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@ikanher
Created January 26, 2022 18:04
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Variational inference with Pyro
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "c84dec81",
"metadata": {},
"outputs": [],
"source": [
"import torch\n",
"import pyro\n",
"\n",
"import matplotlib\n",
"import matplotlib.pyplot as plt\n",
"\n",
"#torch.set_default_dtype(torch.double)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "2f113c94",
"metadata": {},
"outputs": [],
"source": [
"# limits for plots\n",
"t = torch.linspace(-6, 6, 100)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "f4cbe021",
"metadata": {},
"outputs": [],
"source": [
"def plot_contour(t, p, save_fname=None):\n",
" xx, yy = torch.meshgrid(t, t)\n",
"\n",
" t = torch.hstack((xx.reshape(-1).unsqueeze(1), yy.reshape(-1).unsqueeze(1)))\n",
" \n",
" Z = p.log_prob(t).reshape(xx.shape)\n",
" \n",
" cs = plt.contour(xx, yy, Z, levels=12)\n",
" plt.clabel(cs, inline=1, fontsize=10)\n",
"\n",
" if save_fname:\n",
" plt.savefig(save_fname)\n",
" else:\n",
" plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "9866ed79",
"metadata": {},
"outputs": [],
"source": [
"def plot_contours(t, p, q, elbo, save_fname=None, log_space=True):\n",
" xx, yy = torch.meshgrid(t, t)\n",
"\n",
" t = torch.hstack((xx.reshape(-1).unsqueeze(1), yy.reshape(-1).unsqueeze(1)))\n",
"\n",
" Zp = p.log_prob(t).reshape(xx.shape)\n",
" Zq = q.log_prob(t).reshape(xx.shape)\n",
" \n",
" if not log_space:\n",
" Zp = Zp.exp()\n",
" Zq = Zq.exp()\n",
" plt.xlim([-5, 5])\n",
" plt.ylim([-5, 5])\n",
"\n",
" plt.contourf(xx, yy, Zp, levels=12)\n",
" \n",
" cs = plt.contour(xx, yy, Zq, levels=12, colors='black')\n",
" plt.clabel(cs, inline=1, fontsize=10)\n",
" \n",
" plt.title(f'ELBO: {elbo:.5f}')\n",
" \n",
" if save_fname:\n",
" plt.savefig(save_fname)\n",
" else:\n",
" plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 97,
"id": "276f900d",
"metadata": {},
"outputs": [],
"source": [
"def model():\n",
" mus = torch.tensor([[-2., -2.], [1., 1.]])\n",
" sigmas = torch.tensor([[[1., 0.], [0., 2.]], [[2., 0.], [0., 1.]]])\n",
" pis = torch.tensor([0.3, 0.7])\n",
"\n",
" weights = torch.distributions.Categorical(pis)\n",
" comp = torch.distributions.MultivariateNormal(loc=mus, covariance_matrix=sigmas)\n",
"\n",
" mixture = torch.distributions.MixtureSameFamily(weights, comp)\n",
" \n",
" pyro.sample('distribution', mixture)"
]
},
{
"cell_type": "markdown",
"id": "c6d0c24a",
"metadata": {},
"source": [
"# Single Gaussian - diagonal covariance"
]
},
{
"cell_type": "code",
"execution_count": 98,
"id": "2e361c9d",
"metadata": {},
"outputs": [],
"source": [
"def guide():\n",
" m = pyro.param('m', torch.randn(2).exp())\n",
"\n",
" c = pyro.param('c',\n",
" torch.randn(2).exp(),\n",
" pyro.distributions.constraints.positive,\n",
" )\n",
"\n",
" pyro.sample('distribution', pyro.distributions.MultivariateNormal(m, c.diag()))"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "fc708c9e",
"metadata": {},
"outputs": [],
"source": [
"torch.manual_seed(42)\n",
"\n",
"D = 2\n",
"N_iter = 5000\n",
"N_particles = 100\n",
"lr = 1e-2\n",
"\n",
"pyro.enable_validation(True)\n",
"pyro.clear_param_store()\n",
"\n",
"optimizer = pyro.optim.Adam({ 'lr': lr })\n",
"\n",
"svi = pyro.infer.SVI(\n",
" model,\n",
" guide,\n",
" optimizer,\n",
" loss=pyro.infer.Trace_ELBO(num_particles=N_particles, vectorize_particles=True),\n",
