{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Exepected Calibration Error(ECE) and Maximum Calibration Error (MCE)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Theoretical Background\n", "\n", "(True) Expected Calibration Error is defined as the average difference between the predicted probability and the true probability for a particular class. We will label the predicted probability as $\\hat{P}$ and the true probability as $P$ and drop the class of interest label for simplicity.\n", "\n", "$$\n", "\\text{ECE} = \\mathbb{E}_{\\hat{P}} [|\\mathbb{P}(\\hat{Y}=Y|\\hat{P}=p)-p|] = \\int_0^1 |\\mathbb{P}(\\hat{Y}=Y|\\hat{P}=p)-p| \\, dF_{\\hat{P}}(p)\n", "$$\n", "\n", "Some also define the ECE as the average difference between the predicted probability and the true probability of the predicted class. This is similar to the top-class vs class-by-class reliability diagram. We will refer to it as $\\text{ECE}_{top}$.\n", "\n", "$$\n", "\\text{ECE}_{top} = \\mathbb{E}_{\\hat{P_{top}}} [|\\mathbb{P}(\\hat{Y_{top}}=Y_{top}|\\hat{P_{top}}=p_{top})-p_{top}|])\n", "$$\n", "\n", "Similarly, we can also define the Maximum Calibration Error (MCE) as the maximum difference between the predicted and true probabilities:\n", "\n", "$$\n", "\\text{MCE} = \\max_p |\\mathbb{P}(\\hat{Y}=Y|\\hat{P}=p)-p|\n", "$$\n", "\n", "$$\n", "\\text{MCE}_{top} = \\max_{p_{top}}|\\mathbb{P}(\\hat{Y_{top}}=Y_{top}|\\hat{P}=p_{top})-p_{top}|\n", "$$\n", "\n", "### Estimated ECE and MCE\n", "\n", "We can't compute ECE and MCE directly from the data, but we can group the data into bins and compute an Estimated ECE and MCE from the grouped data. In most literature, the estimated ECE and MCE are simply referred to as ECE and MCE. We adopt the same convention but want to remind the reader that the estimated ECE and MCE are not the same as the true ECE and MCE and they heavily depend on the binning method. In the text below, we will use the terms ECE and MCE to refer to the estimated ECE and MCE, and true ECE and MCE to refer to the true ECE and MCE.\n", "\n", "$$\\text{ECE} = \\sum_{m=1}^M \\frac{|B_m|}{n} |acc(B_m) - conf(B_m)|$$\n", "\n", "where M is the number of bins, $B_m$ is the m-th bin, $acc(B_m)$ is the accuracy of the m-th bin, $conf(B_m)$ is the mean predicted probability of the m-th bin, and $n$ is the total number of samples. The ECE-topclass is a simple extension where only the top-class probability is used to group the data. We can define MCE similarly.\n", "\n", "$$\\text{MCE} = \\max_m |acc(B_m) - conf(B_m)|$$\n", "\n", "\n", "Both ECE and MCE group the data based on the predicted probability. This means the resulting ECE and MCE depend on the binning method used. Traditionally, the data are grouped into 10 equal-width bins. However, if the data is not evenly distributed, the resulting ECE and MCE may not be a good representation of the model's calibration. \n", "\n", "Nixon et al. (2019) proposed a new binning method which bins the data into equal-count bins. They refer to the resulting ECE as Adaptive Calibration Error (ACE). The ACE also accounts for all the predictions for all classes. This is equivalent to a sum of ECE for all classes. \n", "\n", "We adopt a modified version of the ACE and aim to measure the true ECE with equal-count binning but ignore the part about summing over all classes. This is equivalent to the ECE but only with equal-count binning. We refer to the equal-width binning ECE as ECE-H and the equal-count binning ECE as ECE-C. Similarly, we will refer to the equal-width binning MCE as MCE-H and the equal-count binning MCE as MCE-C.\n", "\n", "## Pros of ECE and MCE\n", "\n", "ECE and MCE are perhaps the most intuitive metrics for measuring the calibration of a probabilistic model. They are simply the average deviation of the predicted probability from the true probability and the maximum deviation of the predicted probability from the true probability. The ECE and MCE are also easy to compute and interpret. ECE could be computed by doing a weighted average of the reliability diagram based on bin counts and MCE is just the maximum difference between the accuracy and the confidence. Because of that, ECE and MCE are widely used in the machine learning literature.\n", "\n", "## Cons of ECE and MCE\n", "\n", "The biggest disadvantage of using ECE and MCE is that they rely on the binning scheme, and results will depend on the binning scheme and the number of bins. It can be shown that the expected ECE and MCE will always increase with the number of bins and the expected ECE and MCE will change with the number of samples for a fixed number of bins. This causes problems when interpreting the results. We will do a simple experiment in the following section to show this. Because of the above reasons, we recommend using ECE and MCE with other metrics that are not dependent on the binning scheme." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calculating ECE and MCE with calzone" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There is two way to calculate the ECE and MCE in calzone. The first way is by calling the function explicitly. Notice $ECE_H$ is the equal-width binning and $ECE_C$ is the equal-count binning." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Top-class ECE-H: 0.009608653731328977\n", "Top-class MCE-H: 0.03926468843081976\n" ] } ], "source": [ "from calzone.utils import reliability_diagram,data_loader\n", "from calzone.metrics import calculate_ece_mce\n", "import numpy as np\n", "\n", "### loading the data\n", "wellcal_dataloader = data_loader(data_path=\"../../../example_data/simulated_welldata.csv\")\n", "\n", "### calculating the top-class ECE-H\n", "### This is done by setting the class_to_plot=None\n", "reliability,confindence,bin_edges,bin_counts = reliability_diagram(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins=10, class_to_plot=None, is_equal_freq=False)\n", "ece_h_top_class,mce_h_top_class = calculate_ece_mce(reliability,confindence,bin_counts=bin_counts)\n", "print(\"Top-class ECE-H: \",ece_h_top_class)\n", "print(\"Top-class MCE-H: \",mce_h_top_class)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Class 1 ECE-H: 0.01208775955804901\n", "Class 1 MCE-H: 0.04848338618970194\n" ] } ], "source": [ "### We can calculate the class 1 ECE and MCE by setting class_to_plot=1\n", "reliability,confindence,bin_edges,bin_counts = reliability_diagram(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins=10, class_to_plot=1, is_equal_freq=False)\n", "ece_h_classone,mce_h_classone = calculate_ece_mce(reliability,confindence,bin_counts=bin_counts)\n", "print(\"Class 1 ECE-H: \",ece_h_classone)\n", "print(\"Class 1 MCE-H: \",mce_h_classone)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Top-class ECE-C: 0.009458033653818828\n", "Top-class MCE-C: 0.020515047600205505\n", "Class 1 ECE-C: 0.008733966945443138\n", "Class 1 MCE-C: 0.02324031223486256\n" ] } ], "source": [ "### Similarily we can calculate the class 1 ECE-C and top-class ECE-C by setting is_equal_freq=True\n", "reliability,confindence,bin_edges,bin_counts = reliability_diagram(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins=10, class_to_plot=None, is_equal_freq=True)\n", "ece_c_top_class,mce_c_top_class = calculate_ece_mce(reliability,confindence,bin_counts=bin_counts)\n", "reliability,confindence,bin_edges,bin_counts = reliability_diagram(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins=10, class_to_plot=1, is_equal_freq=True)\n", "ece_c_classone,mce_c_classone = calculate_ece_mce(reliability,confindence,bin_counts=bin_counts)\n", "print(\"Top-class ECE-C: \",ece_c_top_class)\n", "print(\"Top-class MCE-C: \",mce_c_top_class)\n", "print(\"Class 1 ECE-C: \",ece_c_classone)\n", "print(\"Class 1 MCE-C: \",mce_c_classone)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The second method is much simpler. We can use the calzone.metrics.CalibrationMetrics class to calculate all type of metrics." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'ECE-H topclass': 0.009608653731328977,\n", " 'ECE-H': 0.01208775955804901,\n", " 'MCE-H topclass': 0.03926468843081976,\n", " 'MCE-H': 0.04848338618970194,\n", " 'ECE-C topclass': 0.009458033653818828,\n", " 'ECE-C': 0.008733966945443138,\n", " 'MCE-C topclass': 0.020515047600205505,\n", " 'MCE-C': 0.02324031223486256}" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from calzone.metrics import CalibrationMetrics\n", "calmetrics = CalibrationMetrics()\n", "calmetrics.calculate_metrics(wellcal_dataloader.labels, wellcal_dataloader.probs, metrics=['ECE-H', 'MCE-H', 'ECE-C', 'MCE-C'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## ECE and MCE as function of bin size" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this section, we want to quickly demonstrate how binning could affect the ECE and MCE." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "range_of_binning = np.arange(10,300,1)\n", "result = np.zeros((len(range_of_binning),8))\n", "for i in range(len(range_of_binning)):\n", " calmetrics = CalibrationMetrics(class_to_calculate=1,num_bins=range_of_binning[i])\n", " result[i,:] = calmetrics.calculate_metrics(wellcal_dataloader.labels, wellcal_dataloader.probs, metrics=['ECE-H', 'MCE-H', 'ECE-C', 'MCE-C'],return_numpy=True)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "plt.plot(range_of_binning,result[:,1], label='ECE Equal Width')\n", "plt.plot(range_of_binning,result[:,5], label='ECE Equal Count')\n", "plt.title('ECE vs Number of Bins (10000 samples)')\n", "#plt.ylim(0, np.max(ece_equal_width)+0.1)\n", "plt.xlabel('Number of Bins')\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that the error goes up as the number of bins increases while equal count and equal width always return different results. Opposite effects can be observed for the number of sample. Therefore, ECE and MCE can only give us a rough estimate of the calibation error of the model." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Reference\n", "Guo, C., Pleiss, G., Sun, Y., & Weinberger, K. Q. (2017). On Calibration of Modern Neural Networks (No. arXiv:1706.04599). arXiv. http://arxiv.org/abs/1706.04599\n", "\n", "Pakdaman Naeini, M., Cooper, G., & Hauskrecht, M. (2015). Obtaining Well Calibrated Probabilities Using Bayesian Binning. Proceedings of the AAAI Conference on Artificial Intelligence, 29(1). https://doi.org/10.1609/aaai.v29i1.9602\n", "\n", "Arrieta-Ibarra, I., Gujral, P., Tannen, J., Tygert, M., & Xu, C. (2022). Metrics of Calibration for Probabilistic Predictions.\n", "\n", "Nixon, J., Dusenberry, M. W., Zhang, L., Jerfel, G., & Tran, D. (2020). Measuring Calibration in Deep Learning.\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [] } ], "metadata": { "kernelspec": { "display_name": "uq", "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": "3.12.0" } }, "nbformat": 4, "nbformat_minor": 2 }