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a bunch of plots from nips submission
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‎Algorithm_comparison_plots.ipynb

+835-22
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‎Categorical_Plots_Final.ipynb

+111-57
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‎Comparison with MIEWRF paper.ipynb

+276
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‎Drosophilia.ipynb

+582
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‎MI Convergence Rates.ipynb

+522
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‎Mixed data.ipynb

+321
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‎Mutual Information Plots.ipynb

+632-7
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‎Mutual Information Settings 2.ipynb

+83-35
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‎Mutual Information Truth.ipynb

+353
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Mutual Information Truths\n",
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"\n",
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"## Normal mutual information"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [
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{
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"ename": "NameError",
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"evalue": "name 'X' is not defined",
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"output_type": "error",
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"traceback": [
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"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
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"\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)",
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"\u001b[0;32m<ipython-input-1-8f0676416654>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m 13\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mmodel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmeans_\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmodel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcovariances_\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 14\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 15\u001b[0;31m \u001b[0mestimate_x_params\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 16\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 17\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mnormal_entropy_f\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmean\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvar\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
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"\u001b[0;31mNameError\u001b[0m: name 'X' is not defined"
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]
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}
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],
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"source": [
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"from scipy.stats import norm\n",
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"from scipy.stats import multivariate_normal\n",
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"import scipy.integrate as integrate\n",
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"import math\n",
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"from sklearn import mixture\n",
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"\n",
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"def estimate_p(y):\n",
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" return y.count(1)/len(y)\n",
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"\n",
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"def estimate_x_params(X):\n",
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" model = mixture.GaussianMixture(n_components = 2, covariance_type = \"full\")\n",
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" model.fit(X)\n",
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" return model.means_, model.covariances_\n",
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" \n",
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"estimate_x_params(X)\n",
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"\n",
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"def normal_entropy_f(t, mean, var):\n",
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" return -norm.pdf(t, mean, var)*np.log(norm.pdf(t, mean, var))\n",
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"\n",
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"def two_mixture_normals_entropy_f(t, mean_1, mean_2, var_1, var_2):\n",
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" return -.5*norm.pdf(t, mean_1, var_1)*np.log(.5*norm.pdf(t, mean_1, var_1) + .5*norm.pdf(t, mean_2, var_2)) - .5*norm.pdf(t, mean_1, var_1)*np.log(.5*norm.pdf(t, mean_1, var_1) + .5*norm.pdf(t, mean_2, var_2))\n",
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"\n",
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"def normal_entropy(var):\n",
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" return .5*np.log(2*math.pi*math.e*var)\n",
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"\n",
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"#NOTE: this doesn't work for mean = 0\n",
65+
"def plugin_estimate_cat_1D(X, y):\n",
66+
" y_param = estimate_p(y)\n",
67+
" x_params = estimate_x_params(X)\n",
68+
" h_y = -y_param*np.log(y_param) - (1 - y_param)*np.log(1 - y_param)\n",
69+
" #h_x_cond_y = integrate.quad(normal_entropy_f, -20, 20, args = (x_params[0][0], x_params[1][0].item()))[0]*.5 + \\\n",
70+
" #integrate.quad(normal_entropy_f, -20, 20, args = (x_params[0][1], x_params[1][1].item()))[0]*.5\n",
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" h_x_cond_y = normal_entropy(x_params[1][0])*.5 + normal_entropy(x_params[1][1])*.5\n",
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" h_x = integrate.quad(two_mixture_normals_entropy_f, -20, 20, args = (x_params[0][0], x_params[0][1], x_params[1][0].item(), x_params[1][1].item()))[0]\n",
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" cond_entropy = h_y - h_x + h_x_cond_y\n",
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" if cond_entropy < 0:\n",
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" return np.array((0))\n",
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" return cond_entropy\n",
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"\n",
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"def truth_1d(mean):\n",
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" h_y = -.5*np.log(.5) - .5*np.log(.5)\n",
80+
" h_x_cond_y = normal_entropy(1)*.5 + normal_entropy(1)*.5\n",
81+
" h_x = integrate.quad(two_mixture_normals_entropy_f, -20, 20, args = (mean, -mean, 1, 1))[0]\n",
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" cond_entropy = h_y - h_x + h_x_cond_y\n",
83+
" if cond_entropy < 0:\n",
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" return np.array((0))\n",
85+
" return cond_entropy\n",
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"\n",
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"\n",
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"def mutual_information_truth():\n",
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" entropy = -.5*np.log(.5) - .5*np.log(.5)\n",
90+
" means = [i*-.2 for i in range(0, 26)]\n",
91+
" means.reverse()\n",
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" means.extend([i*.2 for i in range(1, 26)])\n",
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" truths = []\n",
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" for elem in means:\n",
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" truths.append(entropy - truth_1d(elem))\n",
96+
" #return means, cef_all, plugin_all, truth\n",
97+
" return truths"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Different variances"
105+
]
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},
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{
108+
"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
113+
"from scipy.stats import norm\n",
114+
"from scipy.stats import multivariate_normal\n",
115+
"import scipy.integrate as integrate\n",
116+
"import math\n",
117+
"from sklearn import mixture\n",
118+
"\n",
119+
"def estimate_p(y):\n",
120+
" return y.count(1)/len(y)\n",
121+
"\n",
122+
"def estimate_x_params(X):\n",
123+
" model = mixture.GaussianMixture(n_components = 2, covariance_type = \"full\")\n",
124+
" model.fit(X)\n",
125+
" return model.means_, model.covariances_\n",
126+
