11_polynomial_regression_torch.ipynb

{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"provenance":[{"file_id":"https://github.com/probml/pyprobml/blob/master/notebooks/book1/11/supplementary/poly_regression_torch.ipynb","timestamp":1687574473632}],"toc_visible":true},"kernelspec":{"name":"python3","display_name":"Python 3"},"language_info":{"name":"python"}},"cells":[{"cell_type":"markdown","metadata":{"id":"4kuVeLiRYXhF"},"source":["# Polynomial regression in 1d.\n","Based on sec 4.4 of\n"," http://d2l.ai/chapter_multilayer-perceptrons/underfit-overfit.html"]},{"cell_type":"code","metadata":{"id":"0prfTp1DYTEp"},"source":["import numpy as np\n","import matplotlib.pyplot as plt\n","\n","np.random.seed(seed=1)\n","import math\n","\n","import torch\n","from torch import nn\n","from torch.nn import functional as F\n","from torch.utils import data\n","from IPython import display\n","\n","!mkdir figures # for saving plots\n","\n","import warnings\n","\n","warnings.filterwarnings(\"ignore\")\n","\n","# For reproducing the results on different runs\n","torch.backends.cudnn.deterministic = True\n","torch.manual_seed(hash(\"by removing stochasticity\") % 2**32 - 1)\n","torch.cuda.manual_seed_all(hash(\"so runs are repeatable\") % 2**32 - 1)"],"execution_count":null,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"725IgNzDZhmB"},"source":["# Data"]},{"cell_type":"markdown","metadata":{"id":"iIMUISREY7TR"},"source":["Make some data using this function:\n","\n","**$$y = 5 + 1.2x - 3.4\\frac{x^2}{2!} + 5.6 \\frac{x^3}{3!} + \\epsilon \\text{ where }\n","\\epsilon \\sim \\mathcal{N}(0, 0.1^2).$$**"]},{"cell_type":"code","metadata":{"id":"bkpZVc5GYdf-"},"source":["np.random.seed(42)\n","max_degree = 20  # Maximum degree of the polynomial\n","n_train, n_test = 100, 100  # Training and test dataset sizes\n","true_w = np.zeros(max_degree)  # Allocate lots of empty space\n","true_w[0:4] = np.array([5, 1.2, -3.4, 5.6])\n","\n","features = np.random.normal(size=(n_train + n_test, 1))\n","np.random.shuffle(features)\n","poly_features = np.power(features, np.arange(max_degree).reshape(1, -1))\n","for i in range(max_degree):\n","    poly_features[:, i] /= math.gamma(i + 1)  # `gamma(n)` = (n-1)!\n","# Shape of `labels`: (`n_train` + `n_test`,)\n","labels = np.dot(poly_features, true_w)\n","labels += np.random.normal(scale=0.1, size=labels.shape)"],"execution_count":null,"outputs":[]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"d7sLXgHuZJdd","outputId":"23c591db-c418-41bc-df61-03f1eda575f2"},"source":["# Convert from NumPy ndarrays to tensors\n","true_w, features, poly_features, labels = [\n","    torch.tensor(x, dtype=torch.float32) for x in [true_w, features, poly_features, labels]\n","]\n","\n","print(true_w)"],"execution_count":null,"outputs":[{"output_type":"stream","text":["tensor([ 5.0000,  1.2000, -3.4000,  5.6000,  0.0000,  0.0000,  0.0000,  0.0000,\n","         0.0000,  0.0000,  0.0000,  0.0000,  0.0000,  0.0000,  0.0000,  0.0000,\n","         0.0000,  0.0000,  0.0000,  0.0000])\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"Z515M5AbZjFe"},"source":["# Train/eval loop"]},{"cell_type":"code","metadata":{"id":"eWsTe9jEszao"},"source":["class Accumulator:\n","    \"\"\"For accumulating sums over `n` variables.\"\"\"\n","\n","    def __init__(self, n):\n","        self.data = [0.0] * n\n","\n","    def add(self, *args):\n","        self.data = [a + float(b) for a, b in zip(self.data, args)]\n","\n","    def reset(self):\n","        self.data = [0.0] * len(self.data)\n","\n","    def __getitem__(self, idx):\n","        return self.data[idx]\n","\n","\n","class Animator:\n","    \"\"\"For plotting data in animation.