{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Quantitative sensitivity analysis\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generalized Sobol Indices" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we show how to compute generalized Sobol indices on the **EOQ** model using the algorithm presented in Kucherenko et al. 2012. We import our model function from ``temfpy`` and use the Kucherenko indices function from ``econsa``. " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt # noqa: F401\n", "import numpy as np\n", "\n", "from temfpy.uncertainty_quantification import eoq_model\n", "\n", "# TODO: Reactivate once Tim's PR is ready.\n", "# from econsa.kucherenko import kucherenko_indices # noqa: E265" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The function ``kucherenko_indices`` expects the input function to be broadcastable over rows, that is, a row represents the input arguments for one evaluation. For sampling around the mean parameters we specify a diagonal covariance matrix, where the variances depend on the scaling of the mean. Since the variances of the parameters are unknown prior to our analysis we choose values such that the probability of sampling negative values is negligible. We do this since the **EOQ** model is not defined for negative parameters and the normal sampling does not naturally account for bounds." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def eoq_model_transposed(x):\n", " \"\"\"EOQ Model but with variables stored in columns.\"\"\"\n", " return eoq_model(x.T)\n", "\n", "mean = np.array([1230, 0.0135, 2.15])\n", "cov = np.diag([1, 0.000001, 0.01])\n", "\n", "# indices = kucherenko_indices( # noqa: E265\n", "# func=eoq_model_transposed, # noqa: E265\n", "# sampling_mean=mean, # noqa: E265\n", "# sampling_cov=cov, # noqa: E265\n", "# n_draws=1_000_000, # noqa: E265\n", "# sampling_scheme=\"sobol\", # noqa: E265\n", "# ) # noqa: E265" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we are ready to inspect the results." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "nbsphinx": "hidden" }, "outputs": [], "source": [ "# sobol_first = indices.loc[(slice(None), \"first_order\"), \"value\"].values # noqa: E265\n", "# sobol_total = indices.loc[(slice(None), \"total\"), \"value\"].values # noqa: E265\n", "\n", "# x = np.arange(3) # the label locations # noqa: E265\n", "# width = 0.35 # the width of the bars # noqa: E265\n", "\n", "# fig, ax = plt.subplots() # noqa: E265\n", "# rects1 = ax.bar(x - width / 2, sobol_first, width, label=\"First-order\") # noqa: E265\n", "# rects2 = ax.bar(x + width / 2, sobol_total, width, label=\"Total\") # noqa: E265\n", "\n", "# ax.set_ylim([0, 1]) # noqa: E265\n", "# ax.legend() # noqa: E265\n", "\n", "# ax.set_xticks(x) # noqa: E265\n", "# ax.set_xticklabels([\"$x_0$\", \"$x_1$\", \"$x_2$\"]) # noqa: E265\n", "# ax.legend(); # noqa: E265" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# fig # noqa: E265" ] }, { "source": [ "## Shapley Effects" ], "cell_type": "markdown", "metadata": {} }, { "cell_type": "markdown", "metadata": {}, "source": [ "`econsa` offers an implementation of the algorithm for the computation of Shapley effects as propsoed by Song et al. (2016).\n", "Here we show how to compute Shapley effects using the **EOQ** model as referenced above. We adjust the model in ``temfpy`` to accomodate an n-dimensional array for use in the context of the Shapley effects as implemented in ``econsa``. " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# import necessary packages and functions\n", "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "import chaospy as cp\n", "\n", "from econsa.shapley import get_shapley\n", "from econsa.shapley import _r_condmvn" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Sampling via `x_all` and `x_cond`, and the model of interest `model`\n", "First, we load all neccesary objects for the estimation of Shapley effects. The following objects are needed in the case of Gaussian model inputs.\n", "\n", "- The functions ``x_all`` and ``x_cond`` for (un-)conditional sampling. These functions depend on the distribution from which we are sampling from. For the purposes of this illustration, we will sample from a multivariate normal distribution, but the functions can be tailored to the user's specific needs.