(16) KG , Translation models , Entity embeddings, Nearest neighbors of entities,Relation prediction,Tail prediction.ipynb

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        "id": "rdT5X78peJXu"
      },
      "source": [
        "# Assignment — Knowledge graphs"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 192,
      "metadata": {
        "id": "6tNRVCujeJXx"
      },
      "outputs": [],
      "source": [
        "import pandas as pd\n",
        "from tqdm.notebook import tqdm, trange\n",
        "import numpy as np\n",
        "import requests\n",
        "pd.options.display.max_colwidth = 100\n",
        "from zlib import adler32"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lY0GE2bdeJXy"
      },
      "source": [
        "### Task 1. Freebase dataset (0.0 points)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f6478877"
      },
      "source": [
        "In this assignment we will see how to use the [TorchKGE](https://github.com/torchkge-team/torchkge) library for building knowledge graphs and its embeddings. To begin with we are going to need a knowledge graph, so let us load a standard knowledge graph dataset called _Freebase-15k-237_."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 193,
      "metadata": {
        "id": "facb26f6"
      },
      "outputs": [],
      "source": [
        "df = pd.read_csv(\n",
        "    \"https://raw.githubusercontent.com/netspractice/network-science/main/datasets/freebase-237-merged-and-remapped.csv.gz\", \n",
        "    names=['h', 'r', 't'])"
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              "                                                h  \\\n",
              "0     queens college, city university of new york   \n",
              "1103                                 sharon stone   \n",
              "2210                                        japan   \n",
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              "8840              the perks of being a wallflower   \n",
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              "\n",
              "                                                                                       r  \\\n",
              "0     /education/educational_institution/students_graduates./education/education/student   \n",
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      ],
      "source": [
        "df = df[~df.h.str.startswith('/') & ~df.t.str.startswith('/')]\n",
        "df[::1000].head(10)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
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      "source": [
        "There is h — head (also subject), r — relation (also predicat, label), t — tail (also object). The shape of the dataset is"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 195,
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              "(282560, 3)"
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        "df.shape"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "b3f19608"
      },
      "source": [
        "Let us check the number of unique entities and unique relations.\n",
        "\n",
        "Write a funtion `n_ent_rel` that takes a dataset and returns a number of unique entities and unique relations.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 196,
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      "source": [
        "def n_ent_rel(df):\n",
        "    heads_and_tails = set(df.h) | set(df.t)\n",
        "    tails = set(df.r)\n",
        "    return len(heads_and_tails), len(tails)"
      ]
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          "metadata": {},
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      ],
      "source": [
        "n_ent, n_rel = n_ent_rel(df)\n",
        "assert adler32(str(n_ent + n_ent).encode()) == 50266365\n",
        "n_ent, n_rel"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
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      "source": [
        "We can look at all facts about any entity via pandas API"
      ]
    },
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              "                       h                                        r  \\\n",
              "4107   aleksandr pushkin                /people/person/profession   \n",
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              "                                t  \n",
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              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
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              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 198
        }
      ],
      "source": [
        "df[df.h ==  'aleksandr pushkin'].head()"
      ]
    },
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      "cell_type": "code",
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            "text/plain": [
              "                        h  \\\n",
              "145219  aleksandr pushkin   \n",
              "\n",
              "                                                                         r  \\\n",
              "145219  /influence/influence_node/peers./influence/peer_relationship/peers   \n",
              "\n",
              "                    t  \n",
              "145219  nikolai gogol  "
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      "source": [
        "df[(df.h ==  'aleksandr pushkin') & (df.t == 'nikolai gogol')]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 200,
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        {
          "output_type": "execute_result",
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            "text/plain": [
              "                    h  \\\n",
              "86362   nikolai gogol   \n",
              "269512  nikolai gogol   \n",
              "\n",
              "                                                                         r  \\\n",
              "86362   /influence/influence_node/peers./influence/peer_relationship/peers   \n",
              "269512                             /influence/influence_node/influenced_by   \n",
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              "\n",
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          },
          "metadata": {},
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        }
      ],
      "source": [
        "df[(df.h ==  'nikolai gogol') & (df.t == 'aleksandr pushkin')]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dc9bdf03"
