{ "cells": [ { "cell_type": "markdown", "id": "blessed-strategy", "metadata": {}, "source": [ "# Linear Regression - MLE\n", "\n", "Implementation of the classic linear regression model. Weights are fitted with Maximum Likelihood Estimation using [PyTorch distributions](https://pytorch.org/docs/stable/distributions.html). \n", "\n", "$y \\sim \\mathcal{N}(\\alpha x + \\beta, \\sigma)$\n", "\n", "\n", "## Setting up the environment" ] }, { "cell_type": "code", "execution_count": 1, "id": "exceptional-hawaiian", "metadata": {}, "outputs": [], "source": [ "import os\n", "\n", "import pandas as pd\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "import torch\n", "import torch.nn.functional as F\n", "from sklearn.metrics import r2_score\n", "from sklearn.model_selection import train_test_split\n", "\n", "cwd = os.getcwd()\n", "if cwd.endswith('notebook'):\n", " os.chdir('..')\n", " cwd = os.getcwd()" ] }, { "cell_type": "code", "execution_count": 2, "id": "opposed-hypothesis", "metadata": {}, "outputs": [], "source": [ "sns.set(palette='colorblind', font_scale=1.3)\n", "palette = sns.color_palette()" ] }, { "cell_type": "code", "execution_count": 3, "id": "humanitarian-vision", "metadata": {}, "outputs": [], "source": [ "seed = 444\n", "np.random.seed(seed);\n", "torch.manual_seed(seed);" ] }, { "cell_type": "markdown", "id": "packed-spank", "metadata": {}, "source": [ "## Generate dataset" ] }, { "cell_type": "code", "execution_count": 4, "id": "offensive-gnome", "metadata": {}, "outputs": [], "source": [ "α_actual = 2.6\n", "β_actual = 3.3\n", "σ_actual = 0.7" ] }, { "cell_type": "code", "execution_count": 5, "id": "developing-parameter", "metadata": {}, "outputs": [], "source": [ "def generate_samples(α, β, σ, min_x=-1, max_x=1, n_samples=500):\n", " x = np.linspace(min_x, max_x, n_samples)[:, np.newaxis]\n", " y = α * x + β\n", " dist = torch.distributions.Normal(torch.from_numpy(y), σ)\n", " y_sample = dist.sample()\n", " return x, y, y_sample.detach().numpy()" ] }, { "cell_type": "code", "execution_count": 6, "id": "located-banks", "metadata": {}, "outputs": [], "source": [ "def plot_line(x, y, y_sample):\n", " f, ax = plt.subplots(1, 1, figsize=(12, 6))\n", " ax.plot(x.flatten(), y.flatten(), '-', color=palette[2], linewidth=3)\n", " ax.scatter(x.flatten(), y_sample.flatten(), color=palette[0], alpha=0.8)\n", " ax.set_xlabel('input x')\n", " ax.set_ylabel('output y')\n", " ax.set_title(r'$y \\sim N(\\alpha x + \\beta, \\sigma)$')\n", " return f, ax" ] }, { "cell_type": "code", "execution_count": 7, "id": "limiting-tackle", "metadata": {}, "outputs": [], "source": [ "x, y, y_sample = generate_samples(α_actual, β_actual, σ_actual)" ] }, { "cell_type": "code", "execution_count": 8, "id": "floral-token", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f, _ = plot_line(x, y, y_sample);" ] }, { "cell_type": "code", "execution_count": 9, "id": "twenty-blank", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(500, 1)" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x.shape" ] }, { "cell_type": "markdown", "id": "extra-illinois", "metadata": {}, "source": [ "## Define model" ] }, { "cell_type": "code", "execution_count": 10, "id": "arbitrary-absorption", "metadata": {}, "outputs": [], "source": [ "class LinearNormal(torch.nn.Module):\n", " \n", " def __init__(self):\n", " super().__init__()\n", " self.α = torch.nn.Parameter(torch.randn(()))\n", " self.β = torch.nn.Parameter(torch.randn(()))\n", " self.s = torch.nn.Parameter(torch.randn(()))\n", " \n", " @property\n", " def sigma(self):\n", " return F.softplus(self.s) # ensure σ > 0\n", " \n", " def forward(self, x):\n", " m = self.α * x + self.