UF_MI_power.ipynb

{
  "cells": [
    {
      "cell_type": "code",
      "source": [
        "from proglearn.progressive_learner import ClassificationProgressiveLearner\n",
        "from proglearn.transformers import TreeClassificationTransformer\n",
        "from proglearn.voters import TreeClassificationVoter\n",
        "from proglearn.deciders import SimpleArgmaxAverage\n",
        "\n",
        "from sklearn.tree import DecisionTreeClassifier\n",
        "from joblib import Parallel, delayed\n",
        "from collections import defaultdict\n",
        "from sklearn.utils.fixes import _joblib_parallel_args\n",
        "import threading\n",
        "from sklearn.ensemble._base import _partition_estimators\n",
        "from sklearn.utils.validation import check_is_fitted\n",
        "\n",
        "import numpy as np\n",
        "\n",
        "from sklearn.ensemble import RandomForestClassifier\n",
        "from sklearn.utils.validation import check_X_y, check_array\n",
        "\n",
        "\n",
        "from hyppo.tools import multimodal_independence, indep_sim, rot_ksamp\n",
        "from hyppo.tools import SIMULATIONS\n",
        "from hyppo.ksample._utils import k_sample_transform\n",
        "from tqdm import tqdm\n",
        "from hyppo.tools import * \n",
        "\n",
        "from joblib import Parallel, delayed\n",
        "from scipy.stats import entropy, multivariate_normal\n",
        "from math import ceil\n",
        "\n",
        "\n",
        "import matplotlib.pyplot as plt"
      ],
      "outputs": [],
      "execution_count": 1,
      "metadata": {
        "gather": {
          "logged": 1670871332302
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "class UncertaintyForest:\n",
        "    \"\"\"\n",
        "    A class used to represent an Uncertainty Forest.\n",
        "    Parameters\n",
        "    ----------\n",
        "    n_estimators : int, default=100\n",
        "        The number of trees in the UncertaintyForest\n",
        "    kappa : float, default=np.inf\n",
        "        The coefficient for finite sample correction. If set to the default\n",
        "        value, finite sample correction is not performed.\n",
        "    max_depth : int, default=None\n",
        "        The maximum depth of a tree in the UncertaintyForest.\n",
        "    tree_construction_proportion : float, default=0.5\n",
        "        The proportions of the input data set aside to train each decision\n",
        "        tree. The remainder of the data is used to fill in voting posteriors.\n",
        "    max_features : {\"auto\", \"sqrt\", \"log2\"}, int or float, default=\"auto\"\n",
        "        The number of features to consider when looking for the best split:\n",
        "        - If int, then consider `max_features` features at each split.\n",
        "        - If float, then `max_features` is a fraction and\n",
        "          `round(max_features * n_features)` features are considered at each\n",
        "          split.\n",
        "        - If \"auto\", then `max_features=sqrt(n_features)`.\n",
        "        - If \"sqrt\", then `max_features=sqrt(n_features)` (same as \"auto\").\n",
        "        - If \"log2\", then `max_features=log2(n_features)`.\n",
        "        - If None, then `max_features=n_features`.\n",
        "        Note: the search for a split does not stop until at least one\n",
        "        valid partition of the node samples is found, even if it requires to\n",
        "        effectively inspect more than ``max_features`` features.\n",
        "    poisson_sampler : boolean, default=False\n",
        "        To match the GRF theory [#1grf]_, if True, the number of features\n",
        "        considered at each tree are drawn from a poisson distribution with\n",
        "        mean equal to `max_features`.\n",
        "    n_jobs : int, default=None\n",
        "        The number of jobs to run in parallel. ``-1`` means use all\n",
        "        processors. None equates to 1.\n",
        "    max_samples : int or float, default=None\n",
        "        The number of samples to draw from X (without replacement) to train\n",
        "        each tree.\n",
        "        - If None, then draw `X.shape[0]` samples.\n",
        "        - If int, then draw `max_samples` samples.\n",
        "        - If float, then draw `max_samples * X.shape[0]` samples. Thus,\n",
        "          `max_samples` should be in the interval `(0, 1)`.\n",
        "        Note: The number of samples used to learn the tree will be further\n",
        "        reduced per the `tree_construction_proportion` value.\n",
        "    honest_prior : {\"ignore\", \"uniform\", \"empirical\"}, default=\"ignore\"\n",
        "        Method for dealing with empty leaves during evaluation of a test\n",
        "        sample. If \"ignore\", trees in which the leaf is empty are not used in\n",
        "        the prediction. If \"uniform\", the prior tree posterior is 1/(number of\n",
        "        classes). If \"empirical\", the prior tree posterior is the relative\n",
        "        class frequency in the voting subsample. If all tree leaves are empty,\n",
        "        \"ignore\" will use the empirical prior and the others will use their\n",
        "        respective priors.\n",
        "    tree_kwargs : dict, default={}\n",
        "        Named arguments to be passed to each\n",
        "        sklearn.tree.DecisionTreeClassifier tree used in the construction\n",
        "        of the forest in addition to the above parameters.\n",
        "    Attributes\n",
        "    ----------\n",
        "    transformers_ : list of sklearn.tree.DecisionTreeClassifier\n",
        "        The collection of fitted trees.\n",
        "    voters_ : list of proglearn.voter.TreeClassificationVoter\n",
        "        The collection of honest voters for leaves in matching trees in\n",
        "        `self.estimators_` at the same index.\n",
        "    n_features_ : int\n",
        "        The number of features when `fit` is performed.\n",
        "    tree_kwargs_ : dict\n",
        "        Full set of keyword arguments passed to the Forest transformer.\n",
        "    References\n",
        "    ----------\n",
        "    .. [#1grf] Athey, Susan, Julie Tibshirani and Stefan Wager.\n",
