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ricardoV94/multiple_changepoint_marginalization.ipynb

Last active July 7, 2024 13:33
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multiple_changepoint_marginalization.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Context\n",
"\n",
"This notebook is a follow up to an excelent [notebook](https://colab.research.google.com/drive/1kRW-X2z5GBsNFtN0dDvPo21yGT0ASosJ?usp=sharing) by [ckrapu](https://discourse.pymc.io/u/ckrapu), originally shared in this [Discourse issue](https://discourse.pymc.io/t/hierarchical-changepoint-detection/10789)\n",
"\n",
"It attempts to sample the first iteration model, marginalizing over the number of changepoints. This relies on a not-yet merged PR in pymc-experimental: https://github.com/pymc-devs/pymcx/pull/91"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "D8VNQICRbIEK"
},
"source": [
"# Changepoint models\n",
"\n",
"Identifying structural breaks in data is an important problem to folks that frequently work with time series data. Some examples of how people have dealt with the problem of a single changepoint can be found [here](https://cscherrer.github.io/post/bayesian-changepoint/) and [here](https://mc-stan.org/docs/2_23/stan-users-guide/change-point-section.html). \n",
"\n",
"Generally, the setup looks like this: we have some data $X_t$ indexed by a discrete time coordinate $t \\in \\{1,...,T\\}$ and a parametric submodel linking the distribution of $X$ to another quantity $\\mu_t$ which depends on the temporal coordinate and which render $X_1,...,X_T$ conditionally independent given the quantity $\\mu_t$. For the case of a linear Gaussian model with a single change point, we have\n",
"\n",
"\n",
"$$a_1, a_2 \\sim N(0, \\sigma^2_\\mu)$$\n",
"\n",
"$$\\tau \\sim \\text{DiscreteUniform}(\\{1,...,T\\})$$\n",
"\n",
"$$\\mu_t = \\left\\{\n",
" \\begin{array}{l}\n",
" a_1 \\text{ if } t < \\tau \\\\\n",
" a_2 \\text{ if } t \\ge \\tau\n",
" \\end{array}\n",
" \\right. $$\n",
"\n",
"$$X_t \\sim N(\\mu_t, \\sigma_\\epsilon)$$\n",
"\n",
"with your scale priors of choice on the variance parameters $\\sigma_\\epsilon$ and $\\sigma_\\mu$. Now, one of the main conceptual problems with this model is that you need to assume it has a single changepoint. You can relax that assumption by extending this model to include more $\\tau$ and $a$ parameters, but you'll still need to specify the number of them ahead of time. \n",
"\n",
"Relaxing the assumption on the number of parameters is, for the most part, a solved problem in the research community (see [here](https://www.sciencedirect.com/science/article/abs/pii/S0167715297000503) and [here](https://repository.upenn.edu/cgi/viewcontent.cgi?article=1376&context=statistics_papers) for a few representative examples). Unfortunately, these require the analyst to implement the inference techniques presented by hand; these are often Gibbs samplers or similar. Wouldn't it be nice to just be able to use a PPL and write down the forward process instead?\n",
"\n",
"That's the point of this notebook - we'll walk through a construction of a changepoint model plus inference in PyMC which is considerably more straightforward than a handwritten sampler. "
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "XuRuGxmcfbDX"
},
"source": [
"We'll start by simulating some data over 50 timesteps; there are 4 changepoints \n",
"and the model's likelihood is Gaussian. We will use a standard set of imports for working with PyMC and set the seed for repeatability."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"id": "xoHV2lhYbIf8"
},
"outputs": [],
"source": [
"import arviz as az\n",
"import pymc as pm\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import scipy.special as sp\n",
"import aesara.tensor as at\n",
"from collections import Counter\n",
"from IPython.display import set_matplotlib_formats\n",
"import xarray as xr"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "MAMECjBVU6lG"
},
"source": [
"# Simulating a dataset"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "gEdVVufPiP6x"
},
"source": [
"Since the generative process for this data is simple, the code required to simulate data is relatively short. We begin by sampling the changepoints and then adding offsets for each changepoint to the mean value of the data. We then perturb this mean with normal noise variates to create simulated observations."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"id": "f3NdjpDy_Ifb"
