Created
November 24, 2023 13:08
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a short example of local fdr outlier detection
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{ | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"id": "c53910f2-582d-495b-9421-670a936579c7", | |
"metadata": {}, | |
"source": [ | |
"the \"local FDR\" technique can be useful for detecting outliers in a large sample" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 1, | |
"id": "116bf9ee-b3ce-4688-b0c2-958e1e5c6668", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"%pylab is deprecated, use %matplotlib inline and import the required libraries.\n", | |
"Populating the interactive namespace from numpy and matplotlib\n" | |
] | |
} | |
], | |
"source": [ | |
"%pylab inline" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"id": "fab5f3c4-87a0-4611-86d6-7c2c4f514386", | |
"metadata": {}, | |
"source": [ | |
"here's a sample signal with some outliers" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 40, | |
"id": "661e8ca9-2c3e-4816-a99b-955221167793", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"[<matplotlib.lines.Line2D at 0x7fa0cd942750>]" | |
] | |
}, | |
"execution_count": 40, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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", | |
"text/plain": [ | |
"<Figure size 640x480 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"x = np.random.randn(32*1024)\n", | |
"outliers = np.random.randint(x.size, size=20)\n", | |
"x[outliers] = 6.0\n", | |
"plot(x, '.')\n", | |
"plot(outliers, x[outliers], 'ro', alpha=0.3)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"id": "71968808-b992-4ac5-9f2e-e262b6b5e571", | |
"metadata": {}, | |
"source": [ | |
"we can construct a guassian approximation of the central density using a histogram and polynomial fit," | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 92, | |
"id": "751d2f92-8d47-4642-b71b-7f3fcdfd4243", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stderr", | |
"output_type": "stream", | |
"text": [ | |
"/tmp/ipykernel_91609/3199614652.py:14: RuntimeWarning: divide by zero encountered in log\n", | |
" plot(bx, np.log(fx))\n" | |
] | |
}, | |
{ | |
"data": { | |
"text/plain": [ | |
"Text(0.5, 0, 'x')" | |
] | |
}, | |
"execution_count": 92, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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", | |
"text/plain": [ | |
"<Figure size 640x480 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"# histogram original samples\n", | |
"fx, bx_ = np.histogram(x, 100, density=True)\n", | |
"bx = bx_[:-1] + (bx_[1] - bx_[0])/2\n", | |
"\n", | |
"# histogram without the tails\n", | |
"pct_exclude = 2.5\n", | |
"q5, q95 = np.percentile(x, [pct_exclude, 100 - pct_exclude])\n", | |
"fx90, _ = np.histogram(x[ (q5 < x) * (x < q95) ], bx_, density=True)\n", | |
"\n", | |
"# fit a 2-order polynomial == gaussian on logarithmic scale\n", | |
"quad90 = np.polyfit(bx[fx90>0], np.log(fx90[fx90>0]), 2)\n", | |
"\n", | |
"# show it\n", | |
"plot(bx, np.log(fx))\n", | |
"plot(bx, np.polyval(quad90, bx))\n", | |
"\n", | |
"legend(('log p(x)', 'gaussian approx'))\n", | |
"xlabel('x')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"id": "cbbfd396-59a3-4106-b8f6-081ebf0ec839", | |
"metadata": {}, | |
"source": [ | |
"now we can apply that approximation to the full set of samples to detect outliers," | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 91, | |
"id": "6e92d24c-403e-4cb6-940b-3232772879d2", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"[<matplotlib.lines.Line2D at 0x7fa0cbf0c890>]" | |
] | |
}, | |
"execution_count": 91, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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", | |
"text/plain": [ | |
"<Figure size 640x480 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"llx = np.polyval(quad90, x)\n", | |
"hits = llx < np.log(0.001)\n", | |
"\n", | |
"plot(x)\n", | |
"plot(np.argwhere(hits)[:,0], x[hits], 'ro', alpha=0.4)" | |
] | |
} | |
], | |
"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": "3.11.5" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 5 | |
} |
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