\"\"\"\n","\n","    def __init__(\n","        self,\n","        xlabel=None,\n","        ylabel=None,\n","        legend=None,\n","        xlim=None,\n","        ylim=None,\n","        xscale=\"linear\",\n","        yscale=\"linear\",\n","        fmts=(\"-\", \"m--\", \"g-.\", \"r:\"),\n","        nrows=1,\n","        ncols=1,\n","        figsize=(3.5, 2.5),\n","    ):\n","        # Incrementally plot multiple lines\n","        if legend is None:\n","            legend = []\n","        # d2l.use_svg_display()\n","        display.set_matplotlib_formats(\"svg\")\n","        self.fig, self.axes = plt.subplots(nrows, ncols, figsize=figsize)\n","        if nrows * ncols == 1:\n","            self.axes = [\n","                self.axes,\n","            ]\n","        # Use a lambda function to capture arguments\n","        self.config_axes = lambda: set_axes(self.axes[0], xlabel, ylabel, xlim, ylim, xscale, yscale, legend)\n","        self.X, self.Y, self.fmts = None, None, fmts\n","\n","    def add(self, x, y):\n","        # Add multiple data points into the figure\n","        if not hasattr(y, \"__len__\"):\n","            y = [y]\n","        n = len(y)\n","        if not hasattr(x, \"__len__\"):\n","            x = [x] * n\n","        if not self.X:\n","            self.X = [[] for _ in range(n)]\n","        if not self.Y:\n","            self.Y = [[] for _ in range(n)]\n","        for i, (a, b) in enumerate(zip(x, y)):\n","            if a is not None and b is not None:\n","                self.X[i].append(a)\n","                self.Y[i].append(b)\n","        self.axes[0].cla()\n","        for x, y, fmt in zip(self.X, self.Y, self.fmts):\n","            self.axes[0].plot(x, y, fmt)\n","        self.config_axes()\n","        display.display(self.fig)\n","        display.clear_output(wait=True)"],"execution_count":null,"outputs":[]},{"cell_type":"code","metadata":{"id":"IOz7XrEytC3I"},"source":["# Incrementally update loss metrics during training\n","def evaluate_loss(net, data_iter, loss):\n","    \"\"\"Evaluate the loss of a model on the given dataset.\"\"\"\n","    metric = Accumulator(2)  # Sum of losses, no. of examples\n","    for X, y in data_iter:\n","        out = net(X)\n","        y = y.reshape(out.shape)\n","        l = loss(out, y)\n","        metric.add(l.sum(), l.numel())\n","    return metric[0] / metric[1]\n","\n","\n","def load_array(data_arrays, batch_size, is_train=True):\n","    \"\"\"Construct a PyTorch data iterator.\"\"\"\n","    dataset = data.TensorDataset(*data_arrays)\n","    return data.DataLoader(dataset, batch_size, shuffle=is_train)\n","\n","\n","def set_axes(axes, xlabel, ylabel, xlim, ylim, xscale, yscale, legend):\n","    \"\"\"Set the axes for matplotlib.\"\"\"\n","    axes.set_xlabel(xlabel)\n","    axes.set_ylabel(ylabel)\n","    axes.set_xscale(xscale)\n","    axes.set_yscale(yscale)\n","    axes.set_xlim(xlim)\n","    axes.set_ylim(ylim)\n","    if legend:\n","        axes.legend(legend)\n","    axes.grid()\n","\n","\n","def accuracy(y_hat, y):\n","    \"\"\"Compute the number of correct predictions.\"\"\"\n","    if len(y_hat.shape) > 1 and y_hat.shape[1] > 1:\n","        y_hat = d2l.argmax(y_hat, axis=1)\n","    cmp = y_hat.to(y.dtype) == y\n","    return float(torch.sum(cmp.to(y.dtype)))"],"execution_count":null,"outputs":[]},{"cell_type":"code","metadata":{"id":"JJ0E3F-3t6Wt"},"source":["def train_epoch(net, train_iter, loss, updater):\n","    \"\"\"The training loop defined in Chapter 3.