        "        \"Generalized Random Forests\", Annals of Statistics, 2019.\n",
        "    \"\"\"\n",
        "\n",
        "    def __init__(\n",
        "        self,\n",
        "        n_estimators=100,\n",
        "        kappa=np.inf,\n",
        "        max_depth=None,\n",
        "        tree_construction_proportion=0.63,\n",
        "        max_features=\"auto\",\n",
        "        poisson_sampler=False,\n",
        "        max_samples=None,\n",
        "        n_jobs=None,\n",
        "        honest_prior=\"ignore\",\n",
        "        weighted_trees=False,\n",
        "        min_samples_leaf=1,\n",
        "        min_samples_split=2,\n",
        "        min_impurity_decrease=0.0,\n",
        "    ):\n",
        "        self.n_estimators = n_estimators\n",
        "        self.kappa = kappa\n",
        "        self.max_depth = max_depth\n",
        "        self.tree_construction_proportion = tree_construction_proportion\n",
        "        self.max_features = max_features\n",
        "        self.poisson_sampler = poisson_sampler\n",
        "        self.max_samples = max_samples\n",
        "        self.n_jobs = n_jobs\n",
        "        self.honest_prior = honest_prior\n",
        "        self.verbose = 0\n",
        "        self.weighted_trees = weighted_trees\n",
        "        self.min_samples_leaf = min_samples_leaf\n",
        "        self.min_samples_split = min_samples_split\n",
        "        self.min_impurity_decrease = min_impurity_decrease\n",
        "        \n",
        "\n",
        "    def fit(self, X, y):\n",
        "        \"\"\"\n",
        "        fits forest to data X with labels y\n",
        "        Parameters\n",
        "        ----------\n",
        "        X : array of shape [n_samples, n_features]\n",
        "            The data that will be trained on\n",
        "        y : array of shape [n_samples]\n",
        "            The label for cluster membership of the given data\n",
        "        Returns\n",
        "        -------\n",
        "        self : UncertaintyForest\n",
        "            The object itself.\n",
        "        \"\"\"\n",
        "        X, y = check_X_y(X, y)\n",
        "\n",
        "        self.n_samples_, self.n_features_ = X.shape\n",
        "        self.n_classes_ = len(np.unique(y))\n",
        "        self.empirical_prior_ = np.bincount(y, minlength=self.n_classes_) / len(y)\n",
        "\n",
        "        self.transformers_ = [\n",
        "            DecisionTreeClassifier(\n",
        "                max_features = self.max_features,\n",
        "                max_depth = self.max_depth,\n",
        "                min_samples_leaf = self.min_samples_leaf,\n",
        "                min_samples_split = self.min_samples_split,\n",
        "                min_impurity_decrease = self.min_impurity_decrease,\n",
        "                )\n",
        "            for _ in range(self.n_estimators)\n",
        "        ]\n",
        "\n",
        "        # Source https://github.com/scikit-learn/scikit-learn/blob/95119c13a/sklearn/ensemble/_forest.py#L387\n",
        "        self.transformers_, self.transformer_indices_ = list(zip(\n",
        "            *Parallel(n_jobs=self.n_jobs, verbose=self.verbose, **_joblib_parallel_args(prefer=\"threads\"))(\n",
        "                delayed(_parallel_build_trees)(\n",
        "                    X, y, tree, self.n_samples_, self.n_classes_,\n",
        "                    self.honest_prior, self.tree_construction_proportion,\n",
        "                    self.kappa, self.weighted_trees)\n",
        "                for tree in self.transformers_)\n",
        "                ))\n",
        "\n",
        "        return self\n",
        "\n",
        "    def predict_proba(self, X):\n",
        "        \"\"\"\n",
        "        estimates class posteriors for each example in input data X.\n",
        "        Parameters\n",
        "        ----------\n",
        "        X : array of shape [n_samples, n_features]\n",
        "            The data whose posteriors we are estimating.\n",
        "        Returns\n",
        "        -------\n",
        "        y_proba_hat : ndarray of shape [n_samples, n_classes]\n",
        "            posteriors per example\n",
        "        \"\"\"\n",
        "        X = self._validate_X_predict(X)\n",
        "        n_jobs, _, _ = _partition_estimators(self.n_estimators, self.n_jobs)\n",
        "\n",
        "        # avoid storing the output of every estimator by summing them here\n",
        "        posteriors = np.zeros((X.shape[0], self.n_classes_), dtype=np.float64)\n",
        "        lock = threading.Lock()\n",
        "\n",
        "        Parallel(n_jobs=n_jobs, verbose=self.verbose, **_joblib_parallel_args(require=\"sharedmem\"))(\n",
        "            delayed(_accumulate_prediction)(tree.tree_.predict, X, posteriors, lock, None, self.weighted_trees)\n",
        "            for tree in self.transformers_)\n",
        "\n",
        "        # Normalize to unit length, due to prior weighting\n",
        "        zero_mask = posteriors.sum(1) == 0\n",
        "        posteriors[~zero_mask] /= posteriors[~zero_mask].sum(1, keepdims=True)\n",
        "        posteriors[zero_mask] = self.empirical_prior_\n",
        "\n",
        "        return posteriors\n",
        "\n",
        "    def _validate_X_predict(self, X):\n",
        "        \"\"\"\n",
        "        From sklearn\n",
        "        Validate X whenever one tries to predict, apply, predict_proba.\"\"\"\n",
        "        check_is_fitted(self)\n",
        "\n",
        "        return self.transformers_[0]._validate_X_predict(X, check_input=True)\n",
        "\n",
        "    def predict(self, X):\n",
        "        \"\"\"\n",
        "        predicts class labels for each example in input data X.\n",
        "        Parameters\n",
        "        ----------\n",
        "        X : array of shape [n_samples, n_features]\n",
        "            The data on which we are performing inference.\n",
        "        Returns\n",
        "        -------\n",
        "        y_hat : ndarray of shape [n_samples]\n",
        "            predicted class label per example\n",
        "        \"\"\"\n",
        "        return self.predict_proba(X).argmax(1)\n",