" \n",
127+
"def normal_entropy_f(t, mean, var):\n",
128+
" return -norm.pdf(t, mean, var)*np.log(norm.pdf(t, mean, var))\n",
129+
"\n",
130+
"def two_mixture_normals_entropy_f(t, mean_1, mean_2, var_1, var_2):\n",
131+
" return -.5*norm.pdf(t, mean_1, var_1)*np.log(.5*norm.pdf(t, mean_1, var_1) + .5*norm.pdf(t, mean_2, var_2)) - .5*norm.pdf(t, mean_1, var_1)*np.log(.5*norm.pdf(t, mean_1, var_1) + .5*norm.pdf(t, mean_2, var_2))\n",
132+
"\n",
133+
"def normal_entropy(var):\n",
134+
" return .5*np.log(2*math.pi*math.e*var)\n",
135+
"\n",
136+
"#NOTE: this doesn't work for mean = 0\n",
137+
"def plugin_estimate_cat_1D(X, y):\n",
138+
" y_param = estimate_p(y)\n",
139+
" x_params = estimate_x_params(X)\n",
140+
" h_y = -y_param*np.log(y_param) - (1 - y_param)*np.log(1 - y_param)\n",
141+
" #h_x_cond_y = integrate.quad(normal_entropy_f, -20, 20, args = (x_params[0][0], x_params[1][0].item()))[0]*.5 + \\\n",
142+
" #integrate.quad(normal_entropy_f, -20, 20, args = (x_params[0][1], x_params[1][1].item()))[0]*.5\n",
143+
" h_x_cond_y = normal_entropy(x_params[1][0])*.5 + normal_entropy(x_params[1][1])*.5\n",
144+
" h_x = integrate.quad(two_mixture_normals_entropy_f, -20, 20, args = (x_params[0][0], x_params[0][1], x_params[1][0].item(), x_params[1][1].item()))[0]\n",
145+
" cond_entropy = h_y - h_x + h_x_cond_y\n",
146+
" if cond_entropy < 0:\n",
147+
" return np.array((0))\n",
148+
" return cond_entropy\n",
149+
"\n",
150+
"def truth_1d(mean):\n",
151+
" h_y = -.5*np.log(.5) - .5*np.log(.5)\n",
152+
" h_x_cond_y = normal_entropy(1)*.5 + normal_entropy(3)*.5\n",
153+
" h_x = integrate.quad(two_mixture_normals_entropy_f, -20, 20, args = (mean, -mean, 1, math.sqrt(3)))[0]\n",
154+
" cond_entropy = h_y - h_x + h_x_cond_y\n",
155+
" if cond_entropy < 0:\n",
156+
" return np.array((0))\n",
157+
" return cond_entropy\n",
158+
"\n",
159+
"\n",
160+
"def mutual_information_truth():\n",
161+
" entropy = -.5*np.log(.5) - .5*np.log(.5)\n",
162+
" means=[i*.2 for i in range(0, 26)]\n",
163+
" truths = []\n",
164+
" for elem in means:\n",
165+
" mi = entropy - truth_1d(elem)\n",
166+
" if mi < 0:\n",
167+
" truths.append(0)\n",
168+
" else:\n",
169+
" truths.append((entropy - truth_1d(elem))/entropy)\n",
170+
" #return means, cef_all, plugin_all, truth\n",
171+
" return truths"
172+
]
173+
},
174+
{
175+
"cell_type": "code",
176+
"execution_count": 28,
177+
"metadata": {},
178+
"outputs": [],
179+
"source": [
180+
"truths_diff_covar = mutual_information_truth()"
181+
]
182+
},
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{
184+
"cell_type": "code",
185+
"execution_count": 29,
186+
"metadata": {},
187+
"outputs": [
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{
189+
"name": "stdout",
190+
"output_type": "stream",
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"text": [
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"[0, 0, 0, 0, 0, 0.00139387239137524, 0.0923354486255463, 0.17983487386233699, 0.26014481159701247, 0.3311346125243729, 0.39191714540163064, 0.4424935478389682, 0.4834711645708754, 0.5158388832981347, 0.5407855870838623, 0.5595579047838196, 0.5733562865659112, 0.5832668885594593, 0.5902244414373682, 0.5949996896546803, 0.5982044676085582, 0.6003078952265687, 0.6016582208033919, 0.602506180664179, 0.6030271057430278, 0.6033401961717422]\n"
193+
]
194+
}
195+
],
196+
"source": [
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"print(truths_diff_covar)"
198+
]
199+
},
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{
201+
"cell_type": "markdown",
202+
"metadata": {},
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"source": [
204+
"## Different ps"
205+
]
206+
},
207+
{
208+
"cell_type": "code",
209+
"execution_count": 19,
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"metadata": {},
211+
"outputs": [],
212+
"source": [
213+
"from scipy.stats import norm\n",
214+
"from scipy.stats import multivariate_normal\n",
215+
"import scipy.integrate as integrate\n",
216+
"import math\n",
217+
"from sklearn import mixture\n",
218+
"\n",
219+
"def estimate_p(y):\n",
220+
" return y.count(1)/len(y)\n",
221+
"\n",
222+
"def estimate_x_params(X):\n",
223+
" model = mixture.GaussianMixture(n_components = 2, covariance_type = \"full\")\n",
224+
" model.fit(X)\n",
225+
" return model.means_, model.covariances_\n",
226+
" \n",
227+
"\n",
228+
"def normal_entropy_f(t, mean, var):\n",
229+
" return -norm.pdf(t, mean, var)*np.log(norm.pdf(t, mean, var))\n",
230+
"\n",
231+
"def two_mixture_normals_entropy_f(t, mean_1, mean_2, var_1, var_2, prob):\n",
232+
" return -prob*norm.pdf(t, mean_1, var_1)*np.log(prob*norm.pdf(t, mean_1, var_1) + (prob)*norm.pdf(t, mean_2, var_2)) - (1-prob)*norm.pdf(t, mean_1, var_1)*np.log((1-prob)*norm.pdf(t, mean_1, var_1) + (1-prob)*norm.pdf(t, mean_2, var_2))\n",
233+
"\n",
234+
"def normal_entropy(var):\n",
235+
" return .5*np.log(2*math.pi*math.e*var)\n",
236+
"\n",
237+
"#NOTE: this doesn't work for mean = 0\n",
238+
"def plugin_estimate_cat_1D(X, y):\n",
239+
" y_param = estimate_p(y)\n",
240+
" x_params = estimate_x_params(X)\n",
241+
" h_y = -y_param*np.log(y_param) - (1 - y_param)*np.log(1 - y_param)\n",
242+
" #h_x_cond_y = integrate.quad(normal_entropy_f, -20, 20, args = (x_params[0][0], x_params[1][0].item()))[0]*.5 + \\\n",
243+
" #integrate.quad(normal_entropy_f, -20, 20, args = (x_params[0][1], x_params[1][1].item()))[0]*.5\n",
244+
" h_x_cond_y = normal_entropy(x_params[1][0])*.5 + normal_entropy(x_params[1][1])*.5\n",
245+
" h_x = integrate.quad(two_mixture_normals_entropy_f, -20, 20, args = (x_params[0][0], x_params[0][1], x_params[1][0].item(), x_params[1][1].item()))[0]\n",
246+
" cond_entropy = h_y - h_x + h_x_cond_y\n",
247+
" if cond_entropy < 0:\n",
248+
" return np.array((0))\n",
249+
" return cond_entropy\n",
250+
"\n",
251+
"def truth_1d(prob):\n",
252+
" h_y = -prob*np.log(prob) - (1-prob)*np.log(1-prob)\n",
253+
" h_x_cond_y = normal_entropy(1)*prob + normal_entropy(1)*(1-prob)\n",
254+
" h_x = integrate.quad(two_mixture_normals_entropy_f, -20, 20, args = (1, -1, 1, 1, prob))[0]\n",
255+
" cond_entropy = h_y - h_x + h_x_cond_y\n",
256+
" if cond_entropy < 0:\n",
257+
" return np.array((0))\n",
258+
" return cond_entropy\n",
259+
"\n",
260+
"\n",
261+
"def mutual_information_truth():\n",
262+
" probs = [i*.02 for i in range(1, 26)]\n",
263+
" truths = []\n",
264+
" for elem in probs:\n",
265+
" entropy = -elem*np.log(elem) - (1-elem)*np.log(1 - elem)\n",
266+
" truths.append(entropy - truth_1d(elem))\n",
267+
" #return means, cef_all, plugin_all, truth\n",
268+
" return truths"
269+
]
270+
},
271+
{
272+
"cell_type": "code",
273+
"execution_count": 20,
274+
"metadata": {},
275+
"outputs": [],
276+
"source": [
277+
"truths=mutual_information_truth()"
278+
]
279+
},
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{
281+
"cell_type": "code",
282+
"execution_count": 22,
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"metadata": {},
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"outputs": [
285+
{
286+
"data": {
287+
"text/plain": [
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"[-0.2582772469333816,\n",
289+
" -0.18837221247894043,\n",
290+
" -0.12934883771250916,\n",
291+
" -0.07754698844452623,\n",
292+
" -0.031233386821665654,\n",
293+
" 0.010608631059595974,\n",
294+
" 0.048647124850824675,\n",
295+
" 0.08335351918822936,\n",
296+
" 0.11507724880731518,\n",
297+
" 0.14408606332507468,\n",
298+
" 0.17059160121826666,\n",
299+
" 0.19476356787385918,\n",
300+
" 0.21674055691830674,\n",
301+
" 0.2366369572343613,\n",
302+
" 0.25454794184177987,\n",
303+
" 0.27055309735931277,\n",
304+
" 0.28471911766804203,\n",
305+
" 0.29710183458058814,\n",
306+
" 0.30774776635099443,\n",
307+
" 0.3166953067961429,\n",
308+
" 0.32397563997903966,\n",
309+
" 0.3296134400392592,\n",
310+
" 0.3336273982452863,\n",
311+
" 0.3360306068768478,\n",
312+
" 0.3368308203468321]"
313+
]
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},
315+
"execution_count": 22,
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"metadata": {},
317+
"output_type": "execute_result"
318+
}
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],
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"source": [
321+
"[elem for elem in truths]"
322+
]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
339+
"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.7.0"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}

‎Mutual Information.ipynb

+105-88
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‎Posterior_plots final.ipynb

+218-16
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‎Untitled.ipynb

-6
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