},
"outputs": [],
"source": [
"np.random.seed(827)\n",
"rng = np.random.default_rng(827)\n",
"\n",
"T = 50\n",
"noise_sd_true = 0.15\n",
"n_cps_true = 4\n",
"\n",
"def simulate_data(T, n_changepoints, noise_sd=0.15):\n",
" cp_times = np.sort(np.random.choice(T, size=n_cps_true))\n",
" cp_deltas = np.random.randn(n_cps_true)\n",
"\n",
" noiseless = np.zeros(T)\n",
" start_time = 0\n",
"\n",
" for cp_time, cp_delta in zip(cp_times, cp_deltas):\n",
" noiseless[start_time:cp_time] += cp_delta\n",
" start_time = cp_time\n",
"\n",
" xs = noiseless + np.random.randn(T) * noise_sd_true\n",
" return xs, noiseless, cp_times, cp_deltas \n",
"\n",
"xs, noiseless, cp_times_true, cp_deltas_true = simulate_data(T, n_cps_true)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 9, 22, 37, 45])"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cp_times_true"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([-0.26203003, 0.47949834, -0.37238606, 0.09406072])"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cp_deltas_true"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "s_zDGssQihSd"
},
"source": [
"As we can see below, the green changepoints do clearly correspond to changes in the level of the time series. However, not all of them are obvious - the last one, in particular, is a relatively small jump."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 301
},
"id": "kTssO46aiN3T",
"outputId": "83cd9247-6a72-4205-dd87-9b7eab93eff1"
},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 900x300 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(9,3))\n",
"plt.plot(xs, marker='o', color='k', label='Observed data')\n",
"plt.plot(noiseless, color='g', label='Noise-free mean value')\n",
"\n",
"for i, cp in enumerate(cp_times_true):\n",
" if i == 0:\n",
" label = 'Change point'\n",
" else:\n",
" label=None\n",
" plt.axvline(cp, color='g', linestyle='--',label=label)\n",
"\n",
"plt.legend()\n",
"\n",
"plt.xlabel('Timestep',fontsize=12)\n",
"plt.ylabel('$X(t)$',fontsize=18);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Model with changepoints marginalized"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pm.DiscreteUniform.dist(0, 2, size=2000).eval().max()"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.random.choice(2, size=2000).max()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will try to help NUTS by marginalizing over the number of changepoints, using experimental featuer from pymc_experimental"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"from pymc_experimental.marginal_model import MarginalModel"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"max_cp_inference = 10\n",
"tiled_times = np.arange(T)[:, None].repeat(max_cp_inference, axis=1)\n",
"\n",
"with MarginalModel() as m:\n",
" # Not implemented yet, but otherwise a nice way to specify more informed prior\n",
"# n_cps = pm.Truncated(\"n_cps\", pm.Poisson.dist(5), 0, T)\n",
" n_cps = pm.DiscreteUniform(\"n_cps\", 0, max_cp_inference)\n",
" \n",
" # We can't marginalize `cp_times` because each dim contributes non-independently to the likelihood\n",
" # It doesn't make sense to consider cp_times of 0 or T, as we can't observe changes\n",
" cp_times = pm.DiscreteUniform(\"cp_times\", 1, T-1, shape=max_cp_inference)\n",
"\n",
" cp_sd = pm.HalfNormal('cp_sd', sigma=2)\n",
" cp_deltas = pm.Normal('cp_deltas', cp_sd, shape=max_cp_inference)\n",
" \n",
" global_mean = pm.Normal('global_mean', sigma=1)\n",
" noise_sd = pm.HalfNormal('noise_sd', sigma=1)\n",
" \n",
" cp_times_sorted = cp_times.sort()\n",
" is_timestep_past_cp = (tiled_times >= cp_times_sorted[None, :].repeat(T, axis=0))\n",
" cp_contrib = at.sum(cp_deltas[:n_cps] * is_timestep_past_cp[:, :n_cps], axis=1)\n",
" \n",
" mu = global_mean + cp_contrib\n",
" pm.Normal('likelihood', mu=mu, sigma=noise_sd, observed=xs)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"m.marginalize([n_cps])"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
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],
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]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Multiprocess sampling (4 chains in 4 jobs)\n",
"CompoundStep\n",
">Metropolis: [cp_times]\n",
">NUTS: [cp_sd, cp_deltas, global_mean, noise_sd]\n"
]
},
{
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"\n",
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" /* gets rid of default border in Firefox and Opera. */\n",
