epistemic uncertainty with variational layers working
This commit is contained in:
ritchie46 committed
1 parent
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commit
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1 file changed
+345
-28
@@ -14,21 +14,23 @@
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"from torch import nn\n",
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"from sklearn import datasets\n",
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"from torch.utils.data import DataLoader, TensorDataset\n",
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"from sklearn.preprocessing import StandardScaler"
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"from sklearn.preprocessing import StandardScaler\n",
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"import torch.distributions as dist\n",
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"from dataclasses import dataclass"
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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": 394,
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"execution_count": 397,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"<matplotlib.collections.PathCollection at 0x7f6d652fbfd0>"
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"<matplotlib.collections.PathCollection at 0x7fa823b1cc50>"
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]
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},
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"execution_count": 394,
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"execution_count": 397,
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"metadata": {},
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"output_type": "execute_result"
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},
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@@ -74,7 +76,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 395,
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"execution_count": 401,
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"metadata": {},
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"outputs": [],
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"source": [
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@@ -84,7 +86,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 396,
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"execution_count": 4,
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"metadata": {},
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"outputs": [],
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"source": [
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@@ -114,12 +116,12 @@
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},
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{
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"cell_type": "code",
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"execution_count": 397,
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"execution_count": 5,
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"metadata": {},
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"outputs": [
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{
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"data": {
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truncated
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"image/png": 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"text/plain": [
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"<Figure size 1152x432 with 1 Axes>"
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]
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@@ -139,14 +141,14 @@
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},
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{
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"cell_type": "code",
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"execution_count": 398,
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"execution_count": 6,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"tensor(0.4997)\n"
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"tensor(0.5057)\n"
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]
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}