        "\n",
        "    def predict_proba_honest(self, X, voters=True):\n",
        "        \"\"\"\n",
        "        Returns predicted posteriors of the training data, excluding trees a\n",
        "        sample was used in construction of.\n",
        "        Parameters\n",
        "        ----------\n",
        "        X : array of shape [n_samples, n_features]\n",
        "            The data on which the forest was fit to.\n",
        "        Returns\n",
        "        -------\n",
        "        y_proba_hat : ndarray of shape [n_samples, n_classes]\n",
        "            posteriors per example\n",
        "        \"\"\"\n",
        "        X = self._validate_X_predict(X)\n",
        "        n_jobs, _, _ = _partition_estimators(self.n_estimators, self.n_jobs)\n",
        "\n",
        "        # avoid storing the output of every estimator by summing them here\n",
        "        posteriors = np.zeros((X.shape[0], self.n_classes_), dtype=np.float64)\n",
        "        lock = threading.Lock()\n",
        "\n",
        "        if voters:\n",
        "            Parallel(n_jobs=n_jobs, verbose=self.verbose, **_joblib_parallel_args(require=\"sharedmem\"))(\n",
        "                delayed(_accumulate_prediction)(tree.tree_.predict, X, posteriors, lock, honest_indices)\n",
        "                for tree, honest_indices in zip(self.transformers_, self.voter_indices_))\n",
        "        else:\n",
        "            Parallel(n_jobs=n_jobs, verbose=self.verbose, **_joblib_parallel_args(require=\"sharedmem\"))(\n",
        "                delayed(_accumulate_prediction)(tree.tree_.predict, X, posteriors, lock, indices)\n",
        "                for tree, indices in zip(self.transformers_, self.transformer_indices_))\n",
        "\n",
        "        # Normalize to unit length, due to prior weighting\n",
        "        zero_mask = posteriors.sum(1) == 0\n",
        "        posteriors[~zero_mask] /= posteriors[~zero_mask].sum(1, keepdims=True)\n",
        "        posteriors[zero_mask] = self.empirical_prior_\n",
        "\n",
        "        return posteriors\n",
        "\n",
        "\n",
        "    @property\n",
        "    def voter_indices_(self):\n",
        "        if not hasattr(self, \"transformer_indices_\"):\n",
        "            raise AttributeError(\"Model has not been fitted. Please fit first.\")\n",
        "        return [\n",
        "            np.setdiff1d(np.arange(self.n_samples_), transformer_indices)\n",
        "            for transformer_indices in self.transformer_indices_]\n",
        "\n",
        "\n",
        "def _parallel_build_trees(\n",
        "    X, y, tree, n_samples_, n_classes_,\n",
        "    honest_prior, tree_construction_proportion,\n",
        "    kappa, weighted_trees):\n",
        "        # https://github.com/scikit-learn/scikit-learn/blob/95119c13a/sklearn/ensemble/_forest.py#L140\n",
        "        \"\"\"\n",
        "        Private function used to fit a single tree in parallel.\"\"\"\n",
        "\n",
        "        transformer_indices = np.random.choice(\n",
        "            n_samples_,\n",
        "            int(tree_construction_proportion * n_samples_),\n",
        "            replace=False)  # No bootstrapping\n",
        "        voter_indices = np.setdiff1d(\n",
        "            np.arange(n_samples_), transformer_indices)\n",
        "\n",
        "        sample_weight = np.ones((n_samples_,), dtype=np.float64)\n",
        "        sample_counts = np.bincount(\n",
        "            transformer_indices, minlength=n_samples_)\n",
        "        sample_weight *= sample_counts\n",
        "\n",
        "        #tree = tree.fit(X, y, sample_weight=sample_weight, check_input=False) ### Why using y, rather than X[transformer_indices,:],y[transformer_indices]\n",
        "        tree = tree.fit(X[transformer_indices,:],y[transformer_indices], sample_weight=sample_weight[transformer_indices], check_input=False)\n",
        "        \n",
        "        honest_leaves = tree.apply(X[voter_indices])\n",
        "        # empirical_prior = np.bincount(\n",
        "        #     y[voter_indices], minlength=n_classes_)\n",
        "\n",
        "        # if honest_prior == 'ignore':\n",
        "        #     posterior_dict = defaultdict(lambda: np.zeros(n_classes_))\n",
        "        # elif honest_prior == 'empirical':\n",
        "        #     posterior_dict = defaultdict(lambda: empirical_prior)\n",
        "        # elif honest_prior == 'uniform':\n",
        "        #     posterior_dict = defaultdict(lambda: np.ones(n_classes_) / n_classes_)\n",
        "\n",
        "        tree.tree_.value[:, :, :] = 0 # empirical_prior\n",
        "\n",
        "        for leaf_id, yval in zip(honest_leaves, y[voter_indices]):\n",
        "            # posterior_dict[leaf_id][yval] += 1\n",
        "            tree.tree_.value[leaf_id][0, yval] += 1\n",
        "\n",
        "        # for leaf_id in np.unique(honest_leaves):\n",
        "        #     leaf_id_indices = np.where(honest_leaves == leaf_id)[0]\n",
        "        #     correction = 1 / (kappa * len(leaf_id_indices))\n",
        "        #     posterior = correction * empirical_prior + \\\n",
        "        #         (1 - correction) * np.bincount(\n",
        "        #             y[voter_indices[leaf_id_indices]],\n",
        "        #             minlength=n_classes_) / len(leaf_id_indices)\n",
        "        #     posterior_dict[leaf_id] = posterior * (len(leaf_id_indices) if weighted_trees else 1)\n",
        "\n",
        "        return tree, transformer_indices\n",
        "\n",
        "\n",
        "def _accumulate_prediction(predict, X, out, lock, honest_indices=None, weighted_trees=False):\n",
        "    \"\"\"\n",
        "    See https://github.com/scikit-learn/scikit-learn/blob/95119c13af77c76e150b753485c662b7c52a41a2/sklearn/ensemble/_forest.py#L460\n",
        "    This is a utility function for joblib's Parallel.\n",
        "    It can't go locally in ForestClassifier or ForestRegressor, because joblib\n",
        "    complains that it cannot pickle it when placed there.\n",
        "    \"\"\"\n",
        "\n",
        "    # predict = DecisionTreeClassifier.tree_.predict\n",
        "    if honest_indices is not None:\n",
