{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Sequential Monte Carlo\n", "\n", ":::{post} Oct 19, 2021\n", ":tags: SMC \n", ":category: beginner\n", ":::" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Running on PyMC v4.0.0b6\n" ] } ], "source": [ "import arviz as az\n", "import numpy as np\n", "import pymc as pm\n", "import pytensor.tensor as pt\n", "\n", "print(f\"Running on PyMC v{pm.__version__}\")" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "az.style.use(\"arviz-darkgrid\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Sampling from distributions with multiple peaks with standard MCMC methods can be difficult, if not impossible, as the Markov chain often gets stuck in either of the minima. A Sequential Monte Carlo sampler (SMC) is a way to ameliorate this problem.\n", "\n", "As there are many SMC flavors, in this notebook we will focus on the version implemented in PyMC.\n", "\n", "SMC combines several statistical ideas, including [importance sampling](https://en.wikipedia.org/wiki/Importance_sampling), tempering and MCMC. By tempering we mean the use of an auxiliary _temperature_ parameter to control the sampling process. To see how tempering can help let's write the posterior as:\n", "\n", "$$p(\\theta \\mid y)_{\\beta} \\propto p(y \\mid \\theta)^{\\beta} \\; p(\\theta)$$\n", "\n", "When $\\beta=0$ we have that $p(\\theta \\mid y)_{\\beta=0}$ is the prior distribution and when $\\beta=1$ we recover the _true_ posterior. We can think of $\\beta$ as a knob we can use to gradually _fade up_ the likelihood. This can be useful as in general sampling from the prior is easier than sampling from the posterior distribution. Thus we can use $\\beta$ to control the transition from an easy to sample distribution to a harder one.\n", "\n", "A summary of the algorithm is:\n", "\n", "1. Initialize $\\beta$ at zero and stage at zero.\n", "2. Generate N samples $S_{\\beta}$ from the prior (because when $\\beta = 0$ the tempered posterior is the prior).\n", "3. Increase $\\beta$ in order to make the effective sample size equals some predefined value (we use $Nt$, where $t$ is 0.5 by default).\n", "4. Compute a set of N importance weights $W$. The weights are computed as the ratio of the likelihoods of a sample at stage $i+1$ and stage $i$.\n", "5. Obtain $S_{w}$ by re-sampling according to $W$.\n", "6. Use $W$ to compute the mean and covariance for the proposal distribution, a MVNormal.\n", "7. For stages other than 0 use the acceptance rate from the previous stage to estimate `n_steps`.\n", "8. Run N independent Metropolis-Hastings (IMH) chains (each one of length `n_steps`), starting each one from a different sample in $S_{w}$. Samples are IMH as the proposal mean is the of the previous posterior stage and not the current point in parameter space.\n", "9. Repeat from step 3 until $\\beta \\ge 1$.\n", "10. The final result is a collection of $N$ samples from the posterior\n", "\n", "The algorithm is summarized in the next figure, the first subplot shows 5 samples (orange dots) at some particular stage. The second subplot shows how these samples are reweighted according to their posterior density (blue Gaussian curve). The third subplot shows the result of running a certain number of IMH steps, starting from the reweighted samples $S_{w}$ in the second subplot, notice how the two samples with the lower posterior density (smaller circles) are discarded and not used to seed new Markov chains.\n", "\n", "![SMC stages](smc.png)\n", "\n", "\n", "SMC samplers can also be interpreted in the light of genetic algorithms, which are biologically-inspired algorithms that can be summarized as follows:\n", "\n", "1. Initialization: set a population of individuals\n", "2. Mutation: individuals are somehow modified or perturbed\n", "3. Selection: individuals with high _fitness_ have higher chance to generate _offspring_.\n", "4. Iterate by using individuals from 3 to set the population in 1.\n", "\n", "If each _individual_ is a particular solution to a problem, then a genetic algorithm will eventually produce good solutions to that problem. One key aspect is to generate enough diversity (mutation step) in order to explore the solution space and hence avoid getting trap in local minima. Then we perform a _selection_ step to _probabilistically_ keep reasonable solutions while also keeping some diversity. Being too greedy and short-sighted could be problematic, _bad_ solutions in a given moment could lead to _good_ solutions in the future.\n", "\n", "For the SMC version implemented in PyMC we set the number of parallel Markov chains $N$ with the `draws` argument. At each stage SMC will use independent Markov chains to explore the _tempered posterior_ (the black arrow in the figure). The final samples, _i.e_ those stored in the `trace`, will be taken exclusively from the final stage ($\\beta = 1$), i.e. the _true_ posterior (\"true\" in the mathematical sense).