(15) GNN , Graph convolution as matrix product , as message passing ,  GAE , Graph attention network , GraphSAGE neighbor sampling.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "HHXNf2ELZI1M"
   },
   "source": [
    "# Assignment — Graph neural networks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "uhVr-XkwZI1Q"
   },
   "outputs": [],
   "source": [
    "from sklearn.manifold import TSNE\n",
    "import torch\n",
    "from tqdm.notebook import trange\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from torch.optim import Adam\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.metrics import balanced_accuracy_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "pCz1CEL_ZI1S"
   },
   "source": [
    "### CORA dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "8217ac0c",
    "outputId": "8bdb2a08-06ac-49cb-d43d-569ed54ebfa4"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "\u001b[31mERROR: pip's dependency resolver does not currently take into account all the packages that are installed. This behaviour is the source of the following dependency conflicts.\n",
      "datascience 0.10.6 requires folium==0.2.1, but you have folium 0.8.3 which is incompatible.\u001b[0m\n",
      "\u001b[?25h"
     ]
    }
   ],
   "source": [
    "!pip install dgl dglgo -f https://data.dgl.ai/wheels/repo.html -q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "97f7e59c",
    "outputId": "1df1cc74-afd9-47d0-d329-adad63e57ac7"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "DGL backend not selected or invalid.  Assuming PyTorch for now.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Setting the default backend to \"pytorch\". You can change it in the ~/.dgl/config.json file or export the DGLBACKEND environment variable.  Valid options are: pytorch, mxnet, tensorflow (all lowercase)\n"
     ]
    }
   ],
   "source": [
    "import dgl\n",
    "from dgl.data import CoraGraphDataset\n",
    "from dgl import function as fn\n",
    "from dgl.nn import SAGEConv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "id": "b9a52628"
   },
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings(action='ignore', category=UserWarning)\n",
    "warnings.simplefilter(action='ignore', category=FutureWarning)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "6f992762"
   },
   "source": [
    "The Cora dataset consists of 2708 scientific publications classified into one of seven classes. The citation network consists of 10556/2 links. Let us take a closer look at this dataset. Each publication in the dataset is described by a 0/1-valued word vector indicating the absence/presence of the corresponding word from the dictionary. The dictionary consists of 1433 unique words."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "3876dd0c",
    "outputId": "a39553fc-f877-442e-aa40-47f26a31012e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Downloading /root/.dgl/cora_v2.zip from https://data.dgl.ai/dataset/cora_v2.zip...\n",
      "Extracting file to /root/.dgl/cora_v2\n",
      "Finished data loading and preprocessing.\n",
      "  NumNodes: 2708\n",
      "  NumEdges: 10556\n",
      "  NumFeats: 1433\n",
      "  NumClasses: 7\n",
      "  NumTrainingSamples: 140\n",
      "  NumValidationSamples: 500\n",
      "  NumTestSamples: 1000\n",
      "Done saving data into cached files.\n"
     ]
    }
   ],
   "source": [
    "data = CoraGraphDataset(force_reload=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "60459d90",
    "outputId": "a69c3855-43bf-4369-e7cd-7203fe70f3a8"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Graph(num_nodes=2708, num_edges=10556,\n",
       "      ndata_schemes={'train_mask': Scheme(shape=(), dtype=torch.bool), 'val_mask': Scheme(shape=(), dtype=torch.bool), 'test_mask': Scheme(shape=(), dtype=torch.bool), 'label': Scheme(shape=(), dtype=torch.int64), 'feat': Scheme(shape=(1433,), dtype=torch.float32)}\n",
       "      edata_schemes={'__orig__': Scheme(shape=(), dtype=torch.int64)})"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "graph = data[0]\n",
    "graph"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "8e97b108"
   },
   "source": [
    "Adjacency matrix can be obtained as follows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "2cc92084",
    "outputId": "75604032-c104-438a-a101-8899c4b10686"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[0., 1., 1.,  ..., 0., 0., 0.],\n",
       "        [1., 0., 0.,  ..., 0., 0., 0.],\n",
       "        [1., 0., 0.,  ..., 0., 0., 0.],\n",
       "        ...,\n",
       "        [0., 0., 0.,  ..., 0., 0., 0.],\n",
       "        [0., 0., 0.,  ..., 0., 0., 1.],\n",
       "        [0., 0., 0.,  ..., 0., 1., 0.]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "adj = graph.adj().to_dense()\n",
    "adj"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "613d60e2"
   },
   "source": [
    "Feature matrix is stored in node features `feat`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "ffe904f8",
    "outputId": "f42617fd-0f5e-4c62-d5b6-d443df1cc222"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([2708, 1433])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tensor([[0.0000, 0.0000, 0.0000,  ..., 0.0000, 0.0000, 0.0000],\n",
       "        [0.0000, 0.0000, 0.0000,  ..., 0.0000, 0.0000, 0.0000],\n",
       "        [0.0000, 0.0000, 0.0000,  ..., 0.0000, 0.0000, 0.0000],\n",
       "        ...,\n",
       "        [0.0000, 0.0000, 0.0000,  ..., 0.0000, 0.0000, 0.0000],\n",
       "        [0.0000, 0.0000, 0.0000,  ..., 0.0000, 0.0000, 0.0000],\n",
       "        [0.0000, 0.0000, 0.0000,  ..., 0.0000, 0.0526, 0.0000]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "feat = graph.ndata['feat']\n",
    "print(feat.shape)\n",
    "feat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "a22e2f36"
   },
   "source": [
    "In DGL, Cora feature matrix are normalized so that the sum per row is 1. Labels are represent type of the publication, they are stored in `label`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "9c85b87c",
    "outputId": "9e323a7b-f29b-4126-b607-acd554424735"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([4, 4, 4,  ..., 4, 3, 3])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "label = graph.ndata['label']\n",
    "label"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "8ffdf1c0"
   },
   "source": [
    "Here are train, validation and test masks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "a0cb7ad4",
    "outputId": "9524430e-b773-43fb-a6b5-2df778e018d1"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([False, False,  True,  ..., False, False, False]),\n",
       " tensor([False, False, False,  ..., False, False, False]),\n",
       " tensor([ True,  True, False,  ..., False, False, False]))"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_mask = graph.ndata['train_mask']\n",
    "val_mask = graph.ndata['val_mask']\n",
    "test_mask = graph.ndata['test_mask']\n",
    "val_mask, train_mask, test_mask"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "PnQ4ubEnZI1Y"
   },
   "source": [
    "### Task 1. Graph convolution as matrix product (0 points)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ddc79913"