        "        proba = predict(X[honest_indices])\n",
        "    else:\n",
        "        proba = predict(X)\n",
        "    if not weighted_trees:\n",
        "        zero_mask = proba.sum(1) == 0\n",
        "        proba[~zero_mask] /= proba[~zero_mask].sum(1, keepdims=True)\n",
        "    with lock:\n",
        "        if honest_indices is not None:\n",
        "            out[honest_indices] += proba\n",
        "        else:\n",
        "            out += proba"
      ],
      "outputs": [],
      "execution_count": 2,
      "metadata": {
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "gather": {
          "logged": 1670871332474
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "class UFTest_permute_tree:\n",
        "    def __init__(self, uf):\n",
        "        self.name = 'UF'\n",
        "        self.uf = uf\n",
        "        self.fit_ = False\n",
        "        \n",
        "    def statistic(self, X, y):\n",
        "        y = y.ravel()\n",
        "        if not self.fit_:\n",
        "            self.uf = self.uf.fit(X, y)\n",
        "            self.y_ = y\n",
        "            if hasattr(self, \"honest_leaf_indices_\"):\n",
        "                assert hasattr(self, \"transformer_leaf_indices_\")\n",
        "                del self.honest_leaf_indices_\n",
        "                del self.transformer_leaf_indices_\n",
        "            self.fit_ = True\n",
        "        if not hasattr(self, \"honest_leaf_indices_\"):\n",
        "            self.honest_leaf_indices_ = []\n",
        "            self.transformer_leaf_indices_ = []\n",
        "            for tree, voter_indices, transformer_indices in zip(self.uf.transformers_, self.uf.voter_indices_, self.uf.transformer_indices_):\n",
        "                self.honest_leaf_indices_.append(tree.apply(X[voter_indices]))\n",
        "                self.transformer_leaf_indices_.append(tree.apply(X[transformer_indices]))\n",
        "\n",
        "        _, counts = np.unique(y, return_counts=True)\n",
        "        H_Y = entropy(counts, base=np.exp(1))\n",
        "        H_YX = self._refit_apply_oob(X, self.y_) # changed from y to self.y_ as does the permutation internally per tree\n",
        "        return max(H_Y - H_YX, 0)\n",
        "        #return H_YX/100\n",
        "\n",
        "    def _refit_apply_oob(self, X, y):\n",
        "        posteriors = np.zeros((X.shape[0], self.uf.n_classes_), dtype=np.float64)\n",
        "        # posteriors = np.zeros((X.shape[0], self.uf.n_estimators, self.uf.n_classes_), dtype=np.float64)\n",
        "\n",
        "        for tree, honest_leaf_indices, voter_indices, tranformer_leaf_indices, transformer_indices in zip(\n",
        "            self.uf.transformers_, self.honest_leaf_indices_, self.uf.voter_indices_, self.transformer_leaf_indices_, self.uf.transformer_indices_):\n",
        "        # for tree_idx, (honest_leaf_indices, voter_indices) in enumerate(zip(self.honest_leaf_indices_, self.uf.voter_indices_)):\n",
        "            tree.tree_.value[:, :, :] = 0\n",
        "\n",
        "            y_voters = y[voter_indices]\n",
        "            np.random.shuffle(y_voters)\n",
        "            for leaf_id, yval in zip(honest_leaf_indices, y_voters):\n",
        "                tree.tree_.value[leaf_id][0, yval] += 1\n",
        "\n",
        "            leaf_indices = np.hstack((honest_leaf_indices, tranformer_leaf_indices))\n",
        "            sample_indices = np.hstack((voter_indices, transformer_indices))\n",
        "\n",
        "            proba = tree.tree_.value[leaf_indices][:, 0, :]\n",
        "            normalizer = proba.sum(axis=1)[:, np.newaxis]\n",
        "            normalizer[normalizer == 0.0] = 1.0 # solves divide by 0 error\n",
        "            proba /= normalizer\n",
        "            posteriors[sample_indices] += proba\n",
        "\n",
        "        # Normalize to unit length, due to prior weighting\n",
        "        zero_mask = posteriors.sum(1) == 0\n",
        "        posteriors[~zero_mask] /= posteriors[~zero_mask].sum(1, keepdims=True)\n",
        "        posteriors[zero_mask] = self.uf.empirical_prior_\n",
        "\n",
        "        return np.mean(entropy(posteriors, base=np.exp(1), axis=1))"
      ],
      "outputs": [],
      "execution_count": 3,
      "metadata": {
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "gather": {
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        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def _perm_stat(calc_stat,X, y, is_distsim = True, permuter = None): \n",
        "    \n",
        "    obs_stat = calc_stat.statistic(X, y)\n",
        "    if permuter is None: \n",
        "        order = np.random.permutation(y.shape[0])\n",
        "    else: \n",
        "        order = permuter()\n",
        "    \n",
        "    if is_distsim: \n",
        "        permy = y[order][:, order]\n",
        "    else: \n",
        "        permy = y[order]\n",
        "    \n",
        "    perm_stat = calc_stat.statistic(X, permy)\n",
        "    \n",
        "    return obs_stat,perm_stat\n",
        "\n",
        "\n",
        "def perm_test(calc_stat,X, y,  alpha = 0.05, is_distsim=True, reps = 1000): \n",
        "\n",
        "    # calculate observed test statistic\n",
        "    stat = calc_stat.statistic(X, y)\n",
        "    #print(stat) \n",
        "    \n",
        "    # calculate null distribution\n",
        "    #null_dist = np.array(Parallel(n_jobs=-2)(delayed(_perm_stat)(test,X, y,is_distsim = False,permuter = None) for rep in range(0,reps)))\n",
        "    # null_dist = []\n",
        "    # for rep in range(0,reps):\n",
        "    #     null_dist.append(_perm_stat(calc_stat,X, y, is_distsim = False, permuter = None))\n",
        "    # #print(null_dist)\n",
        "\n",
        "    alt_dist, null_dist = map(np.float64,\n",
        "            zip(*[_perm_stat(calc_stat, X, y,is_distsim = False) for _ in range(reps)]\n",
        "        ),\n",
        "        )\n",
        "    #pvalue = ((null_dist >= stat).sum() + 1) / (reps + 1)\n",
        "    #pvalue = (null_dist >= stat).sum() / reps\n",
        "    \n",
        "    cutoff = np.sort(null_dist)[ceil(reps * (1 - alpha))]\n",
        "    empirical_power = (1 + (alt_dist >= cutoff).sum()) / (1 + reps)\n",