\n", "\n", "The successive values of $\\beta$ are determined automatically (step 3). The harder the distribution is to sample the closer two successive values of $\\beta$ will be. And the larger the number of stages SMC will take. SMC computes the next $\\beta$ value by keeping the effective sample size (ESS) between two stages at a constant predefined value of half the number of draws. This can be adjusted if necessary by the `threshold` parameter (in the interval [0, 1])-- the current default of 0.5 is generally considered as a good default. The larger this value, the higher the target ESS and the closer two successive values of $\\beta$ will be. This ESS values are computed from the importance weights (step 4) and not from the autocorrelation like those from ArviZ (for example using `az.ess` or `az.summary`). \n", "\n", "Two more parameters that are automatically determined are:\n", "\n", "* The number of steps each Markov chain takes to explore the _tempered posterior_ `n_steps`. This is determined from the acceptance rate from the previous stage.\n", "* The covariance of the MVNormal proposal distribution is also adjusted adaptively based on the acceptance rate at each stage.\n", "\n", "As with other sampling methods, running a sampler more than one time is useful to compute diagnostics, SMC is no exception. PyMC will try to run at least two **SMC _chains_** (do not confuse with the $N$ Markov chains inside each SMC chain).\n", "\n", "Even when SMC uses the Metropolis-Hasting algorithm under the hood, it has several advantages over it:\n", "\n", "* It can sample from distributions with multiple peaks.\n", "* It does not have a burn-in period, it starts by sampling directly from the prior and then at each stage the starting points are already _approximately_ distributed according to the tempered posterior (due to the re-weighting step).\n", "* It is inherently parallel." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solving a PyMC model with SMC\n", "\n", "To see an example of how to use SMC inside PyMC let's define a multivariate Gaussian of dimension $n$ with two modes, the weights of each mode and the covariance matrix." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "n = 4\n", "\n", "mu1 = np.ones(n) * (1.0 / 2)\n", "mu2 = -mu1\n", "\n", "stdev = 0.1\n", "sigma = np.power(stdev, 2) * np.eye(n)\n", "isigma = np.linalg.inv(sigma)\n", "dsigma = np.linalg.det(sigma)\n", "\n", "w1 = 0.1 # one mode with 0.1 of the mass\n", "w2 = 1 - w1 # the other mode with 0.9 of the mass\n", "\n", "\n", "def two_gaussians(x):\n", " log_like1 = (\n", " -0.5 * n * pt.log(2 * np.pi)\n", " - 0.5 * pt.log(dsigma)\n", " - 0.5 * (x - mu1).T.dot(isigma).dot(x - mu1)\n", " )\n", " log_like2 = (\n", " -0.5 * n * pt.log(2 * np.pi)\n", " - 0.5 * pt.log(dsigma)\n", " - 0.5 * (x - mu2).T.dot(isigma).dot(x - mu2)\n", " )\n", " return pm.math.logsumexp([pt.log(w1) + log_like1, pt.log(w2) + log_like2])" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Initializing SMC sampler...\n", "Sampling 4 chains in 4 jobs\n" ] }, { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\n", "
\n", " \n", " 100.00% [100/100 00:00<00:00 Stage: 6 Beta: 1.000]\n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ " " ] } ], "source": [ "with pm.Model() as model:\n", " X = pm.Uniform(\n", " \"X\",\n", " shape=n,\n", " lower=-2.0 * np.ones_like(mu1),\n", " upper=2.0 * np.ones_like(mu1),\n", " initval=-1.0 * np.ones_like(mu1),\n", " )\n", " llk = pm.Potential(\"llk\", two_gaussians(X))\n", " idata_04 = pm.sample_smc(2000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see from the message that PyMC is running four **SMC chains** in parallel. As explained before this is useful for diagnostics. As with other samplers one useful diagnostics is the `plot_trace`, here we use `kind=\"rank_vlines\"` as rank plots as generally more useful than the classical \"trace\"" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'Estimated w1 = 0.907'" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = az.plot_trace(idata_04, compact=True, kind=\"rank_vlines\")\n", "ax[0, 0].axvline(-0.5, 0, 0.9, color=\"k\")\n", "ax[0, 0].axvline(0.5, 0, 0.1, color=\"k\")\n", "f'Estimated w1 = {np.mean(idata_04.posterior[\"X\"] < 0).item():.3f}'" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From the KDE we can see that we recover the modes and even the relative weights seems pretty good. The rank plot on the right looks good too. One SMC chain is represented in blue and the other in orange. The vertical lines indicate deviation from the ideal expected value, which is represented with a black dashed line. If a vertical line is above the reference black dashed line we have more samples than expected, if the vertical line is below the sampler is getting less samples than expected. Deviations like the ones in the figure above are fine and not a reason for concern.