   },
   "source": [
    "Graph convolutional network (GCN) was proposed in [[1]](#references) and defined on an undirected graph as the following propagation rule:\n",
    "\n",
    "$$H^{(l)}=\\sigma\\left(\\tilde D^{-1 / 2} \\tilde A \\tilde D^{-1 / 2} H^{(l-1)} W^{(l)}\\right)$$\n",
    "\n",
    "where $\\tilde A = A + I_N$ is the adjacency matrix with added self-connections. $I_N$ is the identity matrix, $\\tilde D_{ii} = \\sum_j \\tilde A_{ij}$ is the degree matrix and $W^{(l)}$ is trainable matrix at the layer $l$. $\\sigma$ represents non-linear activation function such as ReLU. $H^{(l)}$ is the hidden states at the layer $l$ and $H^{(0)} = X$ is the initial feature matrix.\n",
    "\n",
    "Write a class `GCNMatrixProductLayer` that takes adjacency matrix, hidden states and returns the next hidden states before activation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "deletable": false,
    "id": "7ff5b791",
    "nbgrader": {
     "cell_type": "code",
     "checksum": "a8e8bb1c6da30605ca8ba49a6c4ecfa9",
     "grade": false,
     "grade_id": "cell-b71f48a8f9c231a0",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "class GCNMatrixProductLayer(nn.Module):\n",
    "    def __init__(self, in_dim, out_dim):\n",
    "        super().__init__()\n",
    "        self.dense = nn.Linear(in_dim, out_dim)\n",
    "        \n",
    "    def forward(self, adj, h):\n",
    "        _adj = adj.clone()\n",
    "        _adj = _adj + np.eye(_adj.shape[0], dtype='float32')\n",
    "        degree_norm = _adj.sum(dim=1) **  (- 1 / 2)\n",
    "        _adj = degree_norm[:, None] * _adj * degree_norm[None, :]\n",
    "        # torch.mm(torch.mm(degree_norm, _adj_with_identity), degree_norm)\n",
    "        h = _adj @ self.dense(h)\n",
    "        return h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "deletable": false,
    "editable": false,
    "id": "904fa061",
    "nbgrader": {
     "cell_type": "code",
     "checksum": "508f28b0a571960c10b36bb656874b59",
     "grade": true,
     "grade_id": "cell-59516dd351a3b233",
     "locked": true,
     "points": 0,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "layer = GCNMatrixProductLayer(in_dim=2708, out_dim=10)\n",
    "with torch.no_grad():\n",
    "    layer.dense.weight.fill_(0.1)\n",
    "    layer.dense.bias.fill_(0.1)\n",
    "    h = layer(adj, torch.eye(2708))\n",
    "assert round(h[0, 0].item(), 2) == 0.19"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "1b041722"
   },
   "source": [
    "Write a class `GCNMatrixProduct` that takes the adjacency matrix and feature matrix and performs two-layer convolution with intermediate ReLU activation. The class initialized by input, hidden and output dimensions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "deletable": false,
    "id": "1c9ef4e4",
    "nbgrader": {
     "cell_type": "code",
     "checksum": "856ad1e1e46a477d61fb9ebbde928fa4",
     "grade": false,
     "grade_id": "cell-5cecc368828015e4",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "class GCNMatrixProduct(nn.Module):\n",
    "    def __init__(self, in_dim, hid_dim, out_dim):\n",
    "        super().__init__()\n",
    "        self.conv1 = GCNMatrixProductLayer(in_dim, hid_dim)\n",
    "        self.conv2 = GCNMatrixProductLayer(hid_dim, out_dim)\n",
    "\n",
    "    def forward(self, adj, feat):\n",
    "        h = self.conv1(adj, feat)\n",
    "        h = F.relu(h)\n",
    "        h = self.conv2(adj, h)\n",
    "        return h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "deletable": false,
    "editable": false,
    "id": "13b3e790",
    "nbgrader": {
     "cell_type": "code",
     "checksum": "20891f674b1f17ad9b39e5e7323599cd",
     "grade": true,
     "grade_id": "cell-13a9aa3e489245ee",
     "locked": true,
     "points": 0,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "model = GCNMatrixProduct(2708, 32, 7)\n",
    "logits = model(adj, torch.eye(2708))\n",
    "assert logits.shape == (2708, 7)\n",
    "assert logits.min() < 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "217ab100"
   },
   "source": [
    "Let us create the two-layer GCN for node classification task."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "id": "a83c6c89"
   },
   "outputs": [],
   "source": [
    "model = GCNMatrixProduct(1433, 32, 7)\n",
    "opt = torch.optim.Adam(model.parameters(), lr=0.01)\n",
    "log = []"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "0569ff05"
   },
   "source": [
    "We train the model in semi-supervised setting: propagate information over the full graph, but optimize it by only train cross-entropy loss."
   ]
  },
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   "cell_type": "code",
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_epochs = 200\n",
    "for i in trange(n_epochs):\n",
    "    \n",
    "    logits = model(adj, feat)\n",
    "    train_loss = F.cross_entropy(logits[train_mask], label[train_mask])\n",
    "\n",
    "    opt.zero_grad()\n",
    "    train_loss.backward()\n",
    "    opt.step()\n",
    "\n",
    "    with torch.no_grad():\n",
    "        val_loss = F.cross_entropy(logits[val_mask], label[val_mask])\n",
    "    \n",
    "    log.append([train_loss.item(), val_loss.item()])\n",
    "    \n",
    "plt.plot(np.array(log))\n",
    "plt.title('Loss')\n",
    "plt.legend(['train', 'val'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "9e222fe4"
   },
   "source": [
    "We evaluate the model by balanced accuracy that accounts for inbalanced classes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "deletable": false,
    "editable": false,
    "id": "7945090a",
    "nbgrader": {
     "cell_type": "code",
     "checksum": "b39b99f78ca3f8319ac2b523edc550a9",
     "grade": true,
     "grade_id": "cell-d77d156cd37bfe99",
     "locked": true,
     "points": 0,
     "schema_version": 3,
     "solution": false,
     "task": false
    },
    "outputId": "251365de-ee04-41c1-fe98-6a8d2e3845c1"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Balanced accuracy: 0.80\n"
     ]
    }
   ],
   "source": [
    "with torch.no_grad():\n",
    "    logits = model(adj, feat)\n",
    "y_pred = torch.argmax(logits[test_mask], 1)\n",
    "score = balanced_accuracy_score(label[test_mask], y_pred)\n",
    "assert score > 0.7\n",
    "print(f'Balanced accuracy: {score:.2f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "_CLAz6cAZI1c"
   },
   "source": [
    "### Task 2. Graph convolution as message passing (0 points)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "d23ffa87"
   },
   "source": [
    "The original GCN is computationally expensive for large graphs since it requires to compute matrix product $\\tilde D^{-1 / 2} \\tilde A \\tilde D^{-1 / 2} H^{l}$, that costs $O(|V|^2)$. However, the information is propagated along edges, the number of which is linearly depends on the number of nodes in scale-free networks, that is $O(|V|)$. Message passing framework was proposed in [[2]](#references) to reduce computation costs by representing a graph neural network's layer as the composition of two functions:\n",
    "\n",
    "$$m_{ij}^l = \\text{Message}\\left(h_i^{l-1}, h_j^{l-1}\\right)$$\n",