")\n",
"\n",
"m_hist = torch.zeros((N_iter, D))\n",
"c_hist = torch.zeros((N_iter, D))\n",
"elbo_hist = torch.zeros(N_iter)\n",
"\n",
"for i in range(N_iter):\n",
" svi.step()\n",
"\n",
" m_hist[i] = pyro.param('m')\n",
" c_hist[i] = pyro.param('c')\n",
" elbo_hist[i] = svi.evaluate_loss()"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "e5aad0c4",
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 1080x360 with 3 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"with torch.no_grad():\n",
" fig, axes = plt.subplots(1, 3, figsize=(15, 5))\n",
" axes[0].plot(m_hist)\n",
" axes[0].set_title('$\\mu$')\n",
" axes[1].plot(c_hist)\n",
" axes[1].set_title('$\\sigma$')\n",
" axes[2].plot(elbo_hist)\n",
" axes[2].set_title('ELBO')"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "73bd8229",
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"mus = torch.tensor([[-2., -2.], [1., 1.]])\n",
"sigmas = torch.tensor([[[1., 0.], [0., 2.]], [[2., 0.], [0., 1.]]])\n",
"pis = torch.tensor([0.3, 0.7])\n",
"\n",
"weights = torch.distributions.Categorical(pis)\n",
"comp = torch.distributions.MultivariateNormal(loc=mus, covariance_matrix=sigmas)\n",
"\n",
"p = torch.distributions.MixtureSameFamily(weights, comp)\n",
"\n",
"with torch.no_grad():\n",
" q = torch.distributions.MultivariateNormal(pyro.param('m'), pyro.param('c').diag())\n",
" plot_contours(t, p, q, svi.loss(model, guide))"
]
},
{
"cell_type": "markdown",
"id": "94579516",
"metadata": {},
"source": [
"# Single Gaussian - full rank"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "e3169654",
"metadata": {},
"outputs": [],
"source": [
"def guide():\n",
" m = pyro.param('m', torch.randn(2).exp())\n",
"\n",
" c = pyro.param('c',\n",
" torch.randn(2).diag().exp(),\n",
" pyro.distributions.constraints.positive_definite,\n",
" )\n",
"\n",
" pyro.sample('distribution', pyro.distributions.MultivariateNormal(m, c))"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "2fb7702f",
"metadata": {},
"outputs": [],
"source": [
"torch.manual_seed(42)\n",
"\n",
"D = 2\n",
"N_iter = 5000\n",
"N_particles = 100\n",
"lr = 1e-2\n",
"\n",
"pyro.enable_validation(True)\n",
"pyro.clear_param_store()\n",
"\n",
"optimizer = pyro.optim.Adam({ 'lr': lr })\n",
"\n",
"svi = pyro.infer.SVI(\n",
" model,\n",
" guide,\n",
" optimizer,\n",
" loss=pyro.infer.Trace_ELBO(num_particles=N_particles, vectorize_particles=True),\n",
")\n",
"\n",
"m_hist = torch.zeros((N_iter, D))\n",
"c_hist = torch.zeros((N_iter, D))\n",
"elbo_hist = torch.zeros(N_iter)\n",
"\n",
"svi.step()\n",
"for i in range(N_iter):\n",
" svi.step()\n",
"\n",
" m_hist[i] = pyro.param('m')\n",
" c_hist[i] = pyro.param('c').diag()\n",
" elbo_hist[i] = svi.evaluate_loss()"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "58e36790",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1080x360 with 3 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"with torch.no_grad():\n",
" fig, axes = plt.subplots(1, 3, figsize=(15, 5))\n",
" axes[0].plot(m_hist)\n",
" axes[0].set_title('$\\mu$')\n",
" axes[1].plot(c_hist)\n",
" axes[1].set_title('$\\sigma$')\n",
" axes[2].plot(elbo_hist)\n",
" axes[2].set_title('ELBO')"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "89e53297",
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"mus = torch.tensor([[-2., -2.], [1., 1.]])\n",
"sigmas = torch.tensor([[[1., 0.], [0., 2.]], [[2., 0.], [0., 1.]]])\n",
