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{ | |
"cells": [ | |
{ | |
"cell_type": "code", | |
"execution_count": 1, | |
"id": "bc872a0f-c564-4ec4-956d-17f6470ce145", | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"import numpy as np\n", | |
"import matplotlib.pyplot as plt\n", | |
"import seaborn as sns" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 2, | |
"id": "6ef579b2-463b-435d-9350-5b4cf8850022", | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"n_dim = 100\n", | |
"n_draws = 5000\n", | |
"\n", | |
"mu = np.random.randn(n_draws, n_dim)\n", | |
"sd = np.exp(1 * np.random.randn(n_draws, n_dim))\n", | |
"\n", | |
"init_points = np.random.randn(n_draws, n_dim) * 1000" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 3, | |
"id": "7b530a7c-b038-4f91-bcb6-0f8990dcb79d", | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"grads = -(init_points - mu) / sd**2" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 4, | |
"id": "61f104ba-46cb-4428-8c0d-02daab88dabf", | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"def dist(estimate, true):\n", | |
" \"\"\"Log condition number of diagonal matrix.\"\"\"\n", | |
" eigs = true / estimate\n", | |
" maxval = eigs.max(-1)\n", | |
" minval = eigs.min(-1)\n", | |
" return np.log(maxval / minval)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 5, | |
"id": "39242b0f-b90b-4d5c-8c81-66daac89c7c1", | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"# Using initial identity\n", | |
"dists_identity = dist(sd*sd, np.ones(n_dim))\n", | |
"dists_grad_sq = dist(sd*sd, 1 / (grads * grads))\n", | |
"dists_grad = dist(sd*sd, 1 / np.abs(grads))" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 6, | |
"id": "44064aff-4eb8-422a-bd89-c4bbdce5d87d", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
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\n", | |
"text/plain": [ | |
"<Figure size 640x480 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"sns.kdeplot(dists_identity, label=\"identity\")\n", | |
"sns.kdeplot(dists_grad, label=\"grad\")\n", | |
"sns.kdeplot(dists_grad_sq, label=\"grad_sq\")\n", | |
"plt.legend();" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"id": "dbbd3f69-e853-43fe-b0a4-e9deeb2b1558", | |
"metadata": {}, | |
"outputs": [], | |
"source": [] | |
} | |
], | |
"metadata": { | |
"kernelspec": { | |
"display_name": "pymc-dev", | |
"language": "python", | |
"name": "pymc-dev" | |
}, | |
"language_info": { | |
"codemirror_mode": { | |
"name": "ipython", | |
"version": 3 | |
}, | |
"file_extension": ".py", | |
"mimetype": "text/x-python", | |
"name": "python", | |
"nbconvert_exporter": "python", | |
"pygments_lexer": "ipython3", | |
"version": "3.10.8" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 5 | |
} |
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