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smsharma/covariances.ipynb

Created February 7, 2023 22:14
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covariances.ipynb
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "405cc9da-a883-41ff-98c2-6f1a1ad8b7a6",
"metadata": {},
"outputs": [],
"source": [
"import math\n",
"\n",
"import torch\n",
"import torch.nn as nn\n",
"import torch.distributions as dist"
]
},
{
"cell_type": "markdown",
"id": "bd46eeb4-d861-485e-ab31-fe7c935afb65",
"metadata": {},
"source": [
"## Full covariance loss"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "716367b0-f6ee-44a2-bcee-83ae94cea759",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"torch.Size([64, 9])"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"n_batch = 64 # Batch dimension\n",
"n_params = 3 # Number of parameters\n",
"\n",
"n_tril = int(n_params * (n_params + 1) / 2) # Number of parameters in lower triangular matrix, for symmetric matrix\n",
"\n",
"out = torch.randn((n_batch, n_params + n_tril)) # Dummy output of neural network\n",
"\n",
"out.shape"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "d2be1e07-243e-4802-92f9-9ed9606be366",
"metadata": {},
"outputs": [],
"source": [
"mu, tril = out[:, :n_params], out[:, n_params:] # Separate out mean and lower-triangular elements"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "20389386-5b25-4d0e-a197-b7703e8c9b91",
"metadata": {},
"outputs": [],
"source": [
"def vector_to_Cov(vec):\n",
" \"\"\" Convert unconstrained vector into a positive-diagonal, symmetric covariance matrix\n",
" by converting to cholesky matrix, then doing Cov = L @ L^T \n",
" (https://en.wikipedia.org/wiki/Cholesky_decomposition)\n",
" \"\"\"\n",
" \n",
" D = int((-1.0 + math.sqrt(1.0 + 8.0 * vec.shape[-1])) / 2.0) # Infer dimensionality; D * (D + 1) / 2 = n_tril\n",
" B = vec.shape[0] # Batch dim\n",
" \n",
" # Get indices of lower-triangular matrix to fill\n",
" tril_indices = torch.tril_indices(row=D, col=D, offset=0)\n",
" \n",
" # Fill lower-triangular Cholesky matrix\n",
" L = torch.zeros((B, D, D))\n",
" L[:, tril_indices[0], tril_indices[1]] = vec\n",
" \n",
" # Enforce positive diagonals\n",
" positive_diags = nn.Softplus()(torch.diagonal(L, dim1=-1, dim2=-2))\n",
" L[:, range(L.shape[-1]), range(L.shape[-2])] = positive_diags\n",
" \n",
" # Cov = L @ L^T \n",
" Cov = torch.einsum(\"bij, bkj ->bik\", L, L)\n",
"\n",
" return Cov\n",
"\n",
"Cov = vector_to_Cov(tril)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "45c9a7fe-0335-4717-ac06-9715862fe8af",
"metadata": {},
"outputs": [],
"source": [
"mu_truth = torch.randn((n_batch, n_params)) # Batch of true parameter values\n",
"loss = -dist.MultivariateNormal(loc=mu_truth, covariance_matrix=Cov).log_prob(mu) # Full batch-wise loss"
]
},
{
"cell_type": "markdown",
"id": "20300f3f-9283-4ef6-aea0-25acf7c31901",
"metadata": {},
"source": [
"## Plotting ellipses"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "0b7abede-daa9-4d74-a799-8aba0dffbff2",
"metadata": {},
"outputs": [
{
"data": {
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"text/plain": [
"<Figure size 1200x1200 with 6 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from matplotlib.patches import Ellipse\n",
"from matplotlib.lines import Line2D\n",
"\n",
"def plot_fisher_single(i ,cov, mu, ax, lims, truths, labels) :\n",
" nb=128\n",
" sigma=np.sqrt(cov[i,i])\n",
" x_arr=mu[i]-8*sigma+16*sigma*np.arange(nb)/(nb-1.)\n",
" p_arr=np.exp(-(x_arr-mu[i])**2/(2*sigma**2))\n",
" ax.plot(x_arr,p_arr, color='red') \n",
" ax.axvline(truths[i], color='darkgrey', lw=1.5)\n",
" ax.set_xlim(lims[0][i], lims[1][i])\n",
" ax.set_ylim(-0.02, 1.2)\n",
" ax.set_title(labels[i], fontsize=18.5, y=1.02)\n",
" \n",
" if i == 0:\n",
" custom_lines = [Line2D([0], [0], color='red', lw=4),\n",
" Line2D([0], [0], color='darkgrey', lw=4)]\n",
" \n",
" ax.legend(custom_lines, [\"Posterior\", \"Truth\"], bbox_to_anchor=[6, 0.5], frameon=True, fancybox=True, fontsize=19)\n",
"\n",
"\n",
"def plot_fisher_two(i1, i2, cov, mu, ax, lims, truths, labels) :\n",
" covar=np.zeros([2,2])\n",
" covar[0,0]=cov[i1,i1]\n",
" covar[0,1]=cov[i1,i2]\n",
" covar[1,0]=cov[i2,i1]\n",
" covar[1,1]=cov[i2,i2]\n",
" sig0=np.sqrt(covar[0,0])\n",
" sig1=np.sqrt(covar[1,1])\n",
"\n",
" w,v=np.linalg.eigh(covar)\n",
" \n",
" angle=180*np.arctan2(v[1,0],v[0,0])/np.pi\n",
" a_1s=np.sqrt(2.3*w[0])\n",
" b_1s=np.sqrt(2.3*w[1])\n",
" a_2s=np.sqrt(6.17*w[0])\n",
" b_2s=np.sqrt(6.17*w[1])\n",
"\n",
" centre=np.array([mu[i1],mu[i2]])\n",
" \n",
" e_1s=Ellipse(xy=centre,width=2*a_1s,height=2*b_1s,angle=angle, color='red', lw=2.)\n",
" e_1s.set_fill(False)\n",
" \n",
" e_2s=Ellipse(xy=centre,width=2*a_2s,height=2*b_2s,angle=angle, ls='--', color='red', lw=2.)\n",
" e_2s.set_fill(False)\n",
"\n",
" ax.add_artist(e_1s)\n",
" ax.add_artist(e_2s)\n",
" \n",
" ax.axvline(truths[i1], color='darkgrey', lw=1.5)\n",
" ax.axhline(truths[i2], color='darkgrey', lw=1.5)\n",
"\n",
" ax.set_xlim(lims[0][i1], lims[1][i1])\n",
" ax.set_ylim(lims[0][i2], lims[1][i2])\n",
" \n",
" ax.set_xlabel(labels[i1])\n",
" ax.set_ylabel(labels[i2])\n",
"\n",
"def plot_fisher_all(mu, cov, lims, truths, labels, suptitles, fig=None): \n",
" n_params = len(mu)\n",
" \n",
" if fig is None:\n",
" fig=plt.figure(figsize=(12, 12))\n",
" plt.subplots_adjust(hspace=0, wspace=0)\n",
" for i in np.arange(n_params):\n",
" i_col=i\n",
" for j in np.arange(n_params-i)+i :\n",
" i_row=j\n",
" iplot=i_col+n_params*i_row+1\n",
"\n",
" ax=fig.add_subplot(n_params,n_params,iplot)\n",
" if i==j :\n",
" plot_fisher_single(i, cov, mu, ax, lims, truths, labels)\n",
" ax.text(0.5, 1.5, suptitles[i], \n",
" horizontalalignment='left' if not i==0 else \"center\",\n",
" verticalalignment='center',\n",
" transform = ax.transAxes,\n",
" fontsize=18)\n",
"\n",
" else :\n",
" plot_fisher_two(i, j, cov, mu, ax, lims, truths, labels)\n",
"\n",
" if i_row!=n_params-1 :\n",
" ax.get_xaxis().set_visible(False)\n",
"\n",
" if i_col!=0 :\n",
" ax.get_yaxis().set_visible(False)\n",
"\n",
" if i_col==0 and i_row==0 :\n",
" ax.get_yaxis().set_visible(False)\n",
" \n",
" ax.locator_params(nbins=2)\n",
" [l.set_rotation(45) for l in ax.get_xticklabels()]\n",
" [l.set_rotation(45) for l in ax.get_yticklabels()]\n",
"\n",
" # fig.align_labels()\n",
" # plt.show()\n",
"\n",
"ii = 0 # Which index to plot\n",
"\n",
"# Automatically choose limits as 6-sigma away from central value\n",
"lims = [mu[ii] - 6 * np.sqrt(np.diag(Cov[ii])), mu[ii] + 6 * np.sqrt(np.diag(Cov[ii]))]\n",
"truths = mu_truth[ii]\n",
"\n",
"labels = [\"a\", \"b\", \"c\"]\n",
"suptitles = [\"Param A\", \"Param B\", \"Param C\"]\n",
"\n",
"fig=plt.figure(figsize=(12, 12))\n",
"plot_fisher_all(mu[ii], Cov[ii], lims, truths, labels, suptitles, fig)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "1c36ab71-2124-49f6-979d-8e21053ad17a",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "cf2089a9-cdc3-4093-9b91-5a5a53d6541b",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"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": "3.9.13"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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