    "$$h_i^l = \\text{Reduce}_{j \\in \\mathcal{N}_\\text{in}(i)}\\left(m_{ji}^l\\right)$$\n",
    "\n",
    "where $\\text{Message}(\\cdot)$ is the message function that applied on each edges in the graph and stores computed values (messages) on edges. $\\text{Reduce}_{j \\in \\mathcal{N}_\\text{in}(i)}(\\cdot)$ is the reduce (aka aggregation, reduction) function that applied on each node and aggregates messages from incoming links (mailboxes). \n",
    "\n",
    "<img src='https://raw.githubusercontent.com/netspractice/network-science/main/images/messpass.png' width=600>\n",
    "\n",
    "In particular, GCN can be represented as follows:\n",
    "\n",
    "$$h_i^l = \\sigma \\left(W^l \\sum_{j \\in \\mathcal{N}_\\text{in}(i)}\\frac{h_j^{l-1}}{\\sqrt{|\\mathcal{N}_\\text{in}(j)||\\mathcal{N}_\\text{in}(i)|}}\\right)$$\n",
    "\n",
    "where the message function\n",
    "\n",
    "$$m_{ji}^l = \\frac{W^l h_j^{l-1}}{\\sqrt{|\\mathcal{N}_\\text{in}(j)|}}$$ \n",
    "\n",
    "is the transformed source node's hidden state normalized by the in-degree of the source node. The reduce function\n",
    "\n",
    "$$h_i^l = \\sigma \\left(\\frac{\\sum_{j \\in \\mathcal{N}_\\text{in}(i)} m_{ji}^l}{\\sqrt{|\\mathcal{N}_\\text{in}(i)|}}\\right)$$\n",
    "\n",
    "is the sum over all incoming neighbors' hidden states with in-degree normalization and subsequent activation $\\sigma$. Here we assume that the graph includes self-connections, that is a node is in its neighborhood. We also assume that the graph is equivalent to its undirected representation, that is $A = A^\\top$.\n",
    "\n",
    "In DGL, message passing is applied by `graph.update_all(message_func, reduce_func)` where `message_func` is defined on edges and `reduce_func` on nodes. DGL contains built-in message and reduce functions, but it is also possible to define your own functions. GCN can be implemented using following functions: \n",
    "* message function `fn.copy_src(src='h', out='m')` copies the source node feature `h` into the mailbox `m`\n",
    "* reduce function `fn.sum(msg='m', out='h')` sums messages from mailboxes `m` and save the result into the node feature `h`\n",
    "\n",
    "Write a class `GCNMessagePassingLayer` that takes a graph, hidden states and returns the next hidden states before activation.\n",
    "\n",
    "*Hints:*\n",
    "* _adding node features is similar to adding values to a dictionary: `graph.ndata['h'] = h`_\n",
    "* _in-degrees can be computed by `graph.in_degrees()`_\n",
    "\n",
    "*Remark: `graph.local_scope()` makes all operations isolated from the original graphs.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "deletable": false,
    "id": "f5984036",
    "nbgrader": {
     "cell_type": "code",
     "checksum": "b7285e6772f70805893fd9df8c98dd43",
     "grade": false,
     "grade_id": "cell-7e663cf5c1afa659",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "class GCNMessagePassingLayer(nn.Module):\n",
    "    def __init__(self, in_dim, out_dim):\n",
    "        super().__init__()\n",
    "        self.dense = nn.Linear(in_dim, out_dim)\n",
    "    def forward(self, graph, h):\n",
    "        with graph.local_scope():\n",
    "            graph = graph.add_self_loop()\n",
    "            norm = graph.in_degrees()[:, None] ** (- 1 / 2)\n",
    "            h = self.dense(h)\n",
    "            h = h * norm\n",
    "            graph.ndata[\"h\"] = h\n",
    "            graph.update_all(\n",
    "                fn.copy_src(src=\"h\", out=\"m\"),\n",
    "                fn.sum(msg=\"m\", out=\"h\")\n",
    "            )\n",
    "            h = graph.ndata[\"h\"]\n",
    "            h = h * norm\n",
    "            return h\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "deletable": false,
    "editable": false,
    "id": "5d8f0c5f",
    "nbgrader": {
     "cell_type": "code",
     "checksum": "8073fd1f805718186c8fd3fd29de8351",
     "grade": true,
     "grade_id": "cell-b7b8314f51fe4d0f",
     "locked": true,
     "points": 0,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "layer = GCNMessagePassingLayer(in_dim=2708, out_dim=10)\n",
    "with torch.no_grad():\n",
    "    layer.dense.weight.fill_(0.1)\n",
    "    layer.dense.bias.fill_(0.1)\n",
    "    h = layer(graph, torch.eye(2708))\n",
    "assert round(h[0, 0].item(), 2) == 0.19"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "5fa85c8d"
   },
   "source": [
    "Write a class `GCNMessagePassing` that takes the graph and feature matrix and performs two-layer convolution with intermediate ReLU activation. The class initialized by input, hidden and output dimensions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "deletable": false,
    "id": "c5391849",
    "nbgrader": {
     "cell_type": "code",
     "checksum": "648906ac3877307e03e5e86946e862da",
     "grade": false,
     "grade_id": "cell-0e8fb3b6e5858162",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "class GCNMessagePassing(nn.Module):\n",
    "    def __init__(self, in_dim, hid_dim, out_dim):\n",
    "        super().__init__()\n",
    "        self.conv1 = GCNMessagePassingLayer(in_dim, hid_dim)\n",
    "        self.conv2 = GCNMessagePassingLayer(hid_dim, out_dim)\n",
    "\n",
    "    def forward(self, adj, feat):\n",
    "        h = self.conv1(adj, feat)\n",
    "        h = F.relu(h)\n",
    "        h = self.conv2(adj, h)\n",
    "        return h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "deletable": false,
    "editable": false,
    "id": "f6c274e7",
    "nbgrader": {
     "cell_type": "code",
     "checksum": "39b9ccecacba09fdee61474dd14c580d",
     "grade": true,
     "grade_id": "cell-bbdfaaf84f5f19cf",
     "locked": true,
     "points": 0,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "model = GCNMessagePassing(2708, 32, 7)\n",
    "logits = model(graph, torch.eye(2708))\n",
    "assert logits.shape == (2708, 7)\n",
    "assert logits.min() < 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "id": "7b8332d3"
   },
   "outputs": [],
   "source": [
    "model = GCNMessagePassing(in_dim=1433, hid_dim=32, out_dim=7)\n",
    "opt = Adam(model.parameters(), lr=0.01)\n",
    "log = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "CgIEmPTJ9rnr"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "8712d82d"
   },
   "source": [
    "We train the model in semi-supervised setting: propagate information over the full graph, but optimize it by only train cross-entropy loss."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 313,
     "referenced_widgets": [
      "0351df69143147e19a9406b5acb85aed",
      "1ff7b1b49b6f4f6c95814b5942f18cdf",
      "cf3d5489823641c7adaeee3a34c972b8",
      "b53e12d8eaca4089a823aa551378b382",
      "defca7b742bd42b897760bd9683386a6",
      "5f6b83bcd2ba4ed7a515bd016aa6732a",
      "54220040475a4f65b141dfe9510d458d",
      "31c05a34f2e6488097f9907d629601c9",
      "c44165fe3aa2403eb96a64ae01bbc5ac",
      "73ade8dc331f49278ff9e59aad6d72cb",
      "27f0c886fc6d423a85e7ed0201d9b530"
     ]
    },
    "id": "628bc120",
    "outputId": "3530dcbb-48b5-4fac-c596-dd78bb83afda"
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "0351df69143147e19a9406b5acb85aed",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/200 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_epochs = 200\n",