β\n", " σ = self.sigma\n", " return torch.distributions.Normal(m, σ)" ] }, { "cell_type": "code", "execution_count": 11, "id": "sonic-trademark", "metadata": {}, "outputs": [], "source": [ "def compute_loss(model, x, y):\n", " out_dist = model(x)\n", " neg_log_likelihood = -out_dist.log_prob(y)\n", " return torch.mean(neg_log_likelihood)\n", "\n", "def compute_rmse(model, x_test, y_test):\n", " model.eval()\n", " pred = model(x_test).sample()\n", " return torch.sqrt(torch.mean((pred - y_test)**2))\n", "\n", "def predict(model, x):\n", " model.eval()\n", " out_dist = model(x)\n", " return out_dist.mean, out_dist.stddev, out_dist" ] }, { "cell_type": "markdown", "id": "described-northeast", "metadata": {}, "source": [ "## Fit linear model" ] }, { "cell_type": "code", "execution_count": 12, "id": "focal-minority", "metadata": {}, "outputs": [], "source": [ "def train_one_step(model, optimizer, x_batch, y_batch):\n", " model.train()\n", " optimizer.zero_grad()\n", " loss = compute_loss(model, x_batch, y_batch)\n", " loss.backward()\n", " optimizer.step()\n", " return loss" ] }, { "cell_type": "code", "execution_count": 13, "id": "aging-premiere", "metadata": {}, "outputs": [], "source": [ "def train(model, optimizer, x_train, x_val, y_train, y_val, n_epochs, batch_size=64, print_every=10):\n", " train_losses, val_losses = [], []\n", " for epoch in range(n_epochs):\n", " batch_indices = sample_batch_indices(x_train, y_train, batch_size)\n", " \n", " batch_losses_t, batch_losses_v, batch_rmse_v = [], [], []\n", " for batch_ix in batch_indices:\n", " b_train_loss = train_one_step(model, optimizer, x_train[batch_ix], y_train[batch_ix])\n", "\n", " model.eval()\n", " b_val_loss = compute_loss(model, x_val, y_val)\n", " b_val_rmse = compute_rmse(model, x_val, y_val)\n", "\n", " batch_losses_t.append(b_train_loss.detach().numpy())\n", " batch_losses_v.append(b_val_loss.detach().numpy())\n", " batch_rmse_v.append(b_val_rmse.detach().numpy())\n", " \n", " train_loss = np.mean(batch_losses_t)\n", " val_loss = np.mean(batch_losses_v)\n", " val_rmse = np.mean(batch_rmse_v)\n", " \n", " train_losses.append(train_loss)\n", " val_losses.append(val_loss)\n", "\n", " if epoch == 0 or (epoch + 1) % print_every == 0:\n", " print(f'Epoch {epoch+1} | Validation loss = {val_loss:.4f} | Validation RMSE = {val_rmse:.4f}')\n", " \n", " _, ax = plt.subplots(1, 1, figsize=(12, 6))\n", " ax.plot(range(1, n_epochs + 1), train_losses, label='Train loss')\n", " ax.plot(range(1, n_epochs + 1), val_losses, label='Validation loss')\n", " ax.set_xlabel('Epoch')\n", " ax.set_ylabel('Loss')\n", " ax.set_title('Training Overview')\n", " ax.legend()\n", " \n", " return train_losses, val_losses\n", "\n", "\n", "def sample_batch_indices(x, y, batch_size, rs=None):\n", " if rs is None:\n", " rs = np.random.RandomState()\n", " \n", " train_ix = np.arange(len(x))\n", " rs.shuffle(train_ix)\n", " \n", " n_batches = int(np.ceil(len(x) / batch_size))\n", " \n", " batch_indices = []\n", " for i in range(n_batches):\n", " start = i * batch_size\n", " end = start + batch_size\n", " batch_indices.append(\n", " train_ix[start:end].tolist()\n", " )\n", "\n", " return batch_indices " ] }, { "cell_type": "code", "execution_count": 14, "id": "interior-renaissance", "metadata": {}, "outputs": [], "source": [ "def compute_train_test_split(x, y, test_size):\n", " x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=test_size)\n", " return (\n", " torch.from_numpy(x_train),\n", " torch.from_numpy(x_test),\n", " torch.from_numpy(y_train),\n", " torch.from_numpy(y_test),\n", " )" ] }, { "cell_type": "code", "execution_count": 15, "id": "federal-theology", "metadata": {}, "outputs": [], "source": [ "model = LinearNormal()\n", "\n", "optimizer = torch.optim.SGD(model.parameters(), lr=5e-3)" ] }, { "cell_type": "code", "execution_count": 16, "id": "boring-grammar", "metadata": {}, "outputs": [], "source": [ "x_train, x_test, y_train, y_test = compute_train_test_split(x, y_sample, test_size=0.2)" ] }, { "cell_type": "code", "execution_count": 17, "id": "tender-tunisia", "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Epoch 1 | Validation loss = 2.9920 | Validation RMSE = 3.8502\n", "Epoch 200 | Validation loss = 2.0640 | Validation RMSE = 2.9241\n", "Epoch 