diff --git a/docs/source/notebooks/Bayes_factor.ipynb b/docs/source/notebooks/Bayes_factor.ipynb index b33efed6c3..5ff368cbe4 100644 --- a/docs/source/notebooks/Bayes_factor.ipynb +++ b/docs/source/notebooks/Bayes_factor.ipynb @@ -16,7 +16,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Running on PyMC3 v3.9.0\n" + "Running on PyMC3 v3.9.1\n" ] } ], @@ -29,7 +29,7 @@ "from scipy.special import betaln\n", "from scipy.stats import beta\n", "\n", - "print('Running on PyMC3 v{}'.format(pm.__version__))" + "print(\"Running on PyMC3 v{}\".format(pm.__version__))" ] }, { @@ -38,7 +38,7 @@ "metadata": {}, "outputs": [], "source": [ - "az.style.use('arviz-darkgrid')" + "az.style.use(\"arviz-darkgrid\")" ] }, { @@ -202,7 +202,7 @@ " alpha, beta = prior\n", " h = np.sum(y)\n", " n = len(y)\n", - " p_y = np.exp(betaln(alpha + h, beta+n-h) - betaln(alpha, beta))\n", + " p_y = np.exp(betaln(alpha + h, beta + n - h) - betaln(alpha, beta))\n", " return p_y" ] }, @@ -230,7 +230,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] @@ -242,11 +242,11 @@ "source": [ "for a, b in priors:\n", " distri = beta(a, b)\n", - " x = np.linspace(0, 1, 100)\n", + " x = np.linspace(0, 1, 300)\n", " x_pdf = distri.pdf(x)\n", - " plt.plot (x, x_pdf, label=r'$\\alpha$ = {:d}, $\\beta$ = {:d}'.format(a, b))\n", + " plt.plot(x, x_pdf, label=r\"$\\alpha$ = {:d}, $\\beta$ = {:d}\".format(a, b))\n", " plt.yticks([])\n", - " plt.xlabel('$\\\\theta$')\n", + " plt.xlabel(\"$\\\\theta$\")\n", " plt.legend()" ] }, @@ -271,7 +271,7 @@ } ], "source": [ - "BF = (beta_binom(priors[1], y) / beta_binom(priors[0], y))\n", + "BF = beta_binom(priors[1], y) / beta_binom(priors[0], y)\n", "print(round(BF))" ] }, @@ -279,7 +279,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We see that the model with the more concentrated prior $Beta(30, 30)$ has $\\approx 5$ times more support than the model with the more extended prior $Beta(1, 1)$. Besides the exact numerical value this should not be surprising since the prior for the most favoured model is concentrated around $\\theta = 0.5$ and the data $y$ has equal number of head and tails, consintent with a value of $\\theta$ around 0.5." + "We see that the model with the more concentrated prior $\\text{beta}(30, 30)$ has $\\approx 5$ times more support than the model with the more extended prior $\\text{beta}(1, 1)$. Besides the exact numerical value this should not be surprising since the prior for the most favoured model is concentrated around $\\theta = 0.5$ and the data $y$ has equal number of head and tails, consintent with a value of $\\theta$ around 0.5." ] }, { @@ -288,7 +288,7 @@ "source": [ "### Sequential Monte Carlo\n", "\n", - "The [Sequential Monte Carlo](SMC2_gaussians.ipynb) sampler is a method that basically progresses by a series of successive interpolated (or *annealed*) sequences from the prior to the posterior. A nice by-product of this process is that we get an estimation of the marginal likelihood. Actually for numerical reasons the returned value is the marginal log likelihood (this helps to avoid underflow)." + "The [Sequential Monte Carlo](SMC2_gaussians.ipynb) sampler is a method that basically progresses by a series of successive *annealed* sequences from the prior to the posterior. A nice by-product of this process is that we get an estimation of the marginal likelihood. Actually for numerical reasons the returned value is the log marginal likelihood (this helps to avoid underflow)." ] }, { @@ -300,25 +300,25 @@ "name": "stderr", "output_type": "stream", "text": [ - "Sample initial stage: ...\n", - "Stage: 0 Beta: 0.090 Steps: 25 Acce: 1.000\n", - "Stage: 1 Beta: 0.735 Steps: 25 Acce: 0.687\n", - "Stage: 2 Beta: 1.000 Steps: 3 Acce: 0.570\n", - "Sample initial stage: ...\n", - "Stage: 0 Beta: 1.000 Steps: 25 Acce: 1.000\n" + "Initializing SMC sampler...\n", + "Multiprocess sampling (2 chains in 2 jobs)\n", + "Stage: 0 Beta: 0.107\n", + "Stage: 1 Beta: 0.843\n", + "Stage: 2 Beta: 1.000\n", + "Initializing SMC sampler...\n", + "Multiprocess sampling (2 chains in 2 jobs)\n", + "Stage: 0 Beta: 1.000\n" ] } ], "source": [ - "n_chains = 1000\n", - "\n", "models = []\n", "traces = []\n", "for alpha, beta in priors:\n", " with pm.Model() as model:\n", - " a = pm.Beta('a', alpha, beta)\n", - " yl = pm.Bernoulli('yl', a, observed=y)\n", - " trace = pm.sample_smc(1000, random_seed=42)\n", + " a = pm.Beta(\"a\", alpha, beta)\n", + " yl = pm.Bernoulli(\"yl\", a, observed=y)\n", + " trace = pm.sample_smc(1000, random_seed=42, parallel=True)\n", " models.append(model)\n", " traces.append(trace)" ] @@ -329,16 +329,21 @@ "metadata": {}, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "5.0\n" - ] + "data": { + "text/plain": [ + "array([5., 5.])" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" } ], "source": [ - "BF_smc = np.exp(models[1].marginal_log_likelihood - models[0].marginal_log_likelihood)\n", - "print(round(BF_smc))" + "BF_smc = np.exp(\n", + " traces[1].report.log_marginal_likelihood - traces[0].report.log_marginal_likelihood\n", + ")\n", + "np.round(BF_smc)" ] }, { @@ -347,7 +352,31 @@ "source": [ "As we can see from the previous cell, SMC gives essentially the same answer as the analytical calculation! \n", "\n", - "The advantage of using SMC is that we can use it to compute the _marginal likelihood_ for a wider range of models as a closed-form expression is no longer needed. The cost we pay for this flexibility is a more expensive computation. We should take into account that for more complex models a more accurate estimation of the _marginal likelihood_ will most likely need a larger number of `draws`. Additionally, a larger number of `n_steps` may help, specially if after stage 1 we notice that SMC uses a number of steps that are close to `n_steps`, i.e. SMC is having trouble to automatically reduce this number. " + "We obtain an array with two values, one per SMC run. As with other samplers PyMC3 attempts to run the sampler more than one time. Having independent samples may help diagnose the performace of the sampler.