        "    # correct for a p-value of 0. This is because, with bootstrapping\n",
        "    # permutations, a p-value of 0 is incorrect\n",
        "    # if pvalue == 0:\n",
        "    #     pvalue = 1 / reps\n",
        "\n",
        "    #return stat, pvalue, null_dist\n",
        "    #print(stat, pvalue, null_dist)\n",
        "    return empirical_power"
      ],
      "outputs": [],
      "execution_count": 4,
      "metadata": {
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "gather": {
          "logged": 1670871340948
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def find_dim(sim):\n",
        "    \"\"\"Find dimension maximum for the simulation.\"\"\"\n",
        "    if sim not in SIMULATIONS.keys():\n",
        "        raise ValueError(\"Invalid simulation\")\n",
        "\n",
        "    if sim in [\"joint_normal\", \"sin_four_pi\", \"sin_sixteen_pi\", \"multiplicative_noise\"]:\n",
        "        dim = 10\n",
        "    elif sim in [\"multimodal_independence\", \"uncorrelated_bernoulli\", \"logarithmic\"]:\n",
        "        dim = 100\n",
        "    elif sim in [\"linear\", \"exponential\", \"cubic\"]:\n",
        "        dim = 1000\n",
        "    elif sim in [\"square\", \"diamond\"]:\n",
        "        dim = 40\n",
        "    else:\n",
        "        dim = 20\n",
        "\n",
        "    return dim\n",
        "\n",
        "\n",
        "def find_dim_range(dim):\n",
        "    \"\"\"Create list of dimension range to calculate power for.\"\"\"\n",
        "    if dim < 20:\n",
        "        lim = 10\n",
        "    else:\n",
        "        lim = 20\n",
        "\n",
        "    dim_range = list(range(int(dim / lim), dim + 1, int(dim / lim)))\n",
        "    if int(dim / lim) != 1:\n",
        "        dim_range.insert(0, 1)\n",
        "    return dim_range"
      ],
      "outputs": [],
      "execution_count": 5,
      "metadata": {
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "gather": {
          "logged": 1670871343048
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def empirical_power(test,sim,power_reps = 10,reps = 1000,sample_size = 100):\n",
        "    #dim = \n",
        "    #dim_range = find_dim_range(find_dim(sim))\n",
        "    dim_range = range(1,10)\n",
        "    \n",
        "    Empirical_Power = []\n",
        "\n",
        "    for j in dim_range:\n",
        "        empirical_power = []\n",
        "    \n",
        "        for i in range(0,power_reps):\n",
        "            #x,y_ = multimodal_independence(n = sample_size,p = 1,prob = 0.5)\n",
        "            #x, y_ = indep_sim(sim, n=sample_size, p=j,noise=True) \n",
        "            #X, y = indep_sim(sim, n=sample_size, p=j,noise=True) ## indep_sim\n",
        "            x, y_ = rot_ksamp(sim, n=sample_size, p=j,noise=True)#ksample\n",
        "            print(x.shape,y_.shape)\n",
        "            X, y = k_sample_transform([x, y_]) #ksample\n",
        "            # if y.shape[1] == 1:\n",
        "            #     y = y.ravel()\n",
        "            y = y.astype(int) #ksample\n",
        "            #print(X.shape)\n",
        "            empirical_power_i = perm_test(test,X, y,alpha = 0.05,is_distsim = False,reps = reps)\n",
        "            print(empirical_power_i)\n",
        "            empirical_power.append(empirical_power_i)\n",
        "            # stat.append(stat_i)\n",
        "            # null_dist[i,:] = null_dist_i\n",
        "        Empirical_Power.append(np.mean(empirical_power))\n",
        "        print(empirical_power)\n",
        "\n",
        "    return Empirical_Power\n"
      ],
      "outputs": [],
      "execution_count": 13,
      "metadata": {
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "gather": {
          "logged": 1670871679989
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "SIMULATIONS.keys()"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 10,
          "data": {
            "text/plain": "dict_keys(['linear', 'exponential', 'cubic', 'joint_normal', 'step', 'quadratic', 'w_shaped', 'spiral', 'uncorrelated_bernoulli', 'logarithmic', 'fourth_root', 'sin_four_pi', 'sin_sixteen_pi', 'square', 'two_parabolas', 'circle', 'ellipse', 'diamond', 'multiplicative_noise', 'multimodal_independence'])"
          },
          "metadata": {}
        }
      ],
      "execution_count": 10,
      "metadata": {
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "gather": {
          "logged": 1670871634044
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "simulations = SIMULATIONS.keys()\n",
        "# test = UFTest_permute_tree(\n",
        "#     uf = UncertaintyForest(\n",
        "#         n_estimators=100,\n",
        "#         tree_construction_proportion=0.5,\n",
        "#         kappa=np.inf,\n",
        "#         min_samples_leaf=5,\n",
        "#         honest_prior=\"ignore\",\n",
        "#         max_features=\"auto\",\n",
        "#         n_jobs=-1,\n",
        "#         max_samples = None\n",
        "#     )\n",
        "# )"
      ],
      "outputs": [],
      "execution_count": 11,
      "metadata": {
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "gather": {
          "logged": 1670871635939
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "for sim in simulations:\n",
        "    print(sim)\n",
        "\n",
        "    test = UFTest_permute_tree(\n",
        "    uf = UncertaintyForest(\n",
        "        n_estimators=100,\n",
        "        tree_construction_proportion=0.5,\n",
        "        kappa=np.inf,\n",
        "        min_samples_leaf=5,\n",
        "        honest_prior=\"ignore\",\n",
        "        max_features=\"auto\",\n",
        "        n_jobs=-1,\n",
        "        max_samples = None\n",
        "    )\n",
        ")\n",
        "    Empirical_Power = empirical_power(test,sim)\n",
        "    np.savetxt(\n",
        "        \"{}_{}_testin.csv\".format(sim, 'uf'),\n",
        "        Empirical_Power,\n",
        "        delimiter=\",\",\n",
        "    )\n",