" border: none;\n",
" /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
" background-size: auto;\n",
" }\n",
" progress:not([value]), progress:not([value])::-webkit-progress-bar {\n",
" background: repeating-linear-gradient(45deg, #7e7e7e, #7e7e7e 10px, #5c5c5c 10px, #5c5c5c 20px);\n",
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},
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{
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"\n",
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" <progress value='8000' class='' max='8000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
" 100.00% [8000/8000 06:39&lt;00:00 Sampling 4 chains, 0 divergences]\n",
" </div>\n",
" "
],
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},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
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"text": [
"Sampling 4 chains for 1_500 tune and 500 draw iterations (6_000 + 2_000 draws total) took 400 seconds.\n"
]
}
],
"source": [
"with m:\n",
" trace = pm.sample(tune=1500, chains=4, draws=500, random_seed=rng)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"No divergences!!!"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
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" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>mean</th>\n",
" <th>sd</th>\n",
" <th>hdi_3%</th>\n",
" <th>hdi_97%</th>\n",
" <th>mcse_mean</th>\n",
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" <th>ess_bulk</th>\n",
" <th>ess_tail</th>\n",
" <th>r_hat</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>cp_times[0]</th>\n",
" <td>24.256</td>\n",
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" </tr>\n",
" <tr>\n",
" <th>cp_times[1]</th>\n",
" <td>40.992</td>\n",
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" <tr>\n",
" <th>cp_times[2]</th>\n",
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" <tr>\n",
" <th>cp_times[3]</th>\n",
" <td>36.684</td>\n",
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" <tr>\n",
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" <tr>\n",
" <th>cp_times[5]</th>\n",
" <td>19.262</td>\n",
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" <tr>\n",
" <th>cp_times[7]</th>\n",
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" <tr>\n",
" <th>cp_times[8]</th>\n",
" <td>28.334</td>\n",
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" <tr>\n",
" <th>cp_times[9]</th>\n",
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" <tr>\n",
" <th>cp_deltas[0]</th>\n",
" <td>0.312</td>\n",
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" <td>-0.256</td>\n",
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" <td>269.0</td>\n",
" <td>1.13</td>\n",
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" <tr>\n",
" <th>cp_deltas[1]</th>\n",
" <td>0.166</td>\n",
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" <tr>\n",
" <th>cp_deltas[2]</th>\n",
" <td>-0.070</td>\n",
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" <th>cp_deltas[3]</th>\n",
" <td>-0.104</td>\n",
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" <td>0.014</td>\n",
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" <th>cp_deltas[7]</th>\n",
" <td>0.343</td>\n",
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" <td>0.006</td>\n",
" <td>784.0</td>\n",
" <td>647.0</td>\n",
" <td>1.01</td>\n",
" </tr>\n",
" <tr>\n",
" <th>noise_sd</th>\n",
" <td>0.145</td>\n",
" <td>0.019</td>\n",
" <td>0.111</td>\n",
" <td>0.181</td>\n",
" <td>0.002</td>\n",
" <td>0.002</td>\n",
" <td>48.0</td>\n",
" <td>57.0</td>\n",
" <td>1.06</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" mean sd hdi_3% hdi_97% mcse_mean mcse_sd ess_bulk \\\n",
"cp_times[0] 24.256 17.229 1.000 47.000 8.301 6.320 5.0 \n",
"cp_times[1] 40.992 4.821 36.000 49.000 0.547 0.388 73.0 \n",
"cp_times[2] 22.595 12.367 9.000 48.000 5.797 4.407 6.0 \n",
"cp_times[3] 36.684 9.548 22.000 48.000 4.414 3.340 7.0 \n",
"cp_times[4] 40.497 5.281 35.000 49.000 0.660 0.469 67.0 \n",
"cp_times[5] 19.262 14.065 1.000 46.000 6.697 5.089 5.0 \n",
"cp_times[6] 33.946 15.123 4.000 49.000 7.146 5.425 7.0 \n",
"cp_times[7] 28.802 13.438 9.000 49.000 6.275 4.755 5.0 \n",
"cp_times[8] 28.334 14.984 1.000 47.000 7.218 5.496 5.0 \n",
"cp_times[9] 14.959 13.127 1.000 43.000 6.027 4.555 5.0 \n",
"cp_deltas[0] 0.312 0.355 -0.256 0.848 0.074 0.053 24.0 \n",
"cp_deltas[1] 0.166 0.564 -0.841 0.893 0.193 0.141 10.0 \n",