\n", + "\n", + "The advantage of using SMC to compute the (log) marginal likelihood is that we can use it for a wider range of models as a closed-form expression is no longer needed. The cost we pay for this flexibility is a more expensive computation. Notice that SMC (with a metropolis kernel as implemented in PyMC3) is not as efficient or robust as gradient-based samplers like NUTS. As the dimensionality of the problem increases a more accurate estimation of the posterior and the _marginal likelihood_ will requiere a larger number of `draws`. Additionally, a larger number of `n_steps` may help, specially if after stage 1 we notice that SMC uses a number of steps that are close to `n_steps`, i.e. SMC is having trouble to automatically reduce this number.\n", + "\n", + "You can check the number of steps per stage by doing:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "([8, 9, 11], [8, 9, 11])" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "traces[0].report.nsteps" ] }, { @@ -363,14 +392,14 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "/dependencies/arviz/arviz/data/io_pymc3.py:89: FutureWarning: Using `from_pymc3` without the model will be deprecated in a future release. Not using the model will return less accurate and less useful results. Make sure you use the model argument or call from_pymc3 within a model context.\n", + "/home/osvaldo/proyectos/00_BM/arviz/arviz/data/io_pymc3.py:89: FutureWarning: Using `from_pymc3` without the model will be deprecated in a future release. Not using the model will return less accurate and less useful results. Make sure you use the model argument or call from_pymc3 within a model context.\n", " FutureWarning,\n" ] }, @@ -418,25 +447,25 @@ "a 0.5 0.05 0.41 0.59" ] }, - "execution_count": 9, + "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "az.summary(traces[0], var_names='a', kind='stats').round(2)" + "az.summary(traces[0], var_names=\"a\", kind=\"stats\").round(2)" ] }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "/dependencies/arviz/arviz/data/io_pymc3.py:89: FutureWarning: Using `from_pymc3` without the model will be deprecated in a future release. Not using the model will return less accurate and less useful results. Make sure you use the model argument or call from_pymc3 within a model context.\n", + "/home/osvaldo/proyectos/00_BM/arviz/arviz/data/io_pymc3.py:89: FutureWarning: Using `from_pymc3` without the model will be deprecated in a future release. Not using the model will return less accurate and less useful results. Make sure you use the model argument or call from_pymc3 within a model context.\n", " FutureWarning,\n" ] }, @@ -472,7 +501,7 @@ " a\n", " 0.5\n", " 0.04\n", - " 0.42\n", + " 0.43\n", " 0.57\n", " \n", " \n", @@ -481,16 +510,16 @@ ], "text/plain": [ " mean sd hdi_3% hdi_97%\n", - "a 0.5 0.04 0.42 0.57" + "a 0.5 0.04 0.43 0.57" ] }, - "execution_count": 10, + "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "az.summary(traces[1], var_names='a', kind='stats').round(2)" + "az.summary(traces[1], var_names=\"a\", kind=\"stats\").round(2)" ] }, { @@ -502,14 +531,34 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "traces[0]" + ] + }, + { + "cell_type": "code", + "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "/dependencies/pymc3/pymc3/sampling.py:1618: UserWarning: samples parameter is smaller than nchains times ndraws, some draws and/or chains may not be represented in the returned posterior predictive sample\n", + "/home/osvaldo/proyectos/00_BM/pymc3/pymc3/sampling.py:1618: UserWarning: samples parameter is smaller than nchains times ndraws, some draws and/or chains may not be represented in the returned posterior predictive sample\n", " \"samples parameter is smaller than nchains times ndraws, some draws \"\n" ] }, @@ -530,8 +579,8 @@ " background: #F44336;\n", " }\n", " \n", - " \n", - " 100.00% [100/100 00:01<00:00]\n", + " \n", + " 100.00% [100/100 00:00<00:00]\n", " \n", " " ], @@ -559,8 +608,8 @@ " background: #F44336;\n", " }\n", " \n", - " \n", - " 100.00% [100/100 00:01<00:00]\n", + " \n", + " 100.00% [100/100 00:00<00:00]\n", " \n", " " ], @@ -573,7 +622,7 @@ }, { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -586,13 +635,13 @@ "_, ax = plt.subplots(figsize=(9, 6))\n", "ppc_0 = pm.sample_posterior_predictive(traces[0], 100, models[0], size=(len(y), 20))\n", "ppc_1 = pm.sample_posterior_predictive(traces[1], 100, models[1], size=(len(y), 20))\n", - "for m_0, m_1 in zip(ppc_0['yl'].T, ppc_1['yl'].T):\n", - " az.plot_kde(np.mean(m_0, 0), ax=ax, plot_kwargs={'color':'C0'})\n", - " az.plot_kde(np.mean(m_1, 0), ax=ax, plot_kwargs={'color':'C1'})\n", - "ax.plot([], label='model_0')\n", - "ax.plot([], label='model_1')\n", + "for m_0, m_1 in zip(ppc_0[\"yl\"].T, ppc_1[\"yl\"].T):\n", + " az.plot_kde(np.mean(m_0, 0), ax=ax, plot_kwargs={\"color\": \"C0\"})\n", + " az.plot_kde(np.mean(m_1, 0), ax=ax, plot_kwargs={\"color\": \"C1\"})\n", + "ax.plot([], label=\"model_0\")\n", + "ax.plot([], label=\"model_1\")\n", "ax.legend()\n", - "ax.set_xlabel('$\\\\theta$')\n", + "ax.set_xlabel(\"$\\\\theta$\")\n", "ax.set_yticks([]);" ] }, @@ -605,20 +654,22 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "arviz 0.8.3\n", - "pymc3 3.9.0\n", - "numpy 1.18.5\n", - "last updated: Fri Jun 12 2020 \n", + "arviz 0.8.3\n", + "json 2.0.9\n", + "numpy 1.18.1\n", + "pymc3 3.9.1\n", + "autopep8 1.5\n", + "last