"pis = torch.tensor([0.3, 0.7])\n",
"\n",
"weights = torch.distributions.Categorical(pis)\n",
"comp = torch.distributions.MultivariateNormal(loc=mus, covariance_matrix=sigmas)\n",
"\n",
"p = torch.distributions.MixtureSameFamily(weights, comp)\n",
"\n",
"with torch.no_grad():\n",
" q = torch.distributions.MultivariateNormal(pyro.param('m'), pyro.param('c'))\n",
" plot_contours(t, p, q, svi.loss(model, guide))"
]
},
{
"cell_type": "markdown",
"id": "8f171229",
"metadata": {},
"source": [
"# GMM"
]
},
{
"cell_type": "code",
"execution_count": 123,
"id": "b7d6611c",
"metadata": {},
"outputs": [],
"source": [
"def guide():\n",
" pis = pyro.param(\n",
" 'pis',\n",
" torch.nn.functional.softmax(torch.randn(2).exp(), dim=0),\n",
" pyro.distributions.constraints.simplex,\n",
" )\n",
"\n",
" weights = torch.distributions.Categorical(pis)\n",
"\n",
" ms = pyro.param('ms', torch.randn((2,2)))\n",
"\n",
" cs = pyro.param('cs',\n",
" torch.randn((2, 2)).exp().diag_embed(),\n",
" pyro.distributions.constraints.positive_definite,\n",
" )\n",
"\n",
" comp = torch.distributions.MultivariateNormal(loc=ms, covariance_matrix=cs)\n",
"\n",
" mixture = pyro.distributions.MixtureSameFamily(weights, comp)\n",
"\n",
" pyro.sample('distribution', mixture)"
]
},
{
"cell_type": "code",
"execution_count": 130,
"id": "08513398",
"metadata": {},
"outputs": [],
"source": [
"torch.manual_seed(42)\n",
"\n",
"D = 2\n",
"N_iter = 1000\n",
"N_particles = 100\n",
"lr = 1e-2\n",
"\n",
"pyro.enable_validation(True)\n",
"pyro.clear_param_store()\n",
"\n",
"optimizer = pyro.optim.Adam({ 'lr': lr })\n",
"\n",
"svi = pyro.infer.SVI(\n",
" model,\n",
" guide,\n",
" optimizer,\n",
" loss=pyro.infer.Trace_ELBO(num_particles=N_particles, vectorize_particles=True),\n",
")\n",
"\n",
"elbo_hist = torch.zeros(N_iter)\n",
"\n",
"svi.step()\n",
"for i in range(N_iter):\n",
" loss = svi.step()\n",
" elbo_hist[i] = loss"
]
},
{
"cell_type": "code",
"execution_count": 139,
"id": "724a9e68",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"with torch.no_grad():\n",
" plt.plot(elbo_hist)\n",
" plt.title('ELBO')"
]
},
{
"cell_type": "code",
"execution_count": 132,
"id": "0d4f0a64",
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# form the `p` distribution\n",
"mus = torch.tensor([[-2., -2.], [1., 1.]])\n",
"sigmas = torch.tensor([[[1., 0.], [0., 2.]], [[2., 0.], [0., 1.]]])\n",
"pis = torch.tensor([0.3, 0.7])\n",
"\n",
"weights = torch.distributions.Categorical(pis)\n",
"comp = torch.distributions.MultivariateNormal(loc=mus, covariance_matrix=sigmas)\n",
"p = torch.distributions.MixtureSameFamily(weights, comp)\n",
"\n",
"# form the `q` distribution\n",
"weights = torch.distributions.Categorical(pyro.param('pis'))\n",
"comp = torch.distributions.MultivariateNormal(loc=pyro.param('ms'), covariance_matrix=pyro.param('cs'))\n",
"q = pyro.distributions.MixtureSameFamily(weights, comp)\n",
"\n",
"with torch.no_grad():\n",
" plot_contours(t, p, q, svi.loss(model, guide))"
]
},
{
"cell_type": "code",
"execution_count": 133,
"id": "fc81ea0a",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"tensor([0.6994, 0.3006], grad_fn=<DivBackward0>)"
]
},
"execution_count": 133,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pyro.param('pis')"
]
},
{
"cell_type": "code",
"execution_count": 134,
"id": "915899ff",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"tensor([[ 1.0019, 1.0007],\n",