\n", "\n", "- A mean vector and covariance matrix of the model inputs. They are necessary for sampling conducted by the above two functions in the case of a Gaussian distribution.\n", "\n", "- The ``model`` the user wishes to perform sensitivity analysis (SA) on that maps model inputs to a model output. Here we consider the **EOQ** model." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "# Mean vector and covariance matrix of the model inputs.\n", "n_inputs = 3\n", "mean = np.array([5.345, 0.0135, 2.15])\n", "cov = np.diag([1, 0.000001, 0.01])" ] }, { "source": [ "### Choosing `n_perms`\n", "Since we are conducting SA on a model with three inputs, the number of permutations on which the computation algorithm is based is $3! = 6$. For larger number of inputs it might be worthwhile to consider only a subset of all permutations. E.g. for a model with 10 inputs, there are 3,628,800 permutations. Considering all permutations could be computationally infeasible. Thus, ``get_shapley`` allows the user to set a specific number of permutations by the argument ``n_perms``." ], "cell_type": "markdown", "metadata": {} }, { "source": [ "### Choosing the number of Monte Carlo (MC) runs `n_output`, `n_outer`, and `n_inner`\n", "$N_V$, $N_O$, and $N_I$ denote the function arguments ``n_output``, ``n_outer``, and ``n_inner``, respectively. For the algorithm by Song et al. (2016) these three MC simulations are needed. The number of model evaluations required for the estimation of Shapley effects by ``get_shapley`` are given by\n", "\n", "$$N_V+m \\cdot N_I \\cdot N_O \\cdot (k-1),$$\n", "\n", "where $m$ denotes the number of permutations, ``n_perms``, and $k$ the number of inputs, ``n_inputs``.\n", "\n", "Song et al. (2016) show that choosing $N_I = 3$ is optimal. $N_V$ needs to be large enough to reliably estimate the total output variance, $V[Y]$. Given these choices, $N_O$ is chosen to consume the rest of the computational budget." ], "cell_type": "markdown", "metadata": {} }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "# Model for which senstivity analysis is being performed.\n", "def eoq_model_ndarray(x, r=0.1):\n", " \"\"\"EOQ Model that accepts ndarray.\"\"\"\n", " m = x[:, 0]\n", " c = x[:, 1]\n", " s = x[:, 2] \n", " return np.sqrt((24 * m * s) / (r * c)) " ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "# Function for unconditional sampling.\n", "def x_all(n):\n", " distribution = cp.MvNormal(mean, cov)\n", " return distribution.sample(n)\n", "\n", "# Function for conditional sampling in the case of Gaussian inputs.\n", "def x_cond(n, subset_j, subsetj_conditional, xjc):\n", " if subsetj_conditional is None:\n", " cov_int = np.array(cov)\n", " cov_int = cov_int.take(subset_j, axis = 1)\n", " cov_int = cov_int[subset_j]\n", " distribution = cp.MvNormal(mean[subset_j], cov_int)\n", " return distribution.sample(n)\n", " else:\n", " return _r_condmvn(n, mean=mean, cov=cov, dependent_ind=subset_j, given_ind=subsetj_conditional, x_given=xjc)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "# Estimate Shapley effects using the exact method.\n", "np.random.seed(1234)\n", "method = \"exact\"\n", "n_perms = None\n", "n_output = 10 ** 4\n", "n_outer = 10 ** 3\n", "n_inner = 3\n", "\n", "exact_shapley = get_shapley(method, eoq_model_ndarray, x_all, x_cond, n_perms, n_inputs, n_output, n_outer, n_inner)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ " Shapley effects std. errors CI_min CI_max\n", "X1 0.828423 0.008709 0.811353 0.845493\n", "X2 0.130322 0.004717 0.121077 0.139568\n", "X3 0.041255 0.012115 0.017509 0.065000" ], "text/html": "
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Shapley effectsstd. errorsCI_minCI_max
X10.8284230.0087090.8113530.845493
X20.1303220.0047170.1210770.139568
X30.0412550.0121150.0175090.065000
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" }, "metadata": {}, "execution_count": 12 } ], "source": [ "exact_shapley" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "# Estimate Shapley effects using the random method.\n", "np.random.seed(1234)\n", "method = \"random\"\n", "n_perms = 5\n", "n_output = 10 ** 4\n", "n_outer = 10 ** 3\n", "n_inner = 3\n", "\n", "random_shapley = get_shapley(method, eoq_model_ndarray, x_all, x_cond, n_perms, n_inputs, n_output, n_outer, n_inner)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ " Shapley effects std. errors CI_min CI_max\n", "X1 0.817302 0.015392 0.787134 0.847470\n", "X2 0.129110 0.003608 0.122037 0.136182\n", "X3 0.053588 0.013530 0.027069 0.080108" ], "text/html": "