      },
      "source": [
        "Let us try to find some facts in this dataset. For example, what is Harrison Ford's nationality? (\"harrison ford\" in the dataset)\n",
        "\n",
        "Write a function `harrison_ford_nationality` that takes a dataset and returns the nationality.\n",
        "\n",
        "_Hint: use `pandas.Series.str.contains` method_"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 201,
      "metadata": {
        "deletable": false,
        "nbgrader": {
          "cell_type": "code",
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        "id": "4e6bb702"
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      "outputs": [],
      "source": [
        "def harrison_ford_nationality(df):\n",
        "    f = (df.h == \"harrison ford\") & (df.r.str.contains(\"nationality\"))\n",
        "    tmp = df[f]\n",
        "    return tmp.iloc[0].t"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 202,
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "33ecca395ecdf947984d8d303239d6e8",
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          "grade_id": "cell-e20681a97039cdf6",
          "locked": true,
          "points": 0,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "4320c1f6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "7373d8c5-f4f5-40b9-e265-9beb0cb15c80"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "'united states of america'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {},
          "execution_count": 202
        }
      ],
      "source": [
        "assert adler32(harrison_ford_nationality(df).encode()) == 1948191013\n",
        "harrison_ford_nationality(df)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "473842ae"
      },
      "source": [
        "More tricky question: who are film directors of movies where Harrison Ford was?\n",
        "\n",
        "Write a function `made_films_with_harrison_ford` that returns a set of directors' names."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 203,
      "metadata": {
        "deletable": false,
        "nbgrader": {
          "cell_type": "code",
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        },
        "id": "2f0f48bf"
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      "outputs": [],
      "source": [
        "def made_films_with_harrison_ford(df):\n",
        "    f = (df.h == \"harrison ford\") & df.r.str.contains(\"actor\")\n",
        "    set_of_films_with_ford = set(df[f].t)\n",
        "    f = df.t.isin(set_of_films_with_ford) & df.r.str.contains(\"director\")\n",
        "    return set(df[f].h)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 204,
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "2eb7754948b26f5dd5ea253755fa788b",
          "grade": true,
          "grade_id": "cell-f3dbc03094dcbb5b",
          "locked": true,
          "points": 0,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "57e619bd",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "659f48b9-c689-4a16-8635-0aec52ec9c4b"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{'francis ford coppola',\n",
              " 'george lucas',\n",
              " 'jon favreau filmography',\n",
              " 'kathryn bigelow',\n",
              " 'mike nichols',\n",
              " 'ridley scott',\n",
              " 'robert zemeckis',\n",
              " 'steven spielberg'}"
            ]
          },
          "metadata": {},
          "execution_count": 204
        }
      ],
      "source": [
        "directors = made_films_with_harrison_ford(df)\n",
        "assert adler32(str(sorted(directors)).encode()) == 3798415057\n",
        "directors"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mUsxUpjoeJX6"
      },
      "source": [
        "### Task 2. Translation models (0.0 points)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4b1fe0e9"
      },
      "source": [
        "TransE (translations in the embedding space) is a method which models relationships by interpreting them as translations operating on the low-dimensional embeddings of the entities.\n",
        "\n",
        "Let us implement the model using TorchKGE — a Python module for knowledge graph embedding relying solely on Pytorch."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 205,
      "metadata": {
        "id": "d59878ae",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "33d96b3d-1b8c-4b3d-f1d8-a8a43420626f"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Requirement already satisfied: torchkge==0.16.25 in /usr/local/lib/python3.7/dist-packages (0.16.25)\n",
            "Requirement already satisfied: pandas in /usr/local/lib/python3.7/dist-packages (from torchkge==0.16.25) (1.3.5)\n",
            "Requirement already satisfied: torch>=1.2.0 in /usr/local/lib/python3.7/dist-packages (from torchkge==0.16.25) (1.11.0+cu113)\n",
            "Requirement already satisfied: tqdm in /usr/local/lib/python3.7/dist-packages (from torchkge==0.16.25) (4.64.0)\n",
            "Requirement already satisfied: typing-extensions in /usr/local/lib/python3.7/dist-packages (from torch>=1.2.0->torchkge==0.16.25) (4.2.0)\n",
            "Requirement already satisfied: numpy>=1.17.3 in /usr/local/lib/python3.7/dist-packages (from pandas->torchkge==0.16.25) (1.21.6)\n",
            "Requirement already satisfied: pytz>=2017.3 in /usr/local/lib/python3.7/dist-packages (from pandas->torchkge==0.16.25) (2022.1)\n",
            "Requirement already satisfied: python-dateutil>=2.7.3 in /usr/local/lib/python3.7/dist-packages (from pandas->torchkge==0.16.25) (2.8.2)\n",
            "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.7/dist-packages (from python-dateutil>=2.7.3->pandas->torchkge==0.16.25) (1.15.0)\n"
          ]
        }
      ],
      "source": [
        "!pip install torchkge==0.16.25 "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 206,
      "metadata": {
        "id": "ca8a243b"
      },
      "outputs": [],
      "source": [
        "import torch\n",
        "from torch import nn\n",
        "import torch.nn.functional as F\n",
        "from torchkge import KnowledgeGraph\n",
        "from torchkge.utils import Trainer\n",
        "from torchkge.evaluation import LinkPredictionEvaluator\n",
        "from torchkge.models.interfaces import TranslationModel\n",
        "from torch.nn.init import xavier_uniform_"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "913de2fd"
      },
      "source": [
