{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "9e4d2938",
   "metadata": {},
   "source": [
    "# Regularization hyperparameter choice in `sparsesurv`"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24658b42",
   "metadata": {},
   "source": [
    "We established before that sparsity and performance of a distilled model can be affected significantly by the choice of the teacher model class. In non-distilled sparse models, such as the Lasso, performance is also highly dependent on the degree of sparsity. In distilled models this seems to be much less the case [1, 2].\n",
    "\n",
    "Still, there are situations in which one may wish to choose a specific sparsity level, or err on the side of choosing a higher/lower level of sparsity."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "23bb301e",
   "metadata": {},
   "source": [
    "## Baseline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2ab46c74",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "from sparsesurv.utils import transform_survival\n",
    "from sklearn.decomposition import PCA\n",
    "from sparsesurv._base import KDSurv\n",
    "from sparsesurv.cv import KDPHElasticNetCV, KDEHMultiTaskLassoCV, KDAFTElasticNetCV\n",
    "from sparsesurv.utils import transform_survival\n",
    "from sklearn.pipeline import make_pipeline\n",
    "from sksurv.linear_model import CoxPHSurvivalAnalysis\n",
    "from sparsesurv.aft import AFT\n",
    "from sparsesurv.eh import EH\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "df = pd.read_csv(\"https://zenodo.org/records/10027434/files/OV_data_preprocessed.csv?download=1\")\n",
    "X = df.iloc[:, 3:].to_numpy()\n",
    "y = transform_survival(time=df.OS_days.values, event=df.OS.values)\n",
    "\n",
    "X_train = X[:200]\n",
    "X_test = X[200:]\n",
    "y_train = y[:200]\n",
    "y_test = y[200:]\n",
    "\n",
    "pipe_cox_efron = KDSurv(\n",
    "            teacher=make_pipeline(\n",
    "                StandardScaler(),\n",
    "                PCA(n_components=16),\n",
    "                CoxPHSurvivalAnalysis(ties=\"efron\"),\n",
    "            ),\n",
    "            student=make_pipeline(\n",
    "                StandardScaler(),\n",
    "                KDPHElasticNetCV(\n",
    "                    tie_correction=\"efron\",\n",
    "                    l1_ratio=0.9,\n",
    "                    eps=0.01,\n",
    "                    n_alphas=100,\n",
    "                    cv=5,\n",
    "                    stratify_cv=True,\n",
    "                    seed=None,\n",
    "                    shuffle_cv=False,\n",
    "                    cv_score_method=\"linear_predictor\",\n",
    "                    n_jobs=1,\n",
    "                    alpha_type=\"min\",\n",
    "                ),\n",
    "            ),\n",
    "        )\n",
    "\n",
    "pipe_cox_efron.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "5ec0004f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "169"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "np.sum(pipe_cox_efron.student[1].coef_ != 0.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6b8da529",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5244498777506112"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sksurv.metrics import concordance_index_censored\n",
    "concordance_index_censored(y_test[\"event\"], y_test[\"time\"], pipe_cox_efron.predict(X_test))[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5c5a5c6",
   "metadata": {},
   "source": [
    "By default, `sparsesurv` fits models with no limit on the number of non-zero coefficients, beyond what is implied by the regularizers. In addition, `sparsesurv` uses `alpha_type=\"min\"` by default, thus choosing the regularization hyperparameter which maximizes the score, which will often be rather high (as evidenced by 168 non-zero coefficients in the ovarian cancer example above).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b4cfde7",
   "metadata": {},
   "source": [
    "## Explicitly limiting the number of non-zero coefficients"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c38879c0",
   "metadata": {},
   "source": [
    "One alternative is explicitly limiting the number of non-zero coefficients. Below, we select the regularization hyperparameter with the maximum that score that has 50 non-zero coefficients or less."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "cfffc0bd",
   "metadata": {},
   "outputs": [],
   "source": [
    "pipe_cox_efron = KDSurv(\n",
    "            teacher=make_pipeline(\n",
    "                StandardScaler(),\n",
    "                PCA(n_components=16),\n",
    "                CoxPHSurvivalAnalysis(ties=\"efron\"),\n",
    "            ),\n",
    "            student=make_pipeline(\n",
    "                StandardScaler(),\n",
    "                KDPHElasticNetCV(\n",
    "                    tie_correction=\"efron\",\n",
    "                    l1_ratio=0.9,\n",
    "                    eps=0.01,\n",
    "                    n_alphas=100,\n",
    "                    cv=5,\n",
    "                    stratify_cv=True,\n",
    "                    seed=None,\n",
    "                    shuffle_cv=False,\n",
    "                    cv_score_method=\"linear_predictor\",\n",
    "                    n_jobs=1,\n",
    "                    alpha_type=\"min\",\n",
    "                    max_coef=50\n",
    "                ),\n",
    "            ),\n",
    "        )\n",
    "\n",
    "pipe_cox_efron.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "b0b9c18b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "47"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(pipe_cox_efron.student[1].coef_ != 0.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "03ce2c44",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5138549307253464"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "concordance_index_censored(y_test[\"event\"], y_test[\"time\"], pipe_cox_efron.predict(X_test))[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "645855c3",