    "for i in trange(n_epochs):\n",
    "    \n",
    "    logits = model(graph, feat)\n",
    "    train_loss = F.cross_entropy(logits[train_mask], label[train_mask])\n",
    "\n",
    "    opt.zero_grad()\n",
    "    train_loss.backward()\n",
    "    opt.step()\n",
    "\n",
    "    with torch.no_grad():\n",
    "        val_loss = F.cross_entropy(logits[val_mask], label[val_mask])\n",
    "    \n",
    "    log.append([train_loss.item(), val_loss.item()])\n",
    "    \n",
    "plt.plot(np.array(log))\n",
    "plt.title('Loss')\n",
    "plt.legend(['train', 'val'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "deletable": false,
    "editable": false,
    "id": "709249ab",
    "nbgrader": {
     "cell_type": "code",
     "checksum": "d96adaccfb3d3494968ec7a788b7db10",
     "grade": true,
     "grade_id": "cell-5ec89b78a948cb61",
     "locked": true,
     "points": 0,
     "schema_version": 3,
     "solution": false,
     "task": false
    },
    "outputId": "255b210d-5054-4527-be7b-6b339e6334b2"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Balanced accuracy: 0.80\n"
     ]
    }
   ],
   "source": [
    "with torch.no_grad():\n",
    "    logits = model(graph, feat)\n",
    "y_pred = torch.argmax(logits[test_mask], 1)\n",
    "score = balanced_accuracy_score(label[test_mask], y_pred)\n",
    "assert score > 0.7\n",
    "print(f'Balanced accuracy: {score:.2f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Z7fPEGOaZI1e"
   },
   "source": [
    "### Task 3. Graph auto-encoder (3 points)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "53670340"
   },
   "source": [
    "Graph auto-encoder (GAE) was proposed in [[3]](#references) as a simple node embedding model that incorporates node features. The model is consists of two parts:\n",
    "* GCN node encoder $Z = \\text{GCN}(X, A)$ where $X$ is the feature matrix\n",
    "* Dot product decoder $\\hat A = \\sigma(ZZ^\\top)$ where $\\sigma$ is the sigmoid function\n",
    "\n",
    "Write a class `DotProductDecoder` that takes node embeddgins and returns dot product before activation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "deletable": false,
    "id": "15c460db",
    "nbgrader": {
     "cell_type": "code",
     "checksum": "94fc1408b8ccdeccd59e8c5d6f6aa5c4",
     "grade": false,
     "grade_id": "cell-a67dd0513e743f58",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "class DotProductDecoder(nn.Module):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "    def forward(self, z):\n",
    "        # YOUR CODE HERE\n",
    "        z_t = z.t()\n",
    "        A = F.relu(z@ z_t)\n",
    "        return A\n",
    "        #raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "deletable": false,
    "editable": false,
    "id": "c730e093",
    "nbgrader": {
     "cell_type": "code",
     "checksum": "627e49028327bee50ff18660bc952fb5",
     "grade": true,
     "grade_id": "cell-4f9b59eac548798b",
     "locked": true,
     "points": 1,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "decoder = DotProductDecoder()\n",
    "assert torch.all(decoder(torch.eye(2)[:, :1]) * 2 == torch.tensor([[2, 0], [0, 0]]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "34fb8d87"
   },
   "source": [
    "The GAE is trained to reconstruct the adjacency matrix, that is the decoder can be considered as the link prediction model. The reconstruction loss is the binary cross entropy between the adjacency matrix $A$ and reconstructed adjacency matrix $\\hat A$. To overcome the imbalance between positive and negative edges, the loss is computed with positive weights — the number of negative exaples divided by the number of positive examples, that is $(|V|^2 - E)/E$.\n",
    "\n",
    "Write a class `ReconstructionLoss` that takes reconstructed adjacency matrix and computes the binary cross entropy with positive weights `F.binary_cross_entropy_with_logits(label, target, pos_weights=...)`. The class is initialized by the adjacency matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "deletable": false,
    "id": "38651b0b",
    "nbgrader": {
     "cell_type": "code",
     "checksum": "e94ea2e39a78930a13843e844add7ee2",
     "grade": false,
     "grade_id": "cell-725f9456c5768b1e",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "class ReconstructionLoss:\n",
    "    def __init__(self, adj):\n",
    "      super().__init__()\n",
    "      self.adj = adj\n",
    "      v = adj.shape[0]**2\n",
    "      e = torch.sum(adj)\n",
    "      self.weight = (v-e)/e\n",
    "        # YOUR CODE HERE\n",
    "        #raise NotImplementedError()\n",
    "    \n",
    "    def __call__(self, rec_adj):\n",
    "        return F.binary_cross_entropy_with_logits(rec_adj, self.adj, pos_weight=self.weight)\n",
    "        # YOUR CODE HERE\n",
    "        #raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "deletable": false,
    "editable": false,
    "id": "575a9887",
    "nbgrader": {
     "cell_type": "code",
     "checksum": "6822debfb10e4c8eaffb38f83d7011bd",
     "grade": true,
     "grade_id": "cell-e6b239111250755e",
     "locked": true,
     "points": 1,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "rec_loss = ReconstructionLoss(torch.eye(2))\n",
    "assert round(rec_loss(1 - torch.eye(2)).item(), 4) == 1.0032"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "e9403b0b"
   },
   "source": [
    "Here we initialize encoder, decoder, reconstruction loss and optimizer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "id": "0eb7900b"
   },
   "outputs": [],
   "source": [
    "encoder = GCNMessagePassing(in_dim=1433, hid_dim=64, out_dim=32)\n",
    "decoder = DotProductDecoder()\n",
    "rec_loss = ReconstructionLoss(adj)\n",
    "opt = Adam(encoder.parameters(), lr=0.02)\n",
    "log = []"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "6b5b5f88"
   },
   "source": [
    "Complete the training loop for GAE. Train the model in unsupervised setting: calculate the reconstruction loss over all edges."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 313,
     "referenced_widgets": [
      "777356f463f54d348bfac17130ce17e4",
      "4eb4c7ca08bb48ffa48855e41422a679",
      "c3e173c06cf84109b52a5d3d8e88fbdd",
      "89f8303c6cdc4248ba0fbcb0e90143de",
      "e1076b51d8084b2ba789dad839852601",
      "05ec7b23371b448388f84d3d23844275",
      "49e0fc7c80204a21abe4de517fce456f",
      "33debd563ed34d658725cd0aeb89aab1",
      "ecd75c98792246789c1161e89b702169",
      "b74518bcd224470aa746c26b8e1054ba",
      "246e4afe159d42dbbbf7ffd06b37e46c"
     ]
    },
    "deletable": false,
    "id": "26457fa7",
    "nbgrader": {
     "cell_type": "code",
     "checksum": "e25fc920277cbb62e8b52c82bd0732c0",
     "grade": false,
     "grade_id": "cell-f1fe4005cbb20b73",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    },
    "outputId": "593ea4dc-ac97-4b1c-d1a6-91183b1152f2"
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "777356f463f54d348bfac17130ce17e4",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/400 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_epochs = 400\n",
    "for i in trange(n_epochs):\n",
    "\n",
    "  logits = encoder(graph, feat)\n",
