{ "cells": [ { "cell_type": "markdown", "id": "12b428e4", "metadata": {}, "source": [ "# Bayesian inference for differentiable agent-based models with variational inference\n", "\n", "In this tutorial, we will discuss how model gradients - provided by implementing agent-based models (ABMs) in differentiable programming languages - can help with certain calibration and optimisation tasks. In particular, we will use the [blackbirds](https://github.com/arnauqb/blackbirds) package [1] to calibrate an ABM using generalised variational inference (GVI). \n", "Let's start by providing a short introduction to GVI. Given an ABM with parameters $\\theta$, observed data $y$, a prior distribution $\\pi$ over the parameters, a loss function $\\ell$ that captures the discrepancy between the behaviour of the ABM at parameter values $\\theta$ and data $y$, and a positive real hyperparameter $w > 0$, the goal of GVI is to approximate the generalised posterior distribution \n", "\n", "$$\n", "\\pi(\\theta|y) \\propto \\exp(-\\ell(\\theta, y)/w)\\pi(\\theta) \n", "$$\n", "\n", "with a simpler distribution $q_\\phi(\\theta)$, which is parameterized by parameters $\\phi$. The choice $\\ell(\\theta, y) = - \\log p(y | \\theta)$ and $w = 1$ corresponds to classical Bayesian inference (i.e., the posterior $\\pi(\\theta|y) \\propto p(y | \\theta)\\pi(\\theta)$).\n", "\n", "We can define the best fitting distribution $q_\\phi^*(\\theta)$ as the one with parameters $\\phi^*$ that minimises the Kullback-Leibler divergence $D$ from $q_\\phi(\\theta)$ to $\\pi(\\theta|y)$.\n", "\n", "Then, the optimal $q_\\phi^*$ is given by \n", "\n", "$$\n", "q_\\phi^*(\\theta) = \\arg\\min_\\phi \\left\\{ \\mathbb E_{q_\\phi(\\theta)} \\left[ \\ell (\\theta, y)/w \\right] + D(q_\\phi || \\pi) \\right\\}.\n", "$$\n", "\n", "Luckily, we do not need to worry too much about the details of the optimization process, as the `blackbirds` package takes care of that for us. We only need to provide the ABM (implemented in PyTorch, potentially with suitably defined surrogate gradients), the observed data, and the prior distribution over the parameters. Let's see how this works in practice.\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "fc4f65f2", "metadata": {}, "outputs": [], "source": [ "#!pip install blackbirds" ] }, { "cell_type": "code", "execution_count": 1, "id": "94f3f11e", "metadata": {}, "outputs": [], "source": [ "import torch\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "from blackbirds.infer.vi import VI" ] }, { "cell_type": "markdown", "id": "ff8577d9", "metadata": {}, "source": [ "# 2. Simple example: Bayesian inference for a Bernoulli random walk model\n", "\n", "In the previous tutorial we implemented a differentiable random walk model with discrete steps. We reimplement this below:" ] }, { "cell_type": "code", "execution_count": 2, "id": "9c53fb93", "metadata": {}, "outputs": [], "source": [ "def random_walk(theta, n_timesteps, tau=0.5):\n", " x = torch.tensor([0.0])\n", " for i in range(n_timesteps - 1):\n", " logits = torch.hstack((theta, 1 - theta)).log()\n", " xi = torch.nn.functional.gumbel_softmax(logits, tau=tau, hard=True)[0]\n", " next_x = x[-1] + 2 * xi - 1\n", " x = torch.hstack((x, next_x))\n", " return x\n", "\n", "def logit_random_walk(logit_theta, n_timesteps, tau=0.5):\n", " return random_walk(torch.sigmoid(logit_theta), n_timesteps, tau)" ] }, { "cell_type": "markdown", "id": "98e33310", "metadata": {}, "source": [ "Let's generate some synthetic data and use the `blackbirds` package to calibrate the model." ] }, { "cell_type": "code", "execution_count": 3, "id": "3169f4f6", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Generate synthetic data\n", "n_timesteps = 100\n", "theta_true = torch.tensor([0.2])\n", "x_true = random_walk(theta_true, n_timesteps)\n", "fig, ax = plt.subplots()\n", "ax.plot(x_true, label='True')" ] }, { "cell_type": "markdown", "id": "a39fa97f", "metadata": {}, "source": [ "Let's take a Gaussian prior over $\\theta$:" ] }, { "cell_type": "code", "execution_count": 4, "id": "67a0f8e9", "metadata": {}, "outputs": [], "source": [ "prior = torch.distributions.Normal(torch.logit(torch.tensor(0.9)), 1.0)" ] }, { "cell_type": "markdown", "id": "222fd046", "metadata": {}, "source": [ "Let's also take a Gaussian variational family with learnable mean and variance:" ] }, { "cell_type": "code", "execution_count": 5, "id": "bbfe5382", "metadata": {}, "outputs": [], "source": [ "class TrainableGaussian(torch.nn.Module):\n", " def __init__(self):\n", " super().