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@cheind
Last active May 24, 2018 05:17
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import numpy as np\n",
"import torch\n",
"import torch.nn\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Testdata\n",
"\n",
"generate noisy training samples"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def gen_data(n, w=0.5, b=10, sigma=0.2):\n",
" x = np.linspace(-10, 10, n)\n",
" y = x * w + b + np.random.randn(n)*sigma\n",
" return x, y"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"x,y = gen_data(40)\n",
"tx = torch.tensor(x, dtype=torch.float32)\n",
"ty = torch.tensor(y, dtype=torch.float32)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"(-10, 10)"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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"text/plain": [
"<matplotlib.figure.Figure at 0x272fb706eb8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.scatter(x, y)\n",
"plt.ylim(0,20)\n",
"plt.xlim(-10,10)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Joint Probability Model\n",
"\n",
"We set up the log joint probability whose posterior we try to approximate by the variational distribution q.\n",
"\n",
"Joint model assumes the generative process is given by with\n",
"\n",
"\\begin{align}\n",
"p(w) &\\sim \\mathcal{N}(0,\\sigma_w) \\\\\n",
"p(b) &\\sim \\mathcal{N}(0,\\sigma_b) \\\\\n",
"p(y \\mid x,w,b) &\\sim \\mathcal{N}(wx+b, \\sigma_y)\n",
"\\end{align}\n",
"\n",
"We assume very uninformed priors over the latent variables $\\mathbf{z}=\\{w,b\\}$. Instead of probabilities we use the log of probabilities."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def lnormal(x, u, sigma):\n",
" '''Log of normal distribution.Don't confuse with log-normal distribution'''\n",
" n = torch.log(1. / (torch.tensor(np.sqrt(2 * np.pi)) * sigma)).to(torch.float32)\n",
" return n - (x - u)**2 / (2*sigma**2)"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"pw = lambda w: lnormal(w, torch.tensor(0.), torch.tensor(100.))\n",
"pb = lambda b: lnormal(b, torch.tensor(0.), torch.tensor(100.))\n",
"py = lambda y, w, b, x: lnormal(y, w*x+b, torch.tensor(0.2)).sum()\n",
"pj = lambda y, w, b, x: pw(w) + pb(b) + py(y, w, b, x)"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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5HV2B0cSi8sSB+GQe+W4LDQN8GNenIbLiLdj3C/R4Faq3cjo8pQpOtaZww9sQ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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x272fdd2def0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def plot_log_prob_w(b=10):\n",
" '''Plots the change of the log-prob by varying w for a given b'''\n",
" x = np.arange(-5,5,0.25, dtype=np.float32)\n",
" y = np.array([pj(ty, w, b, tx).item() for w in x])\n",
" plt.plot(x,y, label=f'b={b}')\n",
" plt.legend()\n",
"\n",
"plot_log_prob_w(b=10)\n",
"plot_log_prob_w(b=5)"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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wLLYNHyCmhRBA1jbYn+rjicE9bOlcW8bdFXBzhwI8/xtLeOUhfBv4CvCdk577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\nRzpc0LyITy6rrMSEJQ12jt7LhxZ976w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+/7zAOWUhWK1GhodmGB6aWZL1CzNihSH97uTX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\nY+P/AfW+5HqpfjJnAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x272fdc7c5f8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def plot_log_prob_wb():\n",
" w, b = np.meshgrid(np.linspace(-10,10,100, dtype=np.float32), np.linspace(-20,20,100, dtype=np.float32))\n",
" tw, tb = torch.tensor(w.ravel()), torch.tensor(b.ravel())\n",
" z = np.array([pj(ty, ww, bb, tx).item() for ww,bb in zip(tw, tb)])\n",
" z = z.reshape(100,100)\n",
" cs = plt.contour(w, b, z)\n",
" plt.clabel(cs, inline=1, fontsize=10)\n",
" \n",
"plot_log_prob_wb()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Inference\n",
"\n",
"We first set up the the variational distribution $q(\\mathbf{z};\\mathbf{\\theta})$ to approximate $p(\\mathbf{z} \\mid x,y)$. We assume $q$ factors as $$q(\\mathbf{z};\\mathbf{\\theta}) = \\prod_i q_i(z_i;\\theta_i)$$ with $q_i(z_i;\\mathbf{\\theta}_i) \\sim \\mathcal{N}(\\mu_i, \\sigma_i)$ where $\\mathbf{\\theta}_i = \\{\\mu_i, \\sigma_i\\}$."