    "  A = decoder(logits)\n",
    "  loss = rec_loss(A)\n",
    "  \n",
    "  opt.zero_grad()\n",
    "  loss.backward()\n",
    "  opt.step()\n",
    "\n",
    "    \n",
    "  log.append(loss.item())\n",
    "\n",
    "\n",
    "plt.plot(np.array(log))\n",
    "plt.title('Loss')\n",
    "plt.show()\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "63152cb4"
   },
   "source": [
    "We evaluate GAE by obtaining node embeddings via GCN encoder and training the logistic regression for node classification task."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "deletable": false,
    "editable": false,
    "id": "8219af43",
    "nbgrader": {
     "cell_type": "code",
     "checksum": "ef3b36a212c279031e8dd78a9afeae0e",
     "grade": true,
     "grade_id": "cell-85a3ec5453dd8fc2",
     "locked": true,
     "points": 1,
     "schema_version": 3,
     "solution": false,
     "task": false
    },
    "outputId": "0bca6f9a-9f51-45da-877d-e348f3b9b99b"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Balanced accuracy: 0.73\n"
     ]
    }
   ],
   "source": [
    "with torch.no_grad():\n",
    "    X = encoder.forward(graph, feat).numpy()\n",
    "y = label.numpy()\n",
    "\n",
    "lr = LogisticRegression()\n",
    "lr.fit(X[train_mask], y[train_mask])\n",
    "\n",
    "y_true = y[test_mask]\n",
    "y_pred = lr.predict(X[test_mask])\n",
    "score = balanced_accuracy_score(y_true, y_pred)\n",
    "assert score >= 0.6\n",
    "print(f'Balanced accuracy: {score:.2f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ba9a163e"
   },
   "source": [
    "Let us visualize node embeddings via t-SNE."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 499
    },
    "id": "7bd996e0",
    "outputId": "627854fd-39ba-4794-c7ef-3f7ecf39a155"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xy_emb = TSNE(n_components=2).fit_transform(X)\n",
    "plt.figure(figsize=(8, 8))\n",
    "plt.title('Node embeddings of graph auto-encoder')\n",
    "scatter = plt.scatter(xy_emb[:, 0], xy_emb[:, 1], c=label, s=10, cmap=plt.cm.Set2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "46be1142"
   },
   "source": [
    "Note that GAE is the simplest encoder-decoder graph model that can be extended to the variational graph auto-encoder (VGAE) [[3]](#references) and GraphVAE [[4]](#references)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "n1GySznuZI1i"
   },
   "source": [
    "### Task 4. Graph attention network (4 points)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "dda10446"
   },
   "source": [
    "The graph attention network (GAT) was proposed in [[5]](#references). The idea behind GAT is based on the multi-head self-attention mechanism [[6]](#references). The graph attention layer is defined by message passing as follows:\n",
    "\n",
    "$$h_i^{l} = \\sum_{j \\in \\mathcal{N}(i)}\\alpha_{ij}^{l}W_\\text{node}^{l}h_j^{l-1}$$\n",
    "\n",
    "where $\\alpha_{ij}$ is the attention score defined on each edge:\n",
    "\n",
    "$$\\alpha_{ij}^{l} = \\text{Softmax}_i(e_{ij}^{l})$$\n",
    "\n",
    "where $e_{ij}^{l}$ is the edge hidden state obtained by the linear transformation of concatenatenated nodes' hidden states and subsequent LeakyReLU activation:\n",
    "\n",
    "$$e_{ij}^{l} = \\text{LeakyReLU}(W_\\text{edge}^l[W_\\text{node}^{l}h_i^{l-1}||W_\\text{node}^{l}h_j^{l-1}])$$\n",
    "\n",
    "where $[\\cdot||\\cdot]$ is concatenation. The multi-head self-attention is defined by different types of attention score (heads) $(\\alpha_{ij}^{l})_0, (\\alpha_{ij}^{l})_1, ..., (\\alpha_{ij}^{l})_N,$. The final node's hidden state is obtained by concatenation all heads' outputs."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ed046bcf"
   },
   "source": [
    "Here is the GAT layer that calculates nodes' preliminary hidden states by `self.fc` ($W_\\text{node}$) layer and copies them to the node feature `z`, then concatenates them on edges by `edge_cat` function and copies to the edge feature `z`, then calculates attention score by `self.attn_fc` ($W_\\text{edge}$) layer and performs message passing. At the end, it concatenates the next hidden states from all heads.\n",
    "\n",
    "_Remark: `graph.apply_edges` applies an edge-wise function on all edges in the graph._"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "deletable": false,
    "editable": false,
    "id": "7df03d73",
    "nbgrader": {
     "cell_type": "code",
     "checksum": "196cc47282c1195fda00e09bd227fe79",
     "grade": false,
     "grade_id": "cell-21314765531e0c74",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "class GATLayer(nn.Module):\n",
    "    def __init__(self, in_dim, out_dim, n_heads):\n",
    "        super().__init__()\n",
    "        self.fc = nn.Linear(in_dim, out_dim)\n",
    "        self.n_heads = n_heads\n",
    "        attn_fc = []\n",
    "        for _ in range(n_heads):\n",
    "            attn_fc.append(nn.Linear(2 * out_dim, 1))\n",
    "        self.attn_fc = nn.ModuleList(attn_fc)\n",
    "        \n",
    "    def forward(self, graph, feat):\n",
    "        with graph.local_scope():\n",
    "            graph = graph.add_self_loop()\n",
    "            graph.ndata['z'] = self.fc(feat)\n",
    "            graph.apply_edges(edge_cat)\n",
    "            edge_z = graph.edata['z']\n",
    "            h = []\n",
    "            for i in range(self.n_heads):\n",
    "                graph.edata['e'] = F.leaky_relu(self.attn_fc[i](edge_z))\n",
    "                graph.update_all(message_func, reduce_func)\n",
    "                h.append(graph.ndata['h'])\n",
    "            return torch.cat(h, dim=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "fe1864c2"
   },
   "source": [
    "In DGL, we can implement specific functions that can be applied on edges or nodes. Let us define an edge-wise function that concatenates nodes' preliminary hidden states `z` and copies them to the edge feature `z`. It takes a batch of edges `dgl.udf.EdgeBatch` which contains source node features in the attribute `src`, destination node features in the attribute `dst` and edge features in the attribute `data`. For example:\n",
    "* `edges.src['z']` is the source node feature `z`\n",
    "* `edges.dst['z']` is the destination node feature `z`\n",
    "* `edges.data['e']` is the edges feature `e`\n",
    "\n",
    "Write a function `edge_cat` that takes a batch of edges and returns a dictionary where the key is `z` and the value is concatenated the source node feature `z` and the destination node feature `z`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "deletable": false,
    "id": "5b35055e",
    "nbgrader": {
     "cell_type": "code",
     "checksum": "668cbae4fbc494c01a25c8b354f258ea",
     "grade": false,
     "grade_id": "cell-ce362a06bda2e6de",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "def edge_cat(edges):\n",
    "    return {'z': torch.cat((edges.src['z'],edges.dst['z']),dim=1)}\n",
    "    # YOUR CODE HERE\n",
    "    #raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "deletable": false,
    "editable": false,
    "id": "2dba9efa",
    "nbgrader": {
     "cell_type": "code",
     "checksum": "04a8035313508d82117b7cf138a93a3a",