__init__()\n", " self.mu = torch.nn.Parameter(torch.zeros(1))\n", " self.sigma = torch.nn.Parameter(torch.ones(1))\n", "\n", " def sample(self, n):\n", " sigma = torch.clamp(self.sigma**2, 1e-2, 1e6)\n", " dist = torch.distributions.Normal(self.mu, sigma)\n", " theta = dist.rsample((n,))\n", " logprob = dist.log_prob(theta)\n", " return theta, logprob\n", "\n", " def log_prob(self, *args):\n", " sigma = torch.clamp(self.sigma**2, 1e-2, 1e6)\n", " dist = torch.distributions.Normal(self.mu, sigma)\n", " logprob = dist.log_prob(*args)\n", " return logprob" ] }, { "cell_type": "markdown", "id": "1606967f", "metadata": {}, "source": [ "Finally, for the sake of demonstration, let's take the energy distance\n", "\n", "$$\n", " \\ell(\\theta, y) = 2\\mathbb{E}_{x \\sim \\mathbb{P}_{\\theta}, y \\sim \\mathbb{P}_{*}}\\left[|| x - y ||\\right] - \\mathbb{E}_{y, y' \\sim \\mathbb{P}_{*}}\\left[|| y - y' ||\\right] - \\mathbb{E}_{x, x' \\sim \\mathbb{P}_{\\theta}}\\left[|| x - x' ||\\right]\n", "$$\n", "\n", "between the distributions $\\mathbb{P}_{\\theta}$ and $\\mathbb{P}_{^*}$ over simulated and true increments, respectively, as our loss function:" ] }, { "cell_type": "code", "execution_count": 6, "id": "465ed2a3", "metadata": {}, "outputs": [], "source": [ "def loss(logit_theta, y):\n", " x = logit_random_walk(logit_theta, n_timesteps)\n", " x_diff = x.diff().unsqueeze(-1)\n", " y_diff = y.diff().unsqueeze(-1)\n", " xx = torch.cdist(x_diff, x_diff, p=1.0).sum() / ((n_timesteps - 1)**2 - (n_timesteps - 1))\n", " yx = torch.cdist(y_diff, x_diff, p=1.0).mean()\n", " total = 2*yx - xx # We omit the final term since this is constant with respect to theta\n", " return total" ] }, { "cell_type": "markdown", "id": "5789247d", "metadata": {}, "source": [ "Let's approximate the posterior:" ] }, { "cell_type": "code", "execution_count": 7, "id": "7586b4e3", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ " 56%|████████████████████████████████████████████████▉ | 556/1000 [02:27<01:57, 3.77it/s, loss=2.1, reg.=0.123, total=2.23, best loss=1.92, epochs since improv.=100]\n" ] } ], "source": [ "torch.manual_seed(0)\n", "q = TrainableGaussian()\n", "optimizer = torch.optim.Adam(q.parameters(), lr=5e-3)\n", "vi = VI(loss,\n", " posterior_estimator=q,\n", " prior=prior,\n", " optimizer=optimizer,\n", " w = 1, # this is a relative weight between the loss and the KL term\n", " n_samples_per_epoch=30\n", " )\n", "vi.run(x_true, n_epochs=1000, max_epochs_without_improvement=100)" ] }, { "cell_type": "markdown", "id": "4b88d2e2", "metadata": {}, "source": [ "Finally, let's get samples from the posterior we learned from the variational procedure:" ] }, { "cell_type": "code", "execution_count": 9, "id": "fd737f50", "metadata": {}, "outputs": [], "source": [ "N_SAMPLES = 10_000\n", "q.load_state_dict(vi.best_estimator_state_dict)\n", "posterior_samples, posterior_sample_log_probs = q.sample(N_SAMPLES)" ] }, { "cell_type": "markdown", "id": "da692fd5", "metadata": {}, "source": [ "We can estimate the same posterior with standard Monte Carlo, to check how accurate it is (note: this method does not use gradients):" ] }, { "cell_type": "code", "execution_count": 11, "id": "ce5794e1", "metadata": {}, "outputs": [], "source": [ "torch.manual_seed(0)\n", "prior_samples = prior.sample((N_SAMPLES,))\n", "losses = torch.tensor([loss(prior_samples[i], x_true) for i in range(prior_samples.shape[0])])\n", "log_weight_norm = torch.logsumexp(-losses, 0)\n", "weights = torch.exp(-losses - log_weight_norm)\n", "true_post_samples = prior_samples[torch.distributions.Categorical(weights).sample((N_SAMPLES,))]" ] }, { "cell_type": "markdown", "id": "061ee8bc", "metadata": {}, "source": [ "Now let's compare everything with some plots:" ] }, { "cell_type": "code", "execution_count": 12, "id": "e8cdfebc", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.hist(true_post_samples.reshape(-1).numpy(), alpha=0.1, label=\"True posterior\",\n", " bins=100, color='b', density=True)\n", "plt.hist(posterior_samples.detach().reshape(-1).numpy(), \n", " bins=100, alpha=0.1, color='r', label=\"Variational posterior\", density=True);\n", "plt.hist(prior_samples.reshape(-1).numpy(), \n", " bins=100, alpha=0.1, color='g', label=\"Prior\", density=True);\n", "plt.legend()" ] }, { "cell_type": "markdown", "id": "78c075ba", "metadata": {}, "source": [ "We can repeat the variational procedure with a score-based gradient, instead of pathwise:" ] }, { "cell_type": "code", "execution_count": 13, "id": "6869d8c0", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ " 56%|████████████████████████████████████████████████▎ | 556/1000 [00:40<00:32, 13.67it/s, loss=2.01, reg.=0.238, total=2.25, best loss=1.93, epochs since improv.=100]\n" ] } ], "source": [ "torch.manual_seed(0)\n", "q = TrainableGaussian()\n", "optimizer = torch.optim.Adam(q.parameters(), lr=5e-3)\n", "vi = VI(loss,\n", " posterior_estimator=q,\n", " prior=prior,\n", " optimizer=optimizer,\n", " w = 1, # this is a relative weight between the loss and the KL term\n", " n_samples_per_epoch=30,\n", " gradient_estimation_method='score'\n", " )\n", "vi.run(x_true, n_epochs=1000, max_epochs_without_improvement=100)" ] }, { "cell_type": "code", "execution_count": 19, "id": "a96744b6", "metadata": {}, "outputs": [], "source": [ "q.load_state_dict(vi.best_estimator_state_dict)\n", "score_posterior_samples, _ = q.sample(N_SAMPLES)" ] }, { "cell_type": "code", "execution_count": 20, "id": "d1df7ee2", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.hist(true_post_samples.reshape(-1).numpy(), alpha=0.1, label=\"True posterior\",\n", " bins=100, color='b', density=True)\n", "plt.hist(score_posterior_samples.detach().reshape(-1).numpy(), \n", " bins=100, alpha=0.1, color='purple', label=\"Variational post. (score)\", density=True);\n", "plt.hist(prior_samples.reshape(-1).numpy(), \n", " bins=100, alpha=0.1, color='g', label=\"Prior\", density=True);\n", "plt.legend(loc='upper left')" ] }, { "cell_type": "markdown", "id": "169c00a8", "metadata": {}, "source": [ "We can assess the accuracy by looking at a distance, such as the energy distance, between the (approximate) ground-truth posterior and variational posteriors:" ] }, { "cell_type": "code", "execution_count": 16, "id": "4af48dcc", "metadata": {}, "outputs": [], "source": [ "def ed(x, y):\n", " Bx, By = x.shape[0], y.shape[0]\n", " xx = torch.cdist(x, x, p=1.0).sum() / (Bx**2 - Bx)\n", " yy = torch.cdist(y, y, p=1.0).sum() / (By**2 - By)\n", " yx = torch.cdist(y, x, p=1.0).mean()\n", " total = 2*yx - xx - yy\n", " return total" ] }, { "cell_type": "code", "execution_count": 17, "id": "7c2953f5", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "tensor(0.0042)" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ed(true_post_samples.unsqueeze(-1), posterior_samples).detach()" ] }, { "cell_type": "code", "execution_count": 18, "id": "d34dfa37", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "tensor(0.0289)" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ed(true_post_samples.unsqueeze(-1), score_posterior_samples).detach()" ] }, { "cell_type": "markdown", "id": "2a787026", "metadata": {}, "source": [ "In this case, the pathwise gradient has given us a better posterior (in the sense that the score-based gradient has given us a larger energy distance to the approximate ground-truth posterior)." ] }, { "cell_type": "markdown", "id": "b6f630aa", "metadata": {}, "source": [ "# 3. More complicated example: ABM of clustered volatility in financial markets" ] }, { "cell_type": "markdown", "id": "0ba72da5", "metadata": {}, "source": [ "We now consider a second more complicated example, which we take from our ICAIF 2023 paper on \"Gradient-assisted calibration for financial agent-based models\" (Dyer et al., 2023). (Further experiments from this paper available in [this repository](https://github.com/joelnmdyer/gradient_assisted_calibration_abm/tree/main).)