"cp_deltas[2] -0.070 0.611 -0.938 0.847 0.236 0.174 8.0 \n",
"cp_deltas[3] -0.104 0.597 -1.078 0.738 0.242 0.180 7.0 \n",
"cp_deltas[4] 0.047 0.654 -1.079 1.142 0.186 0.135 15.0 \n",
"cp_deltas[5] 0.014 0.852 -1.105 1.840 0.233 0.169 14.0 \n",
"cp_deltas[6] 0.323 0.820 -1.325 1.933 0.033 0.059 558.0 \n",
"cp_deltas[7] 0.343 0.944 -1.410 2.192 0.028 0.027 1143.0 \n",
"cp_deltas[8] 0.370 1.024 -1.724 2.158 0.027 0.024 1456.0 \n",
"cp_deltas[9] 0.341 1.013 -1.617 2.180 0.027 0.026 1431.0 \n",
"global_mean -0.298 0.100 -0.499 -0.125 0.010 0.007 90.0 \n",
"cp_sd 0.336 0.253 0.000 0.763 0.008 0.006 784.0 \n",
"noise_sd 0.145 0.019 0.111 0.181 0.002 0.002 48.0 \n",
"\n",
" ess_tail r_hat \n",
"cp_times[0] 11.0 2.04 \n",
"cp_times[1] 68.0 1.04 \n",
"cp_times[2] 6.0 2.18 \n",
"cp_times[3] 4.0 1.62 \n",
"cp_times[4] 45.0 1.03 \n",
"cp_times[5] 21.0 2.54 \n",
"cp_times[6] 6.0 1.63 \n",
"cp_times[7] 32.0 2.15 \n",
"cp_times[8] 13.0 2.38 \n",
"cp_times[9] 10.0 2.38 \n",
"cp_deltas[0] 269.0 1.13 \n",
"cp_deltas[1] 25.0 1.34 \n",
"cp_deltas[2] 264.0 1.44 \n",
"cp_deltas[3] 63.0 1.54 \n",
"cp_deltas[4] 82.0 1.27 \n",
"cp_deltas[5] 167.0 1.22 \n",
"cp_deltas[6] 746.0 1.23 \n",
"cp_deltas[7] 955.0 1.04 \n",
"cp_deltas[8] 1313.0 1.00 \n",
"cp_deltas[9] 801.0 1.00 \n",
"global_mean 274.0 1.04 \n",
"cp_sd 647.0 1.01 \n",
"noise_sd 57.0 1.06 "
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"az.summary(trace)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"R-hat is awful, but we don't care about those changepoint specific variables that correspond to implausible number of changepoints. The global parameters make sense at least:"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 1200x400 with 3 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"az.plot_posterior(\n",
" trace, var_names=[\"noise_sd\", \"cp_sd\", \"global_mean\"], \n",
" ref_val=[noise_sd_true, cp_deltas_true.std(), noiseless[0]],\n",
" figsize=(12, 4)\n",
");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Recovering the marginalized variable and checking inference"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's recover the marginalized variable `n_cps`, so that we can see what he model actually predicts for the mean and changepoints"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"with pm.Model() as recover_m:\n",
" n_cps = pm.DiscreteUniform(\"n_cps\", 0, max_cp_inference)\n",
" cp_times = pm.DiscreteUniform(\"cp_times\", 1, T-1, shape=max_cp_inference)\n",
"\n",
" # We need to disable transforms so that we can use the posterior points directly\n",
" # As the transformed draws are not saved\n",
" cp_sd = pm.HalfNormal('cp_sd', sigma=2, transform=None)\n",
" cp_deltas = pm.Normal('cp_deltas', cp_sd, shape=max_cp_inference)\n",
" \n",
" global_mean = pm.Normal('global_mean', sigma=1)\n",
" noise_sd = pm.HalfNormal('noise_sd', sigma=1, transform=None)\n",
" \n",
" cp_times_sorted = cp_times.sort()\n",
" is_timestep_past_cp = (tiled_times >= cp_times_sorted[None, :].repeat(T, axis=0))\n",
" cp_contrib = at.sum(cp_deltas[:n_cps] * is_timestep_past_cp[:, :n_cps], axis=1)\n",
" \n",
" mu = pm.Deterministic(\"mu\", global_mean + cp_contrib)\n",
" \n",
" llike = pm.Normal('likelihood', mu=mu, sigma=noise_sd, observed=xs)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"# Only the likelihood depends directly on n_cps, so we create a logp function that only considers those two\n",
"logp_fn = recover_m.compile_fn(\n",
" recover_m.logp([n_cps, llike]), \n",
" inputs=recover_m.value_vars,\n",
" on_unused_input=\"ignore\",\n",
" point_fn=False\n",
")"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2000"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from pymc.util import dataset_to_point_list\n",
"points, _ = dataset_to_point_list(az.extract(trace), sample_dims=(\"sample\",))\n",
"len(points)"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([-259.7478298 , -138.74512393, -123.36547779, -291.10229905,\n",
" -394.30545815, -31.77460832, -60.62234883, -91.30291365,\n",
" 20.99261401, 20.8252028 , 19.37766871])"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# logp for first point\n",
"logps = np.array([logp_fn(**points[0], n_cps=n_cps) for n_cps in range(0, max_cp_inference + 1)])\n",
"logps"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"8"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# For simplicity we will take the argmax, instead of sampling from the logps\n",