        "<img src='https://github.com/netspractice/ml-on-graphs/raw/main/assignment_knowledge_graph_embedding/kge.png' width=300>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "d24c0ca2"
      },
      "source": [
        "The basic idea behind the model is that the functional relation induced by the $r$-labeled edges corresponds to a translation of the embeddings, i.e. we want that $h + r \\approx t$ when ($h$, $r$, $t$) holds ($t$ should be a nearest neighbor of $h + r$), while $h + r$ should be far away from $t$ otherwise. Thereby, TransE scoring function is negative distance between $h+r$ and $t$\n",
        "\n",
        "$$f(h, r, t) = -||h + r - t||$$\n",
        "\n",
        "where $||\\cdot||$ is L1 or L2 norm. The goal of the optimization procedure is learning optimal embeddings, such that the scoring function is able to assign high scores to positive statements and low scores to statements unlikely to be true. The most common loss function is Margin Loss that can be represented as\n",
        "\n",
        "$$L = \\text{ReLU}\\left(\\gamma - f(h, r, t) + f(h', r, t')\\right)$$\n",
        "\n",
        "where $\\gamma > 0$ is a \"margin\" hyperparameter, the triplet $(h, r, t)$ is in a training set (positive) and the $(h', r, t')$ is in a set of *corrupted* (negative) triplets, that are composed of training triplets with either the head or tail replaced by a random entity (but not both at the same time)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "87808531"
      },
      "source": [
        "We will use TorchKGE TranslationModel as a base for TransE class, here are some auxiliary methods: \n",
        "\n",
        "* `normalize_parameters` applies `L2` normalization for training stability\n",
        "* `get_embeddings` returns the tensors representing entities and relations\n",
        "* `lp_prep_cands` gets entities and relations embeddings for link prediction training process\n",
        "* `forward` returns scores for positive triplets (`h`, `r`, `t`) and negative triplets (`nh`, `r`, `nt`)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 207,
      "metadata": {
        "id": "7280f803"
      },
      "outputs": [],
      "source": [
        "class BaseTransE(TranslationModel):\n",
        "    def __init__(self, num_entities, num_relations, dim=100):\n",
        "        super(BaseTransE, self).__init__(num_entities, num_relations, dissimilarity_type='L2')\n",
        "        self.num_entities = num_entities\n",
        "        self.num_relations = num_relations\n",
        "        self.dim = dim\n",
        "        self.ent_embeddings = nn.Embedding(num_entities, self.dim)\n",
        "        self.rel_embeddings = nn.Embedding(num_relations, self.dim)\n",
        "        \n",
        "    def normalize_parameters(self):\n",
        "        self.ent_embeddings.weight.data = F.normalize(self.ent_embeddings.weight.data, p=2, dim=1)\n",
        "\n",
        "    def get_embeddings(self):\n",
        "        self.normalize_parameters()\n",
        "        return self.ent_embeddings.weight.data, self.rel_embeddings.weight.data\n",
        "        \n",
        "    def lp_prep_cands(self, h_idx, t_idx, r_idx):\n",
        "        b_size = h_idx.shape[0]\n",
        "\n",
        "        h_emb = self.ent_embeddings(h_idx)\n",
        "        t_emb = self.ent_embeddings(t_idx)\n",
        "        r_emb = self.rel_embeddings(r_idx)\n",
        "\n",
        "        candidates = self.ent_embeddings.weight.data.view(1, self.num_entities, self.dim)\n",
        "        candidates = candidates.expand(b_size, self.num_entities, self.dim)\n",
        "\n",
        "        return h_emb, t_emb, candidates, r_emb\n",
        "    \n",
        "    def forward(self, h, t, nh, nt, r):\n",
        "        return self.scoring_function(h, t, r), self.scoring_function(nh, nt, r)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ca3ee02b"
      },
      "source": [
        "Write a function `scoring_function` that takes a tensor `h`, `t`, `r` with triplets of the shape (number of triplets) and returns its L2 scores. For training stability, apply L2 normalization (`F.normalize`  with `p=2`) on entities embeddings before computing the scores. Note that `h`, `t`, `r` are tensors with integer IDs of entities and relations."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 208,
      "metadata": {
        "deletable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "b28acb89a574281b6b491dc2a892fa97",
          "grade": false,
          "grade_id": "cell-10c450a856899a4f",
          "locked": false,
          "schema_version": 3,
          "solution": true,
          "task": false
        },
        "id": "d0011822"
      },
      "outputs": [],
      "source": [
        "class TransE(BaseTransE):\n",
        "    def scoring_function(self, h, t, r):\n",
        "        h_emb = self.ent_embeddings(h)\n",
        "        t_emb = self.ent_embeddings(t)\n",
        "        r_emb = self.rel_embeddings(r)\n",
        "\n",
        "        h_emb = F.normalize(h_emb, p=2, dim=1)\n",
        "        t_emb = F.normalize(t_emb, p=2, dim=1)\n",
        "        score = (h_emb + r_emb) - t_emb\n",
        "        return -torch.norm(score, p=2, dim=1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 209,
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "cbdaf22fe01f7bfe4d19358cfa593ddf",
          "grade": true,
          "grade_id": "cell-89f5ccbf84380079",
          "locked": true,
          "points": 0,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "fdd6e41d"
      },
      "outputs": [],
      "source": [
        "model = TransE(num_entities=5, num_relations=2, dim=2)\n",
        "\n",
        "h = torch.LongTensor([1, 1, 1])\n",
        "r = torch.LongTensor([0, 1, 1])\n",
        "t = torch.LongTensor([2, 2, 3])\n",
        "\n",
        "with torch.no_grad():\n",
        "    scores = model.scoring_function(h, t, r).numpy()\n",
        "assert scores.shape == (3, ) # 3 triplets"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1460dae6"
      },
      "source": [
        "Complete the class `MarginLoss` so that computes the losses among scores and returns an average loss. Positive and negative scores are tensors of the shape (number of triplets)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 210,
      "metadata": {
        "deletable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "e152703e15d1c0adb58fa5f20649adcc",
          "grade": false,
          "grade_id": "cell-3fb7cb717cb420cb",
          "locked": false,
          "schema_version": 3,
          "solution": true,
