{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import arviz as az\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pymc3 as pm\n", "import theano\n", "\n", "from pymc3.ode import DifferentialEquation\n", "from scipy.integrate import odeint\n", "\n", "plt.style.use(\"seaborn-darkgrid\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# GSoC 2019: Introduction of pymc3.ode API\n", "by [Demetri Pananos](https://dpananos.github.io/posts/2019/08/blog-post-21/)\n", "\n", "Ordinary differential equations (ODEs) are a convenient mathematical framework for modelling the temporal dynamics of a system in disciplines from engineering to ecology. Though most analyses focus on bifurcations and stability of fixed points, parameter and uncertainty estimates are more salient in systems of practical interest, such as population pharmacokinetics and pharmacodynamics.\n", "\n", "\n", "Both parameter estimation and uncertainty propagation are handled elegantly by the Bayesian framework. In this notebook, I showcase how PyMC3 can be used to do inference for differential equations using the `ode` submodule. While the current implementation is quite flexible and well integrated, more complex models can easily become slow to estimate. A new package that integrates the much faster `sundials` package into PyMC3 called `sunode` can be found [here](https://github.com/aseyboldt/sunode). \n", "\n", "\n", "## Catching Up On Differential Equations\n", "\n", "A differential equation is an equation relating an unknown function's derivative to itself. We usually write differentual equations as \n", "\n", "$$ \\mathbf{y}' = f(\\mathbf{y},t,\\mathbf{p}) \\quad \\mathbf{y}(t_0) = \\mathbf{y}_0 $$\n", "\n", "Here, $\\mathbf{y}$ is the unknown function, $t$ is time, and $\\mathbf{p}$ is a vector of parameters. The function $f$ can be either scalar or vector valued.\n", "\n", "Only a small subset of differential equations have an analytical solution. For most differential equations of applied interest, numerical methods must be used to obtain approximate solutions.\n", "\n", "\n", "## Doing Bayesian Inference With Differential Equations\n", "\n", "PyMC3 uses Hamiltonian Monte Carlo (HMC) to obtain samples from the posterior distribution. HMC requires derivatives of the ODE's solution with respect to the parameters $p$. The `ode` submodual automatically computes appropriate derivatives so you don't have to. All you have to do is \n", "\n", "* Write the differential equation as a python function\n", "* Write the model in PyMC3\n", "* Hit the Inference Button $^{\\text{TM}}$\n", "\n", "Let's see how this is done in practice with a small example.\n", "\n", "## A Differential Equation For Freefall\n", "\n", "An object of mass $m$ is brought to some height and allowed to fall freely until it reaches the ground. A differential equation describing the object's speed over time is \n", "\n", "$$ y' = mg - \\gamma y $$\n", "\n", "The force the object experiences in the downwards direction is $mg$, while the force the object experiences in the opposite direction (due to air resistance) is proportional to how fast the object is presently moving. Let's assume the object starts from rest (that is, that the object's initial velocity is 0). This may or may not be the case. To showcase how to do inference on initial conditions, I will first assume the object starts from rest, and then relax that assumption later.\n", "\n", "Data on this object's speed as a function of time is shown below. The data may be noisy because of our measurement tools, or because the object is an irregular shape, thus leading to times during freefall when the object is more/less aerodynamic. Let's use this data to estimate the proportionality constant for air resistance." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# For reproducibility\n", "np.random.seed(20394)\n", "\n", "\n", "def freefall(y, t, p):\n", " return 2.0 * p[1] - p[0] * y[0]\n", "\n", "\n", "# Times for observation\n", "times = np.arange(0, 10, 0.5)\n", "gamma, g, y0, sigma = 0.4, 9.8, -2, 2\n", "y = odeint(freefall, t=times, y0=y0, args=tuple([[gamma, g]]))\n", "yobs = np.random.normal(y, 2)\n", "\n", "fig, ax = plt.subplots(dpi=120)\n", "plt.plot(times, yobs, label=\"observed speed\", linestyle=\"dashed\", marker=\"o\", color=\"red\")\n", "plt.plot(times, y, label=\"True speed\", color=\"k\", alpha=0.5)\n", "plt.legend()\n", "plt.xlabel(\"Time (Seconds)\")\n", "plt.ylabel(r\"$y(t)$\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To specify and ordinary differential equation with pyMC3, use the `DifferentialEquation` class. This class takes as arguments:\n", "\n", "* `func`: A function specifying the differential equation (i.e. $f(\\mathbf{y},t,\\mathbf{p})$).\n", "* `times`: An array of times at which data was observed.\n", "* `n_states`: The dimension of $f(\\mathbf{y},t,\\mathbf{p})$.\n", "* `n_theta`: The dimension of $\\mathbf{p}$.\n", "* `t0`: Optional time to which the initial condition belongs.\n", "\n", "The argument `func` needs to be written as if `y` and `p` are vectors. So even when your model has one state and/or one parameter, you should explicitly write `y[0]` and/or `p[0]`.\n", "\n", "Once the model is specified, we can use it in our pyMC3 model by passing parameters and initial conditions. `DifferentialEquation` returns a flattened solution, so you will need to reshape it to the same shape as your observed data in the model.\n", "\n", "Shown below is a model to estimate $\\gamma$ in the ODE above." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Sequential sampling (2 chains in 1 job)\n", "NUTS: [gamma, sigma]\n" ] }, { "data": { "text/html": [ "\n", "
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"outputs": [ { "data": { "image/png": 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\n", 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\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "with pm.Model() as model2:\n", " sigma = pm.HalfCauchy(\"sigma\", 1)\n", " gamma = pm.Lognormal(\"gamma\", 0, 1)\n", " # A prior on the acceleration due to gravity\n", " g = pm.Lognormal(\"g\", pm.math.log(10), 2)\n", "\n", " # Notice now I have passed g to the odeparams argument\n", " ode_solution = ode_model(y0=[0], theta=[gamma, g])\n", "\n", " Y = pm.Normal(\"Y\", mu=ode_solution, sigma=sigma, observed=yobs)\n", "\n", " prior = pm.sample_prior_predictive()\n", " trace = pm.sample(2000, tune=1000, target_accept=0.9, cores=1)\n", " posterior_predictive = pm.sample_posterior_predictive(trace)\n", "\n", " data = az.from_pymc3(trace=trace, prior=prior, posterior_predictive=posterior_predictive)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "az.plot_posterior(data);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The uncertainty in the acceleration due to gravity has increased our uncertainty in the proportionality constant.\n", "\n", "Finally, we can do inference on the initial condition. If this object was brought to its initial height by an airplane, then turbulent air might have made the airplane move up or down, thereby changing the initial velocity of the object. \n", "\n", "Doing inference on the initial condition is as easy as specifying a prior for the initial condition, and then passing the initial condition to `ode_model`." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Sequential sampling (2 chains in 1 job)\n", "NUTS: [y0, g, gamma, sigma]\n" ] }, { "data": { "text/html": [ "\n", "
