspace(xmin,xmax,300)[np.newaxis,:]
transformer = lambda a: a
if 'transformer' in kwargs:
transformer = kwargs['transformer']
a = self.model(transformer(s),weights[:,c])
# plot counting cost
t = np.sign(a).flatten()
ax.plot(s.flatten(),t,linewidth = 4,color = 'b',zorder = 2)
# pretty up panel
title = 'class ' + str(c+1) + ' versus all'
ax.set_title(title,fontsize = 14)
def confusion_matrix(self,w):
# compute predicted labels
y_hat = np.sign(self.model(self.x,w))
# determine indices of real and predicted label values
ind1 = np.argwhere(self.y == +1)
ind1 = [v[1] for v in ind1]
ind2 = np.argwhere(self.y == -1)
ind2 = [v[1] for v in ind2]
ind3 = np.argwhere(y_hat == +1)
ind3 = [v[1] for v in ind3]
ind4 = np.argwhere(y_hat == -1)
ind4 = [v[1] for v in ind4]
# compute elements of confusion matrix
A = len(list(set.intersection(*[set(ind1), set(ind3)])))
B = len(list(set.intersection(*[set(ind1), set(ind4)])))
C = len(list(set.intersection(*[set(ind2), set(ind3)])))
D = len(list(set.intersection(*[set(ind2), set(ind4)])))
return A,B,C,D