          "task": false
        },
        "id": "6996f6b3"
      },
      "outputs": [],
      "source": [
        "class MarginLoss(nn.Module):\n",
        "    def __init__(self, margin):\n",
        "        super().__init__()\n",
        "        self.margin = margin\n",
        "    def forward(self, positive_scores, negative_scores):\n",
        "        return F.relu(self.margin - positive_scores + negative_scores).mean()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 211,
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "ddad8c020d3e0fe7112475c8f7a059fd",
          "grade": true,
          "grade_id": "cell-b28b48d0354bf7be",
          "locked": true,
          "points": 0,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "1c789666"
      },
      "outputs": [],
      "source": [
        "loss_fn = MarginLoss(margin=0.5)\n",
        "torch.manual_seed(0)\n",
        "positive_scores = torch.randn(8)\n",
        "negative_scores = torch.randn(8)\n",
        "loss = loss_fn(positive_scores, negative_scores)\n",
        "assert loss.shape == torch.Size([])\n",
        "assert round(loss.item(), 2) == 0.79"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "40e66c15"
      },
      "source": [
        "Let us look at the WikiDataSet that presents country-specific subgraphs of Wikidata."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 212,
      "metadata": {
        "id": "39f768ae"
      },
      "outputs": [],
      "source": [
        "url = 'https://raw.githubusercontent.com/netspractice/network-science/main/datasets/countries_edges.tsv'\n",
        "open('countries_edges.tsv', 'wb').write(requests.get(url).content)\n",
        "url = 'https://raw.githubusercontent.com/netspractice/network-science/main/datasets/countries_entities.tsv'\n",
        "open('countries_entities.tsv', 'wb').write(requests.get(url).content)\n",
        "url = 'https://raw.githubusercontent.com/netspractice/network-science/main/datasets/countries_relations.tsv'\n",
        "open('countries_relations.tsv', 'wb').write(requests.get(url).content);"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 213,
      "metadata": {
        "id": "6430aa5b"
      },
      "outputs": [],
      "source": [
        "edges = pd.read_csv('countries_edges.tsv', sep='\t').values\n",
        "entity_labels = pd.read_csv('countries_entities.tsv', sep='\t', index_col=0).label.values\n",
        "relation_labels = pd.read_csv('countries_relations.tsv', sep='\t', index_col=0).label.values"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 214,
      "metadata": {
        "id": "cac5db83",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "outputId": "0f7b7cb3-4aa4-48f9-d13f-1ffc9d2f11f3"
      },
      "outputs": [
        {
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          "data": {
            "text/plain": [
              "         h                    r              t\n",
              "0  Belgium              country        Belgium\n",
              "1  Belgium  diplomatic relation     Luxembourg\n",
              "2  Belgium  diplomatic relation          Italy\n",
              "3  Belgium  diplomatic relation        Germany\n",
              "4  Belgium  diplomatic relation  Liechtenstein"
            ],
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              "      <td>Belgium</td>\n",
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              "      <th>1</th>\n",
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              "      <td>diplomatic relation</td>\n",
              "      <td>Luxembourg</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>Belgium</td>\n",
              "      <td>diplomatic relation</td>\n",
              "      <td>Italy</td>\n",
              "    </tr>\n",
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              "      <th>3</th>\n",
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              "      <td>diplomatic relation</td>\n",
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              "      <th>4</th>\n",
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          },
          "metadata": {},
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        }
      ],
      "source": [
        "edges_labeled = np.stack([entity_labels[edges[:, 0]], \n",
        "                          entity_labels[edges[:, 1]], \n",
        "                          relation_labels[edges[:, 2]]], axis=1)\n",
        "\n",
        "df = pd.DataFrame(edges_labeled, columns=['h', 't', 'r'])[['h', 'r', 't']]\n",
        "df.head()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "96e03f08"
      },
      "source": [
        "Here are unique relations with the number of triplets"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 215,
      "metadata": {
        "id": "1d4ef2bd",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "05dbfe74-cd3e-4311-9872-a175c930d56e"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "r\n",
              "applies to jurisdiction                                        1\n",
              "basic form of government                                       3\n",
              "biological process                                             1\n",
              "capital                                                       34\n",
              "capital of                                                    25\n",
              "contains administrative territorial entity                    94\n",
              "country                                                     1339\n",
              "country of citizenship                                         5\n",
              "country of origin                                              1\n",
              "culture                                                        3\n",
              "designated as terrorist by                                     9\n",
              "different from                                               113\n",
              "diplomatic relation                                         6145\n",
              "enclave within                                                 3\n",
              "facet of                                                      13\n",
              "family                                                         1\n",
              "followed by                                                  332\n",
              "follows                                                      316\n",
              "founded by                                                    11\n",