     "grade": true,
     "grade_id": "cell-ac20c7b9a52d701a",
     "locked": true,
     "points": 0.67,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "class EdgeBatch:\n",
    "    def __init__(self):\n",
    "        self.src = {'z': torch.arange(10).tile(3, 1)}\n",
    "        self.dst = {'z': torch.arange(10, 20).tile(3, 1)}\n",
    "        self.data = {'e': torch.arange(20).tile(5, 1)}\n",
    "edges = EdgeBatch()\n",
    "res = edge_cat(edges)\n",
    "assert res['z'].shape == (3, 20)\n",
    "assert torch.all(res['z'][0] == torch.arange(20))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "554ac592"
   },
   "source": [
    "Next, implement the message function. Message function simply copies the source nodes' feature `z` and edges' feature `e` into mailboxes `z` and `e`.\n",
    "\n",
    "Write a function `message_func` that takes a batch of edges and returns a dictionary:\n",
    "* the key is `z`, the value is source nodes' feature `z`\n",
    "* the key is `e`, the value is edges' feature `e`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "deletable": false,
    "id": "a2e0475d",
    "nbgrader": {
     "cell_type": "code",
     "checksum": "8cc00e8a928114f9d63558d06f42a931",
     "grade": false,
     "grade_id": "cell-3a18badcbd54139b",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "def message_func(edges):\n",
    "    return {'z': edges.src['z'],\n",
    "            'e': edges.data['e']}\n",
    "    # YOUR CODE HERE\n",
    "    #raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "deletable": false,
    "editable": false,
    "id": "ed8c7b78",
    "nbgrader": {
     "cell_type": "code",
     "checksum": "c856676cd953bc1526a4e30294757ecd",
     "grade": true,
     "grade_id": "cell-2ef6cc6f7d9b708f",
     "locked": true,
     "points": 0.67,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "class EdgeBatch:\n",
    "    def __init__(self):\n",
    "        self.src = {'z': torch.arange(10).tile(3, 1)}\n",
    "        self.dst = {'z': torch.arange(10, 20).tile(3, 1)}\n",
    "        self.data = {'e': torch.arange(20).tile(5, 1)}\n",
    "edges = EdgeBatch()\n",
    "res = message_func(edges)\n",
    "assert res['z'].shape == (3, 10)\n",
    "assert torch.all(res['z'][0] == torch.arange(10))\n",
    "assert res['e'].shape == (5, 20)\n",
    "assert torch.all(res['e'][0] == torch.arange(20))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "4f41c262"
   },
   "source": [
    "The reduce funtion takes a batch of nodes `dgl.udf.NodeBatch` and calculates the next hidden states of nodes by summation of preliminary hidden states `z` weighted by attention score:\n",
    "$$\\alpha_{ij} = \\text{Softmax}_i(e_{ij})$$\n",
    "$$h_i = \\sum_{j \\in \\mathcal{N}(i)}\\alpha_{ij}z_j$$\n",
    "\n",
    "The batch of nodes contains incoming messages in the attribute `mailbox` of the shape (N, D, 1), where N is the number of nodes in the batch, D is the number of messages received per node for this node batch. \n",
    "\n",
    "Write a function `reduce_func` that takes a batch of nodes with mailboxes `z` and `e` and returns a dictionary where the key is `h`, the value is the next hidden states of nodes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {
    "deletable": false,
    "id": "e5dd2e63",
    "nbgrader": {
     "cell_type": "code",
     "checksum": "95573749111fe5a7223ef0070b2d0874",
     "grade": false,
     "grade_id": "cell-fa9346fd8971f05b",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "def reduce_func(nodes):\n",
    "  e = nodes.mailbox['e']\n",
    "  z = nodes.mailbox['z']\n",
    "  a = F.softmax(e,dim = 1)\n",
    "  h = torch.sum(a*z,dim = 1)\n",
    "  return {'h':h} \n",
    "    # YOUR CODE HERE\n",
    "    #raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "deletable": false,
    "editable": false,
    "id": "d2bb6114",
    "nbgrader": {
     "cell_type": "code",
     "checksum": "8bcfc66c7f372ac14df93ceefa350d26",
     "grade": true,
     "grade_id": "cell-6cf5795c738e58f8",
     "locked": true,
     "points": 0.67,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "class NodeBatch:\n",
    "    def __init__(self):\n",
    "        self.mailbox = dict()\n",
    "        self.mailbox['e'] = torch.arange(10, 20, dtype=float).tile(3, 1)[..., None]\n",
    "        self.mailbox['z'] = torch.arange(10, dtype=float).tile(3, 1)[..., None]\n",
    "nodes = NodeBatch()\n",
    "assert reduce_func(nodes)['h'].shape == (3, 1)\n",
    "assert round(reduce_func(nodes)['h'][0].item(), 4) == 8.4185"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "a2a14cf4"
   },
   "source": [
    "Write a class `GAT` that takes a graph and a feature matrix and performs two-layer convolution with intermediate ReLU activation. The class initialized by input, hidden, output dimensions and the number of heads in the first layer. The second layer contains a single head."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {
    "deletable": false,
    "id": "56ef1c65",
    "nbgrader": {
     "cell_type": "code",
     "checksum": "48273454d4e693bf7b20e8af8dde5196",
     "grade": false,
     "grade_id": "cell-57ec6b461b254ec6",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "class GAT(nn.Module):\n",
    "    def __init__(self, in_dim, hid_dim, out_dim, n_heads):\n",
    "        super().__init__()\n",
    "        self.conv1 = GATLayer(in_dim, hid_dim, n_heads)\n",
    "        self.conv2 = GATLayer(hid_dim *n_heads, out_dim  , 1)\n",
    "        #self.conv1 = GCNMessagePassingLayer(in_dim, hid_dim)\n",
    "        #self.conv2 = GCNMessagePassingLayer(hid_dim, out_dim)\n",
    "         \n",
    "        # YOUR CODE HERE\n",
    "        #raise NotImplementedError()\n",
    "    def forward(self, graph, feat):\n",
    "        # YOUR CODE HERE\n",
    "        h = self.conv1(graph, feat)\n",
    "        h = F.relu(h)\n",
    "\n",
    "        h = self.conv2(graph, h)\n",
    "        return h\n",
    "        #raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {
    "deletable": false,
    "editable": false,
    "id": "23df8dcd",
    "nbgrader": {
     "cell_type": "code",
     "checksum": "dea3fd3cc1a0f67d8cf0ec2b4d07cfe2",
     "grade": true,
     "grade_id": "cell-fbee928783f27b2a",
     "locked": true,
     "points": 0.67,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "model = GAT(2708, 32, 7, n_heads=4)\n",
    "logits = model.conv1(graph, torch.eye(2708))\n",
    "assert logits.shape == (2708, 128)\n",
    "logits = model(graph, torch.eye(2708))\n",
    "assert logits.shape == (2708, 7)\n",
    "assert logits.min() < 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3c849aec"
   },
   "source": [
    "Let us initialize the model and the optimizer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "id": "5fefc93e"
   },
   "outputs": [],
   "source": [
    "model = GAT(in_dim=1433, hid_dim=16, out_dim=7, n_heads=3)\n",
    "opt = Adam(model.parameters(), lr=0.005, weight_decay=0.001)\n",
    "log = []"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "5e76ba50"
   },
   "source": [
    "We train the model in semi-supervised setting: propagate information over the full graph, but optimize it by only train cross-entropy loss."
