Last active
January 21, 2018 18:03
-
-
Save benbovy/618bce9d2beb84f1affa816b3c127ff3 to your computer and use it in GitHub Desktop.
Inference on Fastscape parameters using PyMC3
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
{ | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# Inference of Fastscape parameters using PyMC3\n", | |
"\n", | |
"Following a bayesian approach, [PyMC3](https://github.com/pymc-devs/pymc3) is a Python package that implements with an expressive API various powerful algorithms such as Monte Carlo Markov Chain (MCMC) samplers or variational inference methods for solving a wide range of inference problems.\n", | |
"\n", | |
"Here we use it to make inference on a few parameters of the Fastscape model (test case). " | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 1, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"import numpy as np\n", | |
"from scipy.stats import ks_2samp\n", | |
"import pymc3 as pm\n", | |
"import theano\n", | |
"import theano.tensor as tt\n", | |
"\n", | |
"import xsimlab\n", | |
"import xtopo\n", | |
"from xtopo.models.fastscape_base import fastscape_base_model\n", | |
"\n", | |
"%matplotlib inline" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 2, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"xsimlab: 0.1.1+2.g857d38b.dirty\n", | |
"xtopo: v0.0.10\n" | |
] | |
} | |
], | |
"source": [ | |
"print('xsimlab:', xsimlab.__version__)\n", | |
"print('xtopo:', xtopo.__version__)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## A simple test case\n", | |
"\n", | |
"As a test case, set \"true\" values for two free parameters: stream power law coefficient $K$ and uplift rate $U$:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 4, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"k_sp_true = 5e-5\n", | |
"u_rate_true = 5e-4" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"The following variables have fixed values for all fastscape simulations:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 3, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"x_size = 101\n", | |
"y_size = 101\n", | |
"spacing = 200.\n", | |
"\n", | |
"time_step = 1e5\n", | |
"time_total = 1e7\n", | |
"\n", | |
"np.random.seed(1234)\n", | |
"init_topography = np.random.rand(y_size, x_size)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"The function belows runs Fastscape (without diffusion). It takes free parameter values and returns flattened arrays of elevation and drainage area at the end of the simulation:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 5, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"fs_model = fastscape_base_model.drop_processes('diffusion')\n", | |
"\n", | |
"\n", | |
"def run_fastscape(k_sp, u_rate):\n", | |
" in_ds = xsimlab.create_setup(\n", | |
" model=fs_model,\n", | |
" clocks={'time': {'end': time_total, 'step': time_step}},\n", | |
" input_vars={\n", | |
" 'grid': {'x_size': x_size, 'y_size': y_size,\n", | |
" 'x_spacing': spacing, 'y_spacing': spacing},\n", | |
" 'flow_routing': {'pit_method': 'mst_linear'},\n", | |
" 'block_uplift': {'u_coef': u_rate},\n", | |
" 'spower': {'k_coef': k_sp, 'm_exp': 0.4, 'n_exp': 1},\n", | |
" 'topography': {'elevation': (('y', 'x'), init_topography)}\n", | |
" },\n", | |
" snapshot_vars={\n", | |
" None: {'topography': 'elevation', 'area': 'area'},\n", | |
" }\n", | |
" )\n", | |
"\n", | |
" out_ds = in_ds.xsimlab.run(model=fs_model)\n", | |
"\n", | |
" return (out_ds.topography__elevation.values.flatten(),\n", | |
" out_ds.area__area.values.flatten())\n" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"We execute this function using the \"true\" parameter values set above to generate some \"ground truth\", i.e., observed distributions of elevation and drainage area:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 6, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"elevation_observed, area_observed = run_fastscape(k_sp_true, u_rate_true)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Next we need to write a custom function for the likelihood, which we define here as inversely proportional to the product of Kolmogorov-Smirnov (K-S) statistics that measure how similar are observed vs. modelled distributions of elevation and drainage area, respectively. The expression of the likelihood might certainly be improved, but for clarity we prefer to keep it simple here. \n", | |
"\n", | |
"(see further below for why we need to use the `@theano.compile.ops.as_op` decorator)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 7, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"@theano.compile.ops.as_op(itypes=[tt.dscalar, tt.dscalar],\n", | |
