{ "cells": [ { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "view-in-github" }, "source": [ "\"Open " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Logistic regression\n", "## Classification with one continuous variable" ] }, { "cell_type": "markdown", "metadata": { "id": "09w3TFe3g3Y2" }, "source": [ "Suppose now that we want to predict the gold standard from the FLAIR values. Fitting a line seems weird, since the outcome can only be 0 or 1. A line would allow for arbitrarily small or large predictions. Similiarly, forcing the prediction to be exactly 0 or 1 leads to difficult optimization problems. A clever solution is to instead model\n", "\n", "$$\n", "P(Y_i = 1 ~|~ X_i)\n", "$$\n", "\n", "where $Y_i$ is the gold standard value (0 or 1 for no lesion or lesion at that voxel, respectively) and $X_i$ is the FLAIR value for voxel $i$. This solves the problem somewhat nicely, but it still leaves some issues unresolved. For example, what does probability even mean in this context? And also probabilities are between 0 and 1, that's better than exactly 0 or 1, but still would create problems.\n", "\n", "For the probability, it's generally a good idea to think about what you're modeling as random in the context. In this case, we're thinking of our voxels as a random sample of FLAIR and gold standard voxel values from some population. This is a meaningful benchmark even if it's not true. We'll find that often in statistics we model data as if it comes from a probability distribution when we know it didn't. We simply know that the probability distribution is a useful model for thinking about the problem.\n", "\n", "As for getting the probabilities from $[0,1]$ to $(-\\infty, \\infty)$, we need a function, preferably a monotonic one. The generally agreed upon choice is the logit (natural log of the odds) function. The logit function of a probability is defined as\n", "\n", "$$\n", "\\eta = \\mathrm{logit}(p) = \\log\\{p / (1 - p)\\}\n", "$$\n", "\n", "where $p$ is the probability and $O = p/(1-p)$ is called the **odds**. Note, you can go backwards from odds to probability with the function $p = O / (1 + O)$. Odds are exactly as used in gambling. If the odds of bet at 1 to 99, then you are saying the probability is $1 / (99 + 1) = 1\\%$. \n", "\n", "Why use odds? There's a couple of reasons why odds are uniquely interprettable. First, there are specific study designs where odds make more sense than probabilities, particularly retrospective ones. Secondly, odds are unique in binomial models where they work out to be particularly tractible to work with. Finally, odds have a unique gambling interpretation. That is, it gives the ratio of a one dollar risk to the return in a fair bet. (A fair bet is where the expected return is 0.) So, when a horse track gives the odds on a horse to be 99 to 1, they are saying that you would get $99 dollars if you bet one dollar and the horse won. This is an implied probability of 99 / (99 + 1) = 99% that the horse loses and 1% probability that the horse wins. Note they don't usually express it as a fraction, they usually espress it as value to 1 or 1 to value. So they would say 99 to 1 (odds against) or 1 to 99 (odds for) so you can easily see how much you'd win for a dollar bet. \n", "\n", "You can go backwards from the logit function to the probability with the expit function. That is, if $\\eta$ is defined as above, then\n", "\n", "$$\n", "p = \\frac{e^{\\eta}}{1 + e^\\eta} = \\frac{1}{1 + e^{-\\eta}}.\n", "$$\n", "\n", "This is sometimes called the **expit** function or **sigmoid**.\n", "\n", "\n", "We model the log of the odds as linear. This is called **logistic regression**.\n", "\n", "$$\n", "\\eta = \\mathrm{logit}\\left\\{ P(Y = 1 ~|~ X) \\right\\}\n", "= \\beta_0 + \\beta_1 X.\n", "$$\n", "\n", "The nice part about this model is that $e^\\beta_1$ has the nice interpretation of the odds ratio associated with a one unit change in $X$.\n", "\n", "This is great, but we still need a function of the probabilities to optimize. We'll use the **cross entropy**. \n", "\n", "$$\n", "-\\sum_{i=1}^n \\left[Y_i \\log\\{P(Y_i = 1 ~|~ X_i)\\} + (1 - Y_i) \\log\\{1 - P(Y_i = 1 ~|~ X_i)\\}\\right].\n", "$$\n", "\n", "This function has the interpretation of being the negative of the log of the probabilities assuming the $Y_i$ are independent. This model doesn't have to hold for the minimization to be useful. \n", "\n", "Plugging our logit model in, the cross entropy now looks like\n", "\n", "$$\n", "-\\sum_{i=1}^n \\left[\n", " Y_i \\eta_i + \\log\\left\\{\\frac{1}{1 + e^\\eta_i} \\right\\} \\right].\n", "$$\n", "\n", "This is the function that we minimize to perform logistic regression. Later on, we'll worry about how to minimize this function. However, today, let's fit logistic regression to some data.