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@ColCarroll
Created February 23, 2018 15:57
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A few experiments comparing NUTS, mean-field ADVI, and full-rank ADVI to ground truth 2d [mixture of] Gaussians
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import theano\n",
"theano.config.compute_test_value = 'raise' # funny bug when first making a theano variable"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Experiments with ADVI\n",
"\n",
"A few computational experiments with ADVI, comparing NUTS, mean-field ADVI, and full-rank ADVI approximations of a distribution."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/colin/miniconda3/envs/scratch3.6/lib/python3.6/site-packages/h5py/__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
" from ._conv import register_converters as _register_converters\n"
]
}
],
"source": [
"%matplotlib inline\n",
"\n",
"import matplotlib\n",
"import numpy as np\n",
"import pymc3 as pm\n",
"import matplotlib.pyplot as plt\n",
"import theano.tensor as tt\n",
"\n",
"plt.style.use('seaborn-dark')"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"def _get_bounds(samples):\n",
" \"\"\"Helper function to draw consistent bounds\"\"\"\n",
" x_max, y_max = 0, 0\n",
" for x_draws, y_draws in samples.values():\n",
" x_max = max(x_max, np.abs(x_draws).max())\n",
" y_max = max(y_max, np.abs(y_draws).max())\n",
" top = max(x_max, y_max)\n",
" return (-top, top)\n",
"\n",
"\n",
"def density_model(Ω):\n",
" \"\"\"This is the \"modeling\" step. \n",
" \n",
" We are using PyMC3, and assuming we get an object Ω that represents some joint\n",
" distribution. We require Ω to have two methods: `logp` and `random`. The logp should also\n",
" be defined in a Theano-compatible fashion so it can compute the gradients.\n",
" \"\"\"\n",
" with pm.Model() as model:\n",
" omega = pm.DensityDist('Ω', Ω.logp, shape=2)\n",
" return model\n",
"\n",
"def sampler(Ω, N=1000):\n",
" \"\"\"This is the \"inference\" step\n",
" \n",
" Note that the only added difficulty in using ADVI is that we have a call to `pm.fit` in order to learn\n",
" the parameters for the mean-field or full-rank approximation.\n",
" \"\"\"\n",
" samples = {'Ground Truth': Ω.random(size=N).T}\n",
" with density_model(Ω):\n",
" samples['NUTS'] = pm.sample(N, step=pm.NUTS(), chains=1)['Ω'].T\n",
" \n",
" for method in ('advi', 'fullrank_advi'):\n",
" inference = pm.fit(n=30000, method=method)\n",
" samples[method] = inference.sample(N)['Ω'].T\n",
" \n",
" return samples\n",
"\n",
"\n",
"def plotter(samples):\n",
" \"\"\"Helper to plot the output of `sampler`. A little flexible in case we want to add more VI methods.\n",
" \"\"\"\n",
" size = int(np.ceil(len(samples) ** 0.5))\n",
" fix, axs = plt.subplots(size, size, figsize=(12, 8))\n",
" bounds = _get_bounds(samples)\n",
" for (label, (x, y)), ax in zip(samples.items(), axs.ravel()):\n",
" ax.plot(x, y, 'o', alpha = 0.5)\n",
" ax.set_title(label)\n",
" ax.axes.set_xlim(bounds)\n",
" ax.axes.set_ylim(bounds)\n",
" \n",
"\n",
"def sample_and_plot(dist):\n",
" \"\"\"For the lazy\"\"\"\n",
" samples = sampler(dist)\n",
" plotter(samples)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 1. Ill-conditioned Gaussian"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"mu = tt.zeros(2,)\n",
"cov = tt.as_tensor([[1e-2, 0.], [0., 1e2]])\n",
"Ω = pm.MvNormal.dist(mu=mu, cov=cov, shape=2, testval=mu)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/colin/miniconda3/envs/scratch3.6/lib/python3.6/site-packages/pymc3/model.py:384: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
" if not np.issubdtype(var.dtype, float):\n",
"Sequential sampling (1 chains in 1 job)\n",
"NUTS: [Ω]\n",
"100%|██████████| 1500/1500 [00:02<00:00, 711.69it/s]\n",
"Only one chain was sampled, this makes it impossible to run some convergence checks\n",
"Average Loss = 0.09657: 100%|██████████| 30000/30000 [00:10<00:00, 2821.92it/s] \n",
"Finished [100%]: Average Loss = 0.097131\n",
"Average Loss = 0.063651: 100%|██████████| 30000/30000 [00:14<00:00, 2015.99it/s]\n",
"Finished [100%]: Average Loss = 0.06198\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fec95127400>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sample_and_plot(Ω)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 2. Strongly correlated Gaussian"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"mu = tt.zeros(2,)\n",
"cov = tt.as_tensor([[50.05, -49.95], [-49.95, 50.05]])\n",
"Ω = pm.MvNormal.dist(mu=mu, cov=cov, shape=2, testval=mu)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/colin/miniconda3/envs/scratch3.6/lib/python3.6/site-packages/pymc3/model.py:384: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
