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Commit 1867ea8a authored by Vincent Schellekens's avatar Vincent Schellekens
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2 - Building intuition for sketched learning.ipynb deleted 100644 → 0
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%% Cell type:markdown id: tags:
# Building intuition for sketched learning
This notebook provides a playground to explore the sketched cost.
First, you can chose one of three tasks to be solved:
1. k-means with $k = 1$ ("1-means") in dimension $d = 2$
1. k-means with $k = 2$ ("1-means") in dimension $d = 1$
1. GMM modeling with $k = 1$ in dimension $d = 1$
The code will generate a dataset in the relevant dimension. Note that you can generate different datasets by changing the random seed to change the datasets. Moreover, you can also add "extra clusters" in the generated dataset (note that in this case, the value of $k$ used in the cost will not match the truth of the dataset!).
Finally, you can also select the parameters of the sketch: its size ($m$) and the scale parameter ($\sigma$).
%% Cell type:code id: tags:
``` python
#%matplotlib widget
%matplotlib notebook
# General imports
import numpy as np
import matplotlib.pyplot as plt
import scipy.stats
# Interactive widget
from ipywidgets import widgets, interact
# We import the pycle toolbox for sketched learning; we will need three submodules
import pycle
from pycle import sketching, compressive_learning, utils
from plot_utils import do_the_plot_for_notebook_2
# Fix the random seed for reproducibility
np.random.seed(0)
```
%% Cell type:code id: tags:
``` python
# f_cost_R is the true statistical learning cost
# f_cost_L is the sketched cost
def f_cost_R(th_0,th_1,X,task):
if task == '1means2D':
C = np.array([[th_0,th_1]]) # centroids are of shape d-by-K, here 1-by-2
return pycle.utils.SSE(X,C)
elif task == '2means1D':
C = np.array([[th_0,th_1]]).T # centroids are of shape d-by-K, here 2-by-1
return pycle.utils.SSE(X,C)
elif task == '1GMM1D':
gmm = (np.array([1.]), np.array([[th_0]]), np.array([[[10**th_1]]]))
return -pycle.utils.loglikelihood_GMM(gmm,X)
def f_cost_L(th_0,th_1,z,Phi,task):
if task == '1means2D':
sketch_centroids = Phi(np.array([[th_0,th_1]]))
return np.linalg.norm(z - sketch_centroids)
elif task == '2means1D': # (assumes centroids have equal weights)
sketch_centroids = 0.5*Phi(np.array([th_0])) + 0.5*Phi(np.array([th_1]))
return np.linalg.norm(z - sketch_centroids)
elif task == '1GMM1D':
gmm = (np.array([1.]), np.array([[th_0]]), np.array([[[10**th_1]]]))
sketch_gaussian = pycle.sketching.fourierSketchOfGMM(gmm,Phi)
return np.linalg.norm(z - sketch_gaussian)
```
%% Cell type:code id: tags:
``` python
tasks = {
'1means2D': '1means2D',
'2means1D': '2means1D',
'1GMM1D': '1GMM1D'
}
seeds = widgets.IntSlider(value=42, min=0, max=100,step=1, description='random seed', continuous_update=False)
extra_ks = widgets.IntSlider(value=0, min=0, max=2,step=1, description='extra clusters', continuous_update=False)
ms = widgets.FloatLogSlider(value=10, min=0, max=3,step=0.1, description='$m$', continuous_update=False)
sigmas = widgets.FloatLogSlider(value=0.1,min=-3,max=2, step=0.1, description='$\sigma$', continuous_update=False)
#plt.ion()
fig = plt.figure(figsize=(10,3.5))
ax1 = fig.add_subplot(131)
ax2 = fig.add_subplot(132)
ax3 = fig.add_subplot(133)
fig.tight_layout(pad=3)
ballsize = 50
markersize = 20
lw = 1.5
cL = 'tab:green'
cR = 'tab:red'
ticksize = 6
plt.rc('xtick',labelsize=ticksize)
plt.rc('ytick',labelsize=ticksize)
@interact(task=tasks,seed=seeds,extra_k=extra_ks,m=ms,sigma=sigmas)
def _(task,seed,extra_k,m,sigma):
if task == '1means2D':
d = 2
k = 1
elif task == '2means1D':
d = 1
k = 2
elif task == '1GMM1D':
d = 1
k = 1
m = int(m)
print("sketch size m = " + str(m))
# Print params
if task == '1means2D':
print(r"task: 1-means in 2d, centroid: c_1 = (theta_1,theta_2)")
elif task == '2means1D':
print(r"task: 2-means in 1d, centroids: c_1 = theta_1, c_2 = theta_2")
elif task == '1GMM1D':
print(r"task: fitting one Gaussian in 1d, GMM: N(mu = theta_1,sigma^2 = theta_2)")
np.random.seed(seed)
n = int(5e3) # Number of samples we want to generate
X = pycle.utils.generatedataset_GMM(d,k+extra_k,n,normalize='l_inf-unit-ball',balanced=False, separation_min=2)
# Sketch
sigma2 = sigma**2
W = pycle.sketching.drawFrequencies("Gaussian",d,m,sigma2)
Phi = pycle.sketching.SimpleFeatureMap("ComplexExponential",W)
z = pycle.sketching.computeSketch(X,Phi)
# Bounds
low_pos = -1
upp_pos = +1
low_var = -3 # in log10 scale
upp_var = 0 # in log10 scale
nTest = 41
# Params to test
if task == '1means2D' or task == '2means1D':
thetas_00 = np.linspace(low_pos,upp_pos,nTest)
thetas_11 = np.linspace(low_pos,upp_pos,nTest)
pos_fine = None
elif task == '1GMM1D':
thetas_00 = np.linspace(low_pos,upp_pos,nTest)
thetas_11 = np.linspace(low_var,upp_var,nTest)
pos_fine = np.linspace(low_pos,upp_pos,5*nTest) # to evaluate the pdf
thetas_0,thetas_1 = np.meshgrid(thetas_00,thetas_11)
# Compute the costs everywhere
cost_R = np.zeros((nTest,nTest))
cost_L = np.zeros((nTest,nTest))
# Exhaustive loop over the grid
for i_0,th_0 in enumerate(thetas_00):
for i_1,th_1 in enumerate(thetas_11):
cost_R[i_0,i_1] = f_cost_R(th_0,th_1,X,task)
cost_L[i_0,i_1] = f_cost_L(th_0,th_1,z,Phi,task)
# Call the dedicated plotting subroutine from plot_utils.py
do_the_plot_for_notebook_2(task,d,ax1,ax2,ax3,thetas_0,thetas_1,X,cost_L,cost_R,ballsize,cR,cL,markersize,lw,pos_fine)
```
%% Cell type:code id: tags:
``` python
```
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