updated: Thu Jun 25 2020 \n", "\n", - "CPython 3.7.7\n", - "IPython 7.15.0\n", + "CPython 3.7.6\n", + "IPython 7.12.0\n", "watermark 2.0.2\n" ] } @@ -645,7 +696,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.10" + "version": "3.7.6" } }, "nbformat": 4, diff --git a/docs/source/notebooks/SMC2_gaussians.ipynb b/docs/source/notebooks/SMC2_gaussians.ipynb index 08922df2d3..4721d8d0df 100644 --- a/docs/source/notebooks/SMC2_gaussians.ipynb +++ b/docs/source/notebooks/SMC2_gaussians.ipynb @@ -4,7 +4,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Sequential Monte Carlo with two gaussians" + "# Sequential Monte Carlo" ] }, { @@ -16,81 +16,106 @@ "name": "stdout", "output_type": "stream", "text": [ - "Running on PyMC3 v3.9.0\n" + "Running on PyMC3 v3.9.1\n" ] } ], "source": [ - "import pymc3 as pm\n", - "import numpy as np\n", + "import arviz as az\n", "import matplotlib.pyplot as plt\n", - "\n", + "import numpy as np\n", + "import pymc3 as pm\n", "import theano.tensor as tt\n", - "import shutil\n", "\n", - "plt.style.use('seaborn-darkgrid')\n", - "print('Running on PyMC3 v{}'.format(pm.__version__))" + "print(\"Running on PyMC3 v{}\".format(pm.__version__))" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "az.style.use(\"arviz-darkgrid\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Sampling from $n$-dimensional distributions with multiple peaks with a standard Metropolis-Hastings algorithm can be difficult, if not impossible, as the Markov chain often gets stuck in either of the minima.\n", + "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", - "A Sequential Monte Carlo sampler (SMC) is a way to overcome this problem, or at least to ameliorate it. SMC samplers are very similar to genetic algorithms, which are biologically-inspired algorithms that can be summarized as follows:\n", + "As there are many SMC flavors, in this notebook we will focus on the version implemented in PyMC3.\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", + "SMC combines several statistical ideas, including [importance sampling](https://en.wikipedia.org/wiki/Importance_sampling), tempering and an MCMC kernel. By tempering we mean the use of an auxiliary _temperature_ parameter to control the sampling process. This is easy to see if we 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 to gradually turn-on 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", - "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) to explore the solution space avoiding getting trap in local minima and then apply _selection_ 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", + "A summary of the algorithm is:\n", "\n", - "Moving into the realm of Bayesian statistics each individual is a point in the _posterior space_, mutations can be done in several ways, a general solution is to use a MCMC method (like Metropolis-Hastings) and run many Markov chains in parallel. The _fitness_ is given by the posterior, points with low posterior density will be removed and points high posterior density will be used as the starting point of a next round of Markov chains (This step is known as _reweighting_ in the SMC literature). The size of the population is kept fixed at some predefined value, so if a point is removed some other point should be used to start at least two new Markov chains.\n", + "1. Initialize $\\beta$ at zero and `stage` at zero.\n", + "2. Sample from the prior a set of samples $S_{\\beta}$ of size $N$. When $\\beta = 0$ the tempered posterior is the prior.\n", + "3. Increase $\\beta$ in order to make the effective sample size (ESS) equals some predefined value. We use $Nt$, where $t$ is the threshold parameter -- by default t=0.5. This means that the default ESS is fixed at half the number of draws.\n", + "4. Compute a set of $N$ importance weights $W$. The weights are computed as the ratio of the tempered likelihoods at stage $i+1$ and stage $i$.\n", + "5. Obtain a new set of samples $S_{w}$ by re-sampling $S_{\\beta}$ according to $W$.\n", + "6. Use the $S_{w}$ to compute the covariance for (multivariate)normal proposal distribution.\n", + "7. For stages other than 0 use the acceptance rate from the previous stage to estimate the scaling of the proposal distribution and to compute `nsteps`.\n", + "8. Run $N$ Metropolis chains (each one of length `n_steps`), starting each one from a different sample $S_{w}$.\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 previous paragraph 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 Metropolis steps, starting from the selected/reweighting samples in the second subplot, notice how the two samples with the lower posterior density (smaller circles) are discarded and not used to seed Markov chains.\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 Metropolis 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 Markov chains.\n", "\n", "![SMC stages](https://github.com/pymc-devs/pymc3/raw/master/docs/source/notebooks/smc.png)\n", "\n", - "So far we have that the SMC sampler is just a bunch of parallel Markov chains, not very impressive, right? Well not that fast. SMC proceed by moving _sequentially_ through a series of stages, starting from a simple to sample distribution until it get to the posterior distribution. All this intermediate distribution (or _tempered posterior distributions_) are controlled by _tempering_ parameter called $\\beta$. SMC takes this idea from other _tempering_ methods originated from a branch of physics known as _statistical mechanics_. The idea is as follow the number of accessible states a _real physical_ system can reach is controlled by the temperature, if the temperature is the lowest possible ($0$ Kelvin) the system is trapped in a single state, on the contrary if the temperature is $\\infty$ all states are equally accessible! In the _statistical mechanics_ literature $\\beta$ is know as the inverse temperature, the higher the more constrained the system is. Going back to the Bayesian statistics context a _natural_ analogy to these physical systems is given by the following formula:\n", "\n", - "$$p(\\theta \\mid y)_{\\beta} \\propto p(y \\mid \\theta)^{\\beta} p(\\theta)$$\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", - "When $\\beta = 0$, the _tempered posterior_ is just the prior and when $\\beta=1$ the _tempered posterior_ is the true posterior. SMC starts with $\\beta = 0$ and progress by always increasing the value of $\\beta$, at each stage, until it reach 1. This is represented in the avobe figure by a narrower Gaussian distribution in the third subplot.\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 avoiding 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 PyMC3 the number of chains is the number of draws. 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.\n", + "For the SMC version implemented in PyMC3 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 from the sampling results of the previous intermediate distribution. SMC will try to keep the effective samples size (ESS) constant. Thus, the harder the distribution is to sample the larger the number of stages SMC will take. In other words the _cooling_ will be slow and the successive values of $\\beta$ will change in small steps.\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", - "* The number of steps each Markov chain takes to explore the _tempered posterior_ (`n_steps`) is determined from the acceptance rate at each stage, SMC use a _tune_interval_ to do this.\n", - "* The width of the proposal distribution (`MultivariateProposal`) is also adjusted adaptively based on the acceptance rate at each stage.\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 (co)variance of the (Multivariate)Normal 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. PyMC3 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 $n$-dimensional 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 distributed according to the tempered posterior (due to the re-weighting step).\n", - "* It is inherently parallel." + "* 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 (PyMC4 will take better advantage of this feature)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "To see an example of how to use SMC inside PyMC3 let's define a multivariate gaussian of dimension $n$, their weights and the covariance matrix. " + "## Solving a PyMC3 model with SMC\n", + "\n", + "To see an example of how to use SMC inside PyMC3 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": 2, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "n = 4\n", "\n", - "mu1 = np.ones(n) * (1. / 2)\n", + "mu1 = np.ones(n) * (1.0 / 2)\n", "mu2 = -mu1\n", "\n", "stdev = 0.1\n", @@ -98,83 +123,264 @@ "isigma = np.linalg.inv(sigma)\n", "dsigma = np.linalg.det(sigma)\n", "\n", - "w1 = 0.1\n", - "w2 = (1 - w1)" + "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", + "def two_gaussians(x):\n", + " log_like1 = (\n", + " -0.5 * n * tt.log(2 * np.pi)\n", + " - 0.5 * tt.log(dsigma)\n", + " - 0.5 * (x - mu1).T.dot(isigma).dot(x - mu1)\n", + " )\n", + " log_like2 = (\n", + " -0.5 * n * tt.log(2 * np.pi)\n", + " - 0.5 * tt.log(dsigma)\n", + " - 0.5 * (x - mu2).T.dot(isigma).dot(x - mu2)\n", + " )\n", + " return pm.math.logsumexp([tt.log(w1) + log_like1, tt.log(w2) + log_like2])" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Initializing SMC sampler...\n", + "Multiprocess sampling (2 chains in 2 jobs)\n", + "Stage: 0 Beta: 0.010\n", + "Stage: 1 Beta: 0.028\n", + "Stage: 2 Beta: 0.064\n", + "Stage: 3 Beta: 0.141\n", + "Stage: 4 Beta: 0.300\n", + "Stage: 5 Beta: 0.608\n", + "Stage: 6 Beta: 1.000\n" + ] + } + ], + "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", + " testval=-1.0 * np.ones_like(mu1),\n", + " )\n", + " llk = pm.Potential(\"llk\", two_gaussians(X))\n", + " trace = pm.sample_smc(2000, parallel=True)\n", + " az_trace = az.from_pymc3(trace)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "The PyMC3 model. Note that we are making two gaussians, where one has `w1` (90%) of the mass:" + "We can see from the message that PyMC3 is running two **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": 3, + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "ax = az.plot_trace(az_trace, 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\");" + ] + }, + { + "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.\n", + "\n", + "We can compute ESS values from the trace returned by `sample_smc`, this is probably an overly optimistic value, as the computation of this ESS value takes autocorrelation into account and each SMC run/chain has low autocorrelation by construction." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "az.plot_ess(az_trace);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Kill your darlings\n", + "\n", + "SMC (with a Metropolis kernel) is not free of problems, as it relies on Metropolis it will deteriorate as the dimensionality of the problem increases and/or if the geometry of the posterior is _weird_ as in hierarchical models. To some extent increasing the number of draws and maybe the number of `n_steps` could help. 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`.\n", + "\n", + "Let's make SMC fails spectacularly. We will run the same model as before, but increasing the dimensionality from 4 to 40." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "n = 40\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\n", + "w2 = 1 - w1" + ] + }, + { + "cell_type": "code", + "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "Sample initial stage: ...\n", - "Stage: 0 Beta: 0.010 Steps: 25 Acce: 1.000\n", - "Stage: 1 Beta: 0.029 Steps: 25 Acce: 0.314\n", - "Stage: 2 Beta: 0.067 Steps: 12 Acce: 0.277\n", - "Stage: 3 Beta: 0.146 Steps: 14 Acce: 0.253\n", - "Stage: 4 Beta: 0.303 Steps: 15 Acce: 0.201\n", - "Stage: 5 Beta: 0.623 Steps: 20 Acce: 0.157\n", - "Stage: 6 Beta: 1.000 Steps: 25 Acce: 0.136\n" + "Initializing SMC sampler...\n", + "Multiprocess sampling (2 chains in 2 jobs)\n", + "Stage: 0 Beta: 0.002\n", + "Stage: 1 Beta: 0.004\n", + "Stage: 2 Beta: 0.006\n", + "Stage: 3 Beta: 0.009\n", + "Stage: 4 Beta: 0.012\n", + "Stage: 5 Beta: 0.017\n", + "Stage: 6 Beta: 0.021\n", + "Stage: 7 Beta: 0.027\n", + "Stage: 8 Beta: 0.034\n", + "Stage: 9 Beta: 0.042\n", + "Stage: 10 Beta: 0.052\n", + "Stage: 11 Beta: 0.064\n", + "Stage: 12 Beta: 0.078\n", + "Stage: 13 Beta: 0.097\n", + "Stage: 14 Beta: 0.122\n", + "Stage: 15 Beta: 0.152\n", + "Stage: 16 Beta: 0.191\n", + "Stage: 17 Beta: 0.240\n", + "Stage: 18 Beta: 0.301\n", + "Stage: 19 Beta: 0.373\n", + "Stage: 20 Beta: 0.462\n", + "Stage: 21 Beta: 0.566\n", + "Stage: 22 Beta: 0.693\n", + "Stage: 23 Beta: 0.854\n", + "Stage: 24 Beta: 1.000\n" ] } ], "source": [ "def two_gaussians(x):\n", - " log_like1 = - 0.5 * n * tt.log(2 * np.pi) \\\n", - " - 0.5 * tt.log(dsigma) \\\n", - " - 0.5 * (x - mu1).T.dot(isigma).dot(x - mu1)\n", - " log_like2 = - 0.5 * n * tt.log(2 * np.pi) \\\n", - " - 0.5 * tt.log(dsigma) \\\n", - " - 0.5 * (x - mu2).T.dot(isigma).dot(x - mu2)\n", - " return tt.log(w1 * tt.exp(log_like1) + w2 * tt.exp(log_like2))\n", + " log_like1 = (\n", + " -0.5 * n * tt.log(2 * np.pi)\n", + " - 0.5 * tt.log(dsigma)\n", + " - 0.5 * (x - mu1).T.dot(isigma).dot(x - mu1)\n", + " )\n", + " log_like2 = (\n", + " -0.5 * n * tt.log(2 * np.pi)\n", + " - 0.5 * tt.log(dsigma)\n", + " - 0.5 * (x - mu2).T.dot(isigma).dot(x - mu2)\n", + " )\n", + " return pm.math.logsumexp([tt.log(w1) + log_like1, tt.log(w2) + log_like2])\n", "\n", "\n", "with pm.Model() as model:\n", - " X = pm.Uniform('X',\n", - " shape=n,\n", - " lower=-2. * np.ones_like(mu1),\n", - " upper=2. * np.ones_like(mu1),\n", - " testval=-1. * np.ones_like(mu1))\n", - " llk = pm.Potential('llk', two_gaussians(X))\n", - " trace = pm.sample_smc(2000)" + " 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", + " testval=-1.0 * np.ones_like(mu1),\n", + " )\n", + " llk = pm.Potential(\"llk\", two_gaussians(X))\n", + " trace = pm.sample_smc(2000, parallel=True)\n", + " az_trace = az.from_pymc3(trace)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Plotting the results using the traceplot:" + "We see that SMC recognizes this is a harder problem and increases the number of stages. Unfortunately in this case that is not enough to recover the correct posterior as we can see in the following plot. \n", + "\n", + "Compare this rank plot with the one obtained in the previous example (n=4). The rank plot is telling us that the _blue chain_ is sampling an excess of low parameter values (ranks below 2000) and is failing to sample from high parameter values. The orange-chain is doing the exact opposite. So basically one SMC chain is exploring one mode and the other SMC chain the other, they are failing to mix and to recover the relative weights of each mode." ] }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 9, "metadata": {}, "outputs": [ { - "name": "stderr", - "output_type": "stream", - "text": [ - "/dependencies/arviz/arviz/data/io_pymc3.py:89: FutureWarning: Using `from_pymc3` without the model will be deprecated in a future release. Not using the model will return less accurate and less useful results. Make sure you use the model argument or call from_pymc3 within a model context.\n", - " FutureWarning,\n" - ] - }, + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "az.plot_trace(az_trace, compact=True, kind=\"rank_vlines\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Even when each SMC run has low autocorrelation by construction the ESS value computed by ArviZ may under some circumstances show problems. This example is such a case, here each SMC chain is basically exploring a single mode and missing the other. When this happens the value of ESS_bulk (computed using `az.summary` or `az.ess`) will be close to the number of modes, for this problem we got ~3. We are working on providing an ESS estimation better tailored to the peculiarities of SMC.\n", + "\n", + "As the ESS value may vary across the parameter space. We also recommend to check the behavior of localized version of ESS. We can do this with `plot_ess`. The recommended value for ESS is at least 400 (dashed gray line)." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ { "data": { - "image/png": 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" ] }, "metadata": {}, @@ -182,24 +388,34 @@ } ], "source": [ - "pm.traceplot(trace);" + "az.plot_ess(az_trace, coords={\"X_dim_0\": slice(0, 5)}); # only the first 6 dimensions" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You may want to repeat the SMC sampling with the failing model as you may get different problems each time." ] }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "pymc3 3.9.0\n", - "numpy 1.18.5\n", - "last updated: Fri Jun 12 2020 \n", + "arviz 0.8.3\n", + "numpy 1.18.1\n", + "autopep8 1.5\n", + "json 2.0.9\n", + "pymc3 3.9.1\n", + "last updated: Mon Jun 29 2020 \n", "\n", - "CPython 3.7.7\n", - "IPython 7.15.0\n", + "CPython 3.7.6\n", + "IPython 7.12.0\n", "watermark 2.0.2\n" ] } @@ -226,7 +442,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.7" + "version": "3.7.6" } }, "nbformat": 4, diff --git a/pymc3/smc/sample_smc.py b/pymc3/smc/sample_smc.py index 11200d1fc2..37fb6f94f5 100644 --- a/pymc3/smc/sample_smc.py +++ b/pymc3/smc/sample_smc.py @@ -14,25 +14,37 @@ import time import logging +import warnings +from collections.abc import Iterable +import multiprocessing as mp +import numpy as np + from .smc import SMC +from ..model import modelcontext +from ..backends.base import MultiTrace +from ..parallel_sampling import _cpu_count + +EXPERIMENTAL_WARNING = ( + "Warning: SMC-ABC is an experimental step method and not yet recommended for use in PyMC3!" +) def sample_smc( - draws=1000, + draws=2000, kernel="metropolis", n_steps=25, - parallel=False, start=None, - cores=None, tune_steps=True, p_acc_rate=0.99, threshold=0.5, epsilon=1.0, dist_func="gaussian_kernel", sum_stat="identity", - progressbar=False, model=None, random_seed=-1, + parallel=False, + chains=None, + cores=None, ): r""" Sequential Monte Carlo based sampling @@ -49,15 +61,9 @@ def sample_smc( The number of steps of each Markov Chain. If ``tune_steps == True`` ``n_steps`` will be used for the first stage and for the others it will be determined automatically based on the acceptance rate and `p_acc_rate`, the max number of steps is ``n_steps``. - parallel: bool - Distribute computations across cores if the number of cores is larger than 1. - Defaults to False. start: dict, or array of dict Starting point in parameter space. It should be a list of dict with length `chains`. When None (default) the starting point is sampled from the prior distribution. - cores: int - The number of chains to run in parallel. If ``None`` (default), it will be automatically - set to the number of CPUs in the system. tune_steps: bool Whether to compute the number of steps automatically or not. Defaults to True p_acc_rate: float @@ -75,11 +81,19 @@ def sample_smc( sum_stat: str or callable Summary statistics. Available options are ``indentity``, ``sorted``, ``mean``, ``median``. If a callable is based it should return a number or a 1d numpy array. - progressbar: bool - Flag for displaying a progress bar. Defaults to False. model: Model (optional if in ``with`` context)). random_seed: int random seed + parallel: bool + Distribute computations across cores if the number of cores is larger than 1. + Defaults to False. + cores : int + The number of chains to run in parallel. If ``None``, set to the number of CPUs in the + system, but at most 4. + chains : int + The number of chains to sample. Running independent chains is important for some + convergence statistics. If ``None`` (default), then set to either ``cores`` or 2, whichever + is larger. Notes ----- @@ -126,52 +140,126 @@ def sample_smc( %282007%29133:7%28816%29>`__ """ + _log = logging.getLogger("pymc3") + _log.info("Initializing SMC sampler...") + + if cores is None: + cores = _cpu_count() + + if chains is None: + chains = max(2, cores) + + _log.info(f"Multiprocess sampling ({chains} chains in {cores} jobs)") + + if random_seed == -1: + random_seed = None + if chains == 1 and isinstance(random_seed, int): + random_seed = [random_seed] + if random_seed is None or isinstance(random_seed, int): + if random_seed is not None: + np.random.seed(random_seed) + random_seed = [np.random.randint(2 ** 30) for _ in range(chains)] + if not isinstance(random_seed, Iterable): + raise TypeError("Invalid value for `random_seed`. Must be tuple, list or int") + + if kernel.lower() == "abc": + warnings.warn(EXPERIMENTAL_WARNING) + if len(modelcontext(model).observed_RVs) != 1: + warnings.warn("SMC-ABC only works properly with models with one observed variable") + + params = ( + draws, + kernel, + n_steps, + start, + tune_steps, + p_acc_rate, + threshold, + epsilon, + dist_func, + sum_stat, + model, + ) + + t1 = time.time() + if parallel: + loggers = [_log] + [None] * (chains - 1) + pool = mp.Pool(cores) + results = pool.starmap( + sample_smc_int, [(*params, random_seed[i], i, loggers[i]) for i in range(chains)] + ) + + pool.close() + pool.join() + else: + results = [] + for i in range(chains): + results.append((sample_smc_int(*params, random_seed[i], i, _log))) + + traces, log_marginal_likelihoods, betas, accept_ratios, nsteps = zip(*results) + trace = MultiTrace(traces) + trace.report._n_draws = draws + trace.report._n_tune = 0 + trace.report._t_sampling = time.time() - t1 + trace.report.log_marginal_likelihood = np.array(log_marginal_likelihoods) + trace.report.betas = betas + trace.report.accept_ratios = accept_ratios + trace.report.nsteps = nsteps + + return trace + + +def sample_smc_int( + draws, + kernel, + n_steps, + start, + tune_steps, + p_acc_rate, + threshold, + epsilon, + dist_func, + sum_stat, + model, + random_seed, + chain, + _log, +): + smc = SMC( draws=draws, kernel=kernel, n_steps=n_steps, - parallel=parallel, start=start, - cores=cores, tune_steps=tune_steps, p_acc_rate=p_acc_rate, threshold=threshold, epsilon=epsilon, dist_func=dist_func, sum_stat=sum_stat, - progressbar=progressbar, model=model, random_seed=random_seed, + chain=chain, ) - - t1 = time.time() - _log = logging.getLogger("pymc3") - _log.info("Sample initial stage: ...") stage = 0 + betas = [] + accept_ratios = [] + nsteps = [] smc.initialize_population() smc.setup_kernel() smc.initialize_logp() while smc.beta < 1: smc.update_weights_beta() - _log.info( - "Stage: {:3d} Beta: {:.3f} Steps: {:3d} Acce: {:.3f}".format( - stage, smc.beta, smc.n_steps, smc.acc_rate - ) - ) - smc.resample() + if _log is not None: + _log.info(f"Stage: {stage:3d} Beta: {smc.beta:.3f}") smc.update_proposal() - if stage > 0: - smc.tune() + smc.resample() smc.mutate() + smc.tune() stage += 1 + betas.append(smc.beta) + accept_ratios.append(smc.acc_rate) + nsteps.append(smc.n_steps) - if smc.parallel and smc.cores > 1: - smc.pool.close() - smc.pool.join() - - trace = smc.posterior_to_trace() - trace.report._n_draws = smc.draws - trace.report._n_tune = 0 - trace.report._t_sampling = time.time() - t1 - return trace + return smc.posterior_to_trace(), smc.log_marginal_likelihood, betas, accept_ratios, nsteps diff --git a/pymc3/smc/smc.py b/pymc3/smc/smc.py index a3707dd821..2bf8d92e41 100644 --- a/pymc3/smc/smc.py +++ b/pymc3/smc/smc.py @@ -16,86 +16,61 @@ import numpy as np from scipy.special import logsumexp -from fastprogress.fastprogress import progress_bar -import multiprocessing as mp -import warnings from theano import function as theano_function from ..model import modelcontext, Point -from ..parallel_sampling import _cpu_count -from ..theanof import inputvars, make_shared_replacements -from ..vartypes import discrete_types +from ..theanof import floatX, inputvars, make_shared_replacements, join_nonshared_inputs from ..sampling import sample_prior_predictive -from ..theanof import floatX, join_nonshared_inputs -from ..step_methods.arraystep import metrop_select -from ..step_methods.metropolis import MultivariateNormalProposal from ..backends.ndarray import NDArray -from ..backends.base import MultiTrace - -EXPERIMENTAL_WARNING = ( - "Warning: SMC-ABC methods are experimental step methods and not yet" - " recommended for use in PyMC3!" -) class SMC: def __init__( self, - draws=1000, + draws=2000, kernel="metropolis", n_steps=25, - parallel=False, start=None, - cores=None, tune_steps=True, p_acc_rate=0.99, threshold=0.5, epsilon=1.0, dist_func="absolute_error", sum_stat="Identity", - progressbar=False, model=None, random_seed=-1, + chain=0, ): self.draws = draws self.kernel = kernel self.n_steps = n_steps - self.parallel = parallel self.start = start - self.cores = cores self.tune_steps = tune_steps self.p_acc_rate = p_acc_rate self.threshold = threshold self.epsilon = epsilon self.dist_func = dist_func self.sum_stat = sum_stat - self.progressbar = progressbar self.model = model self.random_seed = random_seed + self.chain = chain self.model = modelcontext(model) if self.random_seed != -1: np.random.seed(self.random_seed) - if self.cores is None: - self.cores = _cpu_count() - self.beta = 0 self.max_steps = n_steps self.proposed = draws * n_steps self.acc_rate = 1 self.acc_per_chain = np.ones(self.draws) - self.model.marginal_log_likelihood = 0 self.variables = inputvars(self.model.vars) - dimension = sum(v.dsize for v in self.variables) - self.scalings = np.ones(self.draws) * min(1, 2.38 ** 2 / dimension) - self.discrete = np.concatenate( - [[v.dtype in discrete_types] * (v.dsize or 1) for v in self.variables] - ) - self.any_discrete = self.discrete.any() - self.all_discrete = self.discrete.all() + self.dimension = sum(v.dsize for v in self.variables) + self.scalings = np.ones(self.draws) * 2.38 / (self.dimension) ** 0.5 + self.weights = np.ones(self.draws) / self.draws + self.log_marginal_likelihood = 0 def initialize_population(self): """ @@ -128,14 +103,11 @@ def setup_kernel(self): Set up the likelihood logp function based on the chosen kernel """ shared = make_shared_replacements(self.variables, self.model) - self.prior_logp = logp_forw([self.model.varlogpt], self.variables, shared) + self.prior_logp_func = logp_forw([self.model.varlogpt], self.variables, shared) if self.kernel.lower() == "abc": - warnings.warn(EXPERIMENTAL_WARNING) - if len(self.model.observed_RVs) != 1: - warnings.warn("SMC-ABC only works properly with models with one observed variable") simulator = self.model.observed_RVs[0] - self.likelihood_logp = PseudoLikelihood( + self.likelihood_logp_func = PseudoLikelihood( self.epsilon, simulator.observations, simulator.distribution.function, @@ -147,24 +119,17 @@ def setup_kernel(self): self.sum_stat, ) elif self.kernel.lower() == "metropolis": - self.likelihood_logp = logp_forw([self.model.datalogpt], self.variables, shared) + self.likelihood_logp_func = logp_forw([self.model.datalogpt], self.variables, shared) def initialize_logp(self): """ initialize the prior and likelihood log probabilities """ - if self.parallel and self.cores > 1: - self.pool = mp.Pool(processes=self.cores) - priors = self.pool.starmap(self.prior_logp, [(sample,) for sample in self.posterior]) - likelihoods = self.pool.starmap( - self.likelihood_logp, [(sample,) for sample in self.posterior] - ) - else: - priors = [self.prior_logp(sample) for sample in self.posterior] - likelihoods = [self.likelihood_logp(sample) for sample in self.posterior] + priors = [self.prior_logp_func(sample) for sample in self.posterior] + likelihoods = [self.likelihood_logp_func(sample) for sample in self.posterior] - self.priors = np.array(priors).squeeze() - self.likelihoods = np.array(likelihoods).squeeze() + self.prior_logp = np.array(priors).squeeze() + self.likelihood_logp = np.array(likelihoods).squeeze() def update_weights_beta(self): """ @@ -173,11 +138,11 @@ def update_weights_beta(self): """ low_beta = old_beta = self.beta up_beta = 2.0 - rN = int(len(self.likelihoods) * self.threshold) + rN = int(len(self.likelihood_logp) * self.threshold) while up_beta - low_beta > 1e-6: new_beta = (low_beta + up_beta) / 2.0 - log_weights_un = (new_beta - old_beta) * self.likelihoods + log_weights_un = (new_beta - old_beta) * self.likelihood_logp log_weights = log_weights_un - logsumexp(log_weights_un) ESS = int(np.exp(-logsumexp(log_weights * 2))) if ESS == rN: @@ -188,13 +153,10 @@ def update_weights_beta(self): low_beta = new_beta if new_beta >= 1: new_beta = 1 - log_weights_un = (new_beta - old_beta) * self.likelihoods + log_weights_un = (new_beta - old_beta) * self.likelihood_logp log_weights = log_weights_un - logsumexp(log_weights_un) - ll_max = np.max(log_weights_un) - self.model.marginal_log_likelihood += ll_max + np.log( - np.exp(log_weights_un - ll_max).mean() - ) + self.log_marginal_likelihood += logsumexp(log_weights_un) - np.log(self.draws) self.beta = new_beta self.weights = np.exp(log_weights) @@ -205,10 +167,11 @@ def resample(self): resampling_indexes = np.random.choice( np.arange(self.draws), size=self.draws, p=self.weights ) + self.posterior = self.posterior[resampling_indexes] - self.priors = self.priors[resampling_indexes] - self.likelihoods = self.likelihoods[resampling_indexes] - self.tempered_logp = self.priors + self.likelihoods * self.beta + self.prior_logp = self.prior_logp[resampling_indexes] + self.likelihood_logp = self.likelihood_logp[resampling_indexes] + self.posterior_logp = self.prior_logp + self.likelihood_logp * self.beta self.acc_per_chain = self.acc_per_chain[resampling_indexes] self.scalings = self.scalings[resampling_indexes] @@ -216,12 +179,12 @@ def update_proposal(self): """ Update proposal based on the covariance matrix from tempered posterior """ - cov = np.cov(self.posterior, bias=False, rowvar=0) + cov = np.cov(self.posterior, ddof=0, aweights=self.weights, rowvar=0) cov = np.atleast_2d(cov) cov += 1e-6 * np.eye(cov.shape[0]) if np.isnan(cov).any() or np.isinf(cov).any(): raise ValueError('Sample covariances not valid! Likely "draws" is too small!') - self.proposal = MultivariateNormalProposal(cov) + self.cov = cov def tune(self): """ @@ -241,56 +204,30 @@ def tune(self): self.proposed = self.draws * self.n_steps def mutate(self): - """ - Perform mutation step, i.e. apply selected kernel - """ - parameters = ( - self.proposal, - self.scalings, - self.any_discrete, - self.all_discrete, - self.discrete, - self.n_steps, - self.prior_logp, - self.likelihood_logp, - self.beta, - ) - if self.parallel and self.cores > 1: - results = self.pool.starmap( - metrop_kernel, - [ - ( - self.posterior[draw], - self.tempered_logp[draw], - self.priors[draw], - self.likelihoods[draw], - draw, - *parameters, - ) - for draw in range(self.draws) - ], + ac_ = np.empty((self.n_steps, self.draws)) + + proposals = ( + np.random.multivariate_normal( + np.zeros(self.dimension), self.cov, size=(self.n_steps, self.draws) ) - else: - iterator = range(self.draws) - if self.progressbar: - iterator = progress_bar(iterator, display=self.progressbar) - results = [ - metrop_kernel( - self.posterior[draw], - self.tempered_logp[draw], - self.priors[draw], - self.likelihoods[draw], - draw, - *parameters, - ) - for draw in iterator - ] - posterior, acc_list, priors, likelihoods = zip(*results) - self.posterior = np.array(posterior) - self.priors = np.array(priors) - self.likelihoods = np.array(likelihoods) - self.acc_per_chain = np.array(acc_list) - self.acc_rate = np.mean(acc_list) + * self.scalings[:, None] + ) + log_R = np.log(np.random.rand(self.n_steps, self.draws)) + + for n_step in range(self.n_steps): + proposal = floatX(self.posterior + proposals[n_step]) + ll = np.array([self.likelihood_logp_func(prop) for prop in proposal]) + pl = np.array([self.prior_logp_func(prop) for prop in proposal]) + proposal_logp = pl + ll * self.beta + accepted = log_R[n_step] < (proposal_logp - self.posterior_logp) + ac_[n_step] = accepted + self.posterior[accepted] = proposal[accepted] + self.posterior_logp[accepted] = proposal_logp[accepted] + self.prior_logp[accepted] = pl[accepted] + self.likelihood_logp[accepted] = ll[accepted] + + self.acc_per_chain = np.mean(ac_, axis=0) + self.acc_rate = np.mean(ac_) def posterior_to_trace(self): """ @@ -301,7 +238,7 @@ def posterior_to_trace(self): with self.model: strace = NDArray(self.model) - strace.setup(lenght_pos, 0) + strace.setup(lenght_pos, self.chain) for i in range(lenght_pos): value = [] size = 0 @@ -309,60 +246,8 @@ def posterior_to_trace(self): shape, new_size = self.var_info[var] value.append(self.posterior[i][size : size + new_size].reshape(shape)) size += new_size - strace.record({k: v for k, v in zip(varnames, value)}) - return MultiTrace([strace]) - - -def metrop_kernel( - q_old, - old_tempered_logp, - old_prior, - old_likelihood, - draw, - proposal, - scalings, - any_discrete, - all_discrete, - discrete, - n_steps, - prior_logp, - likelihood_logp, - beta, -): - """ - Metropolis kernel - """ - deltas = np.squeeze(proposal(n_steps) * scalings[draw]) - - accepted = 0 - for n_step in range(n_steps): - delta = deltas[n_step] - - if any_discrete: - if all_discrete: - delta = np.round(delta, 0).astype("int64") - q_old = q_old.astype("int64") - q_new = (q_old + delta).astype("int64") - else: - delta[discrete] = np.round(delta[discrete], 0) - q_new = floatX(q_old + delta) - else: - q_new = floatX(q_old + delta) - - ll = likelihood_logp(q_new) - pl = prior_logp(q_new) - - new_tempered_logp = pl + ll * beta - - q_old, accept = metrop_select(new_tempered_logp - old_tempered_logp, q_new, q_old) - - if accept: - accepted += 1 - old_prior = pl - old_likelihood = ll - old_tempered_logp = new_tempered_logp - - return q_old, accepted / n_steps, old_prior, old_likelihood + strace.record(point={k: v for k, v in zip(varnames, value)}) + return strace def logp_forw(out_vars, vars, shared): diff --git a/pymc3/tests/test_smc.py b/pymc3/tests/test_smc.py index ba9dd14979..5bb25e0843 100644 --- a/pymc3/tests/test_smc.py +++ b/pymc3/tests/test_smc.py @@ -79,9 +79,9 @@ def test_ml(self): a = pm.Beta("a", alpha, beta) y = pm.Bernoulli("y", a, observed=data) trace = pm.sample_smc(2000) - marginals.append(model.marginal_log_likelihood) + marginals.append(trace.report.log_marginal_likelihood) # compare to the analytical result - assert abs(np.exp(marginals[1] - marginals[0]) - 4.0) <= 1 + assert abs(np.exp(np.mean(marginals[1]) - np.mean(marginals[0])) - 4.0) <= 1 def test_start(self): with pm.Model() as model: