synthetic_data_exp.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "1aedc8ed-9295-4f13-b713-1f22d7ddc8aa",
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "attachments": {
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    }
   },
   "cell_type": "markdown",
   "id": "7254dae0-4a27-46e4-8877-f3310437ad1c",
   "metadata": {},
   "source": [
    "![draft-top-down-lpm-v1.jpg](attachment:e6e9d9e9-74dd-442f-ba1f-5a6948c8e489.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc47c385-7ec8-4cb0-b5ae-00687305b7cc",
   "metadata": {},
   "source": [
    "# Writing a generative model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ef49c6ba-a66a-4f63-8551-038702356569",
   "metadata": {},
   "outputs": [],
   "source": [
    "import jax.numpy as jnp\n",
    "import jax\n",
    "import genjax\n",
    "import polars as pl\n",
    "import numpy as np\n",
    "from itertools import product\n",
    "from jax.scipy.special import logit\n",
    "from genjax import static_gen_fn\n",
    "from generative_join.modeling import (\n",
    "    aggregate_mean,\n",
    "    importance_sample,\n",
    "    estimate_mu_std,\n",
    "    make_conditions_dict,\n",
    "    estimate_logprobs,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "7c982a10-fff1-4c4b-817f-9b426425680b",
   "metadata": {},
   "outputs": [],
   "source": [
    "from tests.test_synthetic_data import gen_parametrized_z, component_params, component_logprobs, make_health_data\n",
    "from generative_join.modeling import mixture_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "db456bc1-ff76-441b-8d0e-307f22d03c26",
   "metadata": {},
   "outputs": [],
   "source": [
    "@static_gen_fn\n",
    "def make_social_data(key, gen_z, gen_z_args, n_sample, n_importance_samples):\n",
    "    # model for OI social connectedness data\n",
    "    n_importance_samples = n_importance_samples.const\n",
    "\n",
    "    conditions = product(\n",
    "        [0, 1],\n",
    "        [0, 1, 2, 3],\n",
    "    )\n",
    "    conditions = np.array([c for c in conditions])\n",
    "\n",
    "    condition_names = [\"attended_elite_college\", \"region\"]\n",
    "    keys = jax.random.split(key, len(conditions))\n",
    "\n",
    "    trs, ws = jax.vmap(importance_sample, in_axes=(0, None, None, 0, None, None))(\n",
    "        keys, gen_z, gen_z_args, conditions, condition_names, n_importance_samples\n",
    "    )\n",
    "\n",
    "    logprob_conditions = jax.vmap(estimate_logprobs)(ws)\n",
    "\n",
    "    group_sizes = (\n",
    "        genjax.multinomial(jnp.array(n_sample, float), logprob_conditions) @ \"social_group_sizes\"\n",
    "    )\n",
    "    mus, stds = jax.vmap(estimate_mu_std, in_axes=(0, 0, None))(\n",
    "        trs, ws, \"connected\"\n",
    "    )\n",
    "\n",
    "    map_aggregate_mean = genjax.map_combinator(in_axes=(0, 0, 0))(aggregate_mean)\n",
    "    means = map_aggregate_mean(mus, stds, group_sizes) @ \"social_map_aggregate_mean\"\n",
    "\n",
    "    # make dictionary with high_income, male, region, mean(high_life_expectancy), and counts\n",
    "    conditions_dict = make_conditions_dict(conditions, condition_names)\n",
    "    conditions_dict[\"mean(connected)\"] = means\n",
    "    conditions_dict[\"count\"] = group_sizes\n",
    "\n",
    "    return conditions_dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "c834fbea-f82d-430e-ab18-04b2db490741",
   "metadata": {},
   "outputs": [],
   "source": [
    "@static_gen_fn\n",
    "def make_politics_data(gen_z, gen_z_args, n_sample):\n",
    "    # model for cces\n",
    "    map_array = jnp.ones(n_sample.const)\n",
    "    map_gen_z = genjax.map_combinator(in_axes=(None, None, 0))(aux_gen_z)\n",
    "    sample_dict = map_gen_z(gen_z, gen_z_args, map_array) @ \"politics_samples\"\n",
    "\n",
    "    return {k: v for k, v in sample_dict.items() if k in [\"male\", \"region\", \"supports_medicare\", \"vote_republican\"]}\n",
    "    \n",
    "@static_gen_fn\n",
    "def aux_gen_z(gen_z, gen_z_args, _):\n",
    "    # hack while the repeat combinator in genjax remains buggy\n",
    "    return gen_z.inline(*gen_z_args)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0937a8f-248a-48e7-893f-01c009faad37",