"np.argmax(logps)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The most likely `n_cps` for the first draw is 4. Let's now recover the most likely for each point in the posterior"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"6.0085"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"possible_n_cps = list(range(max_cp_inference+1))\n",
"n_cps = np.array([\n",
" np.argmax([\n",
" [logp_fn(**point, n_cps=n_cps) for n_cps in possible_n_cps]\n",
" \n",
" ])\n",
" for point in points\n",
"])\n",
"n_cps.mean()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The posterior mean overshoots the real number of changepoints. I would blame it on the prior?"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"az.plot_posterior(n_cps, ref_val=n_cps_true);"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [],
"source": [
"post = az.extract(trace)\n",
"post[\"n_cps\"] = xr.DataArray(n_cps, dims=\"sample\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"With the `n_cps` recovered we can now also recover any other deterministics of interest, by exploiting `posterior_predictive`"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Sampling: []\n"
]
},
{
"data": {
"text/html": [
"\n",
"<style>\n",
" /* Turns off some styling */\n",
" progress {\n",
" /* gets rid of default border in Firefox and Opera. */\n",
" border: none;\n",
" /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
" background-size: auto;\n",
" }\n",
" progress:not([value]), progress:not([value])::-webkit-progress-bar {\n",
" background: repeating-linear-gradient(45deg, #7e7e7e, #7e7e7e 10px, #5c5c5c 10px, #5c5c5c 20px);\n",
" }\n",
" .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
" background: #F44336;\n",
" }\n",
"</style>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"\n",
" <div>\n",
" <progress value='2000' class='' max='2000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
" 100.00% [2000/2000 00:00&lt;00:00]\n",
" </div>\n",
" "
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"with recover_m:\n",
" mu = pm.sample_posterior_predictive(\n",
" post, sample_dims=[\"sample\"], \n",
" var_names=[\"mu\"],\n",
" random_seed=rng,\n",
" ).posterior_predictive[\"mu\"]\n",
"mu = xr.DataArray(mu.values, dims=(\"sample\", \"mu_dim_0\"))\n",
"post[\"mu\"] = mu "
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [],
"source": [
"def make_inference_plot(trace, xs, noiseless, true_cp, *, figsize=(9,4), n_cp_shown=10):\n",
" T = len(xs)\n",
" top_cp = Counter(\n",
" trace[\"cp_times\"].to_numpy().astype(int).ravel().tolist()\n",
" ).most_common(n_cp_shown)\n",
"\n",
" plt.figure(figsize=figsize)\n",
" plt.plot(noiseless, label='True noiseless values', color='green')\n",
"\n",
" plt.plot(trace['mu'].mean(axis=(0,)), label='Inferred noiseless mean', color='orange')\n",
"\n",
" q10, q90 = np.percentile(trace['mu'], [10,90], axis=(0,))\n",
" plt.fill_between(np.arange(T), q10, q90, color='orange', alpha=0.2)\n",
" plt.plot(xs, linestyle='', color='k', marker='o', label='Observed data')\n",
" for i, cp in enumerate(true_cp):\n",
" if i == 0:\n",
" label = 'True change point'\n",
" else:\n",
" label=None\n",
" plt.axvline(cp, color='g', linestyle='--',label=label)\n",
"\n",
" for i, (t, _) in enumerate(top_cp):\n",
" if i == 0:\n",
" label = 'Inferred change point'\n",
" else:\n",
" label=None\n",
" # The recovered change points seem to be one unit to the left\n",
" # Probably I messed up something in the model specification\n",
" plt.axvline(t+0.1, color='orange', linestyle='--', label=label)\n",
" plt.xlabel('Timestep',fontsize=12)\n",
" plt.ylabel('$X(t)$',fontsize=18)\n",
" plt.legend(loc=(1, .6));"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 900x400 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"make_inference_plot(post, xs, noiseless, cp_times_true, n_cp_shown=6)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"colab": {
"provenance": []
},
"hide_input": false,
"kernelspec": {
"display_name": "pymcx",
"language": "python",
"name": "pymcx"
},
"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"
},
"toc": {
"base_numbering": 1,
"nav_menu": {},
"number_sections": true,
"sideBar": true,
"skip_h1_title": false,
"title_cell": "Table of Contents",
"title_sidebar": "Contents",
"toc_cell": false,
"toc_position": {},
"toc_section_display": true,
"toc_window_display": false
}
},
"nbformat": 4,
"nbformat_minor": 1
}
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