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\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "with pm.Model() as model3:\n", " sigma = pm.HalfCauchy(\"sigma\", 1)\n", " gamma = pm.Lognormal(\"gamma\", 0, 1)\n", " g = pm.Lognormal(\"g\", pm.math.log(10), 2)\n", " # Initial condition prior. We think it is at rest, but will allow for perturbations in initial velocity.\n", " y0 = pm.Normal(\"y0\", 0, 2)\n", "\n", " ode_solution = ode_model(y0=[y0], theta=[gamma, g])\n", "\n", " Y = pm.Normal(\"Y\", mu=ode_solution, sigma=sigma, observed=yobs)\n", "\n", " prior = pm.sample_prior_predictive()\n", " trace = pm.sample(2000, tune=1000, target_accept=0.9, cores=1)\n", " posterior_predictive = pm.sample_posterior_predictive(trace)\n", "\n", " data = az.from_pymc3(trace=trace, prior=prior, posterior_predictive=posterior_predictive)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "az.plot_posterior(data, figsize=(13, 3));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that by explicitly modelling the initial condition, we obtain a much better estimate of the acceleration due to gravity than if we had insisted that the object started at rest." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Non-linear Differential Equations\n", "\n", "The example of an object in free fall might not be the most appropriate since that differential equation can be solved exactly. Thus, `DifferentialEquation` is not needed to solve that particular problem. There are, however, many examples of differential equations which cannot be solved exactly. Inference for these models is where `DifferentialEquation` truly shines.\n", "\n", "Consider the SIR model of infection. This model describes the temporal dynamics of a disease spreading through a homogeneously mixed closed population. Members of the population are placed into one of three cateories: Susceptible, Infective, or Recovered. The differential equations are...\n", "\n", "\n", "$$ \\dfrac{dS}{dt} = - \\beta SI \\quad S(0) = S_0 $$\n", "$$ \\dfrac{dI}{dt} = \\beta SI - \\lambda I \\quad I(0) = I_0 $$\n", "$$ \\dfrac{dR}{dt} = \\lambda I \\quad R(0) = R_0 $$\n", "\n", "With the constraint that $S(t) + I(t) + R(t) = 1 \\, \\forall t$. Here, $\\beta$ is the rate of infection per susceptible and per infective, and $\\lambda$ is the rate of recovery.\n", "\n", "If we knew $S(t)$ and $I(t)$, then we could determine $R(t)$, so we can peel off the differential equation for $R(t)$ and work only with the first two. \n", "\n", "\n", "In the SIR model, it is straight-forward to see that $\\beta, \\gamma$ and $\\beta/2, \\gamma/2$ will produce the same qualitative dynamics but on much different time scales. To study the *quality* of the dynamics, regardless of time scale, applied mathematicians will *non-dimensionalize* differential equations. Non-dimensionalization is the process of introducing scaleless variables into the differential equation to understand the system's dynamics under families of equivalent paramterizations.\n", "\n", "To non-dimensionalize this system, let's scale time by $1/\\lambda$ (we do this because people stay infected for an average of $1/\\lambda$ units of time. It is a straight forward argument to show this. For more, see [1]). Let $t = \\tau/\\lambda$, where $\\tau$ is a unitless variable. Then...\n", "\n", "\n", "$$ \\dfrac{dS}{d\\tau} = \\dfrac{dt}{d\\tau} \\dfrac{dS}{dt} = \\dfrac{1}{\\lambda}\\dfrac{dS}{dt} = -\\dfrac{\\beta}{\\lambda}SI$$\n", "\n", "and \n", "\n", "$$ \\dfrac{dI}{d\\tau} = \\dfrac{dt}{d\\tau} \\dfrac{dI}{dt} = \\dfrac{1}{\\lambda}\\dfrac{dI}{dt} = \\dfrac{\\beta}{\\lambda}SI - I$$\n", "\n", "The quantity $\\beta/\\lambda$ has a very special name. We call it *The R-Nought* ($\\mathcal{R}_0$). It's interpretation is that if we were to drop a single infected person into a population of suceptible individuals, we would expect $\\mathcal{R}_0$ new infections. If $\\mathcal{R}_0>1$, then an epidemic will take place. If $\\mathcal{R}_0\\leq1$ then there will be no epidemic (note, we can show this more rigoursly by studying eigenvalues of the system's Jacobain. For more, see [2]).\n", "\n", "This non-dimensionalization is important because it gives us information about the parameters. If we see an epidemic has occurred, then we know that $\\mathcal{R}_0>1$ which means $\\beta> \\lambda$. Furthermore, it might be hard to place a prior on $\\beta$ because of beta's interpretation. But since $1/\\lambda$ has a simple interpretation, and since $\\mathcal{R}_0>1$, we can obtain $\\beta$ by computing $\\mathcal{R}_0\\lambda$. \n", "\n", "Side note: I'm going to choose a likelihood which certainly violates these constraints, just for exposition on how to use `DifferentialEquation`. In reality, a likelihood which respects these constraints should be chosen." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def SIR(y, t, p):\n", " ds = -p[0] * y[0] * y[1]\n", " di = p[0] * y[0] * y[1] - p[1] * y[1]\n", " return [ds, di]\n", "\n", "\n", "times = np.arange(0, 5, 0.25)\n", "\n", "beta, gamma = 4, 1.0\n", "# Create true curves\n", "y = odeint(SIR, t=times, y0=[0.99, 0.01], args=((beta, gamma),), rtol=1e-8)\n", "# Observational model. Lognormal likelihood isn't appropriate, but we'll do it anyway\n", "yobs = np.random.lognormal(mean=np.log(y[1::]), sigma=[0.2, 0.3])\n", "\n", "plt.plot(times[1::], yobs, marker=\"o\", linestyle=\"none\")\n", "plt.plot(times, y[:, 0], color=\"C0\", alpha=0.5, label=f\"$S(t)$\")\n", "plt.plot(times, y[:, 1], color=\"C1\", alpha=0.5, label=f\"$I(t)$\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Sequential sampling (2 chains in 1 job)\n", "NUTS: [lambda, R0, sigma]\n" ] }, { "data": { "text/html": [ "\n", "
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\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "Sampling 2 chains for 1_000 tune and 2_000 draw iterations (2_000 + 4_000 draws total) took 5339 seconds.\n" ] } ], "source": [ "sir_model = DifferentialEquation(\n", " func=SIR,\n", " times=np.arange(0.25, 5, 0.25),\n", " n_states=2,\n", " n_theta=2,\n", " t0=0,\n", ")\n", "\n", "with pm.Model() as model4:\n", " sigma = pm.HalfCauchy(\"sigma\", 1, shape=2)\n", "\n", " # R0 is bounded below by 1 because we see an epidemic has occurred\n", " R0 = pm.Bound(pm.Normal, lower=1)(\"R0\", 2, 3)\n", " lam = pm.Lognormal(\"lambda\", pm.math.log(2), 2)\n", " beta = pm.Deterministic(\"beta\", lam * R0)\n", "\n", " sir_curves = sir_model(y0=[0.99, 0.01], theta=[beta, lam])\n", "\n", " Y = pm.Lognormal(\"Y\", mu=pm.math.log(sir_curves), sigma=sigma, observed=yobs)\n", "\n", " trace = pm.sample(2000, tune=1000, target_accept=0.9, cores=1)\n", " data = az.from_pymc3(trace=trace)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/dependencies/arviz/arviz/utils.py:654: UserWarning: Keyword argument credible_interval has been deprecated Please replace with hdi_prob\n", " (\"Keyword argument credible_interval has been deprecated \" \"Please replace with hdi_prob\"),\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "az.plot_posterior(data, round_to=2, credible_interval=0.95);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As can be seen from the posterior plots, $\\beta$ is well estimated by leveraging knoweldege about the non-dimensional parameter $\\mathcal{R}_0$ and $\\lambda$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conclusions & Final Thoughts\n", "\n", "ODEs are a really good model for continuous temporal evolution. With the addition of `DifferentialEquation` to PyMC3, we can now use bayesian methods to estimate the parameters of ODEs.\n", "\n", "`DifferentialEquation` is not as fast as compared to Stan's `integrate_ode_bdf`. However, the ease of use of `DifferentialEquation` will allow practitioners to get up and running much quicker with Bayesian estimation for ODEs than Stan (which has a steep learning curve)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "1. Earn, D. J., et al. Mathematical epidemiology. Berlin: Springer, 2008.\n", "2. Britton, Nicholas F. Essential mathematical biology. Springer Science & Business Media, 2012." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "arviz 0.8.3\n", "theano 1.0.4\n", "pymc3 3.9.0\n", "numpy 1.18.5\n", "last updated: Mon Jun 15 2020 \n", "\n", "CPython 3.7.7\n", "IPython 7.15.0\n", "watermark 2.0.2\n" ] } ], "source": [ "%load_ext watermark\n", "%watermark -n -u -v -iv -w" ] } ], "metadata": { "kernelspec": { "display_name": "pymc-dev", "language": "python", "name": "pymc-dev" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.7" } }, "nbformat": 4, "nbformat_minor": 4 }