        "    print(Empirical_Power)\n"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": "linear\n(100, 2) (100, 2)\n0.07792207792207792\n(100, 2) (100, 2)\n0.07492507492507493\n(100, 2) (100, 2)\n0.04195804195804196\n(100, 2) (100, 2)\n0.058941058941058944\n(100, 2) (100, 2)\n0.052947052947052944\n(100, 2) (100, 2)\n0.06493506493506493\n(100, 2) (100, 2)\n0.04895104895104895\n(100, 2) (100, 2)\n0.04295704295704296\n(100, 2) (100, 2)\n0.057942057942057944\n(100, 2) (100, 2)\n0.03996003996003996\n[0.07792207792207792, 0.07492507492507493, 0.04195804195804196, 0.058941058941058944, 0.052947052947052944, 0.06493506493506493, 0.04895104895104895, 0.04295704295704296, 0.057942057942057944, 0.03996003996003996]\n(100, 3) (100, 3)\n0.04495504495504495\n(100, 3) (100, 3)\n0.053946053946053944\n(100, 3) (100, 3)\n0.054945054945054944\n(100, 3) (100, 3)\n0.052947052947052944\n(100, 3) (100, 3)\n0.060939060939060936\n(100, 3) (100, 3)\n0.04895104895104895\n(100, 3) (100, 3)\n0.052947052947052944\n(100, 3) (100, 3)\n0.03796203796203796\n(100, 3) (100, 3)\n0.04195804195804196\n(100, 3) (100, 3)\n0.04995004995004995\n[0.04495504495504495, 0.053946053946053944, 0.054945054945054944, 0.052947052947052944, 0.060939060939060936, 0.04895104895104895, 0.052947052947052944, 0.03796203796203796, 0.04195804195804196, 0.04995004995004995]\n(100, 4) (100, 4)\n0.055944055944055944\n(100, 4) (100, 4)\n0.06893106893106893\n(100, 4) (100, 4)\n0.04295704295704296\n(100, 4) (100, 4)\n0.04895104895104895\n(100, 4) (100, 4)\n0.04695304695304695\n(100, 4) (100, 4)\n0.04495504495504495\n(100, 4) (100, 4)\n0.04195804195804196\n(100, 4) (100, 4)\n0.04095904095904096\n(100, 4) (100, 4)\n0.06493506493506493\n(100, 4) (100, 4)\n0.04795204795204795\n[0.055944055944055944, 0.06893106893106893, 0.04295704295704296, 0.04895104895104895, 0.04695304695304695, 0.04495504495504495, 0.04195804195804196, 0.04095904095904096, 0.06493506493506493, 0.04795204795204795]\n(100, 5) (100, 5)\n0.05094905094905095\n(100, 5) (100, 5)\n0.04295704295704296\n(100, 5) (100, 5)\n0.04795204795204795\n(100, 5) (100, 5)\n0.04595404595404595\n(100, 5) (100, 5)\n0.04095904095904096\n(100, 5) (100, 5)\n0.055944055944055944\n(100, 5) (100, 5)\n0.058941058941058944\n(100, 5) (100, 5)\n0.060939060939060936\n(100, 5) (100, 5)\n0.05194805194805195\n(100, 5) (100, 5)\n0.03596403596403597\n[0.05094905094905095, 0.04295704295704296, 0.04795204795204795, 0.04595404595404595, 0.04095904095904096, 0.055944055944055944, 0.058941058941058944, 0.060939060939060936, 0.05194805194805195, 0.03596403596403597]\n(100, 6) (100, 6)\n0.04695304695304695\n(100, 6) (100, 6)\n0.053946053946053944\n(100, 6) (100, 6)\n0.06993006993006994\n(100, 6) (100, 6)\n0.06293706293706294\n(100, 6) (100, 6)\n0.057942057942057944\n(100, 6) (100, 6)\n0.055944055944055944\n(100, 6) (100, 6)\n0.03596403596403597\n(100, 6) (100, 6)\n0.03596403596403597\n(100, 6) (100, 6)\n0.057942057942057944\n(100, 6) (100, 6)\n0.03896103896103896\n[0.04695304695304695, 0.053946053946053944, 0.06993006993006994, 0.06293706293706294, 0.057942057942057944, 0.055944055944055944, 0.03596403596403597, 0.03596403596403597, 0.057942057942057944, 0.03896103896103896]\n(100, 7) (100, 7)\n0.03896103896103896\n(100, 7) (100, 7)\n0.04995004995004995\n(100, 7) (100, 7)\n0.052947052947052944\n(100, 7) (100, 7)\n0.06993006993006994\n(100, 7) (100, 7)\n0.05194805194805195\n(100, 7) (100, 7)\n0.04895104895104895\n(100, 7) (100, 7)\n0.04195804195804196\n(100, 7) (100, 7)\n0.04095904095904096\n(100, 7) (100, 7)\n0.04695304695304695\n(100, 7) (100, 7)\n0.052947052947052944\n[0.03896103896103896, 0.04995004995004995, 0.052947052947052944, 0.06993006993006994, 0.05194805194805195, 0.04895104895104895, 0.04195804195804196, 0.04095904095904096, 0.04695304695304695, 0.052947052947052944]\n(100, 8) (100, 8)\n0.04895104895104895\n(100, 8) (100, 8)\n0.052947052947052944\n(100, 8) (100, 8)\n0.03796203796203796\n(100, 8) (100, 8)\n0.05194805194805195\n(100, 8) (100, 8)\n0.05194805194805195\n(100, 8) (100, 8)\n0.04495504495504495\n(100, 8) (100, 8)\n0.04595404595404595\n(100, 8) (100, 8)\n0.03396603396603397\n(100, 8) (100, 8)\n0.04095904095904096\n(100, 8) (100, 8)\n0.04195804195804196\n[0.04895104895104895, 0.052947052947052944, 0.03796203796203796, 0.05194805194805195, 0.05194805194805195, 0.04495504495504495, 0.04595404595404595, 0.03396603396603397, 0.04095904095904096, 0.04195804195804196]\n(100, 9) (100, 9)\n0.03396603396603397\n(100, 9) (100, 9)\n0.06493506493506493\n(100, 9) (100, 9)\n0.058941058941058944\n(100, 9) (100, 9)\n0.04195804195804196\n(100, 9) (100, 9)\n0.04995004995004995\n(100, 9) (100, 9)\n0.04695304695304695\n(100, 9) (100, 9)\n0.06493506493506493\n(100, 9) (100, 9)\n0.07992007992007992\n(100, 9) (100, 9)\n0.03596403596403597\n(100, 9) (100, 9)\n0.06293706293706294\n[0.03396603396603397, 0.06493506493506493, 0.058941058941058944, 0.04195804195804196, 0.04995004995004995, 0.04695304695304695, 0.06493506493506493, 0.07992007992007992, 0.03596403596403597, 0.06293706293706294]\n(100, 10) (100, 10)\n0.03896103896103896\n(100, 10) (100, 10)\n0.04695304695304695\n(100, 10) (100, 10)\n0.06493506493506493\n(100, 10) (100, 10)\n0.03896103896103896\n(100, 10) (100, 10)\n0.06493506493506493\n(100, 10) (100, 10)\n0.04295704295704296\n(100, 10) (100, 10)\n0.053946053946053944\n(100, 10) (100, 10)\n0.03496503496503497\n(100, 10) (100, 10)\n0.030969030969030968\n(100, 10) (100, 10)\n0.060939060939060936\n[0.03896103896103896, 0.04695304695304695, 0.06493506493506493, 0.03896103896103896, 0.06493506493506493, 0.04295704295704296, 0.053946053946053944, 0.03496503496503497, 0.030969030969030968, 0.060939060939060936]\n[0.05614385614385614, 0.049950049950049945, 0.05044955044955045, 0.04925074925074925, 0.051648351648351645, 0.04955044955044955, 0.04515484515484516, 0.054045954045954046, 0.04785214785214785]\nexponential\n(100, 2) (100, 2)\n0.04495504495504495\n(100, 2) (100, 2)\n0.057942057942057944\n(100, 2) (100, 2)\n0.04895104895104895\n(100, 2) (100, 2)\n0.04595404595404595\n(100, 2) (100, 2)\n0.07692307692307693\n(100, 2) (100, 2)\n0.04795204795204795\n(100, 2) (100, 2)\n0.060939060939060936\n(100, 2) (100, 2)\n0.03996003996003996\n(100, 2) (100, 2)\n0.054945054945054944\n(100, 2) (100, 2)\n0.06693306693306693\n[0.04495504495504495, 0.057942057942057944, 0.04895104895104895, 0.04595404595404595, 0.07692307692307693, 0.04795204795204795, 0.060939060939060936, 0.03996003996003996, 0.054945054945054944, 0.06693306693306693]\n(100, 3) (100, 3)\n0.04495504495504495\n(100, 3) (100, 3)\n0.03496503496503497\n(100, 3) (100, 3)\n0.054945054945054944\n(100, 3) (100, 3)\n0.04595404595404595\n(100, 3) (100, 