" otypes=[tt.dscalar])\n", | |
"def likelihood(k_sp, u_rate):\n", | |
" elevation, area = run_fastscape(k_sp, u_rate)\n", | |
"\n", | |
" ks_prod = np.prod([ks_2samp(elevation, elevation_observed).statistic,\n", | |
" ks_2samp(area, area_observed).statistic])\n", | |
" \n", | |
" return np.array(1. / ks_prod)\n" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"With a few lines of code, we complete our probabilistic model by setting uniform prior distributions for each of the free parameters and then we draw samples from the posterior distribution using the Metropolis-Hastings algorithm, starting from an approximation of the best fit model:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 8, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stderr", | |
"output_type": "stream", | |
"text": [ | |
"Warning: gradient not available.(E.g. vars contains discrete variables). MAP estimates may not be accurate for the default parameters. Defaulting to non-gradient minimization 'Powell'.\n", | |
"logp = 25.937: 100%|██████████| 130/130 [00:22<00:00, 5.69it/s] \n", | |
"100%|██████████| 1500/1500 [23:21<00:00, 1.07it/s]\n" | |
] | |
} | |
], | |
"source": [ | |
"with pm.Model() as model:\n", | |
" \n", | |
" # set uniform prior probabilities for the free parameters\n", | |
" k_sp = pm.Uniform('k_sp', lower=1e-5, upper=1e-4)\n", | |
" u_rate = pm.Uniform('u_rate', lower=1e-4, upper=1e-3)\n", | |
" \n", | |
" loglike = pm.Potential('loglike', tt.log(likelihood(k_sp, u_rate)))\n", | |
" \n", | |
" start = pm.find_MAP()\n", | |
" step = pm.Metropolis()\n", | |
" \n", | |
" trace = pm.sample(1000, start=start, step=step, njobs=2)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Show inference results with plots (marginal distributions + traces) and summary (bayesian credible intervals) of the sampled posterior:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 12, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"\n", | |
"k_sp:\n", | |
"\n", | |
" Mean SD MC Error 95% HPD interval\n", | |
" -------------------------------------------------------------------\n", | |
" \n", | |
" 0.00006 0.00002 0.00000 [0.00003, 0.00010]\n", | |
"\n", | |
" Posterior quantiles:\n", | |
" 2.5 25 50 75 97.5\n", | |
" |--------------|==============|==============|--------------|\n", | |
" \n", | |
" 0.00002 0.00005 0.00006 0.00008 0.00010\n", | |
"\n", | |
"\n", | |
"u_rate:\n", | |
"\n", | |
" Mean SD MC Error 95% HPD interval\n", | |
" -------------------------------------------------------------------\n", | |
" \n", | |
" 0.00056 0.00019 0.00001 [0.00015, 0.00091]\n", | |
"\n", | |
" Posterior quantiles:\n", | |
" 2.5 25 50 75 97.5\n", | |
" |--------------|==============|==============|--------------|\n", | |
" \n", | |
" 0.00018 0.00045 0.00054 0.00069 0.00094\n", | |
"\n" | |
] | |
}, | |
{ | |
"data": { | |
"image/png": "iVBORw0KGgoAAAANSUhEUgAAA1gAAAEYCAYAAABBWFftAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nE/8fG6jMy91vcZQAAAAASUVORK5CYII=\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x1277cad30>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"pm.traceplot(trace)\n", | |
"pm.summary(trace, roundto=5)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Evaluation of using PyMC3 for our inference problem\n", | |
"\n", | |
"*PROS*\n", | |
"\n", | |
"- We have implemented our inference problem (setup + run + plot/summary) with a very few lines of readable code.\n", | |
"- PyMC3 has many features (samplers, distributions, transforms) and an expressive API for flexible formulation of the inference problem. For example, we might easily introduce discrete variables (e.g., a flag for single-flow vs. multiple-flow routing?) in the probabilistic model.\n", | |
"- PyMC3 is a-priori extensible. We might investigate the possibility of adding the [Neighborhood Algorithm](http://onlinelibrary.wiley.com/doi/10.1046/j.1365-246X.1999.00876.x/abstract) (NA) as an alternative sampler (or ensemble sampler?), if the latter presents a clear advantage over other samplers (at-least for some cases) or for legacy purpose.\n", | |
"\n", | |
"*CONS*\n", | |
"\n", | |
"- Although it doesn't represent a huge obtacle, the dependency of PyMC3 on Theano is overkill and not very useful for our problem (see here below).\n", | |
"- Theano is no longer maintained.\n", | |
"\n", | |
"*Note on the Theano dependency in PyMC3*\n", | |
"\n", | |