" if not np.issubdtype(var.dtype, float):\n",
"Sequential sampling (1 chains in 1 job)\n",
"NUTS: [Ω]\n",
"100%|██████████| 1500/1500 [00:06<00:00, 215.85it/s]\n",
"Only one chain was sampled, this makes it impossible to run some convergence checks\n",
"Average Loss = 2.7394: 100%|██████████| 30000/30000 [00:09<00:00, 3022.32it/s]\n",
"Finished [100%]: Average Loss = 2.744\n",
"Average Loss = 0.83846: 100%|██████████| 30000/30000 [00:17<00:00, 1712.92it/s]\n",
"Finished [100%]: Average Loss = 0.83957\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fec55d49cf8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sample_and_plot(Ω)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 3. Mixture of Gaussians"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"class MoG(object):\n",
" def __init__(self, centers, sds):\n",
" mu_1, mu_2 = centers\n",
" cov_1 = tt.as_tensor([[sds[0], 0], [0, sds[0]]])\n",
" cov_2 = tt.as_tensor([[sds[1], 0], [0, sds[1]]])\n",
"\n",
" self.rvs = [pm.MvNormal.dist(mu=mu_1, cov=cov_1, shape=2),\n",
" pm.MvNormal.dist(mu=mu_2, cov=cov_2, shape=2)]\n",
" \n",
" def random(self, size=1):\n",
" return np.array([rv.random() for rv in np.random.choice(self.rvs, size=size)])\n",
" \n",
" def logp(self, value):\n",
" return pm.math.logsumexp([rv.logp(value) for rv in self.rvs]) - np.log(len(self.rvs))\n"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"Ω = MoG(centers=[np.array([-2, 0]), np.array([2, 0])], sds=[0.1, 0.1])"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/colin/miniconda3/envs/scratch3.6/lib/python3.6/site-packages/pymc3/model.py:384: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
" if not np.issubdtype(var.dtype, float):\n",
"Sequential sampling (1 chains in 1 job)\n",
"NUTS: [Ω]\n",
"100%|██████████| 1500/1500 [00:01<00:00, 957.48it/s]\n",
"Only one chain was sampled, this makes it impossible to run some convergence checks\n",
"Average Loss = 5.969: 100%|██████████| 30000/30000 [00:14<00:00, 2121.74it/s] \n",
"Finished [100%]: Average Loss = 5.9217\n",
"Average Loss = 6.3004: 100%|██████████| 30000/30000 [00:21<00:00, 1409.53it/s]\n",
"Finished [100%]: Average Loss = 6.2906\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fec55d58710>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sample_and_plot(Ω)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 4. Mixture of Gaussians with different scales"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"Ω = MoG(centers=[np.array([-4, 0]), np.array([4, 0])], sds=[2, 0.1])"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/colin/miniconda3/envs/scratch3.6/lib/python3.6/site-packages/pymc3/model.py:384: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
" if not np.issubdtype(var.dtype, float):\n",
"Sequential sampling (1 chains in 1 job)\n",
"NUTS: [Ω]\n",
"100%|██████████| 1500/1500 [00:01<00:00, 932.83it/s]\n",
"Only one chain was sampled, this makes it impossible to run some convergence checks\n",
"Average Loss = 0.70752: 100%|██████████| 30000/30000 [00:13<00:00, 2201.93it/s]\n",
"Finished [100%]: Average Loss = 0.70748\n",
"Average Loss = 0.71185: 100%|██████████| 30000/30000 [00:20<00:00, 1437.01it/s]\n",
"Finished [100%]: Average Loss = 0.71251\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fec4e2c3eb8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sample_and_plot(Ω)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 5. Mixture of non-axis-aligned Gaussians"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"θ = np.pi / 4\n",
"rot_45 = np.array([[np.cos(θ), -np.sin(θ)], [np.sin(θ), np.cos(θ)]])\n",
"Ω = MoG(centers=[rot_45.dot(np.array([-2, 0])), rot_45.dot(np.array([2, 0]))], sds=[0.1, 0.1])"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/colin/miniconda3/envs/scratch3.6/lib/python3.6/site-packages/pymc3/model.py:384: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
" if not np.issubdtype(var.dtype, float):\n",
"Sequential sampling (1 chains in 1 job)\n",
"NUTS: [Ω]\n",
"100%|██████████| 1500/1500 [00:01<00:00, 936.08it/s]\n",
"Only one chain was sampled, this makes it impossible to run some convergence checks\n",
"Average Loss = 10.593: 100%|██████████| 30000/30000 [00:16<00:00, 1829.69it/s]\n",
"Finished [100%]: Average Loss = 10.65\n",
"Average Loss = 6.4672: 100%|██████████| 30000/30000 [00:20<00:00, 1463.15it/s]\n",
"Finished [100%]: Average Loss = 6.4597\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fec4de3afd0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sample_and_plot(Ω)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "scratch3.6",
"language": "python",
"name": "scratch3_6"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.4"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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