\n", "\n", "As previously said SMC internally computes an estimation of the ESS (from importance weights). Those ESS values are not useful for diagnostics as they are a fixed target value. We can compute the ESS values from the trace returned by `sample_smc`, but this is also not a very useful diagnostics, as the computation of this ESS value takes autocorrelation into account and each SMC run/chain has low autocorrelation by construction, for most problems the values of ESS will be either very close to the number of total samples (i.e. draws x chains). In general it will only be a low number if each SMC chain explores a different mode, in that case the value of ESS will be close to the number of modes." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Kill your darlings\n", "\n", "SMC is not free of problems, sampling can deteriorate as the dimensionality of the problem increases, in particular for multimodal posterior or _weird_ geometries as in hierarchical models. To some extent increasing the number of draws could help. Increasing the value of the argument `p_acc_rate` is also a good idea. This parameter controls how the number of steps is computed at each stage. To access the number of steps per stage you can check `trace.report.nsteps`. Ideally SMC will take a number of steps lower than `n_steps`. But if the actual number of steps per stage is `n_steps`, for a few stages, this may be signaling that we should also increase `n_steps`. \n", "\n", "Let's see the performance of SMC when we run the same model as before, but increasing the dimensionality from 4 to 80." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "n = 80\n", "\n", "mu1 = np.ones(n) * (1.0 / 2)\n", "mu2 = -mu1\n", "\n", "stdev = 0.1\n", "sigma = np.power(stdev, 2) * np.eye(n)\n", "isigma = np.linalg.inv(sigma)\n", "dsigma = np.linalg.det(sigma)\n", "\n", "w1 = 0.1 # one mode with 0.1 of the mass\n", "w2 = 1 - w1 # the other mode with 0.9 of the mass\n", "\n", "\n", "def two_gaussians(x):\n", " log_like1 = (\n", " -0.5 * n * pt.log(2 * np.pi)\n", " - 0.5 * pt.log(dsigma)\n", " - 0.5 * (x - mu1).T.dot(isigma).dot(x - mu1)\n", " )\n", " log_like2 = (\n", " -0.5 * n * pt.log(2 * np.pi)\n", " - 0.5 * pt.log(dsigma)\n", " - 0.5 * (x - mu2).T.dot(isigma).dot(x - mu2)\n", " )\n", " return pm.math.logsumexp([pt.log(w1) + log_like1, pt.log(w2) + log_like2])" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Initializing SMC sampler...\n", "Sampling 4 chains in 4 jobs\n" ] }, { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\n", "
\n", " \n", " 100.00% [100/100 00:00<00:00 Stage: 37 Beta: 1.000]\n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ " " ] } ], "source": [ "with pm.Model() as model:\n", " X = pm.Uniform(\n", " \"X\",\n", " shape=n,\n", " lower=-2.0 * np.ones_like(mu1),\n", " upper=2.0 * np.ones_like(mu1),\n", " initval=-1.0 * np.ones_like(mu1),\n", " )\n", " llk = pm.Potential(\"llk\", two_gaussians(X))\n", " idata_80 = pm.sample_smc(2000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that SMC recognizes this is a harder problem and increases the number of stages. We can see that SMC still sample from both modes but now the model with higher weight is being oversampled (we get a relative weight of 0.99 instead of 0.9). Notice how the rank plot looks worse than when n=4." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'Estimated w1 = 0.991'" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = az.plot_trace(idata_80, compact=True, kind=\"rank_vlines\")\n", "ax[0, 0].axvline(-0.5, 0, 0.9, color=\"k\")\n", "ax[0, 0].axvline(0.5, 0, 0.1, color=\"k\")\n", "f'Estimated w1 = {np.mean(idata_80.posterior[\"X\"] < 0).item():.3f}'" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You may want to repeat the SMC sampling for n=80, and change one or more of the default parameters too see if you can improve the sampling and how much time the sampler takes to compute the posterior." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Last updated: Tue May 31 2022\n", "\n", "Python implementation: CPython\n", "Python version : 3.9.7\n", "IPython version : 8.3.0\n", "\n", "xarray: 2022.3.0\n", "\n", "sys : 3.9.7 (default, Sep 16 2021, 13:09:58) \n", "[GCC 7.5.0]\n", "arviz : 0.12.0\n", "numpy : 1.21.5\n", "pytensor: 2.6.2\n", "pymc : 4.0.0b6\n", "\n", "Watermark: 2.3.0\n", "\n" ] } ], "source": [ "%load_ext watermark\n", "%watermark -n -u -v -iv -w -p xarray" ] } ], "metadata": { "interpreter": { "hash": "d4ca51fc2fdee62b1a00ff5126f64ae66836e25d3ba6f45d8551026256283997" }, "kernelspec": { "display_name": "Python 3.9.7 ('base')", "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": "3.9.7" } }, "nbformat": 4, "nbformat_minor": 4 }