"`PyMC3` implements powerful, gradient-based MCMC samplers (e.g., NUTS or HMC), for which the gradient of the posterior probability does not need to have an explicit expression but instead can be calculated automatically (using symbolic or automatic differentation). `PyMC3` delegates this task to the [theano](https://github.com/Theano/Theano) library. Consequently, all variables of a `PyMC3` probabilistic model must be `theano` variable objects (see below). Unfortunately, both the Fastscape implementation and the function used to compute the K-S statistics (taken from the `scipy.stats` package) are not directly compatible with `theano`. Fortunately, the `@theano.compile.ops.as_op()` decorator allows us to convert our likelihood function as a `theano` operator, but it doesn't support automatic differentiation. Given that we cannot manually derive an expression for the gradient of our likelihood we can't use gradient-based samplers here, unless we implement Fastscape (+ the computation of the K-S statistics) using exclusively `theano` operations (*), which would represent too much work (if it's possible). We can still use the gradient-free samplers implemented in `PyMC3` (e.g., Metropolis-Hastings, Slice, [SMC](http://docs.pymc.io/notebooks/SMC2_gaussians.html?highlight=smc)), though.\n", | |
"\n", | |
"(*) TODO: explore the possibility of using [autograd](https://github.com/HIPS/autograd) (automatic differentiation for native Python and Numpy code) and embedding it in a `theano.Op` subclass (instead of using the `as_op` decorator). This sounds very hacky and performances may be poor, though. UPDATE: after reading autograd's tutorial, that would be very very tricky, if even possible.\n", | |
"\n", | |
"*Note on MCMC samplers available in PyMC2/3*\n", | |
"\n", | |
"See [here](http://twiecki.github.io/blog/2014/01/02/visualizing-mcmc/) and [here](https://healthyalgorithms.com/2011/01/28/mcmc-in-python-pymc-step-methods-and-their-pitfalls/) for animations showing how and why MCMC perform well/badly in some situations. " | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Alternative options in Python that may be relevant\n", | |
"\n", | |
"- [Edward](https://github.com/blei-lab/edward): like PyMC3, it also provides tools for MCMC sampling and variational inference (it seems less featured than PyMC3 for MCMC but more featured for variational inference). Unlike PyMC3/Theano, it is built on top of [TensorFlow](https://www.tensorflow.org/), which still lead to the same king of obstacle, i.e., here it would need our likelihood (+ forward model) to be fully expressed as a tensorflow computation graph. Like Theano's `as_op` decorator, `tf.py_func` can be used to warp any Python code as a tensorflow operator, but it has limitations (not serializable). Note: recently edward has been [integrated in tensorflow](https://discourse.edwardlib.org/t/edward-is-officially-moving-into-tensorflow/387).\n", | |
"\n", | |
"- [Emcee](https://github.com/dfm/emcee): implements an affine-invariant ensemble sampler for MCMC (gradient-free), which is known to work well with degenerate, multi-dimensional distributions (see, e.g., [this notebook](https://gist.github.com/benbovy/b40a777c2d52426a3821) for a comparaison of emcee and the NA algorithm for sampling a distribution with high covariances). However, this package only provides the sampler and currently lacks the model specification capabilities and probability distributions that PyMC3 offers. There is [ongoing work](https://github.com/pymc-devs/pymc3/pull/2253) to add this sampler to PyMC3, though.\n", | |
"\n", | |
"- Likelihood-free inference (may be helpful for inference of more advanced landscape evolution models for which the likelihood may become intractable): [elfi](https://github.com/elfi-dev/elfi) or [carl](https://github.com/diana-hep/carl).\n", | |
"\n", | |
"- May be related: [pomegranate](https://github.com/jmschrei/pomegranate), [hmmlearn](https://github.com/hmmlearn/hmmlearn), with scikit-learn compatible API." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": {}, | |
"outputs": [], | |
"source": [] | |
} | |
], | |
"metadata": { | |
"kernelspec": { | |
"display_name": "Python [conda env:fastscape_py36]", | |
"language": "python", | |
"name": "conda-env-fastscape_py36-py" | |
}, | |
"language_info": { | |
"codemirror_mode": { | |
"name": "ipython", | |
"version": 3 | |
}, | |
"file_extension": ".py", | |
"mimetype": "text/x-python", | |
"name": "python", | |
"nbconvert_exporter": "python", | |
"pygments_lexer": "ipython3", | |
"version": "3.6.4" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 2 | |
} |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment