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Sync dag tutorial markdown with notebook
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merajhashemi committed Feb 10, 2025
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106 changes: 16 additions & 90 deletions docs/source/notebooks/plot_dag_learning.ipynb
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"[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/cooper-org/cooper/blob/master/docs/source/notebooks/plot_dag_learning.ipynb)\n",
"\n",
"\n",
"Consider the problem of learning a Directed Acyclic Graph (DAG) on data. This is a common problem in causal inference, where we are interested in learning the causal relationships between variables. In this notebook, we will demonstrate how to learn a DAG on data using a {py:class}`~cooper.formulations.QuadraticPenalty` formulation in **Cooper**.\n"
"Consider the problem of learning a Directed Acyclic Graph (DAG) on data. This is a common problem in causal inference, where we are interested in learning the causal relationships between variables. In this notebook, we will demonstrate how to learn a DAG on data using a {py:class}`~cooper.formulations.QuadraticPenalty` formulation in **Cooper**."
]
},
{
"cell_type": "code",
"execution_count": 92,
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
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},
{
"cell_type": "code",
"execution_count": 93,
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
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"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"Consider a $d$-dimensional random vector ${X_1, X_2, ..., X_d}$. Given $n$ observations of the random vector $X \\in \\mathbb{R}^{n \\times d}$, we are interested in learning a DAG $G = (V, E)$ whose edges represent the dependencies between the variables. We model the DAG via an adjacency matrix $A \\in \\{0, 1\\}^{d \\times d}$, where $A_{ij} = 1$ if there is an edge from $X_i$ to $X_j$ and $A_{ij} = 0$ otherwise.\n",
"\n",
"This problem can be formulated as the following optimization problem:\n",
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},
{
"cell_type": "code",
"execution_count": 94,
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
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},
{
"cell_type": "code",
"execution_count": 103,
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
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},
{
"cell_type": "code",
"execution_count": 102,
"execution_count": null,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"tensor([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
" [0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
" [0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
" [0., 0., 1., 0., 0., 0., 0., 0., 0., 0.],\n",
" [1., 1., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
" [0., 0., 0., 0., 1., 0., 0., 0., 0., 0.],\n",
" [1., 0., 1., 1., 1., 0., 0., 0., 0., 0.],\n",
" [1., 1., 1., 1., 0., 0., 0., 0., 0., 0.],\n",
" [0., 0., 1., 1., 0., 0., 1., 1., 0., 0.],\n",
" [1., 1., 1., 1., 1., 1., 1., 0., 1., 0.]])\n"
]
}
],
"outputs": [],
"source": [
"D = 10\n",
"N = 1000\n",
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},
{
"cell_type": "code",
"execution_count": 97,
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
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},
{
"cell_type": "code",
"execution_count": 99,
"execution_count": null,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Step 0, loss=2201.7742, violation=0.5068, penalty_coefficient=1.0100\n",
"Step 100, loss=1128.9160, violation=0.0110, penalty_coefficient=2.7319\n",
"Step 200, loss=693.1588, violation=0.5280, penalty_coefficient=7.3892\n",
"Step 300, loss=505.0096, violation=0.2386, penalty_coefficient=19.9863\n",
"Step 400, loss=400.4205, violation=0.0640, penalty_coefficient=54.0591\n",
"Step 500, loss=333.4678, violation=0.0208, penalty_coefficient=146.2198\n",
"Step 600, loss=286.8203, violation=0.0070, penalty_coefficient=395.4971\n",
"Step 700, loss=252.3343, violation=0.0024, penalty_coefficient=1069.7448\n",
"Step 800, loss=225.7109, violation=0.0008, penalty_coefficient=2893.4583\n",
"Step 900, loss=204.4717, violation=0.0003, penalty_coefficient=7826.2573\n",
"Final loss: 787.2999, violation: 0.5077, penalty_coefficient: 20342.5723\n"
]
}
],
"outputs": [],
"source": [
"A = torch.nn.Parameter(torch.randn(D, D, device=DEVICE) / math.sqrt(D))\n",
"\n",
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},
{
"cell_type": "code",
"execution_count": 109,
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
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},
{
"cell_type": "code",
"execution_count": 110,
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<Figure size 640x480 with 0 Axes>"
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",
"text/plain": [
"<Figure size 640x480 with 3 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"tensor([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
" [0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
" [0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
" [0., 0., 1., 0., 0., 0., 0., 0., 0., 0.],\n",
" [1., 1., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
" [0., 0., 0., 0., 1., 0., 0., 0., 0., 0.],\n",
" [1., 0., 1., 1., 1., 0., 0., 0., 0., 0.],\n",
" [1., 1., 1., 1., 0., 0., 0., 0., 0., 0.],\n",
" [0., 0., 1., 1., 0., 0., 1., 1., 0., 0.],\n",
" [1., 1., 1., 1., 1., 1., 1., 0., 1., 0.]])\n"
]
}
],
"outputs": [],
"source": [
"# Plot\n",
"\n",
Expand All @@ -441,15 +369,13 @@
"source": [
"## References\n",
"- NOTEARS\n",
"- Seb's paper?\n"
"- Seb's paper?"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "cooper",
"language": "python",
"name": "python3"
"jupytext": {
"formats": "ipynb,md:myst"
},
"language_info": {
"codemirror_mode": {
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