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2730892
Add draft notebook
jessegrabowski Aug 13, 2025
07fcc1e
progress
jessegrabowski Aug 14, 2025
597be35
Fix pattern match
ricardoV94 Aug 14, 2025
a3811f0
update notebook
jessegrabowski Aug 16, 2025
7e408b3
Adding blah blah
jessegrabowski Aug 17, 2025
bc17c86
Blah blah close to done
jessegrabowski Aug 17, 2025
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388 changes: 388 additions & 0 deletions identify_linear_expression.ipynb
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{
"cells": [
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "BK5As0cbUejz",
"jupyter": {
"is_executing": true
}
},
"outputs": [],
"source": [
"import random\n",
"\n",
"from etuples import etuple\n",
"from unification import unify, var\n",
"\n",
"import pytensor.tensor as pt\n",
"from pytensor.graph import rewrite_graph\n",
"from pytensor.graph.fg import FunctionGraph\n",
"from pytensor.graph.rewriting.basic import MergeOptimizer, PatternNodeRewriter, out2in"
]
},
{
"cell_type": "code",
"execution_count": 87,
"metadata": {
"ExecuteTime": {
"end_time": "2025-08-14T11:32:09.438328768Z",
"start_time": "2025-08-14T11:29:54.500174Z"
},
"id": "alNycwOIUzTM"
},
"outputs": [],
"source": [
"def find_optimal_P(P, Q, mc):\n",
" pi = (Q * (P - mc)).sum()\n",
" dpi_dP = pt.grad(pi, P)\n",
" # P_star, success = root(dpi_dP, P, method=\"hybr\", optimizer_kwargs=dict(tol=1e-8))\n",
" # return P_star, success\n",
" return dpi_dP"
]
},
{
"cell_type": "code",
"execution_count": 97,
"metadata": {
"ExecuteTime": {
"end_time": "2025-08-14T11:32:09.440094174Z",
"start_time": "2025-08-14T11:31:54.469010Z"
},
"id": "wVnYGz8GVKb4"
},
"outputs": [],
"source": [
"price_effect = pt.scalar(\"price_effect\")\n",
"price = pt.vector(\"price\")\n",
"trend = pt.vector(\"trend\")\n",
"seasonality = pt.vector(\"seasonality\")\n",
"mc = pt.scalar(\"marginal_cost\")\n",
"\n",
"price_term = price * price_effect\n",
"expected_sales = trend + price_term + seasonality"
]
},
{
"cell_type": "code",
"execution_count": 98,
"metadata": {
"ExecuteTime": {
"end_time": "2025-08-14T11:32:09.440827348Z",
"start_time": "2025-08-14T11:31:54.681476Z"
},
"id": "BeitshYMVkQU"
},
"outputs": [],
"source": [
"expr = find_optimal_P(price, expected_sales, mc=mc)"
]
},
{
"cell_type": "code",
"execution_count": 99,
"metadata": {
"ExecuteTime": {
"end_time": "2025-08-14T11:32:09.443902007Z",
"start_time": "2025-08-14T11:31:54.918556Z"
},
"id": "jugOxL4DcRFN"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Add [id A] 5\n",
" ├─ Mul [id B] 4\n",
" │ ├─ Sub [id C] 3\n",
" │ │ ├─ price [id D]\n",
" │ │ └─ ExpandDims{axis=0} [id E] 2\n",
" │ │ └─ marginal_cost [id F]\n",
" │ └─ ExpandDims{axis=0} [id G] 0\n",
" │ └─ price_effect [id H]\n",
" ├─ trend [id I]\n",
" ├─ Mul [id J] 1\n",
" │ ├─ price [id D]\n",
" │ └─ ExpandDims{axis=0} [id G] 0\n",
" │ └─ ···\n",
" └─ seasonality [id K]\n"
]
},
{
"data": {
"text/plain": [
"<ipykernel.iostream.OutStream at 0x7fcbccd613c0>"