3)\n0.04695304695304695\n(100, 3) (100, 3)\n0.04995004995004995\n(100, 3) (100, 3)\n0.03596403596403597\n(100, 3) (100, 3)\n0.04095904095904096\n(100, 3) (100, 3)\n0.061938061938061936\n(100, 3) (100, 3)\n0.058941058941058944\n[0.04495504495504495, 0.03496503496503497, 0.054945054945054944, 0.04595404595404595, 0.04695304695304695, 0.04995004995004995, 0.03596403596403597, 0.04095904095904096, 0.061938061938061936, 0.058941058941058944]\n(100, 4) (100, 4)\n0.06393606393606394\n(100, 4) (100, 4)\n0.06293706293706294\n(100, 4) (100, 4)\n0.06893106893106893\n(100, 4) (100, 4)\n0.052947052947052944\n(100, 4) (100, 4)\n0.04295704295704296\n(100, 4) (100, 4)\n0.025974025974025976\n(100, 4) (100, 4)\n0.057942057942057944\n(100, 4) (100, 4)\n0.04695304695304695\n(100, 4) (100, 4)\n0.07292707292707293\n(100, 4) (100, 4)\n0.04195804195804196\n[0.06393606393606394, 0.06293706293706294, 0.06893106893106893, 0.052947052947052944, 0.04295704295704296, 0.025974025974025976, 0.057942057942057944, 0.04695304695304695, 0.07292707292707293, 0.04195804195804196]\n(100, 5) (100, 5)\n0.04695304695304695\n(100, 5) (100, 5)\n0.06793206793206794\n(100, 5) (100, 5)\n0.054945054945054944\n(100, 5) (100, 5)\n0.04295704295704296\n(100, 5) (100, 5)\n0.04395604395604396\n(100, 5) (100, 5)\n0.06793206793206794\n(100, 5) (100, 5)\n0.04895104895104895\n(100, 5) (100, 5)\n0.03296703296703297\n(100, 5) (100, 5)\n0.054945054945054944\n(100, 5) (100, 5)\n0.05194805194805195\n[0.04695304695304695, 0.06793206793206794, 0.054945054945054944, 0.04295704295704296, 0.04395604395604396, 0.06793206793206794, 0.04895104895104895, 0.03296703296703297, 0.054945054945054944, 0.05194805194805195]\n(100, 6) (100, 6)\n0.06693306693306693\n(100, 6) (100, 6)\n0.04895104895104895\n(100, 6) (100, 6)\n0.060939060939060936\n(100, 6) (100, 6)\n0.03596403596403597\n(100, 6) (100, 6)\n0.05194805194805195\n(100, 6) (100, 6)\n0.04795204795204795\n(100, 6) (100, 6)\n0.04395604395604396\n(100, 6) (100, 6)\n0.05094905094905095\n(100, 6) (100, 6)\n0.05194805194805195\n(100, 6) (100, 6)\n0.05094905094905095\n[0.06693306693306693, 0.04895104895104895, 0.060939060939060936, 0.03596403596403597, 0.05194805194805195, 0.04795204795204795, 0.04395604395604396, 0.05094905094905095, 0.05194805194805195, 0.05094905094905095]\n(100, 7) (100, 7)\n0.04795204795204795\n(100, 7) (100, 7)\n0.06393606393606394\n(100, 7) (100, 7)\n0.058941058941058944\n(100, 7) (100, 7)\n0.03496503496503497\n(100, 7) (100, 7)\n0.06493506493506493\n(100, 7) (100, 7)\n0.04095904095904096\n(100, 7) (100, 7)\n0.05194805194805195\n(100, 7) (100, 7)\n0.052947052947052944\n(100, 7) (100, 7)\n0.07092907092907093\n(100, 7) (100, 7)\n0.04195804195804196\n[0.04795204795204795, 0.06393606393606394, 0.058941058941058944, 0.03496503496503497, 0.06493506493506493, 0.04095904095904096, 0.05194805194805195, 0.052947052947052944, 0.07092907092907093, 0.04195804195804196]\n(100, 8) (100, 8)\n0.05094905094905095\n(100, 8) (100, 8)\n0.058941058941058944\n(100, 8) (100, 8)\n0.04995004995004995\n(100, 8) (100, 8)\n0.058941058941058944\n(100, 8) (100, 8)\n0.04895104895104895\n(100, 8) (100, 8)\n0.04795204795204795\n(100, 8) (100, 8)\n0.04595404595404595\n(100, 8) (100, 8)\n0.05194805194805195\n(100, 8) (100, 8)\n0.053946053946053944\n(100, 8) (100, 8)\n0.059940059940059943\n[0.05094905094905095, 0.058941058941058944, 0.04995004995004995, 0.058941058941058944, 0.04895104895104895, 0.04795204795204795, 0.04595404595404595, 0.05194805194805195, 0.053946053946053944, 0.059940059940059943]\n(100, 9) (100, 9)\n0.07292707292707293\n(100, 9) (100, 9)\n0.054945054945054944\n(100, 9) (100, 9)\n0.056943056943056944\n(100, 9) (100, 9)\n0.052947052947052944\n(100, 9) (100, 9)\n0.04795204795204795\n(100, 9) (100, 9)\n0.060939060939060936\n(100, 9) (100, 9)\n0.052947052947052944\n(100, 9) (100, 9)\n0.04595404595404595\n(100, 9) (100, 9)\n0.057942057942057944\n(100, 9) (100, 9)\n0.060939060939060936\n[0.07292707292707293, 0.054945054945054944, 0.056943056943056944, 0.052947052947052944, 0.04795204795204795, 0.060939060939060936, 0.052947052947052944, 0.04595404595404595, 0.057942057942057944, 0.060939060939060936]\n(100, 10) (100, 10)\n0.030969030969030968\n(100, 10) (100, 10)\n0.03796203796203796\n(100, 10) (100, 10)\n0.04195804195804196\n(100, 10) (100, 10)\n0.056943056943056944\n(100, 10) (100, 10)\n0.03196803196803197\n(100, 10) (100, 10)\n0.06493506493506493\n(100, 10) (100, 10)\n0.04095904095904096\n(100, 10) (100, 10)\n0.052947052947052944\n(100, 10) (100, 10)\n0.04795204795204795\n(100, 10) (100, 10)\n0.058941058941058944\n[0.030969030969030968, 0.03796203796203796, 0.04195804195804196, 0.056943056943056944, 0.03196803196803197, 0.06493506493506493, 0.04095904095904096, 0.052947052947052944, 0.04795204795204795, 0.058941058941058944]\n[0.05454545454545454, 0.04755244755244755, 0.05374625374625375, 0.05134865134865135, 0.051048951048951054, 0.052947052947052944, 0.05274725274725275, 0.056443556443556454, 0.04655344655344655]\ncubic\n(100, 2) (100, 2)\n0.054945054945054944\n(100, 2) (100, 2)\n0.04895104895104895\n(100, 2) (100, 2)\n0.03496503496503497\n(100, 2) (100, 2)\n0.06993006993006994\n(100, 2) (100, 2)\n0.04995004995004995\n(100, 2) (100, 2)\n0.04895104895104895\n(100, 2) (100, 2)\n0.057942057942057944\n(100, 2) (100, 2)\n0.061938061938061936\n(100, 2) (100, 2)\n0.04495504495504495\n(100, 2) (100, 2)\n0.06793206793206794\n[0.054945054945054944, 0.04895104895104895, 0.03496503496503497, 0.06993006993006994, 0.04995004995004995, 0.04895104895104895, 0.057942057942057944, 0.061938061938061936, 0.04495504495504495, 0.06793206793206794]\n(100, 3) (100, 3)\n0.053946053946053944\n(100, 3) (100, 3)\n0.057942057942057944\n(100, 3) (100, 3)\n0.03896103896103896\n(100, 3) (100, 3)\n0.05094905094905095\n(100, 3) (100, 3)\n0.03796203796203796\n(100, 3) (100, 3)\n0.06293706293706294\n(100, 3) (100, 3)\n0.04495504495504495\n(100, 3) (100, 3)\n0.04995004995004995\n(100, 3) (100, 3)\n0.04995004995004995\n(100, 3) (100, 3)\n0.04995004995004995\n[0.053946053946053944, 0.057942057942057944, 0.03896103896103896, 0.05094905094905095, 0.03796203796203796, 0.06293706293706294, 0.04495504495504495, 0.04995004995004995, 0.04995004995004995, 0.04995004995004995]\n(100, 4) (100, 4)\n0.04195804195804196\n(100, 4) (100, 4)\n0.05194805194805195\n(100, 4) (100, 4)\n0.04795204795204795\n(100, 4) (100, 4)\n0.059940059940059943\n(100, 4) (100, 4)\n0.04395604395604396\n(100, 4) (100, 4)\n0.04295704295704296\n(100, 4) (100, 4)\n0.05194805194805195\n(100, 4) (100, 4)\n0.05094905094905095\n(100, 4) (100, 4)\n0.04395604395604396\n(100, 4) (100, 4)\n0.04395604395604396\n[0.04195804195804196, 0.05194805194805195, 0.04795204795204795, 0.059940059940059943, 0.04395604395604396, 0.04295704295704296, 0.05194805194805195, 0.05094905094905095, 0.04395604395604396, 0.04395604395604396]\n(100, 5) (100, 5)\n0.054945054945054944\n(100, 5) (100, 5)\n0.052947052947052944\n(100, 5) (100, 5)\n0.03996003996003996\n(100, 5) (100, 5)\n0.03696303696303696\n(100, 5) (100, 5)\n0.053946053946053944\n(100, 5) (100, 5)\n0.058941058941058944\n(100, 5) (100, 5)\n0.06593406593406594\n(100, 5) (100, 5)\n"