\n", "\n", "In this model, a collection of $N$ agents trade a single asset over time steps $t = 1, \\ldots, T$, where the price of the asset at time $t$ is written $S_t$. At time $t$, agent $i$ submits an order, which can take on three different possible values; buy and sell are represented with $\\rho_i(t) = 1$ and $−1$, respectively; $\\rho_i(t) = 0$ means that agent $i$ is inactive at this time. \n", "\n", "Agent $i$ decides whether or not to place an order at time $t$ using the rule:\n", "\n", "$$\n", " \\rho_i(t) = \\mathbb{I}_{\\epsilon_t > \\nu_i(t)} - \\mathbb{I}_{\\epsilon_t < -\\nu_i(t)},\n", "$$\n", "\n", "where $\\epsilon_t \\sim \\mathcal{N}(0, \\sigma^2)$ is a common signal received by each agent that forecasts the next time period’s log-returns, \n", "\n", "$$\n", " r_t = \\log S_t / S_{t - 1},\n", "$$\n", "\n", "in the price of the asset. In the above, $\\nu_i(t) > 0$ is the threshold level for agent $i$ at time $t$, which determines the range of values of the public information $\\epsilon_t$ that agent $i$ considers to be significant. The initial values $\\nu_i(0)$ are drawn iid from some probability density function $f_\\gamma$ with parameters $\\gamma$. \n", "\n", "The actual log-returns is then given by\n", "\n", "\\begin{equation}\\label{eq:logret}\n", " r_t = \\frac{\\sum_{i=1}^N \\rho_i(t)}{N\\eta},\n", "\\end{equation}\n", "\n", "where $\\eta > 0$ is a free parameter of the model. Finally, each agent updates their threshold $\\nu_i(t)$ at time $t$ according to\n", "\n", "\\begin{equation}\\label{eq:nu}\n", " \\nu_i(t) = \\mathbb{I}_{u_i(t) < 1/10} \\vert{r_t}\\vert + \\mathbb{I}_{u_i(t) \\geq 1/10} \\nu_i(t-1),\n", "\\end{equation}\n", "\n", "where $u_i(t)$ are iid uniformly distributed random variables on the unit interval $[0,1]$." ] }, { "cell_type": "markdown", "id": "0b78ecde", "metadata": {}, "source": [ "In the above, there are two instances of discrete randomness, with different characteristics:\n", "\n", "- one in the definition of the $\\rho_i(t)$, which all depend on a common random variable $\\epsilon_t$;\n", "- one in the definition of $\\nu_i(t)$.\n", "\n", "To build a differentiable implementation of this model, we need to have a way to pass gradients through these operations. We will need to do this in different ways for each of these, since one of them depends on a shared random variable $\\epsilon_t$ while the other does not." ] }, { "cell_type": "markdown", "id": "384e8508", "metadata": {}, "source": [ "The below is a differentiable implementation of this model, using the Gumbel softmax (Jang et al., 2016) and straight-through (Bengio et al., 2013) surrogate gradient tricks we've encountereed previously:" ] }, { "cell_type": "code", "execution_count": 11, "id": "d90d2185", "metadata": {}, "outputs": [], "source": [ "from blackbirds.models.model import Model\n", "\n", "class RamaCont(Model):\n", " def __init__(self, n_agents, n_timesteps, s, sigmoid_k):\n", " r\"\"\"\n", " Implementation of the Rama Cont model from Rama Cont (2005).\n", "\n", " **Arguments:**\n", "\n", " - `n_agents`: Number of agents\n", " - `n_timesteps`: Number of timesteps\n", " - `s`: Probability of updating the threshold $\\nu_i$.\n", " - `sigmoid_k`: Steepness of the sigmoid function.\n", " \"\"\"\n", " super().__init__()\n", " self.n_agents = n_agents\n", " self.n_timesteps = n_timesteps\n", " self.s = s\n", " self.sigmoid_k = sigmoid_k\n", "\n", " def initialize(self, params):\n", " nu_0 = torch.distributions.LogNormal(params[0], params[1]).rsample(\n", " (self.n_agents,)\n", " )\n", " epsilon_t = torch.zeros(self.n_agents)\n", " order = self.compute_order(epsilon_t, nu_0)\n", " eta = params[3]\n", " returns = self.compute_returns(order, eta) * torch.ones(self.n_agents)\n", " x = torch.vstack((nu_0, epsilon_t, returns))\n", " return x.reshape(1, 3, self.n_agents)\n", "\n", " def step(self, params, x):\n", " # draw epsilon_t from normal distribution\n", " sigma = params[2]\n", " epsilon_t = torch.distributions.Normal(0, sigma).rsample()\n", " # compute order\n", " nu_t = x[-1, 0, :]\n", " order = self.compute_order(epsilon_t, nu_t)\n", " # compute returns\n", " eta = params[3]\n", " returns = self.compute_returns(order, eta)\n", " # update nu_t\n", " new_nu_t = self.compute_new_nu_t(nu_t, self.s, returns)\n", " x = torch.vstack(\n", " (\n", " new_nu_t,\n", " epsilon_t * torch.ones(self.n_agents),\n", " returns * torch.ones(self.n_agents),\n", " )\n", " )\n", " return x.reshape(1, 3, self.n_agents)\n", "\n", " def observe(self, x):\n", " return [x[:, 2, 0]]\n", "\n", " def compute_order_soft(self, epsilon_t, nu_t):\n", " return torch.sigmoid(self.sigmoid_k * (epsilon_t - nu_t)) - torch.sigmoid(\n", " self.sigmoid_k * (-nu_t - epsilon_t)\n", " )\n", "\n", " def compute_order_hard(self, epsilon_t, nu_t):\n", " return (epsilon_t > nu_t).float() - (epsilon_t < -nu_t).float()\n", "\n", " def compute_order(self, epsilon_t, nu_t):\n", " \"\"\"\n", " We do a trick similar to the gumbel-softmax.\n", " \"\"\"\n", " soft = self.compute_order_soft(epsilon_t, nu_t)\n", " return self.compute_order_hard(epsilon_t, nu_t) + soft - soft.detach() # Straight-through gradient\n", "\n", " def compute_returns(self, order, eta):\n", " return 1.0 / (self.n_agents * eta) * order.sum()\n", "\n", " def compute_new_nu_t(self, nu_t, s, returns):\n", " probs = s * torch.ones(self.n_agents)\n", " probs = torch.vstack((probs, 1.0 - probs)).transpose(0, 1)\n", " q = torch.nn.functional.gumbel_softmax(probs.log(), tau=0.1, hard=True)[:, 0] # Gumbel softmax gradient\n", " return torch.abs(returns) * q + (1 - q) * nu_t\n", "\n", " def trim_time_series(self, x):\n", " return x\n", "\n", "# Parameterise with the log10 of parameters, to make parameter space unbounded\n", "class LogModel(RamaCont):\n", " def initialize(self, params):\n", " return super().initialize(10 ** params)\n", " def step(self, params, x):\n", " return super().step(10 ** params, x)" ] }, { "cell_type": "code", "execution_count": 32, "id": "3a39a401", "metadata": {}, "outputs": [], "source": [ "model = LogModel(n_agents = 1000, n_timesteps=100, s=0.1, sigmoid_k=5.0)" ] }, { "cell_type": "markdown", "id": "596f4a79", "metadata": {}, "source": [ "Now we generate the \"true\" data set:" ] }, { "cell_type": "code", "execution_count": 17, "id": "dcf2cdd0", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "true_parameters = torch.log10(torch.tensor([1., 0.5, 1., .7]))\n", "true_data = model.run_and_observe(true_parameters)\n", "plt.plot(true_data[0]);" ] }, { "cell_type": "markdown", "id": "191dc3ed", "metadata": {}, "source": [ "We use as loss the maximum mean discrepancy between the empirical and simulated distributions of log-returns:" ] }, { "cell_type": "code", "execution_count": 13, "id": "b7411bdc", "metadata": {}, "outputs": [], "source": [ "from blackbirds.losses import SingleOutput_SimulateAndMMD" ] }, { "cell_type": "code", "execution_count": 34, "id": "91ed97ef", "metadata": {}, "outputs": [], "source": [ "class MMDLoss:\n", " def __init__(self, *args, offset=0., **kwargs):\n", " self.mmd_calculator = SingleOutput_SimulateAndMMD(*args, **kwargs)\n", " self.offset = offset\n", " \n", " def __call__(self, *args, **kwargs):\n", " loss = self.mmd_calculator(*args, **kwargs)\n", " return loss - self.offset" ] }, { "cell_type": "markdown", "id": "c2ecb56e", "metadata": {}, "source": [ "We take the variational family in this case to be a normalising flow (a flexible class of neural density estimators):" ] }, { "cell_type": "code", "execution_count": 18, "id": "dbfbe2ed", "metadata": {}, "outputs": [], "source": [ "#!pip install normflows" ] }, { "cell_type": "code", "execution_count": 19, "id": "c9034998", "metadata": {}, "outputs": [], "source": [ "import normflows as nf\n", "\n", "def make_flow():\n", " torch.manual_seed(1)\n", " base = nf.distributions.base.DiagGaussian(len(true_parameters))\n", " num_layers = 5\n", " latent_size = len(true_parameters)\n", " flows = []\n", " for i in range(num_layers):\n", " param_map = nf.nets.MLP([2, 50, 50, latent_size], init_zeros=True)\n", " flows.append(nf.flows.AffineCouplingBlock(param_map))\n", " flows.append(nf.flows.Permute(latent_size, mode='swap'))\n", " return nf.NormalizingFlow(base, flows)" ] }, { "cell_type": "markdown", "id": "87d3d702", "metadata": {}, "source": [ "Finally, taking a multivariate Normal prior, we can find a posterior corresponding to this choice of loss and model:" ] }, { "cell_type": "code", "execution_count": 20, "id": "140ea3c9", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 100/100 [01:08<00:00, 1.45it/s, loss=-.992, reg.=0.00772, total=-.984, best loss=-.994, epochs since improv.=14]\n" ] } ], "source": [ "# Define prior density\n", "prior = torch.distributions.MultivariateNormal(torch.zeros(4), 1.0 * torch.eye(len(true_parameters)))\n", "# Instantiate q_{\\phi}\n", "path_estimator = make_flow()\n", "torch.manual_seed(1)\n", "mmd_loss = MMDLoss(model=model, y=true_data[0], offset=1.)\n", "optimizer = torch.optim.AdamW(path_estimator.parameters(), lr=1e-3)\n", "# Optimise\n", "vi = VI(loss=mmd_loss, \n", " posterior_estimator=path_estimator, \n", " prior=prior, \n", " optimizer=optimizer, \n", " n_samples_per_epoch=10,\n", " w=0.001,\n", " log_tensorboard=True,\n", " gradient_estimation_method=\"pathwise\",\n", " gradient_clipping_norm=1.0)\n", "vi.run(true_data[0], n_epochs=100, max_epochs_without_improvement=100);" ] }, { "cell_type": "markdown", "id": "d042cc3a", "metadata": {}, "source": [ "We can then, e.g., look at the posterior:" ] }, { "cell_type": "code", "execution_count": 21, "id": "6d3f8674", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "tensor([1.4796])\n" ] } ], "source": [ "path_estimator.load_state_dict(vi.best_estimator_state_dict)\n", "with torch.no_grad():\n", " log_posterior_density_of_true_parameters = path_estimator.log_prob(true_parameters.unsqueeze(0))\n", " print(log_posterior_density_of_true_parameters)\n", " path_samples = path_estimator.sample(10000)[0].detach().numpy()\n", "samples_prior = prior.sample((10000,)).numpy()" ] }, { "cell_type": "code", "execution_count": 22, "id": "2c6b78fa", "metadata": {}, "outputs": [], "source": [ "#!pip install pygtc" ] }, { "cell_type": "code", "execution_count": 23, "id": "c27c9619", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "try:\n", " import pygtc\n", " pygtc.plotGTC([path_samples, samples_prior],\n", " figureSize=4, truths = true_parameters.numpy(), \n", " chainLabels = [\"Learned posterior\", \"Prior\", ], \n", " paramNames = [r\"$\\log\\alpha$\", r\"$\\log\\beta$\", r\"$\\log\\sigma$\", r\"$\\log\\eta$\"],\n", " colorsOrder=['blues', 'oranges']);\n", "except AttributeError:\n", " import matplotlib.patches as mpatches\n", " path_patch = mpatches.Patch(color='blue', label='Learned posterior')\n", " prior_patch = mpatches.Patch(color='orange', label='Prior')\n", " plt.gcf().legend(handles=[path_patch, prior_patch], loc='upper right', bbox_to_anchor=(.95,0.9))" ] }, { "cell_type": "markdown", "id": "84231673", "metadata": {}, "source": [ "## Bonus material 1: Point estimation" ] }, { "cell_type": "markdown", "id": "d0e1f2b4", "metadata": {}, "source": [ "Point estimation of parameters can also be performed using the model gradients. Consider searching for the model parameters $\\theta^*$ such that the maximum mean discrepancy between the distribution of simulated and real log returns -- respectively, $\\mathbb{P}_{\\theta}$ and $\\hat{\\mathbb{P}}$ -- is minimised, i.e.\n", "\n", "$$\n", " \\theta^* := \\arg\\min_{\\theta \\in \\Theta} \\text{MMD}(\\mathbb{P}_{\\theta}, \\hat{\\mathbb{P}}).\n", "$$\n", "\n", "This is an example of minimum distance estimation (see, e.g., [5] below). Provided we use a differentiable kernel in the MMD estimates, we can continue ti backpropagate through everything and find this $\\theta^*$ with gradient-assisted search. We do this below." ] }, { "cell_type": "code", "execution_count": 70, "id": "c923bf1d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Starting at tensor([-0.1391, -0.0815, -0.0320, 0.0738], requires_grad=True)\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ " 14%|██████████████████████▏ | 285/2000 [02:10<13:04, 2.19it/s, Current loss=0.00278, Best loss=-.00511, Epochs since last improvement=100]\n" ] } ], "source": [ "torch.manual_seed(101)\n", "log_pars = torch.tensor([torch.randn(1)*0.1 for i in range(4)], requires_grad=True)\n", "print(\"Starting at\", log_pars)\n", "\n", "from tqdm import tqdm\n", "# Increase number of time steps for improved estimates of MMD\n", "model = LogModel(n_agents = 1000, n_timesteps=500, s=0.1, sigmoid_k=5.0)\n", "mmd_loss = MMDLoss(true_data[0], model)\n", "\n", "n_epochs = 2000\n", "loss_hist = []\n", "param_hist = []\n", "optimizer = torch.optim.Adam([log_pars], lr=0.05)\n", "iterator = tqdm(range(n_epochs))\n", "best_loss = float('inf')\n", "m = 0\n", "max_epochs_no_improvement = 100\n", "\n", "# Optimisation loop\n", "for i in iterator:\n", " optimizer.zero_grad()\n", " l = mmd_loss(log_pars, true_data[0])\n", " l.backward()\n", " # clip norm this is important to avoid exploding gradients\n", " torch.nn.utils.clip_grad_norm_(log_pars, 1)\n", " optimizer.step()\n", " loss_hist.append(l.item())\n", " if l.item() < best_loss:\n", " best_loss = l.item()\n", " m = 0\n", " m += 1\n", " if m > max_epochs_no_improvement:\n", " break\n", " param_hist.append(10 ** log_pars.detach())\n", " iterator.set_postfix({\"Current loss\":l.item(), \"Best loss\":best_loss, \"Epochs since last improvement\":m})" ] }, { "cell_type": "markdown", "id": "1a8f44d4", "metadata": {}, "source": [ "Let's see how close we are to the true parameters:" ] }, { "cell_type": "code", "execution_count": 71, "id": "c24a933c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 2, figsize=(10, 5))\n", "par_names = [r\"$\\gamma_0$\", r\"$\\gamma_1$\", r\"$\\eta$\", r\"$\\sigma$\"]\n", "ax[0].plot(loss_hist)\n", "ax[0].set_title(\"Loss\")\n", "ax[0].set_xlabel(\"Epoch\")\n", "ax[0].set_ylabel(\"Loss\")\n", "ax[1].set_title(\"Estimated parameters\")\n", "for i in range(4):\n", " ax[1].plot([par[i] for par in param_hist], \n", " label = \"Estimated {0}\".format(par_names[i]), \n", " color = \"C{0}\".format(i))\n", " ax[1].axhline(10**true_parameters[i], \n", " color=\"C{0}\".format(i), \n", " linestyle=\"--\", \n", " label=\"True {0}\".format(par_names[i]))\n", "ax[1].set_xlabel(\"Epoch\")\n", "ax[1].legend()" ] }, { "cell_type": "markdown", "id": "0c8dbd47", "metadata": {}, "source": [ "## Bonus material 2: Estimating the classical Bayesian posterior with variational inference" ] }, { "cell_type": "markdown", "id": "d41993e6", "metadata": {}, "source": [ "In this section, we'll do the same as in Section 2 but now using the negative log-likelihood as the loss function in the variational procedure." ] }, { "cell_type": "markdown", "id": "36ec959f", "metadata": {}, "source": [ "We will use a Beta prior over $\\theta$." ] }, { "cell_type": "code", "execution_count": 5, "id": "807afea6", "metadata": {}, "outputs": [], "source": [ "beta_shape_1 = torch.tensor(2.)\n", "beta_shape_2 = torch.tensor(2.)\n", "prior = torch.distributions.Beta(beta_shape_1, beta_shape_2)" ] }, { "cell_type": "markdown", "id": "6b163f95", "metadata": {}, "source": [ "Now we need to choose a variational family for $q$. We will use another Beta distribution with trainable shape parameters." ] }, { "cell_type": "code", "execution_count": 6, "id": "9fb76017", "metadata": { "lines_to_next_cell": 0 }, "outputs": [], "source": [ "class TrainableBeta(torch.nn.Module):\n", " def __init__(self):\n", " super().__init__()\n", " self.par_1 = torch.nn.Parameter(torch.ones(1)*2)\n", " self.par_2 = torch.nn.Parameter(torch.ones(1)*2)\n", "\n", " def sample(self, n):\n", " dist = torch.distributions.Beta(self.par_1, self.par_2)\n", " theta = dist.rsample((n,))\n", " logprob = dist.log_prob(theta)\n", " return theta, logprob" ] }, { "cell_type": "markdown", "id": "d18bfafb", "metadata": {}, "source": [ "Now we need to specify the loss $\\ell(\\theta, y)$. We know that a Beta prior is conjugate for Bernoulli distribution in the context of the classical posterior (i.e., when taking $\\ell(\\theta, y) = - \\log p(y | \\theta)$). We will therefore use this, since it will allow us to check the accuracy of the variational posterior:" ] }, { "cell_type": "code", "execution_count": 7, "id": "339103df", "metadata": { "lines_to_next_cell": 0 }, "outputs": [], "source": [ "def diffed_clamped(y):\n", " y_diffed = y.diff()\n", " y_diffed_clamped = (y_diffed + 1.) / 2.\n", " return y_diffed_clamped\n", "\n", "def loss(theta, y):\n", " y_diffed_clamped = diffed_clamped(y)\n", " log_prob = torch.distributions.Binomial(len(y_diffed_clamped), theta).log_prob(y_diffed_clamped.sum())\n", " return -log_prob.squeeze()" ] }, { "cell_type": "markdown", "id": "6c175c50", "metadata": {}, "source": [ "And we have all the ingredients!" ] }, { "cell_type": "code", "execution_count": null, "id": "c751db85", "metadata": { "lines_to_next_cell": 0 }, "outputs": [], "source": [ "q = TrainableBeta()\n", "optimizer = torch.optim.Adam(q.parameters(), lr=1e-2)\n", "vi = VI(loss,\n", " posterior_estimator=q,\n", " prior=prior,\n", " optimizer=optimizer,\n", " w = 1, # this is a relative weight between the loss and the KL term,\n", " n_samples_per_epoch=500\n", " )\n", "vi.run(x_true, n_epochs=2500, max_epochs_without_improvement=500)" ] }, { "cell_type": "code", "execution_count": 9, "id": "2e53ddc0", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# we can now inspect the loss\n", "loss_df = pd.DataFrame(vi.losses_hist)\n", "loss_df.plot(xlabel='Epoch', ylabel='Loss');" ] }, { "cell_type": "code", "execution_count": 10, "id": "ae39b714", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# and we can check the trained posterior\n", "\n", "n_samples = 10_000\n", "x_true_diffed_clamped = diffed_clamped(x_true)\n", "n_draws = len(x_true_diffed_clamped)\n", "variational_posterior_samples = q.sample(n_samples)[0].detach().numpy()\n", "true_posterior_samples = torch.distributions.Beta(beta_shape_1 + x_true_diffed_clamped.sum(),\n", " beta_shape_2 + n_draws - x_true_diffed_clamped.sum()\n", " ).sample((n_samples,)).numpy()\n", "\n", "fig, ax = plt.subplots()\n", "ax.hist(true_posterior_samples, bins=50, alpha=0.5, label='True posterior')\n", "ax.hist(variational_posterior_samples, bins=50, alpha=0.5, label='Learned posterior')\n", "ax.legend();\n", "ax.set_xlim([0,1]);" ] }, { "cell_type": "markdown", "id": "6d730318", "metadata": {}, "source": [ "We could improve upon this approximation by running the optimisation procedure for longer. Note that this section did not make use of gradients of the model output with respect to the input parameters, since the log-likelihood function does not use simulated samples from the model." ] }, { "cell_type": "markdown", "id": "5259bb9a", "metadata": {}, "source": [ "# References" ] }, { "cell_type": "markdown", "id": "d8e33f63", "metadata": {}, "source": [ "[1] Quera-Bofarull, A., Dyer, J., Calinescu, A., Farmer, J. D., & Wooldridge, M. (2023). BlackBIRDS: Black-Box Inference foR Differentiable Simulators. Journal of Open Source Software, 8(89).\n", "\n", "[2] Dyer, Joel, et al. \"Gradient-assisted calibration for financial agent-based models.\" Proceedings of the Fourth ACM International Conference on AI in Finance. 2023.\n", "\n", "[3] Bengio, Yoshua, Nicholas Léonard, and Aaron Courville. \"Estimating or propagating gradients through stochastic neurons for conditional computation.\" arXiv preprint arXiv:1308.3432 (2013).\n", "\n", "[4] Jang, Eric, Shixiang Gu, and Ben Poole. \"Categorical reparameterization with gumbel-softmax.\" arXiv preprint arXiv:1611.01144 (2016).\n", "\n", "[5] Briol, Francois-Xavier, et al. \"Statistical inference for generative models with maximum mean discrepancy.\" arXiv preprint arXiv:1906.05944 (2019).\n", "\n", "[6] Dyer, Joel. \"Variational Bayesian Inference for Agent based Models.\" INET Oxford YouTube Channel, [https://www.youtube.com/watch?v=ria0aKWztGE](https://www.youtube.com/watch?v=ria0aKWztGE) (2023)." ] } ], "metadata": { "kernelspec": { "display_name": "icaif_code", "language": "python", "name": "icaif_code" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.12" } }, "nbformat": 4, "nbformat_minor": 5 }