              "has contributing factor                                        1\n",
              "has part                                                     121\n",
              "headquarters location                                          8\n",
              "history of topic                                               2\n",
              "instance of                                                   18\n",
              "located in present-day administrative territorial entity       7\n",
              "located in the administrative territorial entity             212\n",
              "located on terrain feature                                    13\n",
              "location                                                       5\n",
              "location of formation                                          1\n",
              "member of                                                     36\n",
              "merged into                                                    3\n",
              "named after                                                   14\n",
              "opposite of                                                    2\n",
              "owned by                                                       2\n",
              "part of                                                      121\n",
              "partially coincident with                                      4\n",
              "permanent duplicated item                                      2\n",
              "replaced by                                                  462\n",
              "replaces                                                     414\n",
              "said to be the same as                                         8\n",
              "separated from                                                15\n",
              "shares border with                                          1395\n",
              "significant event                                              6\n",
              "subclass of                                                    6\n",
              "territory claimed by                                          18\n",
              "territory overlaps                                             4\n",
              "time period                                                    8\n",
              "topic's main category                                          2\n",
              "twinned administrative body                                    2\n",
              "Name: r, dtype: int64"
            ]
          },
          "metadata": {},
          "execution_count": 215
        }
      ],
      "source": [
        "df.r.groupby(df.r).count()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "767c8128"
      },
      "source": [
        "Convert our dataset into a TorchKGE knowledge graph"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 216,
      "metadata": {
        "id": "e315fd6c"
      },
      "outputs": [],
      "source": [
        "kg = KnowledgeGraph(\n",
        "    pd.DataFrame(edges_labeled, columns=['from', 'to', 'rel']))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7cd9ac15"
      },
      "source": [
        "Split the dataset into train and test set. What differs from the standard method of randomly sampling N points to make up our test set, is that our data points are two entities linked by some relationship, and we need to take care to ensure that all entities are represented in train and test sets by at least one triple.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 217,
      "metadata": {
        "id": "86485e1b"
      },
      "outputs": [],
      "source": [
        "kg_train, kg_test = kg.split_kg()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "45027cae"
      },
      "source": [
        "Create required objects: model, loss, optimizer and trainer."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 218,
      "metadata": {
        "id": "949a0024"
      },
      "outputs": [],
      "source": [
        "model = TransE(kg_train.n_ent, kg_train.n_rel, dim=64)\n",
        "criterion = MarginLoss(margin=0.5)\n",
        "optimizer = torch.optim.Adam(model.parameters(), lr=0.005)\n",
        "\n",
        "trainer = Trainer(\n",
        "    model, criterion, kg_train, n_epochs=500, \n",
        "    batch_size=2048, optimizer=optimizer)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ddd51ca4"
      },
      "source": [
        "During training, positive triplets are selected, negative triplets are generated, margin loss is calculated and then the gradient step is performed."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 219,
      "metadata": {
        "id": "26513e9f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 49,
          "referenced_widgets": [
            "4d2349b3b0c741af900d20cb1dff6886",
            "59c53ed4c7d34c70ab6cfdd2bdb04c38",
            "31c9fbe8688f43dc984c898c583b4d32",
            "ac5f547c595f4d479c8ecc813c418345",
            "73aa4aa539cf4355ac5c25d3be0a06e2",
            "2a46b511189a445f8de6583721766601",
            "aa8c4e0600724b1db24a847e4fda9830",
            "b98f975d1dbb48d1bcdfda4278fc1881",
            "69c470d9836b4173bf027b59f7d9747f",
            "85ed2a1f151c41a184d138c2f042e324",
            "774ae9563b9f47ae8286149f4ac7d41c"
          ]
        },
        "outputId": "64f403dd-1abf-42c9-d66b-afe4558a5407"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "  0%|          | 0/500 [00:00<?, ?epoch/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "4d2349b3b0c741af900d20cb1dff6886"
            }
          },
          "metadata": {}
        }
      ],
      "source": [
        "trainer.run()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "b27a7911"
      },
      "source": [
        "Let us evaluate our model on the link prediction task"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 220,
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "a299a76160d560f54404e83da29d3379",
          "grade": true,
          "grade_id": "cell-e6b0a4e916e8c503",
          "locked": true,
          "points": 0,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "ba2026aa",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 49,
          "referenced_widgets": [
            "b67936bdf11c4a588c6d09e0bd179186",
            "ee47ca771c784ea5abf701005b2cb948",
            "a6410fdfc632403ab5528b6f48b17601",
            "be22475b882346ddbdc685c6b12a17d8",
            "8a0ce9e6615f4811a6eb3d6a9ad8ad7c",
            "cf208f3d6ec0487b9659e5512b197ca2",
            "a4371f95ae2d47a1b1df1a8b141921fa",
            "bdcf5d1ae2f140a6bab5415cb58e3be1",
            "9c6d2efa64bf4a8f978c18ddd259b3a6",
            "137a6f9b26ba4b15aabd98e4e5138105",
            "f0ff88c0f84c41a68e10d946a579f542"
          ]
        },
        "outputId": "2da2ee8a-918e-43d2-f1c2-2f68bcb35048"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Link prediction evaluation:   0%|          | 0/17 [00:00<?, ?batch/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "b67936bdf11c4a588c6d09e0bd179186"
            }
          },
          "metadata": {}
        }
      ],
      "source": [
        "evaluator = LinkPredictionEvaluator(model, kg_test)\n",
        "evaluator.evaluate(b_size=128)\n",
        "\n",
        "assert evaluator.hit_at_k(k=10)[0] > 0.3\n",
        "assert evaluator.mean_rank()[0] < 70\n",
        "assert evaluator.mrr()[0] > 0.1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 221,
      "metadata": {
        "id": "ba1f7516",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "fad3d137-f6ea-464a-e9e0-6ca78fd63644"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Hit@10: 0.3337\n",
            "Mean Rank: 66.4624\n",
            "MRR: 0.1389\n"
          ]
        }
      ],
      "source": [
        "print('Hit@10: {:.4f}'.format(evaluator.hit_at_k(k=10)[0]))\n",
        "print('Mean Rank: {:.4f}'.format(evaluator.mean_rank()[0]))\n",
        "print('MRR: {:.4f}'.format(evaluator.mrr()[0]))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4c2ce4e5"
      },
      "source": [
        "`Hit@k` indicates how many times in average a true triple was ranked in the top-k.\n",
        "\n",
        "`Mean Rank` is a mean rank of the true entity when replacing alternatively head and tail in any fact of the dataset.\n",
        "\n",
        "`MRR` is an average of mean recovery rank for head and tail replacement."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cvv2UBLCeJYE"
      },
      "source": [
        "### Task 3. Entity embeddings (2.5 points)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 222,
      "metadata": {
        "id": "a0fc34f6"
      },
      "outputs": [],
      "source": [
        "from sklearn.decomposition import TruncatedSVD\n",
        "from sklearn.cluster import k_means\n",
        "import matplotlib.pyplot as plt\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5433cf80"
      },
      "source": [
        "Similarly to node embedding visualization, we can plot 2D embeddings of entities of knowledge graph.\n",
        "\n",
        "Write a function `ent_embeddgins` that takes the model, transforms entity embeddings into 2-dimenstional space via SVD, then finds 2 clusters via k-means and finally returns a tuple: np.array with embeddings and 0/1 labels of clusters."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 223,
      "metadata": {
        "deletable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "17f1706f3d95cf3e2c3d9107ca211a69",
          "grade": false,
          "grade_id": "cell-c79123779965d790",
          "locked": false,
          "schema_version": 3,
          "solution": true,
          "task": false
        },
        "id": "dbc9b605"
      },
      "outputs": [],
      "source": [
        "def ent_embeddgins(model):\n",
        "    svd = TruncatedSVD()\n",
        "    output = svd.fit_transform(np.array(model.ent_embeddings.weight.data))\n",
        "    centroids , labels , interia  = k_means(output,2)\n",
        "    return output , labels\n",
        "    # YOUR CODE HERE\n",
        "    #raise NotImplementedError()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 224,
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "9b9bd3f420bac9892056ac2c1f37c0b2",
          "grade": true,
          "grade_id": "cell-c4d5a66741d71c62",
          "locked": true,
          "points": 2.5,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "6cbae81a"
      },
      "outputs": [],
      "source": [
        "ent_emb, labels = ent_embeddgins(model)\n",
        "assert ent_emb.shape == (1810, 2)\n",
        "assert labels.shape == (1810,)\n",
        "n_label1 = (labels == 1).sum()\n",
        "n_label0 = (labels == 0).sum()\n",
        "assert 0.14 < min(n_label1, n_label0) / max(n_label1, n_label0) < 0.18"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 225,
      "metadata": {
        "id": "7fe88cd5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 336
        },
        "outputId": "f34f142c-66a4-49e6-eb7f-085b01d45577"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x360 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "plt.figure(figsize=(8, 5))\n",
        "colors = np.array(plt.cm.tab10.colors)\n",
        "plt.scatter(ent_emb[:, 0], ent_emb[:, 1], s=10, c=colors[labels])\n",
        "plt.title('Entity embeddings')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "595b2ba3"
      },
      "source": [
        "Let us look at some randomly chosen entities from each cluster. Here we use `kg.ent2ix` dictionary to get labels of entities."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 226,
      "metadata": {
        "id": "6b09c78c",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "505ce79c-bd67-4dd2-f84f-baa4a51c5b10"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "First cluster:  Commonwealth realm of Kenya, Kaluga Soviet Republic, Goa, Daman and Diu, French Second Republic, Republic of Venice, Amarasi, regne de Zion, Kingdom of Gumma, Republica de la Comrat, Repubblica dell'Alto Monferrato\n",
            "\n",
            "Second cluster:  Tajikistan, Libya, Kingdom of the Netherlands, Nepal, Kingdom of Bulgaria, Villes libres de Menton et Roquebrune, Republic of Cyprus, Maldives, Artsakh, Sahrawi Arab Democratic Republic\n"
          ]
        }
      ],
      "source": [
        "ent_labels = np.array(list(kg.ent2ix.keys()))\n",
        "print('First cluster: ', ', '.join(\n",
        "    np.random.permutation(ent_labels[labels == 0])[:10]))\n",
        "print()\n",
        "print('Second cluster: ', ', '.join(\n",
        "    np.random.permutation(ent_labels[labels == 1])[:10]))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eG4A-qY5eJYF"
      },
      "source": [
        "### Task 4. Nearest neighbors of entities (2.5 points)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 227,
      "metadata": {
        "id": "669adc04"
      },
      "outputs": [],
      "source": [