   "metadata": {},
   "source": [
    "# Running the generative model forward"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "371c969e-632b-45ce-86bd-2b979b38d349",
   "metadata": {},
   "outputs": [],
   "source": [
    "key = jax.random.PRNGKey(0)\n",
    "keys = jax.random.split(key, 5)\n",
    "n_sample = 1000\n",
    "n_importance_samples = 10000\n",
    "args = (component_logprobs, component_params, gen_parametrized_z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "3b332eb3-8602-4b78-a7fc-d6db81e2db7f",
   "metadata": {},
   "outputs": [],
   "source": [
    "health_tr = make_health_data.simulate(keys[0], (keys[1], mixture_model, args, n_sample, genjax.Pytree.const(n_importance_samples)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "c2688709-92fe-42bb-9484-6dc879fb23fe",
   "metadata": {},
   "outputs": [],
   "source": [
    "social_tr = make_social_data.simulate(keys[2], (keys[3], mixture_model, args, n_sample, genjax.Pytree.const(n_importance_samples)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "899bdc67-5004-44f0-bcad-d8e8159e1472",
   "metadata": {},
   "outputs": [],
   "source": [
    "politics_tr = make_politics_data.simulate(keys[4], (mixture_model, args, genjax.Pytree.const(n_sample)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "ae7a0a95-49e8-4fe5-91b8-62c73f27c77f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def trace_to_df(tr):\n",
    "    tr_dict = {k: np.array(v) for k, v in tr.get_retval().items()}\n",
    "    return pl.from_dict(tr_dict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "a31c0b2b-4114-424e-b801-34449b1a1409",
   "metadata": {},
   "outputs": [],
   "source": [
    "politics_df = trace_to_df(politics_tr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "b961ebdd-cc7e-4d8c-94c1-6826a03fb0dc",
   "metadata": {},
   "outputs": [],
   "source": [
    "health_df = trace_to_df(health_tr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "232819ee-bcf1-49e3-9535-79f391281452",
   "metadata": {},
   "outputs": [],
   "source": [
    "social_df = trace_to_df(social_tr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "08a7366b-48a7-44d3-87c4-d1ac7862b0ea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><style>\n",
       ".dataframe > thead > tr,\n",
       ".dataframe > tbody > tr {\n",
       "  text-align: right;\n",
       "  white-space: pre-wrap;\n",
       "}\n",
       "</style>\n",
       "<small>shape: (9, 5)</small><table border=\"1\" class=\"dataframe\"><thead><tr><th>statistic</th><th>male</th><th>region</th><th>supports_medicare</th><th>vote_republican</th></tr><tr><td>str</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td></tr></thead><tbody><tr><td>&quot;count&quot;</td><td>1000.0</td><td>1000.0</td><td>1000.0</td><td>1000.0</td></tr><tr><td>&quot;null_count&quot;</td><td>0.0</td><td>0.0</td><td>0.0</td><td>0.0</td></tr><tr><td>&quot;mean&quot;</td><td>0.45</td><td>1.053</td><td>0.372</td><td>0.406</td></tr><tr><td>&quot;std&quot;</td><td>0.497743</td><td>1.154783</td><td>0.48358</td><td>0.49133</td></tr><tr><td>&quot;min&quot;</td><td>0.0</td><td>0.0</td><td>0.0</td><td>0.0</td></tr><tr><td>&quot;25%&quot;</td><td>0.0</td><td>0.0</td><td>0.0</td><td>0.0</td></tr><tr><td>&quot;50%&quot;</td><td>0.0</td><td>1.0</td><td>0.0</td><td>0.0</td></tr><tr><td>&quot;75%&quot;</td><td>1.0</td><td>2.0</td><td>1.0</td><td>1.0</td></tr><tr><td>&quot;max&quot;</td><td>1.0</td><td>3.0</td><td>1.0</td><td>1.0</td></tr></tbody></table></div>"
      ],
      "text/plain": [
       "shape: (9, 5)\n",
       "┌────────────┬──────────┬──────────┬───────────────────┬─────────────────┐\n",
       "│ statistic  ┆ male     ┆ region   ┆ supports_medicare ┆ vote_republican │\n",
       "│ ---        ┆ ---      ┆ ---      ┆ ---               ┆ ---             │\n",
       "│ str        ┆ f64      ┆ f64      ┆ f64               ┆ f64             │\n",
       "╞════════════╪══════════╪══════════╪═══════════════════╪═════════════════╡\n",
       "│ count      ┆ 1000.0   ┆ 1000.0   ┆ 1000.0            ┆ 1000.0          │\n",
       "│ null_count ┆ 0.0      ┆ 0.0      ┆ 0.0               ┆ 0.0             │\n",