" [-1.9983, -1.9954]], requires_grad=True)"
]
},
"execution_count": 134,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pyro.param('ms')"
]
},
{
"cell_type": "code",
"execution_count": 135,
"id": "8d6adf64",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"tensor([[[ 1.9964e+00, -1.4542e-03],\n",
" [-1.4542e-03, 9.9935e-01]],\n",
"\n",
" [[ 1.0015e+00, 4.5516e-03],\n",
" [ 4.5516e-03, 2.0081e+00]]], grad_fn=<UnsafeViewBackward>)"
]
},
"execution_count": 135,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pyro.param('cs')"
]
},
{
"cell_type": "markdown",
"id": "18b0aa40",
"metadata": {},
"source": [
"# Custom ELBO"
]
},
{
"cell_type": "code",
"execution_count": 123,
"id": "9ae56c5d",
"metadata": {},
"outputs": [],
"source": [
"def guide():\n",
" pis = pyro.param(\n",
" 'pis',\n",
" torch.nn.functional.softmax(torch.randn(2).exp(), dim=0),\n",
" pyro.distributions.constraints.simplex,\n",
" )\n",
"\n",
" weights = torch.distributions.Categorical(pis)\n",
"\n",
" ms = pyro.param('ms', torch.randn((2,2)))\n",
"\n",
" cs = pyro.param('cs',\n",
" torch.randn((2, 2)).exp().diag_embed(),\n",
" pyro.distributions.constraints.positive_definite,\n",
" )\n",
"\n",
" comp = torch.distributions.MultivariateNormal(loc=ms, covariance_matrix=cs)\n",
"\n",
" mixture = pyro.distributions.MixtureSameFamily(weights, comp)\n",
"\n",
" pyro.sample('distribution', mixture)"
]
},
{
"cell_type": "code",
"execution_count": 130,
"id": "10cc3452",
"metadata": {},
"outputs": [],
"source": [
"torch.manual_seed(42)\n",
"\n",
"D = 2\n",
"N_iter = 1000\n",
"N_particles = 100\n",
"lr = 1e-2\n",
"\n",
"pyro.enable_validation(True)\n",
"pyro.clear_param_store()\n",
"\n",
"optimizer = pyro.optim.Adam({ 'lr': lr })\n",
"\n",
"svi = pyro.infer.SVI(\n",
" model,\n",
" guide,\n",
" optimizer,\n",
" loss=pyro.infer.Trace_ELBO(num_particles=N_particles, vectorize_particles=True),\n",
")\n",
"\n",
"elbo_hist = torch.zeros(N_iter)\n",
"\n",
"svi.step()\n",
"for i in range(N_iter):\n",
" loss = svi.step()\n",
" elbo_hist[i] = loss"
]
},
{
"cell_type": "code",
"execution_count": 139,
"id": "375a50cf",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"with torch.no_grad():\n",
" plt.plot(elbo_hist)\n",
" plt.title('ELBO')"
]
},
{
"cell_type": "code",
"execution_count": 132,
"id": "fdc6d552",
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# form the `p` distribution\n",
"mus = torch.tensor([[-2., -2.], [1., 1.]])\n",
"sigmas = torch.tensor([[[1., 0.], [0., 2.]], [[2., 0.], [0., 1.]]])\n",
"pis = torch.tensor([0.3, 0.7])\n",
"\n",
"weights = torch.distributions.Categorical(pis)\n",
"comp = torch.distributions.MultivariateNormal(loc=mus, covariance_matrix=sigmas)\n",
"p = torch.distributions.MixtureSameFamily(weights, comp)\n",
"\n",
"# form the `q` distribution\n",
"weights = torch.distributions.Categorical(pyro.param('pis'))\n",
"comp = torch.distributions.MultivariateNormal(loc=pyro.param('ms'), covariance_matrix=pyro.param('cs'))\n",
"q = pyro.distributions.MixtureSameFamily(weights, comp)\n",
"\n",
"with torch.no_grad():\n",
" plot_contours(t, p, q, svi.loss(model, guide))"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "d7407392",
"metadata": {},
"outputs": [],
"source": []
}
],
"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": "3.9.7"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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