\n" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "id": "ifAqCb45ib3s" }, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import seaborn as sns\n", "import matplotlib.pyplot as plt\n", "import sklearn.linear_model as lm\n", "## this sets some style parameters\n", "sns.set()\n", "\n", "## Read in the data and display a few rows\n", "dat = pd.read_csv(\"https://raw.githubusercontent.com/bcaffo/ds4bme_intro/master/data/oasis.csv\")" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 357 }, "id": "y6wr4aBFiuAS", "outputId": "82a2be1d-4914-44e8-a17d-1ccfdb6f13e9" }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## Plot the data\n", "sns.scatterplot(x = 'FLAIR', y = 'GOLD_Lesions', data = dat);\n" ] }, { "cell_type": "markdown", "metadata": { "id": "x_z1yMIuqaij" }, "source": [ "Let's now fit the model. Again we're going to split into training and test data. But, now we're not going to do it manually since we have to load a library that has a function to do this." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "id": "3e1JpcHcqkUB" }, "outputs": [], "source": [ "x = dat[['FLAIR']]\n", "y = dat.GOLD_Lesions\n", "trainFraction = .75\n", "\n", "## Once again hold out some data\n", "sample = np.random.uniform(size = 100) < trainFraction\n", "xtrain = x[ sample]\n", "ytrain = y[ sample]\n", "xtest = x[~sample]\n", "ytest = y[~sample]\n" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "id": "Ap2VTA3yr5Nm" }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/bcaffo/miniconda3/envs/ds4bio_new/lib/python3.10/site-packages/sklearn/linear_model/_logistic.py:1182: FutureWarning: `penalty='none'`has been deprecated in 1.2 and will be removed in 1.4. To keep the past behaviour, set `penalty=None`.\n", " warnings.warn(\n" ] } ], "source": [ "lr = lm.LogisticRegression(fit_intercept=True, penalty='none');\n", "fit = lr.fit(xtrain, ytrain)" ] }, { "cell_type": "markdown", "metadata": { "id": "sM07ock_hp1w" }, "source": [ "Let's look at the parameters fit from the model" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "tH0jHnilhtTU", "outputId": "3b21e47c-6c6b-4892-aff4-3dbb48fea609" }, "outputs": [ { "data": { "text/plain": [ "[-3.172226261083505, 2.0243779471793184]" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "beta0, beta1 = [fit.intercept_[0], fit.coef_[0][0]]\n", "[beta0, beta1]" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 392 }, "id": "etcphjtOu8F-", "outputId": "312d3ce4-49ef-4c72-bcb8-daffe893b3cf" }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/bcaffo/miniconda3/envs/ds4bio_new/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.\n", " with pd.option_context('mode.use_inf_as_na', True):\n", "/home/bcaffo/miniconda3/envs/ds4bio_new/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.\n", " with pd.option_context('mode.use_inf_as_na', True):\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 1000\n", "xplot = np.linspace(-1, 5, n)\n", "eta = beta0 + beta1 * xplot\n", "p = 1 / (1 + np.exp(-eta))\n", "\n", "sns.scatterplot(x = 'FLAIR', y = 'GOLD_Lesions', data = dat, hue = 'GOLD_Lesions');\n", "sns.lineplot(x = xplot, y = p);\n", "\n", "## Of course, scikit has a predict\n", "## function so that you don't have to do this manually\n", "#yplot = fit.predict_proba(xplot.reshape((n, 1)))\n", "#sns.lineplot(xplot, yplot[:, 1])\n" ] }, { "cell_type": "markdown", "metadata": { "id": "_klq2nybjmnJ" }, "source": [ "Now let's evaluate the test set." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "zYG1FVHqhQRt", "outputId": "144ced78-0fa6-4237-a748-b9ae9954bf14" }, "outputs": [ { "data": { "text/plain": [ "array([0.793, 0.867, 0.714])" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "## This predicts the classes using a 50% probability cutoff\n", "yhat_test = fit.predict(xtest)\n", "\n", "## double checking that if you want\n", "#all(yhat_test == (fit.predict_proba(xtest)[:, 1] > .5))\n", "\n", "accuracy = np.mean(yhat_test == ytest)\n", "sensitivity = np.mean(yhat_test[ytest == 1] == ytest[ytest == 1])\n", "specificity = np.mean(yhat_test[ytest == 0] == ytest[ytest == 0])\n", "np.round([accuracy, sensitivity, specificity], 3)\n" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 301 }, "id": "Z4guOe34xFaD", "outputId": "2f45105d-dd6c-4762-f8e5-9a39cc2f6746" }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.metrics import accuracy_score, roc_curve, auc\n", "\n", "ptest = fit.predict_proba(xtest)[:, 1]\n", "fpr, tpr, thresholds = roc_curve(ytest, ptest)\n", "roc_auc = auc(fpr, tpr)\n", "plt.figure()\n", "lw = 2\n", "plt.plot(fpr, tpr, color='darkorange',\n", " lw=lw, label='ROC curve (area = %0.2f)' % roc_auc)\n", "plt.plot([0, 1], [0, 1], color='navy', lw=lw, linestyle='--')\n", "plt.xlim([-0.05, 1.05])\n", "plt.ylim([-0.05, 1.05])\n", "plt.xlabel('False Positive Rate')\n", "plt.ylabel('True Positive Rate')\n", "plt.title('Receiver operating characteristic example')\n", "plt.legend(loc=\"lower right\")\n", "plt.show()\n" ] } ], "metadata": { "colab": { "collapsed_sections": [], "include_colab_link": true, "name": "notebook4.ipynb", "provenance": [] }, "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": "3.10.13" } }, "nbformat": 4, "nbformat_minor": 4 }