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],
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@@ -166,7 +168,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 399,
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"execution_count": 7,
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"metadata": {},
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"outputs": [],
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"source": [
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@@ -177,7 +179,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 451,
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"execution_count": 398,
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"metadata": {},
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"outputs": [],
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"source": [
|
||||
@@ -214,19 +216,20 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 452,
|
||||
"execution_count": 411,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def elbo(y_pred, y, mu, log_var):\n",
|
||||
" sigma = log_var.exp()**0.5\n",
|
||||
" # likelihood of observing y given Variational mu and sigma\n",
|
||||
" likelihood = ll_gaussian(y, mu, log_var)\n",
|
||||
" likelihood = dist.Normal(mu, sigma).log_prob(y)\n",
|
||||
" \n",
|
||||
" # prior probability of y_pred\n",
|
||||
" log_prior = ll_gaussian(y_pred, 0, torch.log(torch.tensor(1.)))\n",
|
||||
" log_prior = dist.Normal(0, 1).log_prob(y_pred)\n",
|
||||
" \n",
|
||||
" # variational probability of y_pred\n",
|
||||
" log_p_q = ll_gaussian(y_pred, mu, log_var)\n",
|
||||
" log_p_q = dist.Normal(mu, sigma).log_prob(y_pred) \n",
|
||||
" \n",
|
||||
" # by taking the mean we approximate the expectation\n",
|
||||
" return (likelihood + log_prior - log_p_q).mean()\n",
|
||||
@@ -240,7 +243,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 453,
|
||||
"execution_count": 412,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
@@ -259,14 +262,14 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 454,
|
||||
"execution_count": 413,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"tensor(0.5258)\n"
|
||||
"tensor(0.5246)\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -277,7 +280,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 455,
|
||||
"execution_count": 414,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
@@ -291,22 +294,22 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 464,
|
||||
"execution_count": 415,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"<matplotlib.collections.PolyCollection at 0x7f6d648794e0>"
|
||||
"<matplotlib.collections.PolyCollection at 0x7fa823623e80>"
|
||||
]
|
||||
},
|
||||
"execution_count": 464,
|
||||
"execution_count": 415,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": "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 truncated
|
||||
"text/plain": [
|
||||
"<Figure size 1152x432 with 1 Axes>"
|
||||
]
|
||||
@@ -326,7 +329,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 300,
|
||||
"execution_count": 14,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
@@ -334,7 +337,304 @@
|
||||
" reconstruction_error = (0.5 * (y - y_pred)**2).sum()\n",
|
||||
" kl_divergence = (-0.5 * torch.sum(1 + log_var - mu**2 - log_var.exp()))\n",
|
||||
"\n",
|
||||
" return (reconstruction_error + kl_divergence).sum()"
|
||||
" return reconstruction_error + kl_divergence"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$ Q(w) = \\mathcal{N}(\\mu_{\\theta}, \\sigma^2_{\\theta}) $ "
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 369,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<Figure size 432x288 with 1 Axes>"
|
||||
]
|
||||
},
|
||||
"metadata": {
|
||||
"needs_background": "light"
|
||||
},
|
||||
"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"# def f(x, sigma=0.07):\n",
|
||||
"# return (x**2 + x) / 3500 + torch.randn_like(x) * sigma\n",
|
||||
"\n",
|
||||
"# plt.scatter(X, f(X))\n",
|
||||
"\n",
|
||||
"# Y = f(X)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 372,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"tensor([[ 0.2131, 0.6623, -1.0420, -0.2947, -0.2779, -0.3666, -0.1316, -0.5020,\n",
|
||||
" 1.4475, -0.7042],\n",
|
||||