        }
      ],
      "execution_count": 14,
      "metadata": {
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "gather": {
          "logged": 1670871637938
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "fig, ax = plt.subplots(nrows=4, ncols=5, figsize=(25, 20))\n",
        "plt.suptitle(\n",
        "    \"Multivariate Independence Testing (Increasing Dimension)\",\n",
        "    y=0.93,\n",
        "    va=\"baseline\",\n",
        "    )\n",
        "\n",
        "for i, row in enumerate(ax):\n",
        "    for j, col in enumerate(row):\n",
        "        count = 5 * i + j\n",
        "        sim = list(SIMULATIONS.keys())[count]\n",
        "        est_power = np.genfromtxt( \"{}_{}.csv\".format(sim, 'uf'),delimiter=\",\",)\n",
        "        col.plot(range(1,10),est_power)\n",
        "        col.set_yticks([0, 1])\n",
        "        #col.yticks(np.arange(0, 1.2, step=0.2))\n",
        "        #col.show()\n",
        "        col.set_title(list(SIMULATIONS.keys())[count])"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 2500x2000 with 20 Axes>",
            "image/png": 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          },
          "metadata": {}
        }
      ],
      "execution_count": 123,
      "metadata": {
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "gather": {
          "logged": 1670814472941
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "circle_uf_ksample = np.loadtxt(\"circle_uf.csv\")\n",
        "cubic_uf_ksample = np.loadtxt(\"cubic_uf.csv\")\n",
        "diamond_uf_ksample = np.loadtxt(\"diamond_uf.csv\")\n",
        "ellipse_uf_ksample = np.loadtxt(\"ellipse_uf.csv\")\n",
        "exponential_uf_ksample = np.loadtxt(\"exponential_uf.csv\")\n",
        "fourth_root_uf_ksample = np.loadtxt(\"fourth_root_uf.csv\")\n",
        "linear_uf_ksample = np.loadtxt(\"linear_uf.csv\")\n",
        "joint_normal_uf_ksample = np.loadtxt(\"joint_normal_uf.csv\")\n",
        "logarithmic_uf_ksample = np.loadtxt(\"logarithmic_uf.csv\")\n",
        "multimodal_independence_uf_ksample = np.loadtxt(\"multimodal_independence_uf.csv\")"
      ],
      "outputs": [],
      "execution_count": 80,
      "metadata": {
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "gather": {
          "logged": 1670787562860
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def sig(x):\n",
        " return 1/(1 + np.exp(-x))"
      ],
      "outputs": [],
      "execution_count": 99,
      "metadata": {
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "gather": {
          "logged": 1670788495520
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "ite = 100\n",
        "reps = 1000\n",
        "sample_size = 200\n",
        "#stat = []\n",
        "#null_dist = np.zeros((ite,reps))\n",
        "dim_range = range(1,21,1)\n",
        "Empirical_Power = []\n",
        "for j in dim_range:\n",
        "    empirical_power = []\n",
        "    for i in range(0,ite):\n",
        "        X, y_ = indep_sim('linear', n=sample_size, p=j,noise=True)\n",
        "        #print(sig(y_))\n",
        "        y = np.round(sig(y_)).astype(int)\n",
        "        #plt.scatter(y_,y)\n",
        "        print(X.shape,y.shape)\n",
        "        print(sum(y))\n",
        "        empirical_power_i = perm_test(test,X, y,alpha = 0.05,is_distsim = False,reps = reps)\n",
        "        print(empirical_power_i)\n",
        "        empirical_power.append(empirical_power_i)\n",
        "    Empirical_Power.append(np.mean(empirical_power))\n",
        "    print(empirical_power)\n"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
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        }
      ],
      "execution_count": 147,
      "metadata": {
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "gather": {
          "logged": 1670821433124
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "np.save('Empirical_Power_linear_20dim_ind_100ite.npy',Empirical_Power)"
      ],
      "outputs": [],
      "execution_count": 151,
      "metadata": {
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "gather": {
          "logged": 1670871222037
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(np.arange(1,21,1),Empirical_Power)\n",
        "plt.yticks(np.arange(0,1.2,0.2))\n",
        "plt.xticks(np.arange(1,21,1))\n",
        "plt.title('Linear Set Independence Testing (Increasing Dimension)')\n"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 152,
          "data": {
            "text/plain": "Text(0.5, 1.0, 'Linear Set Independence Testing (Increasing Dimension)')"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 640x480 with 1 Axes>",
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "execution_count": 152,
      "metadata": {
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "gather": {
          "logged": 1670871225374
        }
      }
    }
  ],
  "metadata": {
    "kernelspec": {
      "name": "python38-azureml",
      "language": "python",
      "display_name": "Python 3.8 - AzureML"
    },
    "language_info": {
      "name": "python",
      "version": "3.8.5",
      "mimetype": "text/x-python",
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "pygments_lexer": "ipython3",
      "nbconvert_exporter": "python",
      "file_extension": ".py"
    },
    "kernel_info": {
      "name": "python38-azureml"
    },
    "microsoft": {
      "host": {
        "AzureML": {
          "notebookHasBeenCompleted": true
        }
      }
    },
    "nteract": {
      "version": "nteract-front-end@1.0.0"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 2
}