   ]
  },
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_epochs = 120\n",
    "for i in trange(n_epochs):\n",
    "    \n",
    "    logits = model(graph, feat)\n",
    "    train_loss = F.cross_entropy(logits[train_mask], label[train_mask])\n",
    "\n",
    "    opt.zero_grad()\n",
    "    train_loss.backward()\n",
    "    opt.step()\n",
    "\n",
    "    with torch.no_grad():\n",
    "        val_loss = F.cross_entropy(logits[val_mask], label[val_mask])\n",
    "    \n",
    "    log.append([train_loss.item(), val_loss.item()])\n",
    "    \n",
    "plt.plot(np.array(log))\n",
    "plt.title('Loss')\n",
    "plt.legend(['train', 'val'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "deletable": false,
    "editable": false,
    "id": "e66301f3",
    "nbgrader": {
     "cell_type": "code",
     "checksum": "79efdeca8d9bd270d2ef0955d5fe5f4f",
     "grade": true,
     "grade_id": "cell-11d791f5122b19f3",
     "locked": true,
     "points": 0.67,
     "schema_version": 3,
     "solution": false,
     "task": false
    },
    "outputId": "08945887-7f7d-441c-d8cb-3f98d315c7af"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Balanced accuracy: 0.77\n"
     ]
    }
   ],
   "source": [
    "with torch.no_grad():\n",
    "    logits = model(graph, feat)\n",
    "y_pred = torch.argmax(logits[test_mask], 1)\n",
    "score = balanced_accuracy_score(label[test_mask], y_pred)\n",
    "assert score > 0.7\n",
    "print(f'Balanced accuracy: {score:.2f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "d1c7e216"
   },
   "source": [
    "We can explain model's predictions using GAT — neighbors with large attention score have the great impact to model's prediction. Let us calculate the neighbors importance using the attention score.\n",
    "\n",
    "Write a function `neighbor_importance` that takes a node index for which we want to explain the prediction, a trained GAT, a graph and a feature matrix. It returns a tuple:\n",
    "* np.array with indices of neighbors\n",
    "* np.array with attention scores on the first GAT layer for each neighbor. Attention score is averaged among all heads.\n",
    "\n",
    "_Hint: use `graph.predecessors` to obtain neighbors_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "id": "49a81627",
    "nbgrader": {
     "cell_type": "code",
     "checksum": "bbc1d91f57b98dfcf437581e2b38a755",
     "grade": false,
     "grade_id": "cell-409230373547e910",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "def neighbor_importance(expl_node, model, graph, feat):\n",
    "    with torch.no_grad(), graph.local_scope():\n",
    "        graph = graph.add_self_loop()\n",
    "        # YOUR CODE HERE\n",
    "        raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false,
    "id": "4c6190ac",
    "nbgrader": {
     "cell_type": "code",
     "checksum": "e120b8bff1738540880015ee455dcb5f",
     "grade": true,
     "grade_id": "cell-9f74e551dbc38adf",
     "locked": true,
     "points": 0.6499999999999999,
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   },
   "outputs": [],
   "source": [
    "neigh, attn = neighbor_importance(1941, model, graph, feat)\n",
    "assert type(neigh) == type(attn) == np.ndarray\n",
    "assert neigh.shape == attn.shape == (7, )\n",
    "assert round(attn.sum(), 2) == 1\n",
    "assert 1397 == neigh[attn.argmax()] or 1937 == neigh[attn.argmax()]\n",
    "plt.bar(neigh.astype('str'), attn)\n",
    "plt.xlabel('Node')\n",
    "plt.ylabel('Attention')\n",
    "plt.title('Neighbor importance')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "t51m-VOBZI1n"
   },
   "source": [
    "### Task 5. Neighbor sampling with GraphSAGE (3 points)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "308322f8"
   },
   "source": [
    "GraphSAGE (SAmple and AggreGatE) was proposed in [[7]](#references) as a model for inductive representation learning on large graph. There are two main things:\n",
    "* Neighbor sampling allows to train models in mini-batches, that is the model can be trained on large graphs and it also can represent previously unseen nodes (semi-supervised inductive learning)\n",
    "* Aggregation is perfomed separately on neighboring nodes and the node itself, that can be considered as \"skip-connections\" in graph neural networks\n",
    "\n",
    "Neighbor sampling is a technique to construct a message flow graph by randomly sampled neighbors of a target node.\n",
    "\n",
    "<img src='https://raw.githubusercontent.com/netspractice/network-science/main/images/neighbor_sampling.png' width=800>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "4bddb502"
   },
   "source": [
    "In DGL, neighbor sampling is performed by `NodeDataLoader`. First, we create sets of indices with train, validation and test nodes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "c056e85a",
    "outputId": "6ba49b68-57bf-44f1-f336-feef70e675d6"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([ 3,  7, 24, 34, 52]),\n",
       " tensor([ 2,  6,  9, 10, 22]),\n",
       " tensor([0, 1, 4, 5, 8]))"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_nids = graph.nodes()[train_mask]\n",
    "val_nids = graph.nodes()[val_mask]\n",
    "test_nids = graph.nodes()[test_mask]\n",
    "train_nids[:5], val_nids[:5], test_nids[:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "1a59f3e7"
   },
   "source": [
    "Next, we create `NeighborSampler` with given number of neighbors for each layer of our network. Let it be 4 neihbors for the first layer and 4 neighbors for the second. Next, we create dataloader with the sampler."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "292d1347",
    "outputId": "39a56bc5-3623-4854-91e1-3e2e52c29df5"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "140"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sampler = dgl.dataloading.NeighborSampler(fanouts=[4, 4])\n",
    "train_dataloader = dgl.dataloading.NodeDataLoader(graph, train_nids, sampler, batch_size=1)\n",
    "len(train_dataloader)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "f2ae454c"
   },
   "source": [
    "We have set batch size is 1, that is each batch contains a single target node. The number of train nodes is 140. Dataloader iterates over:\n",
    "* input nodes — the nodes from which we collect messages in the first layer\n",
    "* output nodes — the target nodes that aggregate messages from neighbors in the second layers\n",
    "* message flow graphs — list of graphs for layers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "bb6cba51",
    "outputId": "0dbe79e1-e824-4b8d-b80e-fda8138c79e7"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([3, 5, 1, 4, 0, 2, 7, 8, 6]), tensor([3]))"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for input_nodes, output_nodes, mfgs in train_dataloader:\n",
    "    break\n",
    "input_nodes, output_nodes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "04190b37"
   },
   "source": [
    "We see that the target node 0 aggregates messages from 0, 633, 1862, etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "49567254",
    "outputId": "e17eb4ee-38ab-4a44-f1da-e068632c1920"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([1, 2, 3, 4]), tensor([0, 0, 0, 0]))"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mfgs[1].edges()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "16cdf063"
   },
   "source": [
    "The message flow graph (MFG) for the second layer consists of neighbors of the target nodes. Note that indices of nodes in MFG differs from indices in the original graph to optimize the message passing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "b95d9250",
    "outputId": "0522594b-7f5b-4feb-a37a-ce033072b641"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([0, 1, 2, 3, 4]), tensor([0]))"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mfgs[1].srcnodes(), mfgs[1].dstnodes()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "fd8edf40"
   },
   "source": [
    "MFG is bipartite, that is messages are passing from neighbors (source nodes) 0, 1, 2, 3 to the target (destination) node 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "d6e130d0",
    "outputId": "b944e868-1e7d-4faa-e89d-b1ac2ef4935e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([4, 5, 2, 1, 5, 6, 7, 2, 1, 0, 8, 4, 8, 0, 1, 6, 5, 0, 8, 2]),\n",