\"\"\"\n","    # Set the model to training mode\n","    if isinstance(net, torch.nn.Module):\n","        net.train()\n","    # Sum of training loss, sum of training accuracy, no. of examples\n","    metric = Accumulator(3)\n","    for X, y in train_iter:\n","        # Compute gradients and update parameters\n","        y_hat = net(X)\n","        l = loss(y_hat, y)\n","\n","        # Using PyTorch in-built optimizer & loss criterion\n","        updater.zero_grad()\n","        l.backward()\n","        updater.step()\n","        metric.add(float(l) * len(y), accuracy(y_hat, y), y.numel())\n","\n","    # Return training loss and training accuracy\n","    return metric[0] / metric[2], metric[1] / metric[2]"],"execution_count":null,"outputs":[]},{"cell_type":"code","metadata":{"id":"bjh-JnZfZRDz"},"source":["# SGD optimization\n","\n","\n","def train(train_features, test_features, train_labels, test_labels, num_epochs=400, batch_size=50):\n","    loss = nn.MSELoss()\n","    input_shape = train_features.shape[-1]\n","    # Switch off the bias since we already catered for it in the polynomial\n","    # features\n","    net = nn.Sequential(nn.Linear(input_shape, 1, bias=False))\n","    batch_size = min(batch_size, train_labels.shape[0])\n","    train_iter = load_array((train_features, train_labels.reshape(-1, 1)), batch_size)\n","    test_iter = load_array((test_features, test_labels.reshape(-1, 1)), batch_size, is_train=False)\n","    trainer = torch.optim.SGD(net.parameters(), lr=0.01)\n","    animator = Animator(\n","        xlabel=\"epoch\", ylabel=\"loss\", yscale=\"log\", xlim=[1, num_epochs], ylim=[1e-3, 1e2], legend=[\"train\", \"test\"]\n","    )\n","    for epoch in range(num_epochs):\n","        train_epoch(net, train_iter, loss, trainer)\n","        if epoch == 0 or (epoch + 1) % 20 == 0:\n","            animator.add(epoch + 1, (evaluate_loss(net, train_iter, loss), evaluate_loss(net, test_iter, loss)))\n","    print(\"weight:\", net[0].weight.data.numpy())"],"execution_count":null,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"vSO6NjB-ZlTs"},"source":["# Degree 3 (matches true function)\n","\n","Train and test loss are similar (no over or underfitting),\n","Loss is small, since matches true function. Estimated parameters are close to the true ones.\n","\n"]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/","height":284},"id":"e3KhBZKVZXgD","outputId":"1d48a01d-3bec-4dd6-9e3b-8620c9e9f2ff"},"source":["# Pick the first four dimensions, i.e., 1, x, x^2/2!, x^3/3! from the\n","# polynomial features\n","train(poly_features[:n_train, :4], poly_features[n_train:, :4], labels[:n_train], labels[n_train:])"],"execution_count":null,"outputs":[{"output_type":"stream","text":["weight: [[ 4.966272   1.7361481 -3.319803   4.646927 ]]\n"],"name":"stdout"},{"output_type":"display_data","data":{"text/plain":["<Figure size 252x180 with 1 Axes>"],"image/svg+xml":"<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Created with matplotlib (https://matplotlib.org/) -->\n<svg height=\"184.455469pt\" version=\"1.1\" viewBox=\"0 0 263.421875 184.455469\" 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loss.\n","However, SGD itself has a regularizing effect (even in full batch mode),\n","so I cannot reproduce overfitting (even though it would occur using a second order optimizer)."]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/","height":352},"id":"FSm_LDL-Z69f","outputId":"808fcbfb-05b6-45c6-89ee-9e6735c4ef5d"},"source":["# Pick all the dimensions from the polynomial features\n","train(\n","    poly_features[:n_train, :],\n","    poly_features[n_train:, :],\n","    labels[:n_train],\n","    labels[n_train:],\n","    num_epochs=2000,\n","    batch_size=n_train,\n",")"],"execution_count":null,"outputs":[{"output_type":"stream","text":["weight: [[ 4.93541479e+00  1.33025610e+00 -3.02163672e+00  4.94317865e+00\n","  -8.01379859e-01  1.77049351e+00 -2.12022990e-01  4.42835212e-01\n","   1.22528784e-01  6.39166236e-02 -1.53294966e-01  1.37772217e-01\n","  -2.55810306e-03 -9.48211923e-02  1.58452168e-01  1.67681873e-01\n","  -7.38579556e-02 -6.81523979e-02 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