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# In order to ensure a positive standard deviation during training, we instead optimize the log of the variance.\n",
"qwu = torch.tensor(0., requires_grad=True)\n",
"qwlv = torch.tensor(-4.0, requires_grad=True) # logvar\n",
"qbu = torch.tensor(5., requires_grad=True)\n",
"qblv = torch.tensor(-4.0, requires_grad=True) # logvar\n",
"\n",
"to_std = lambda lv: torch.exp(lv*0.5)\n",
"\n",
"qj = lambda z0, z1: lnormal(z0, qwu, to_std(qwlv)) + lnormal(z1, qbu, to_std(qblv))\n",
"\n",
"def sampleq(n):\n",
" with torch.no_grad():\n",
" return torch.randn(n)*to_std(qwlv) + qwu, torch.randn(n)*to_std(qblv) + qbu"
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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6gL2NiL51MnZfNEx4iaw27wTTvNqonvku+fxL1Os5AKLReyYFPvNOAoG5J3OU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\nCMpLgDrRAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x272fda67630>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def plot_prior():\n",
" plt.scatter(x,y)\n",
" \n",
" lx = np.linspace(-10,10,100)\n",
" w = np.random.randn(10)*to_std(qwlv).item() + qwu.item()\n",
" b = np.random.randn(10)*to_std(qblv).item() + qbu.item() \n",
" for i in range(10):\n",
" plt.plot(lx, lx*w[i] + b[i])\n",
" plt.plot(lx, lx*qwu.item() + qbu.item(), 'k', label='expected') \n",
" plt.legend()\n",
"\n",
"plot_prior()"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def zero_grad(elems):\n",
" [e.grad.zero_() for e in elems]\n",
"\n",
"def elbo_grad(nsamples=30): \n",
" z0, z1 = sampleq(nsamples)\n",
" for i in range(nsamples):\n",
" qe = qj(z0[i], z1[i])\n",
" pe = pj(ty, z0[i], z1[i], tx)\n",
" s = (pe - qe) / nsamples \n",
" qe.backward(gradient=s) # scale by s and accumulate gradients "
]
},
{
"cell_type": "code",
"execution_count": 61,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[tensor(0.1421), tensor(5.1898), tensor(-3.9884), tensor(-3.9946)]\n",
"[tensor(0.5345), tensor(6.9471), tensor(-4.1288), tensor(-4.0306)]\n",
"[tensor(0.5337), tensor(8.0812), tensor(-4.2751), tensor(-4.0239)]\n",
"[tensor(0.5100), tensor(8.8417), tensor(-4.3897), tensor(-4.0267)]\n",
"[tensor(0.4861), tensor(9.3255), tensor(-4.4999), tensor(-4.0362)]\n",
"[tensor(0.4794), tensor(9.5853), tensor(-4.5870), tensor(-4.0395)]\n",
"[tensor(0.4876), tensor(9.7566), tensor(-4.6749), tensor(-4.0439)]\n",
"[tensor(0.4921), tensor(9.8669), tensor(-4.7407), tensor(-4.0504)]\n",
"[tensor(0.4951), tensor(9.9191), tensor(-4.8190), tensor(-4.0567)]\n",
"[tensor(0.5040), tensor(9.9541), tensor(-4.8843), tensor(-4.0599)]\n"
]
}
],
"source": [
"qp = [qwu, qbu, qwlv, qblv]\n",
"#qp = [qwu, qbu]\n",
"\n",
"lr = 1e-5\n",
"for i in range(500):\n",
" elbo_grad(nsamples=100)\n",
" with torch.no_grad():\n",
" for p in qp:\n",
" p += p.grad * lr \n",
" zero_grad(qp)\n",
" if i % 50 == 0: print(qp)"
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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WVRuot1gZ5uHE00FetHf4//U6DSYLa1P1LInP4WhxLW52Gp7o15pJPYLwcrxw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\nRK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x272fdc64048>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def plot_posterior():\n",
" plt.scatter(x,y)\n",
" \n",
" lx = np.linspace(-10,10,100)\n",
" w = np.random.randn(10)*to_std(qwlv).item() + qwu.item()\n",
" b = np.random.randn(10)*to_std(qblv).item() + qbu.item() \n",
" for i in range(10):\n",
" plt.plot(lx, lx*w[i] + b[i])\n",
" plt.plot(lx, lx*qwu.item() + qbu.item(), 'k', label='expected') \n",
" plt.legend()\n",
" \n",
"plot_posterior()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.0"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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