       " tensor([0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4]))"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mfgs[0].edges()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "f4b74fcf"
   },
   "source": [
    "The first MFG consists of edges that follow from source nodes in the first layer (0, 1, 2, 3, 4, 5, 6, 7) to sourse nodes in the second layer (0, 1, 2, 3). Let us create train, validation and test dataloaders with batch size 64."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "8c703230",
    "outputId": "3d777849-f1fd-4032-e4cb-17a9f9c241e6"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 8, 16)"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_dataloader = dgl.dataloading.NodeDataLoader(graph, train_nids, sampler, batch_size=64)\n",
    "val_dataloader = dgl.dataloading.NodeDataLoader(graph, val_nids, sampler, batch_size=64)\n",
    "test_dataloader = dgl.dataloading.NodeDataLoader(graph, test_nids, sampler, batch_size=64)\n",
    "len(train_dataloader), len(val_dataloader), len(test_dataloader)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "a7f1688b"
   },
   "source": [
    "GraphSAGE is defined by message passing:\n",
    "\n",
    "$$h_i^l = W^l[h_i^{l-1} || \\text{Aggregation}_{j \\in \\mathcal{N}(i)}(h_j^{l-1})]$$\n",
    "\n",
    "where $[\\cdot||\\cdot]$ is concatenation. Aggregation function may be represented by average, maximum or LSTM. Let us define two-layer GraphSAGE with average aggregation and intermediate ReLU activation. `SAGEConv` layer takes the MFG and features of source node, returns the hidden of destinations nodes.\n",
    "\n",
    "Write a function `forward` that takes MFGs, feature matrix for input nodes and returns the next hidden states of output nodes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {
    "deletable": false,
    "id": "1c6d212a",
    "nbgrader": {
     "cell_type": "code",
     "checksum": "a8240c388d4a88c8baba1ad933da82ab",
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     "grade_id": "cell-42631ac0523a62a7",
     "locked": false,
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    }
   },
   "outputs": [],
   "source": [
    "class GraphSAGE(nn.Module):\n",
    "    def __init__(self, in_dim, hid_dim, out_dim):\n",
    "        super().__init__()\n",
    "        self.conv1 = SAGEConv(in_dim, hid_dim, aggregator_type='mean')\n",
    "        self.conv2 = SAGEConv(hid_dim, out_dim, aggregator_type='mean')\n",
    "\n",
    "    def forward(self, mfgs, feat):\n",
    "        h = self.conv1(mfgs, feat)\n",
    "        h = F.relu(h())\n",
    "        h = self.conv2(mfgs, h)\n",
    "        return h\n",
    "        # YOUR CODE HERE\n",
    "        #raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "e747b35e"
   },
   "source": [
    "We train the model in semi-supervised setting: propagate information over the full graph, but optimize it by only train cross-entropy loss.\n",
    "\n",
    "Write a function `train_epoch` that takes GraphSAGE model, train dataloader, validation dataloader, the full feature matrix, labels and optimizer. It returns a tuple: the average train loss and the average validation loss. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "id": "d43c50da",
    "nbgrader": {
     "cell_type": "code",
     "checksum": "73d95920bbbccb1a805f27142fe43168",
     "grade": false,
     "grade_id": "cell-7a7eb641f7d14a3b",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
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   },
   "outputs": [],
   "source": [
    "def train_epoch(model, train_dataloader, val_dataloader, feat, label, opt):\n",
    "\n",
    "    logits = model(train_dataloader, feat)\n",
    "    train_loss = F.cross_entropy(logits[train_mask], label[train_mask])\n",
    "\n",
    "    opt.zero_grad()\n",
    "    train_loss.backward()\n",
    "    opt.step()\n",
    "\n",
    "    with torch.no_grad():\n",
    "        val_loss = F.cross_entropy(logits[val_mask], label[val_mask])\n",
    "    \n",
    "    log.append([train_loss.item(), val_loss.item()])\n",
    "    \n",
    "    # YOUR CODE HERE\n",
    "    #raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false,
    "id": "8776fb7b",
    "nbgrader": {
     "cell_type": "code",
     "checksum": "680b7450b92d8a2c0f5eaa77d0749eba",
     "grade": true,
     "grade_id": "cell-a6c94febdc58013b",
     "locked": true,
     "points": 1.5,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "model = GraphSAGE(1433, 16, 7)\n",
    "opt = Adam(model.parameters(), lr=0.1)\n",
    "train_loss, val_loss = train_epoch(model, train_dataloader, val_dataloader, feat, label, opt)\n",
    "assert type(train_loss) == float\n",
    "assert type(val_loss) == float\n",
    "assert 1.8 < train_loss < 2.2\n",
    "assert 1.8 < val_loss < 2.2\n",
    "train_loss, val_loss = train_epoch(model, train_dataloader, val_dataloader, feat, label, opt)\n",
    "train_loss, val_loss = train_epoch(model, train_dataloader, val_dataloader, feat, label, opt)\n",
    "assert train_loss < val_loss"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "e5530e48"
   },
   "source": [
    "Initialize the model and optimizers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "a58dff00"
   },
   "outputs": [],
   "source": [
    "model = GraphSAGE(1433, 16, 7)\n",
    "opt = Adam(model.parameters(), lr=0.01)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "28def0b8"
   },
   "source": [
    "Train the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "55698c78"
   },
   "outputs": [],
   "source": [
    "log = []\n",
    "n_epochs = 50\n",
    "for i in trange(n_epochs):\n",
    "    train_loss, val_loss = train_epoch(model, train_dataloader, val_dataloader, feat, label, opt)\n",
    "    log.append([train_loss, val_loss])\n",
    "plt.plot(np.array(log))\n",
    "plt.title('Loss')\n",
    "plt.legend(['train', 'val'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false,
    "id": "9d0c16d2",
    "nbgrader": {
     "cell_type": "code",
     "checksum": "7c5bce0504893fe5753e233815f38af4",
     "grade": true,
     "grade_id": "cell-1f31b207a4f89e8f",
     "locked": true,
     "points": 1.5,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "logits = []\n",
    "for input_nodes, output_nodes, mfgs in test_dataloader:\n",
    "    with torch.no_grad():\n",
    "        logits.append(model(mfgs, feat[input_nodes]))\n",
    "logits = torch.cat(logits)\n",
    "y_pred = torch.argmax(logits, 1)\n",
    "score = balanced_accuracy_score(label[test_mask], y_pred)\n",
    "assert score > 0.7\n",
    "print(f'Balanced accuracy: {score:.2f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "8MiNtnaJZI1w"
   },
   "source": [
    "### References"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "yx1Gi4FdZI1x"
   },
   "source": [
    "<a id='references'></a>\n",
    "\n",
    "[1] Kipf, T. N., & Welling, M. (2016). Semi-Supervised Classification with Graph Convolutional Networks. CoRR, abs/1609.02907. http://arxiv.org/abs/1609.02907\n",
    "\n",
    "[2] Gilmer, J., Schoenholz, S. S., Riley, P. F., Vinyals, O., & Dahl, G. E. (2017). Neural Message Passing for Quantum Chemistry. CoRR, abs/1704.01212. http://arxiv.org/abs/1704.01212\n",
    "\n",
    "[3] Kipf, T. N., & Welling, M. (2016). Variational Graph Auto-Encoders. arXiv. https://doi.org/10.48550/ARXIV.1611.07308\n",
    "\n",
    "[4] Simonovsky, M., & Komodakis, N. (2018). GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders. CoRR, abs/1802.03480. http://arxiv.org/abs/1802.03480\n",
    "\n",
    "[5] VeliДЌkoviД‡, P., Cucurull, G., Casanova, A., Romero, A., LiГІ, P., & Bengio, Y. (2017). Graph Attention Networks. arXiv. https://doi.org/10.48550/ARXIV.1710.10903\n",
    "\n",
    "[6] Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., Kaiser, L., & Polosukhin, I. (2017). Attention Is All You Need. CoRR, abs/1706.03762. http://arxiv.org/abs/1706.03762\n",
    "\n",
    "[7] Hamilton, W. L., Ying, R., & Leskovec, J. (2017). Inductive Representation Learning on Large Graphs. CoRR, abs/1706.02216. http://arxiv.org/abs/1706.02216"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "xX9vu9x5ZI1x"
   },
   "outputs": [],
   "source": []
  }
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