]
},
"execution_count": 99,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Use existing rewrites to simplify expression\n",
"fgraph = FunctionGraph(outputs=[expr], clone=False)\n",
"rewrite_graph(fgraph, include=(\"canonicalize\",))\n",
"fgraph.dprint()"
]
},
{
"cell_type": "code",
"execution_count": 100,
"metadata": {
"ExecuteTime": {
"end_time": "2025-08-14T11:32:09.445406846Z",
"start_time": "2025-08-14T11:31:55.243098Z"
},
"id": "86-KeCOFWQZU"
},
"outputs": [],
"source": [
"# distribute_mul_over_add = PatternNodeRewriter(\n",
"# (pt.mul, (pt.add, \"x\", \"y\"), \"z\"),\n",
"# (pt.add, (pt.mul, \"x\", \"z\"), (pt.mul, \"y\", \"z\")),\n",
"# )\n",
"\n",
"distribute_mul_over_sub = PatternNodeRewriter(\n",
" (pt.mul, (pt.sub, \"x\", \"y\"), \"z\"),\n",
" (pt.add, (pt.mul, \"x\", \"z\"), (pt.mul, (pt.neg, \"y\"), \"z\")),\n",
")\n",
"\n",
"combine_addition_terms = PatternNodeRewriter(\n",
" (pt.add, (pt.add, \"x\", \"y\"), \"z\", \"x\", \"w\"),\n",
" (pt.add, (pt.mul, \"x\", 2), (pt.add, \"y\", \"z\", \"w\")),\n",
")\n",
"\n",
"# distribute_mul_over_add = out2in(distribute_mul_over_add, name=\"distribute_mul_add\")\n",
"distribute_mul_over_sub = out2in(distribute_mul_over_sub, name=\"distribute_mul_sub\")\n",
"combine_addition_terms = out2in(combine_addition_terms, name=\"combine_addition_terms\")\n",
"\n",
"# distribute\n",
"distribute_mul_over_sub.rewrite(fgraph)\n",
"# merge equivalent terms\n",
"MergeOptimizer().rewrite(fgraph)\n",
"# combine equivalent terms\n",
"combine_addition_terms.rewrite(fgraph)\n",
"# extract rewritten expression\n",
"expr = fgraph.outputs[0]"
]
},
{
"cell_type": "code",
"execution_count": 101,
"metadata": {
"ExecuteTime": {
"end_time": "2025-08-14T11:32:09.446341276Z",
"start_time": "2025-08-14T11:31:56.276558Z"
},
"id": "4qGBap72Xvvn"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Add [id A]\n",
" ├─ Mul [id B]\n",
" │ ├─ Mul [id C]\n",
" │ │ ├─ price [id D]\n",
" │ │ └─ ExpandDims{axis=0} [id E]\n",
" │ │ └─ price_effect [id F]\n",
" │ └─ ExpandDims{axis=0} [id G]\n",
" │ └─ 2 [id H]\n",
" └─ Add [id I]\n",
" ├─ Mul [id J]\n",
" │ ├─ Neg [id K]\n",
" │ │ └─ ExpandDims{axis=0} [id L]\n",
" │ │ └─ marginal_cost [id M]\n",
" │ └─ ExpandDims{axis=0} [id E]\n",
" │ └─ ···\n",
" ├─ trend [id N]\n",
" └─ seasonality [id O]\n"
]
},
{
"data": {
"text/plain": [
"<ipykernel.iostream.OutStream at 0x7fcbccd613c0>"
]
},
"execution_count": 101,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"expr.dprint()"
]
},
{
"cell_type": "code",
"execution_count": 102,
"metadata": {
"ExecuteTime": {
"end_time": "2025-08-14T11:32:09.447033733Z",
"start_time": "2025-08-14T11:31:59.481064Z"
},
"id": "8Fq10k2LcCY-"
},
"outputs": [],
"source": [
"# Create variations of a graph for pattern matching\n",
"rewrites = [\n",
" out2in(\n",
" PatternNodeRewriter((pt.add, \"x\", \"y\"), (pt.add, \"y\", \"x\")),\n",
" name=\"commutative_add\",\n",
" ignore_newtrees=True,\n",
" ),\n",
" out2in(\n",