       "│ mean       ┆ 0.45     ┆ 1.053    ┆ 0.372             ┆ 0.406           │\n",
       "│ std        ┆ 0.497743 ┆ 1.154783 ┆ 0.48358           ┆ 0.49133         │\n",
       "│ min        ┆ 0.0      ┆ 0.0      ┆ 0.0               ┆ 0.0             │\n",
       "│ 25%        ┆ 0.0      ┆ 0.0      ┆ 0.0               ┆ 0.0             │\n",
       "│ 50%        ┆ 0.0      ┆ 1.0      ┆ 0.0               ┆ 0.0             │\n",
       "│ 75%        ┆ 1.0      ┆ 2.0      ┆ 1.0               ┆ 1.0             │\n",
       "│ max        ┆ 1.0      ┆ 3.0      ┆ 1.0               ┆ 1.0             │\n",
       "└────────────┴──────────┴──────────┴───────────────────┴─────────────────┘"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "politics_df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0853d0cc-d382-4dea-a09e-dd89918465bc",
   "metadata": {},
   "source": [
    "# Solving a simple inference problem"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "513f82da-16c8-42a7-91e3-3a6813356eda",
   "metadata": {},
   "source": [
    "As a first example, we'll solve a really simple inference problem\n",
    "- We'll start by placing a simple prior on z, as a mixture"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "41583afe-355c-4a7b-a268-213b15eb36c5",
   "metadata": {},
   "outputs": [],
   "source": [
    "@static_gen_fn\n",
    "def gen_z_prior():\n",
    "    p = genjax.uniform() @ \"p\"\n",
    "\n",
    "    @static_gen_fn\n",
    "    def parametrized_gen_z():\n",
    "        model_choice = genjax.bernoulli(logit(p)) @ \"model\"\n",
    "        model_choice = jnp.array(model_choice, dtype=int)\n",
    "        z = switch(model_choice) @ \"z\"\n",
    "        return z\n",
    "\n",
    "    return parametrized_gen_z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "86877944-7f7b-4c5d-898a-bf9052e13777",
   "metadata": {},
   "outputs": [],
   "source": [
    "@static_gen_fn\n",
    "def model(key):\n",
    "    keys = jax.random.split(key, 2)\n",
    "\n",
    "    p = genjax.uniform() @ \"p\"\n",
    "    component_logprobs = jnp.log(jnp.array([1-p, p]))\n",
    "\n",
    "    args = (component_logprobs, component_params, gen_parametrized_z)\n",
    "    # fix: if I don't inline the calls to health/social data, I get an UnexpectedTracer error when doing\n",
    "    # IS on model. \n",
    "    health_data = make_health_data.inline(keys[0], mixture_model, args, n_sample, genjax.Pytree.const(n_importance_samples))\n",
    "    social_data = make_social_data.inline(keys[1], mixture_model, args, n_sample, genjax.Pytree.const(n_importance_samples))\n",
    "    politics_data = make_politics_data.inline(mixture_model, args, genjax.Pytree.const(n_sample))\n",
    "\n",
    "    return health_data, social_data, politics_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "779b1449-4ba1-4ea8-b92f-6a697672b87c",
   "metadata": {},
   "outputs": [],
   "source": [
    "obs, _ = health_tr.get_choices().merge(social_tr.get_choices())\n",
    "obs, _ = obs.merge(politics_tr.get_choices())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "448424dd-2c76-4474-8eac-c5f36e048110",
   "metadata": {},
   "outputs": [],
   "source": [
    "key = jax.random.PRNGKey(1234)\n",
    "keys = jax.random.split(key, 101)\n",
    "\n",
    "# question I should ask mccoy---how can I ergonomically vmap over the second key here?\n",
    "trs, ws = jax.vmap(model.importance, in_axes=(0, None, None))(keys[1:], obs, (keys[0],))\n",
    "# tr, w = model.importance(keys[1], obs, (keys[0],))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fc66a650-fcc6-495c-8641-d2d75ecbeb8d",
   "metadata": {},
   "outputs": [],
   "source": [
    "probs = np.exp(ws - np.max(ws))\n",
    "probs /= np.sum(probs)\n",
    "plot_df = pl.from_dict({\"p\": trs[\"p\"], \"prob\": probs})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e6c5425a-73a3-437d-aff3-150b874811bb",
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "976a9cc3-b459-4c3c-b5bb-20597fe9ef42",
   "metadata": {},
   "outputs": [],
   "source": [
    "sns.scatterplot(data=plot_df, x=\"p\", y=\"prob\")"
   ]
  }
 ],
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