400 | Validation loss = 1.5080 | Validation RMSE = 1.6508\n", "Epoch 600 | Validation loss = 1.1400 | Validation RMSE = 1.0177\n", "Epoch 800 | Validation loss = 1.1421 | Validation RMSE = 1.0224\n", "Epoch 1000 | Validation loss = 1.1423 | Validation RMSE = 0.9786\n", "Epoch 1200 | Validation loss = 1.1426 | Validation RMSE = 1.0176\n", "Epoch 1400 | Validation loss = 1.1407 | Validation RMSE = 1.0184\n", "Epoch 1600 | Validation loss = 1.1429 | Validation RMSE = 1.0304\n", "Epoch 1800 | Validation loss = 1.1411 | Validation RMSE = 1.0163\n", "Epoch 2000 | Validation loss = 1.1423 | Validation RMSE = 1.0137\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "train(model, optimizer, x_train, x_test, y_train, y_test, n_epochs=2000, print_every=200);" ] }, { "cell_type": "markdown", "id": "consecutive-unemployment", "metadata": {}, "source": [ "## Validation" ] }, { "cell_type": "code", "execution_count": 18, "id": "plain-legislation", "metadata": {}, "outputs": [], "source": [ "y_pred, _, y_dist = predict(model, x_test)\n", "y_pred_sample = y_dist.sample()" ] }, { "cell_type": "code", "execution_count": 19, "id": "collect-australia", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Validation RMSE = 0.9237898387187049\n" ] } ], "source": [ "val_rmse = float(compute_rmse(model, x_test, y_test).detach().numpy())\n", "print(f'Validation RMSE = {val_rmse}')" ] }, { "cell_type": "code", "execution_count": 20, "id": "departmental-acoustic", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Validation R squared = 0.6966485902638072\n" ] } ], "source": [ "val_r2 = r2_score(y_test.detach().numpy(), y_pred_sample.detach().numpy())\n", "print(f'Validation R squared = {val_r2}')" ] }, { "cell_type": "markdown", "id": "proper-timothy", "metadata": {}, "source": [ "## Plot results" ] }, { "cell_type": "code", "execution_count": 21, "id": "correct-pipeline", "metadata": {}, "outputs": [], "source": [ "def plot_results(x, y, y_sample, y_pred, std):\n", " f, ax = plt.subplots(1, 1, figsize=(12, 6))\n", " \n", " x_arg_sort = x.flatten().argsort()\n", " xx = x.flatten()[x_arg_sort]\n", " v = y_pred.flatten()[x_arg_sort]\n", " std_val = std.flatten()[0]\n", " v_err_min = v - 2 * std_val\n", " v_err_max = v + 2 * std_val\n", " \n", " ax.fill_between(\n", " xx, \n", " v_err_min ,\n", " v_err_max, \n", " color=palette[1], \n", " alpha=0.2,\n", " label='2$\\sigma$ error',\n", " )\n", " \n", " ax.plot(xx, y.flatten()[x_arg_sort], '-', color=palette[0], linewidth=2, label='Actual')\n", " ax.scatter(xx, y_sample.flatten()[x_arg_sort], color=palette[0])\n", " \n", " ax.plot(xx, v, '-', color=palette[1], linewidth=2, label='Predicted')\n", " \n", " ax.set_title('Predictions on the validation set')\n", " ax.set_xlabel('input x')\n", " ax.set_ylabel('output y')\n", " ax.legend()\n", " return f, ax" ] }, { "cell_type": "code", "execution_count": 22, "id": "atomic-coordinator", "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f, ax = plot_results(\n", " x_test.detach().numpy(), \n", " α_actual * x_test.detach().numpy() + β_actual, \n", " y_test.detach().numpy(), \n", " y_pred.detach().numpy(), \n", " y_dist.stddev.detach().numpy(),\n", ")" ] }, { "cell_type": "code", "execution_count": 23, "id": "individual-timber", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Actual α = 2.6 | Predicted α = 2.6\n", "Actual β = 3.3 | Predicted β = 3.3\n", "Actual σ = 0.7 | Predicted σ = 0.7\n" ] } ], "source": [ "α_hat = float(model.α.detach().numpy())\n", "β_hat = float(model.β.detach().numpy())\n", "σ_hat = float(y_dist.stddev.detach().numpy()[0])\n", "\n", "print(f'Actual α = {α_actual:.1f} | Predicted α = {α_hat:.1f}')\n", "print(f'Actual β = {β_actual:.1f} | Predicted β = {β_hat:.1f}')\n", "print(f'Actual σ = {σ_actual:.1f} | Predicted σ = {σ_hat:.1f}')" ] }, { "cell_type": "code", "execution_count": null, "id": "micro-majority", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.9" } }, "nbformat": 4, "nbformat_minor": 5 }