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"source": [
"The matrix we want to compute is $H^\\infty$, where\n",
"$$\n",
"H^\\infty_{ij}\n",
" = x_i^T x_j \\Pr_{w \\sim \\mathcal N(0, I)}\\left( w^T x_i \\ge 0, w^T x_j \\ge 0 \\right)\n",
".$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Xie et al (2017) say (and I checked) that this probability is\n",
"$$\n",
"\\frac{1}{2} - \\frac{\\arccos x_i^T x_j}{2 \\pi}\n",
".$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The question is: what does $\\lambda_\\min(H^\\infty)$ look like as a function of $n$? Let's assume uniform $x_i$ for simplicity."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"from scipy import linalg, stats\n",
"\n",
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"sns.set()\n",
"\n",
"from tqdm import tqdm_notebook as tqdm"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"def simulate(n, d):\n",
" X = np.random.normal(size=(n, d))\n",
" X /= np.sqrt((X ** 2).sum(axis=1, keepdims=True))\n",
" \n",
" gram = X @ X.T\n",
" np.maximum(-1, gram, out=gram)\n",
" np.minimum(1, gram, out=gram)\n",
" \n",
" H = gram * (.5 - np.arccos(gram) / (2 * np.pi))\n",
" return linalg.eigvalsh(H, eigvals=(0, 0))[0]"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"import pandas as pd\n",
"evals = pd.DataFrame(columns=['d', 'n', 'est'])\n",
"\n",
"def do_evals(n, d, reps=1, **kw):\n",
" global evals\n",
" chunk = []\n",
" for _ in tqdm(range(reps), **kw) if reps > 1 else [0]:\n",
" chunk.append((d, float(n), simulate(n, d)))\n",
" evals = pd.concat([evals, pd.DataFrame(chunk, columns=['d', 'n', 'est'])])"
]
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"source": [
"for d in tqdm([2, 5, 10]):\n",
" for n in (10 ** np.linspace(2, 3.5, num=10)).astype(int):\n",
" do_evals(n, d, reps=10, desc=f'{d} - {n}')"
]
},
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"metadata": {},
"source": [
"Linear regression: $\\log \\lambda_0 \\approx a \\log n + b$, meaning $\\lambda_0 \\approx \\exp(b) n^a$."
]
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{
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"execution_count": 12,
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\n",
"text/plain": [
"<Figure size 432x864 with 3 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ds = sorted(evals.d.unique())\n",
"\n",
"fig, axes = plt.subplots(len(ds), figsize=(6, 4 * len(ds)), constrained_layout=True)\n",
"for d, ax in zip(ds, axes):\n",
" evs = evals[evals.d == d]\n",
"\n",
" means = evs.set_index('n').est.groupby(level=0).mean()\n",
" means.plot(marker='o', ax=ax)\n",
"\n",
" evs.plot('n', 'est', kind='scatter', ax=ax)\n",
" \n",
" reg = stats.linregress(np.log(evs.n), np.log(evs.est))\n",
" ns = evs.n.unique()\n",
" ax.plot(ns, np.exp(reg.intercept) * ns ** reg.slope, color='r')\n",
"\n",
" ax.set_xscale('log')\n",
" ax.set_yscale('log')\n",
" ax.set_title(f\"d = {d}: $\\\\lambda_0 \\\\approx {np.exp(reg.intercept):.2} \\\\, n^{{ {reg.slope:.3} }}$\")"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python [conda env:py3]",
"language": "python",
"name": "conda-env-py3-py"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.5"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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