        "from sklearn.neighbors import NearestNeighbors"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "e07bdbf6"
      },
      "source": [
        "Let us find a nearest neighbors of Belgium using embedding space.\n",
        "\n",
        "Write a function `similar_countries` that takes a name of country, graph and model and returns a list with names of nearest countries. Use `model.get_embeddings()`."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 240,
      "metadata": {
        "deletable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "2914a4ae39cc291785e97e21b00d67ae",
          "grade": false,
          "grade_id": "cell-fe878bfa8dc0c817",
          "locked": false,
          "schema_version": 3,
          "solution": true,
          "task": false
        },
        "id": "91d490c5"
      },
      "outputs": [],
      "source": [
        "def similar_countries(name, kg, model):\n",
        "    n_emmbedings , rel_emmbedings = model.get_embeddings()\n",
        "    neigh = NearestNeighbors()\n",
        "    neigh.fit(n_emmbedings)\n",
        "    arr_distance , arr_labels = neigh.kneighbors(n_emmbedings[kg.ent2ix[name]].reshape(1, -1))\n",
        "    list_labels= list(arr_labels[0])\n",
        "    ent_val = {v: k for k, v in kg.ent2ix.items()}\n",
        "    output = []\n",
        "    for o in list_labels:\n",
        "      output.append(ent_val[o])\n",
        "    return output  \n",
        "    # YOUR CODE HERE\n",
        "    #raise NotImplementedError()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 241,
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "e38fd671f48cd1c4614f6adda30bd36e",
          "grade": true,
          "grade_id": "cell-0b8b02590a965cc3",
          "locked": true,
          "points": 2.5,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "dee374e6",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6e3bc7be-582f-4a2f-f654-2bd3c36561d4"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "['Belgium',\n",
              " 'Netherlands',\n",
              " 'Luxembourg',\n",
              " 'France',\n",
              " 'Kingdom of the Netherlands']"
            ]
          },
          "metadata": {},
          "execution_count": 241
        }
      ],
      "source": [
        "similar = similar_countries('Belgium', kg, model)\n",
        "assert 'Netherlands' in similar\n",
        "similar"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KOUdxRBUeJYG"
      },
      "source": [
        "### Task 5. Relation prediction (2.5 points)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8bcd2c29"
      },
      "source": [
        "Let us consider these facts:\n",
        "1. Belgium shares border with France\n",
        "2. Belgium shares border with Switzerland\n",
        "3. Belgium shares border with Nigeria\n",
        "\n",
        "Only the fact 1 is truth, but it seems that the fact 2 is more likely than 3."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 230,
      "metadata": {
        "id": "5ed79917",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 112
        },
        "outputId": "c82ebc05-2032-4944-abf2-266e9c9e83fe"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "          h                    r       t\n",
              "8   Belgium  diplomatic relation  France\n",
              "32  Belgium   shares border with  France"
            ],
            "text/html": [
              "\n",
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              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
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              "      <th></th>\n",
              "      <th>h</th>\n",
              "      <th>r</th>\n",
              "      <th>t</th>\n",
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              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>Belgium</td>\n",
              "      <td>diplomatic relation</td>\n",
              "      <td>France</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>32</th>\n",
              "      <td>Belgium</td>\n",
              "      <td>shares border with</td>\n",
              "      <td>France</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-b30febdb-a612-434b-a2a6-73556c9f4aa9')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
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              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
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              "    }\n",
              "  </style>\n",
              "\n",
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              "        const buttonEl =\n",
              "          document.querySelector('#df-b30febdb-a612-434b-a2a6-73556c9f4aa9 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-b30febdb-a612-434b-a2a6-73556c9f4aa9');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 230
        }
      ],
      "source": [
        "df[(df.h == 'Belgium') & (df.t == 'France')]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 231,
      "metadata": {
        "id": "52a2002d",
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          "base_uri": "https://localhost:8080/",
          "height": 49
        },
        "outputId": "020772e7-6296-492a-e150-ac5406933117"
      },
      "outputs": [
        {
          "output_type": "execute_result",
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            "text/plain": [
              "Empty DataFrame\n",
              "Columns: [h, r, t]\n",
              "Index: []"
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              "  </svg>\n",
              "      </button>\n",
              "      \n",
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              "    .colab-df-container {\n",
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              "    .colab-df-convert {\n",
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              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
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              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
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              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
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              "        const buttonEl =\n",
              "          document.querySelector('#df-94b90743-0d68-457d-a460-01c3bad69aa3 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-94b90743-0d68-457d-a460-01c3bad69aa3');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 231