" PatternNodeRewriter((pt.mul, \"x\", \"y\"), (pt.mul, \"y\", \"x\")),\n",
" name=\"commutative_mul\",\n",
" ignore_newtrees=True,\n",
" ),\n",
" out2in(\n",
" PatternNodeRewriter(\n",
" (pt.mul, (pt.mul, \"x\", \"y\"), \"z\"), (pt.mul, \"x\", (pt.mul, \"y\", \"z\"))\n",
" ),\n",
" name=\"associative_mul\",\n",
" ignore_newtrees=True,\n",
" ),\n",
"]\n",
"\n",
"\n",
"def yield_arithmetic_variants(expr, n):\n",
" fgraph = FunctionGraph(outputs=[expr], clone=False)\n",
" while n > 0:\n",
" rewrite = random.choice(rewrites)\n",
" res = rewrite.apply(fgraph)\n",
" n -= 1\n",
" if res:\n",
" yield fgraph.outputs[0]\n",
" yield fgraph.outputs[0]"
]
},
{
"cell_type": "code",
"execution_count": 103,
"metadata": {
"ExecuteTime": {
"end_time": "2025-08-14T11:32:09.447578804Z",
"start_time": "2025-08-14T11:31:59.831774Z"
},
"colab": {
"base_uri": "https://localhost:8080/",
"height": 198
},
"id": "h9K70LGxYJ7E",
"outputId": "793e98c6-4570-43bf-a452-eb6d0d745dc7"
},
"outputs": [
{
"data": {
"text/plain": [
"{~price: price, ~a: Mul.0, ~b: Add.0}"
]
},
"execution_count": 103,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Rewrite graph randomly until we match price * a + b\n",
"a, b, price_ = var(\"a\"), var(\"b\"), var(\"price\")\n",
"pattern = etuple(pt.add, etuple(pt.mul, price_, a), b)\n",
"\n",
"for variant in yield_arithmetic_variants(expr, n=100):\n",
" match_dict = unify(variant, pattern)\n",
" if match_dict and match_dict[price_] is price:\n",
" break\n",
"else:\n",
" raise ValueError(\"No matching variant found\")\n",
"match_dict"
]
},
{
"cell_type": "code",
"execution_count": 104,
"metadata": {
"ExecuteTime": {
"end_time": "2025-08-14T11:32:09.448905279Z",
"start_time": "2025-08-14T11:32:01.264784Z"
},
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "8M-qjXBKa6Db",
"outputId": "cdce40c4-e1dd-4757-f4d6-f368643bb5c1"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"True_div [id A]\n",
" ├─ Neg [id B]\n",
" │ └─ Add [id C]\n",
" │ ├─ Mul [id D]\n",
" │ │ ├─ Neg [id E]\n",
" │ │ │ └─ ExpandDims{axis=0} [id F]\n",
" │ │ │ └─ marginal_cost [id G]\n",
" │ │ └─ ExpandDims{axis=0} [id H]\n",
" │ │ └─ price_effect [id I]\n",
" │ ├─ trend [id J]\n",
" │ └─ seasonality [id K]\n",
" └─ Mul [id L]\n",
" ├─ ExpandDims{axis=0} [id H]\n",
" │ └─ ···\n",
" └─ ExpandDims{axis=0} [id M]\n",
" └─ 2 [id N]\n"
]
},
{
"data": {
"text/plain": [
"<ipykernel.iostream.OutStream at 0x7fcbccd613c0>"
]
},
"execution_count": 104,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"optimal_result = -match_dict[b] / match_dict[a]\n",
"optimal_result.dprint()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"ExecuteTime": {
"end_time": "2025-08-14T11:32:09.449645675Z",
"start_time": "2025-08-14T11:25:52.269957Z"
}
},
"outputs": [],
"source": []
}
],
"metadata": {
"colab": {
"provenance": []
},
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"name": "python"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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