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0 Basic statistics (sol.).ipynb
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0 Basic statistics (sol.).ipynb
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.10.6"
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"version": "3.12.3"
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}
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},
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"nbformat": 4,
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1021
0 CLT.ipynb
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0 CLT.ipynb
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853
2.1 Representation Learning.ipynb
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2.1 Representation Learning.ipynb
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541
3.1 Supervised Regression.ipynb
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3.1 Supervised Regression.ipynb
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1020
3.2 Regression Uncetainties.ipynb
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3.2 Regression Uncetainties.ipynb
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7 Mixture Models.ipynb
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1503
7 Mixture Models.ipynb
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104
Line fits.ipynb
104
Line fits.ipynb
@@ -1,104 +0,0 @@
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||||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "1bba0128",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Simple fits\n",
|
||||
"\n",
|
||||
"Here we are fitting a line from scratch.\n",
|
||||
"In the next notebook, we will do fancier fits with neural networks, but let's start with a basic problem and complicate it as we go along.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 1,
|
||||
"id": "23feddde",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"from typing import Tuple\n",
|
||||
"\n",
|
||||
"import pandas as pd\n",
|
||||
"import numpy as np\n",
|
||||
"import matplotlib.pyplot as plt\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "bb1286f0",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"We start by generating some fake dataset, which is simple enough that we can visualize the results easily. For this reason, the dataset will contain only two variables.\n",
|
||||
"\n",
|
||||
"The simulated example data will be $f(x) = 3 x + \\epsilon$, where $\\epsilon \\sim \\mathcal{N}(\\mu=0, \\sigma=0.5)$.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 2,
|
||||
"id": "5d457cd8",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def generate_data(N: int) -> np.ndarray:\n",
|
||||
" x = 2*np.random.randn(N, 1)\n",
|
||||
" epsilon = 0.5*np.random.randn(N, 1)\n",
|
||||
" z = 3*x + epsilon\n",
|
||||
" return np.concatenate((x, z), axis=1).astype(np.float32)\n",
|
||||
"\n",
|
||||
"data = generate_data(N=1000)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "48433f6f",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"We can fit this line from scratch, assuming $y = f(x) = \\beta x + \\alpha + \\epsilon$, where $\\epsilon$ is a zero-mean Gaussian noise.\n",
|
||||
"\n",
|
||||
"How would you do it? Feel free to use standard Python modules. Look at the solution for a simple mathematical expression for this fit with a full derivation.\n",
|
||||
"\n",
|
||||
"Tip: Look for the documentation for `numpy.linalg.lstsq`."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "85040eef-3558-4531-9bce-4f29d520f86b",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": []
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "5e9170af-ca77-4526-b3d2-e19e77fef44e",
|
||||
"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": "3.10.6"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 5
|
||||
}
|
||||
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Reference in New Issue
Block a user