        }
      ],
      "source": [
        "df[(df.h == 'Belgium') & (df.t == 'Switzerland')]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 232,
      "metadata": {
        "id": "5c5a6e01",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 49
        },
        "outputId": "95a36b2b-e829-4885-da50-b5fcc1d68c49"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Empty DataFrame\n",
              "Columns: [h, r, t]\n",
              "Index: []"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-b9cf28d9-1868-4929-a169-51cbba9c87c6\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>h</th>\n",
              "      <th>r</th>\n",
              "      <th>t</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-b9cf28d9-1868-4929-a169-51cbba9c87c6')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
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              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-b9cf28d9-1868-4929-a169-51cbba9c87c6 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-b9cf28d9-1868-4929-a169-51cbba9c87c6');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 232
        }
      ],
      "source": [
        "df[(df.h == 'Belgium') & (df.t == 'Nigeria')]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "e2e80719"
      },
      "source": [
        "Now we can compare these facts using scoring function of TransE model to check our prior knowledge.\n",
        "\n",
        "Write a function `belgium_facts` that takes a model, a graph and returns 3 values of scoring function for each fact. Use `model.scoring_function` with `torch.no_grad()`."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 233,
      "metadata": {
        "deletable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "d6b24f412af3938aadfd82f350222dcb",
          "grade": false,
          "grade_id": "cell-5feee5e866b961d0",
          "locked": false,
          "schema_version": 3,
          "solution": true,
          "task": false
        },
        "id": "6e484ea3"
      },
      "outputs": [],
      "source": [
        "def belgium_facts(model, kg):\n",
        "    bel_ind = kg.ent2ix['Belgium']\n",
        "    fra_ind = kg.ent2ix['France']\n",
        "    swi_ind = kg.ent2ix['Switzerland']\n",
        "    nig_ind = kg.ent2ix['Nigeria']\n",
        "    border_ind = kg.rel2ix['shares border with']\n",
        "    h = torch.LongTensor([bel_ind, bel_ind, bel_ind])\n",
        "    r = torch.LongTensor([border_ind, border_ind, border_ind])\n",
        "    t = torch.LongTensor([fra_ind, swi_ind, nig_ind])\n",
        "    with torch.no_grad():\n",
        "        scores = model.scoring_function(h,t,r).numpy()\n",
        "    return scores\n",
        "    # YOUR CODE HERE\n",
        "    #raise NotImplementedError()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 234,
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "2f00080d176375341ae1f4e7095a6b19",
          "grade": true,
          "grade_id": "cell-a6b6e4e88ba6569f",
          "locked": true,
          "points": 2.5,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "0c73a43b",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a48aa1e8-6b62-4134-ac29-34d83ba00fae"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-0.5740867 , -0.6991047 , -0.98608255], dtype=float32)"
            ]
          },
          "metadata": {},
          "execution_count": 234
        }
      ],
      "source": [
        "scores = belgium_facts(model, kg)\n",
        "assert scores[0] > scores[1] > scores[2]\n",
        "scores"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kz72QKg7eJYI"
      },
      "source": [
        "### Task 6. Tail prediction (2.5 points)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 235,
      "metadata": {
        "id": "1feb4bc5"
      },
      "outputs": [],
      "source": [
        "from sklearn.neighbors import NearestNeighbors"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eb36ce98"
      },
      "source": [
        "Recall that the main idea of TransE is to learn $h + r \\approx t$, so let us find the closest tails for the head + relation pair.\n",
        "\n",
        "Write a function `soviet_tail` that takes a model, graph and finds 5 nearest neighbors for the pair $h$ is \"Soviet Union\" and $r$ is \"founded by\"."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 236,
      "metadata": {
        "deletable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "803dd88ce8a03a13810ab252b70a682e",
          "grade": false,
          "grade_id": "cell-dbc103d80a938c68",
          "locked": false,
          "schema_version": 3,
          "solution": true,
          "task": false
        },
        "id": "c6f4633a"
      },
      "outputs": [],
      "source": [
        "def soviet_tail(model, kg):\n",
        "  n_emmbedings , rel_emmbedings = model.get_embeddings()\n",
        "  neigh = NearestNeighbors()\n",
        "  neigh.fit(n_emmbedings)\n",
        "  arr_distance , arr_labels = neigh.kneighbors( n_emmbedings[kg.ent2ix['Soviet Union']] + rel_emmbedings[kg.rel2ix['founded by']].reshape(1, -1))\n",
        "  list_labels= list(arr_labels[0])\n",
        "  ent_val = {v: k for k, v in kg.ent2ix.items()}\n",
        "  output = []\n",
        "  for v in list_labels:\n",
        "    output.append(ent_val[v])\n",
        "  return output\n",
        "    # YOUR CODE HERE\n",
        "    #raise NotImplementedError()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 237,
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "1249fc19b4c2a82f809dd83121103d3c",
          "grade": true,
          "grade_id": "cell-ba34f9e5a695e8ca",
          "locked": true,
          "points": 2.5,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "d8d5ab86",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3f13dd2e-609e-42ba-a265-a7e1f9f68d86"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "['Soviet Union',\n",
              " 'Russian Empire',\n",
              " 'Russian Soviet Federative Socialist Republic',\n",
              " 'Transcaucasian Socialist Federative Soviet Republic',\n",
              " 'Russian Republic']"
            ]
          },
          "metadata": {},
          "execution_count": 237
        }
      ],
      "source": [
        "tails = soviet_tail(model, kg)\n",
        "assert 'Russian Soviet Federative Socialist Republic' in tails\n",
        "tails"
      ]
    },
    {
      "cell_type": "code",
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