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Shapley effectsstd. errorsCI_minCI_max
X10.8173020.0153920.7871340.847470
X20.1291100.0036080.1220370.136182
X30.0535880.0135300.0270690.080108
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" }, "metadata": {}, "execution_count": 15 } ], "source": [ "random_shapley" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we plot the ranking of the Shapley values below." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "nbsphinx": "hidden" }, "outputs": [], "source": [ "# comparison of exact and random method ranking\n", "data = {'inputs':['X1', 'X2', 'X3'], 'exact_method':[0.814539, 0.130068, 0.055392],\n", " 'random_method': [0.814734, 0.130517, 0.054749]}\n", "\n", "# covert dict to dataframe for plot\n", "df = pd.DataFrame(data)\n", "\n", "# Set up a grid to plot survival probability against several variables\n", "def ranking(data):\n", " g = sns.PairGrid(data.sort_values(\"exact_method\", ascending=False),\n", " x_vars=data.columns[-2:], y_vars=[\"inputs\"],\n", " height=4, aspect=.9)\n", "\n", " # Draw a dot plot using the stripplot function\n", " g.map(sns.stripplot, size=10, orient=\"h\", linewidth=1, edgecolor=\"w\")\n", "\n", " # Use the same x axis limits on all columns and add better labels\n", " g.set(xlim=(0, 0.9), xlabel=\"Shapley effect\", ylabel=\"\")\n", "\n", " # Use semantically meaningful titles for the columns\n", " titles = [\"exact method\", \"random method\"]\n", "\n", " for ax, title in zip(g.axes.flat, titles):\n", "\n", " # Set a different title for each axes\n", " ax.set(title=title)\n", "\n", " # Make the grid horizontal instead of vertical\n", " ax.xaxis.grid(False)\n", " ax.yaxis.grid(True)\n", "\n", " sns.despine(left=True, bottom=True)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "output_type": "display_data", "data": { "text/plain": "
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\n" }, "metadata": { "needs_background": "light" } } ], "source": [ "# plot for exact and random permutations methods\n", "ranking(data = df)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As noticed above, both methods produce the same ranking. Sometimes, it is neccesary to compare the parameter estimates with their parameter values. A typical application is hypothesis testing, that is, whether the parameter estimates are significant, and what the contribution of significant / insignificant estimates is to the output variance as reflected by their Shapley ranking.\n", "\n", "We can plot the parameter estimates together with their Shapley ranking as shown below:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "nbsphinx": "hidden" }, "outputs": [], "source": [ "# plot for exact permutations method\n", "def ranking_params_shapley(ordered_df):\n", "# The vertical plot is made using the hline function\n", "# I load the seaborn library only to benefit the nice looking feature\n", " plt.hlines(y=my_range, xmin=ordered_df['params'], xmax=ordered_df['shapley_effect'], color='grey', alpha=0.4)\n", " plt.scatter(ordered_df['params'], my_range, color='skyblue', alpha=1, label='params')\n", " plt.scatter(ordered_df['shapley_effect'], my_range, color='green', alpha=0.4 , label='shapley_effect')\n", " plt.legend()\n", " \n", " # Add title and axis names\n", " plt.yticks(my_range, ordered_df['inputs'])\n", " plt.title(\"Comparison of params and Shapley effects\", loc='left')\n", " plt.xlabel('Value of the variables')\n", " plt.ylabel('Group')\n", " \n", "df = {'inputs':['X1', 'X2', 'X3'], 'params':[5.345, 0.0135, 2.15],\n", " 'shapley_effect': [0.814539, 0.130068, 0.055392]}\n", "\n", "df_exact = pd.DataFrame(df)\n", "ordered_df = df_exact.sort_values(by='params')\n", "my_range = range(1,len(df_exact.index)+1)\n" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "output_type": "display_data", "data": { "text/plain": "