   "metadata": {},
   "source": [
    "While explicitly setting the desired degree of sparsity can work well, one may also want a degree of sparsity to be chosen that finds a good trade-off between performance and sparsity."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "110aad98",
   "metadata": {},
   "source": [
    "## Automatically trading-off between sparsity and performance"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8dc0a54a",
   "metadata": {},
   "source": [
    "For this purpose, `sparsesurv` implements two alternative rules, instead of choosing the regularization hyperparameter that maximizes the score:\n",
    "\n",
    "    1. alpha_type=\"1se\" chooses the highest regularization hyperparameter that is within one standard error of the \n",
    "    mean of the best score [3].\n",
    "    \n",
    "    2. alpha_type=\"pcvl\" chooses a regularization hyperparameter less sparse than \"1se\" but more sparse than \"min\"\n",
    "    via a penalization approach [4].\n",
    "    \n",
    "Importantly, `alpha_type=1se` requires `cv_score_method != linear_predictor`, since otherwise calculating a mean score is impossible."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "ef8ee7a8",
   "metadata": {},
   "outputs": [],
   "source": [
    "pipe_cox_efron = KDSurv(\n",
    "            teacher=make_pipeline(\n",
    "                StandardScaler(),\n",
    "                PCA(n_components=16),\n",
    "                CoxPHSurvivalAnalysis(ties=\"efron\"),\n",
    "            ),\n",
    "            student=make_pipeline(\n",
    "                StandardScaler(),\n",
    "                KDPHElasticNetCV(\n",
    "                    tie_correction=\"efron\",\n",
    "                    l1_ratio=0.9,\n",
    "                    eps=0.01,\n",
    "                    n_alphas=100,\n",
    "                    cv=5,\n",
    "                    stratify_cv=True,\n",
    "                    seed=None,\n",
    "                    shuffle_cv=False,\n",
    "                    cv_score_method=\"vvh\",\n",
    "                    n_jobs=1,\n",
    "                    alpha_type=\"1se\"\n",
    "                ),\n",
    "            ),\n",
    "        )\n",
    "\n",
    "pipe_cox_efron.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "ffc98f9d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(pipe_cox_efron.student[1].coef_ != 0.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "11d2b9de",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "concordance_index_censored(y_test[\"event\"], y_test[\"time\"], pipe_cox_efron.predict(X_test))[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "cfa745c1",
   "metadata": {},
   "outputs": [],
   "source": [
    "pipe_cox_efron = KDSurv(\n",
    "            teacher=make_pipeline(\n",
    "                StandardScaler(),\n",
    "                PCA(n_components=16),\n",
    "                CoxPHSurvivalAnalysis(ties=\"efron\"),\n",
    "            ),\n",
    "            student=make_pipeline(\n",
    "                StandardScaler(),\n",
    "                KDPHElasticNetCV(\n",
    "                    tie_correction=\"efron\",\n",
    "                    l1_ratio=0.9,\n",
    "                    eps=0.01,\n",
    "                    n_alphas=100,\n",
    "                    cv=5,\n",
    "                    stratify_cv=True,\n",
    "                    seed=None,\n",
    "                    shuffle_cv=False,\n",
    "                    cv_score_method=\"linear_predictor\",\n",
    "                    n_jobs=1,\n",
    "                    alpha_type=\"pcvl\"\n",
    "                ),\n",
    "            ),\n",
    "        )\n",
    "\n",
    "pipe_cox_efron.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "2b124255",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "51"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(pipe_cox_efron.student[1].coef_ != 0.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "c2fb2b92",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5142624286878565"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "concordance_index_censored(y_test[\"event\"], y_test[\"time\"], pipe_cox_efron.predict(X_test))[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "86fd7829",
   "metadata": {},
   "source": [
    "As seen above, the downside of automatic selection methods, is that they may select completely sparse models if the prediction is not much better than chance, as is the case here."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "039220e6",
   "metadata": {},
   "source": [
    "## References"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1f18949",
   "metadata": {},
   "source": [
    "[1] David Wissel, Nikita Janakarajan, Daniel Rowson, Julius Schulte, Xintian Yuan, Valentina Boeva. \"sparsesurv: Sparse survival models via knowledge distillation.\" (2023, under review).\n",
    "\n",
    "[2] Paul, Debashis, et al. \"“Preconditioning” for feature selection and regression in high-dimensional problems.\" (2008): 1595-1618.\n",
    "\n",
    "\n",
    "[3] Hastie, Trevor, et al. The elements of statistical learning: data mining, inference, and prediction. Vol. 2. New York: Springer, 2009.\n",
    "\n",
    "[4] Ternès, Nils, Federico Rotolo, and Stefan Michiels. \"Empirical extensions of the lasso penalty to reduce the false discovery rate in high‐dimensional Cox regression models.\" Statistics in medicine 35.15 (2016): 2561-2573."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a675767",
   "metadata": {},
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}