" [ 0.2131, 0.6623, -1.0420, -0.2947, -0.2779, -0.3666, -0.1316, -0.5020,\n",
|
||||
" 1.4475, -0.7042],\n",
|
||||
" [ 0.2131, 0.6623, -1.0420, -0.2947, -0.2779, -0.3666, -0.1316, -0.5020,\n",
|
||||
" 1.4475, -0.7042],\n",
|
||||
" [ 0.2131, 0.6623, -1.0420, -0.2947, -0.2779, -0.3666, -0.1316, -0.5020,\n",
|
||||
" 1.4475, -0.7042],\n",
|
||||
" [ 0.2131, 0.6623, -1.0420, -0.2947, -0.2779, -0.3666, -0.1316, -0.5020,\n",
|
||||
" 1.4475, -0.7042],\n",
|
||||
" [ 0.2131, 0.6623, -1.0420, -0.2947, -0.2779, -0.3666, -0.1316, -0.5020,\n",
|
||||
" 1.4475, -0.7042],\n",
|
||||
" [ 0.2131, 0.6623, -1.0420, -0.2947, -0.2779, -0.3666, -0.1316, -0.5020,\n",
|
||||
" 1.4475, -0.7042],\n",
|
||||
" [ 0.2131, 0.6623, -1.0420, -0.2947, -0.2779, -0.3666, -0.1316, -0.5020,\n",
|
||||
" 1.4475, -0.7042],\n",
|
||||
" [ 0.2131, 0.6623, -1.0420, -0.2947, -0.2779, -0.3666, -0.1316, -0.5020,\n",
|
||||
" 1.4475, -0.7042],\n",
|
||||
" [ 0.2131, 0.6623, -1.0420, -0.2947, -0.2779, -0.3666, -0.1316, -0.5020,\n",
|
||||
" 1.4475, -0.7042]], grad_fn=<AddBackward0>)"
|
||||
]
|
||||
},
|
||||
"execution_count": 372,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"class LinearVariational(nn.Module):\n",
|
||||
" \"\"\"\n",
|
||||
" Mean field approximation of dense layer.\n",
|
||||
" \"\"\"\n",
|
||||
" def __init__(self, in_features, out_features, parent, bias=True):\n",
|
||||
" super().__init__()\n",
|
||||
" self.in_features = in_features\n",
|
||||
" self.out_features = out_features\n",
|
||||
" self.include_bias = bias \n",
|
||||
" self.parent = parent\n",
|
||||
" \n",
|
||||
" if getattr(parent, 'accumulated_kl_div', None) is None:\n",
|
||||
" parent.accumulated_kl_div = 0\n",
|
||||
" \n",
|
||||
" # Initialize the variational parameters.\n",
|
||||
" # 𝑄(𝑤)=N(𝜇_𝜃,𝜎2_𝜃)\n",
|
||||
" # Do some random initialization with 𝜎=0.01\n",
|
||||
" self.w_mu = nn.Parameter(\n",
|
||||
" torch.FloatTensor(in_features, out_features).normal_(mean=0, std=0.001)\n",
|
||||
" )\n",
|
||||
" # proxy for variance\n",
|
||||
" # log(1 + exp(ρ))◦ eps\n",
|
||||
" self.w_p = nn.Parameter(\n",
|
||||
" torch.FloatTensor(in_features, out_features).normal_(mean=-2.5, std=0.001)\n",
|
||||
" )\n",
|
||||
" if self.include_bias:\n",
|
||||
" self.b_mu = nn.Parameter(\n",
|
||||
" torch.zeros(out_features)\n",
|
||||
" )\n",
|
||||
" # proxy for variance\n",
|
||||
" self.b_p = nn.Parameter(\n",
|
||||
" torch.zeros(out_features)\n",
|
||||
" )\n",
|
||||
" # learnable prior mixture parameters\n",
|
||||
" # See 3.3. Scale mixture prior\n",
|
||||
" # Weight Uncertainty in Neural Networks (Charles Blundell et al.)\n",
|
||||
" # https://arxiv.org/pdf/1505.05424.pdf\n",
|
||||
" self.pi = nn.Parameter(torch.FloatTensor([0.2]))\n",
|
||||
" self.sigma_1 = nn.Parameter(torch.FloatTensor([1.]))\n",
|
||||
" self.sigma_2 = nn.Parameter(torch.FloatTensor([.1]))\n",
|
||||
" \n",
|
||||
" def log_prior(self, z):\n",
|
||||
" return (self.pi * dist.Normal(0, self.sigma_1).log_prob(z).exp() +\n",
|
||||
" (1 - self.pi) * dist.Normal(0, self.sigma_2).log_prob(z).exp()).log()\n",
|
||||
"\n",
|
||||
" def reparameterize(self, mu, p):\n",
|
||||
" sigma = torch.log(1 + torch.exp(p)) \n",
|
||||
" eps = torch.randn_like(sigma)\n",
|
||||
" return mu + (eps * sigma)\n",
|
||||
" \n",
|
||||
" def kl_divergence(self, z, mu_theta, p_theta, prior_sd=1):\n",
|
||||
" log_prior = dist.Normal(0, prior_sd).log_prob(z) \n",
|
||||
" log_p_q = dist.Normal(mu_theta, torch.log(1 + torch.exp(p_theta))).log_prob(z) \n",
|
||||
"\n",
|
||||
" # reverse the elbo, as we need to maximize the elbo\n",
|
||||
" # - (log_prior - log_p_q) = log_p_q - log_prior\n",
|
||||
" return (log_p_q - log_prior).sum()\n",
|
||||
" \n",
|
||||
"\n",
|
||||
" def forward(self, x):\n",
|
||||
" w = self.reparameterize(self.w_mu, self.w_p)\n",
|
||||
" \n",
|
||||
" if self.include_bias:\n",
|
||||
" b = self.reparameterize(self.b_mu, self.b_p)\n",
|
||||
" else:\n",
|
||||
" b = 0\n",
|
||||
" \n",
|
||||
" z = x @ w + b\n",
|
||||
" \n",
|
||||
" self.parent.accumulated_kl_div += self.kl_divergence(w, \n",
|
||||
" self.w_mu,\n",
|
||||
" self.w_p, \n",
|
||||
" 1.\n",
|
||||
" )\n",
|
||||
" if self.include_bias:\n",
|
||||
" self.parent.accumulated_kl_div += self.kl_divergence(b, \n",
|
||||
" self.b_mu, \n",
|
||||
" self.b_p,\n",
|
||||
" 1.\n",
|
||||
" )\n",
|
||||
" return z\n",
|
||||
" \n",
|
||||
"m = LinearVariational(2, 10, parent=d)\n",
|
||||
"m.forward(torch.ones(10, 2))"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 416,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"tensor([[0.2831],\n",
|
||||
" [0.2831],\n",
|
||||
" [0.2828],\n",
|
||||
" [0.2819],\n",
|
||||
" [0.2813],\n",
|
||||
" [0.2810],\n",
|
||||
" [0.2799],\n",
|
||||
" [0.2791],\n",
|
||||
" [0.2789],\n",
|
||||
" [0.2786]], grad_fn=<SliceBackward>)"
|
||||
]
|
||||
},
|
||||
"execution_count": 416,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"@dataclass\n",
|
||||
"class KL:\n",
|
||||
" accumulated_kl_div = 0\n",
|
||||
"\n",
|
||||
"class Model(nn.Module):\n",
|
||||
" def __init__(self, in_size, hidden_size, out_size):\n",
|
||||
" super().__init__()\n",
|
||||
" \n",
|
||||
" self.kl_loss = KL\n",
|
||||
" \n",
|
||||
" self.layers = nn.Sequential(\n",
|
||||
" LinearVariational(in_size, hidden_size, self.kl_loss),\n",
|
||||
" nn.ReLU(),\n",
|
||||
" LinearVariational(hidden_size, hidden_size, self.kl_loss),\n",
|
||||
" nn.ReLU(),\n",
|
||||
" LinearVariational(hidden_size, out_size, self.kl_loss)\n",
|
||||
" )\n",
|
||||
" \n",
|
||||
" @property\n",
|
||||
" def accumulated_kl_div(self):\n",
|
||||
" return self.kl_loss.accumulated_kl_div\n",
|
||||
" \n",
|
||||
" def reset_kl_div(self):\n",
|
||||
" self.kl_loss.accumulated_kl_div = 0\n",
|
||||
" \n",
|
||||
" def forward(self, x):\n",
|
||||
" return self.layers(x)\n",
|
||||
" \n",
|
||||
"m = Model(1, 20, 1)\n",
|
||||
"m(X)[:10]"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 417,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"tensor(908.0202, grad_fn=<AddBackward0>)"
|
||||
]
|
||||
},
|
||||
"execution_count": 417,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"m.accumulated_kl_div"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 418,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"11374.8408203125\n",
|
||||
"4694.74560546875\n",
|
||||
"5758.109375\n",
|
||||
"5817.72265625\n",
|
||||
"4768.3720703125\n",
|
||||
"4349.931640625\n",
|
||||
"4380.0009765625\n",
|
||||
"4547.62548828125\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"epochs = 2000\n",
|
||||
"\n",
|
||||
"def det_loss(y, y_pred, model):\n",
|
||||
" batch_size = y.shape[0]\n",
|
||||
" reconstruction_error = -dist.Normal(y_pred, .1).log_prob(y).sum() \n",
|
||||
" kl = model.accumulated_kl_div\n",
|
||||
" model.reset_kl_div()\n",
|
||||
" return (reconstruction_error + kl) \n",
|
||||
" \n",
|
||||
"m = Model(1, 20, 1)\n",
|
||||
"optim = torch.optim.Adam(m.parameters(), lr=0.01)\n",
|
||||
"\n",
|
||||
"for epoch in range(epochs):\n",
|
||||
" optim.zero_grad()\n",
|
||||
" y_pred = m(X)\n",
|
||||
" loss = det_loss(y_pred, Y, m)\n",
|
||||
" loss.backward()\n",
|
||||
" optim.step()\n",
|
||||
" \n",
|
||||
" if epoch % 250 == 0:\n",
|
||||
" print(loss.data.item())"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 420,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"with torch.no_grad():\n",
|
||||
" trace = np.array([m(X).flatten().numpy() for _ in range(1000)]).T"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 421,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"q_25, q_95 = np.quantile(trace, [0.05, 0.95], axis=1)"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -345,15 +645,32 @@
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"tensor(0.5044, grad_fn=<MeanBackward0>)"
|
||||
"<matplotlib.collections.PolyCollection at 0x7fa8234d16d8>"
|
||||
]
|
||||
},
|
||||
"execution_count": 422,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": "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 truncated
|
||||
"text/plain": [
|
||||
"<Figure size 1152x432 with 1 Axes>"
|
||||
]
|
||||
},
|
||||
"metadata": {
|
||||
"needs_background": "light"
|
||||
},
|
||||
"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"source": []
|
||||
"source": [
|
||||
"plt.figure(figsize=(16, 6))\n",
|
||||
"plt.plot(X, trace.mean(1))\n",
|
||||
"plt.scatter(X, Y)\n",
|
||||
"plt.fill_between(X.flatten(), q_25, q_95, alpha=0.2)\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
|
||||
Reference in new issue
Block a user