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}, "metadata": { "needs_background": "light" } } ], "source": [ "# plot exact method comparison\n", "ranking_params_shapley(ordered_df)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "nbsphinx": "hidden" }, "outputs": [], "source": [ "# plot random method comparison\n", "df = {'inputs':['X1', 'X2', 'X3'], 'params':[5.345, 0.0135, 2.15],\n", " 'shapley_effect': [0.814734, 0.130517, 0.054749]}\n", "\n", "df_exact = pd.DataFrame(df)\n", "ordered_df = df_exact.sort_values(by='params')\n", "my_range = range(1,len(df_exact.index)+1)\n" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "output_type": "display_data", "data": { "text/plain": "
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\n" }, "metadata": { "needs_background": "light" } } ], "source": [ "# plot random method comparison\n", "ranking_params_shapley(ordered_df)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### When do we use randomly sampled permutations? Choosing `method`\n", "The `exact` method is good for use when the number of parameters is low, depending on the computational time it takes to estimate the model in question. If it is computationally inexpensive to estimate the model for which sensitivity analysis is required, then the `exact` method is always preferable, otherwise the `random` is recommended. A good way to proceed if one suspects that the computational time required to estimate the model is high, having a lot of parameters to conduct SA on is always to commence the exercise with a small number of parameters, e.g. 3, then get a benchmark of the Shapley effects using the `exact` method. Having done that, repeat the exercise using the `random` method on the same vector of parameters, calibrating the `n_perms` argument to make sure that the results produced by the `random` method are the same as the `exact` one. Once this is complete, scale up the exercise using the `random` method, increasing the number of parameters to the desired parameter vector." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Quantile Based Sensitivity Measures" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We show how to compute global sensitivity measures based on quantiles of model's output." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "# import necessary packages and functions\n", "import numpy as np\n", "import pandas as pd\n", "import chaospy as cp\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "\n", "from temfpy.uncertainty_quantification import eoq_model\n", "from econsa.quantile_measures import mc_quantile_measures" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Firstly, we specify the parameters of the function. This function `mc_quantile_measures` is capable of computing numerical results of quantile-based sensitivity measures on various user-provided models. Here we take **EOQ model** from `temfpy` as an example, where the model function is adjusted to accommodate an n-dimensional array. For multivariate distributed samples, the `loc` and `scale` keywords are denoted by a mean vector and a covariance matrix respectively. Considering both efficient computation and good convergence, we set `n_draws` equal to 3000 and $2^{13}$ for brute force and double loop reordering estimators correspondently. Note that the double loop reordering estimator is more efficient than the brute force estimator." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "# model to perform quantile based sensitivity ananlysis\n", "def eoq_model_transposed(x):\n", " \"\"\"EOQ Model but with variables stored in columns.\"\"\"\n", " return eoq_model(x.T)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "# mean and covaraince matrix inputs\n", "mean = np.array([5.345, 0.0135, 2.15])\n", "cov = np.diag([1, 0.000001, 0.01])\n", "n_params = len(mean)\n", "dist_type = \"Normal\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then we are ready to calculate the numerical results using the algorithm presented in Kucherenko et al. 2019." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "# compute quantile measures using brute force estimator\n", "bf_measures = mc_quantile_measures(\"brute force\", eoq_model_transposed, n_params, mean, cov, dist_type, 3000,)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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x_1x_2x_3
Measuresalpha
q_10.02064.01046210.5951926.522037
0.05253.56528711.7648027.126140
0.08447.20363511.8491847.315335
0.11643.58470211.9457587.390247
0.14840.74679212.0746257.493912
...............
