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    "## TD;LR\n",
    "\n",
    "`prob.argmax(axis=1)` を `hack(prob)` に**置き換える** だけで，どんなモデルでも**確実にスコアUP↑**ができる関数 `hack` の紹介です。\n",
    "\n",
    "以下に実装とデモを示しますが，`pip install -U pulp` が事前に必要です。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 実装\n",
    "import pulp  # pip install pulp==2.3\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "N_CLASSES = [404, 320, 345, 674]  # @yCarbonによる推定（過去フォーラム参照）\n",
    "\n",
    "# 制約付き対数尤度最大化問題を解く\n",
    "def hack(prob):\n",
    "    logp = np.log(prob + 1e-16)\n",
    "    N = prob.shape[0]\n",
    "    K = prob.shape[1]\n",
    "\n",
    "    m = pulp.LpProblem('Problem', pulp.LpMaximize)  # 最大化問題\n",
    "\n",
    "    # 最適化する変数(= 提出ラベル)\n",
    "    x = pulp.LpVariable.dicts('x', [(i, j) for i in range(N) for j in range(K)], 0, 1, pulp.LpBinary)\n",
    "    \n",
    "    # log likelihood(目的関数)\n",
    "    log_likelihood = pulp.lpSum([x[(i, j)] * logp[i, j] for i in range(N) for j in range(K)])\n",
    "    m += log_likelihood\n",
    "    \n",
    "    # 各データについて，1クラスだけを予測ラベルとする制約\n",
    "    for i in range(N):\n",
    "        m += pulp.lpSum([x[(i, k)] for k in range(K)]) == 1  # i.e., SOS1\n",
    "    \n",
    "    # 各クラスについて，推定個数の合計に関する制約\n",
    "    for k in range(K):\n",
    "        m += pulp.lpSum([x[(i, k)] for i in range(N)]) == N_CLASSES[k]\n",
    "        \n",
    "    m.solve()  # 解く\n",
    "\n",
    "    assert m.status == 1  # assert 最適 <=>（実行可能解が見つからないとエラー）\n",
    "\n",
    "    x_ast = np.array([[int(x[(i, j)].value()) for j in range(K)] for i in range(N)])  # 結果の取得\n",
    "    return x_ast.argmax(axis=1) # 結果をonehotから -> {0, 1, 2, 3}のラベルに変換"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# デモ\n",
    "prob = model.predict_proba(test_X)\n",
    "\n",
    "# before\n",
    "y = prob.argmax(axis=1) + 1\n",
    "\n",
    "# after\n",
    "y = hack(prob) + 1  # +0.01 ~ 0.02 on LB. depends on your model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 意味がわからない人へ\n",
    "\n",
    "どっちが簡単ですか？\n",
    "\n",
    "- 以下の選択肢から正解を **一つ** 選べ。\n",
    "- 以下の選択肢から正解を **すべて** 選べ。\n",
    "\n",
    "\\#あとは分かるな"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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