Q_20.8520.8511800.1080550.040765
0.8840.8577880.1028970.039315
0.9160.8637970.0993140.036889
0.9480.8713520.0938220.034825
0.9800.8806320.0892500.030119
\n", "

124 rows × 3 columns

\n", "
" ], "text/plain": [ " x_1 x_2 x_3\n", "Measures alpha \n", "q_1 0.020 64.010462 10.595192 6.522037\n", " 0.052 53.565287 11.764802 7.126140\n", " 0.084 47.203635 11.849184 7.315335\n", " 0.116 43.584702 11.945758 7.390247\n", " 0.148 40.746792 12.074625 7.493912\n", "... ... ... ...\n", "Q_2 0.852 0.851180 0.108055 0.040765\n", " 0.884 0.857788 0.102897 0.039315\n", " 0.916 0.863797 0.099314 0.036889\n", " 0.948 0.871352 0.093822 0.034825\n", " 0.980 0.880632 0.089250 0.030119\n", "\n", "[124 rows x 3 columns]" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "bf_measures" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "# compute quantile measures using double loop reordering estimator\n", "dlr_measures = mc_quantile_measures(\"DLR\", eoq_model_transposed, n_params, mean, cov, dist_type, 2 ** 13,)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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x_1x_2x_3
Measuresalpha
q_10.02064.17980910.4148236.285291
0.05252.26739911.0373416.778817
0.08446.31114611.2113026.917412
0.11642.56310311.4078167.013578
0.14840.32109811.6382897.183969
...............
Q_20.8520.8654170.0973120.037271
0.8840.8710060.0934220.035572
0.9160.8768100.0898010.033388
0.9480.8839110.0849700.031119
0.9800.8907280.0816050.027667
\n", "

124 rows × 3 columns

\n", "
" ], "text/plain": [ " x_1 x_2 x_3\n", "Measures alpha \n", "q_1 0.020 64.179809 10.414823 6.285291\n", " 0.052 52.267399 11.037341 6.778817\n", " 0.084 46.311146 11.211302 6.917412\n", " 0.116 42.563103 11.407816 7.013578\n", " 0.148 40.321098 11.638289 7.183969\n", "... ... ... ...\n", "Q_2 0.852 0.865417 0.097312 0.037271\n", " 0.884 0.871006 0.093422 0.035572\n", " 0.916 0.876810 0.089801 0.033388\n", " 0.948 0.883911 0.084970 0.031119\n", " 0.980 0.890728 0.081605 0.027667\n", "\n", "[124 rows x 3 columns]" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dlr_measures" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we are able to visualize the results." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "nbsphinx": "hidden" }, "outputs": [], "source": [ "def plot_quantile_measures(df_measures):\n", " \n", " sns.set_style(\"whitegrid\")\n", " sns.set_context(\"notebook\", font_scale=1.5)\n", "\n", " fig, ax = plt.subplots(figsize=(8,6))\n", " \n", " n_params = len(df_measures.columns)\n", "\n", " style_1 = [f'C{i}s--' for i in range(n_params)]\n", " style_2 = [f'C{i}o--' for i in range(n_params)]\n", "\n", " for q, s in zip([\"Q_1\", \"Q_2\"], [style_1, style_2]):\n", " df_measures.loc[q].plot(ax=ax, style=s, markerfacecolor='none')\n", "\n", " ax.set_title(r\"Values of $Q_i^{(1)}$ and $Q_i^{(2)}$ versus $\\alpha$\")\n", " ax.set_xticks(np.arange(0, 1.1, 0.1))\n", " ax.set_ylabel(\"Measures\")\n", " ax.set_xlabel(r\"$\\alpha$\")\n", "\n", " labels = [f'$Q_{i+1}^{{({p})}}$' for p in [1,2] for i in range(n_params)] \n", " ax.legend(labels,loc='center left', bbox_to_anchor=(1, 0.5), fontsize=15)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot brute force estimates\n", "plot_quantile_measures(bf_measures)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot double loop reordering estimates\n", "plot_quantile_measures(dlr_measures)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The brute force estimator and DLR estimator generate the same ranking of variables for all quantiles: $x_1, x_2, x_3$(in descending order). At $\\alpha=0.5$, measures $Q_i$ reachs their minimun:$i=1$ and maximum:$i=2,3$." ] } ], "metadata": { "kernelspec": { "name": "python3", "display_name": "Python 3.7.10 64-bit ('econsa': conda)" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.10" }, "interpreter": { "hash": "27f73fc847b24c08ac9b7a18ebc71c0304d052de3761b7e57e982a062414d1b0" } }, "nbformat": 4, "nbformat_minor": 4 }