Last active
July 16, 2021 18:27
-
-
Save ljbelenky/3c5661dd5c7a7725992caf07edcfedd2 to your computer and use it in GitHub Desktop.
A random ensemble approach using linear regression
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
{ | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# The Invention of a New Regression Algorithm\n", | |
"\n", | |
"### Disclaimer: \n", | |
"I really don't think this is a new algorithm. I'm sure someone has thought of it before. It's just that I've never heard of it before. Also, while it doesn't perform poorly, it doesn't seem to have much (if any) advantage over good ole' linear regression. This might explain why I've never seen anyone implement it before.\n", | |
"\n", | |
"## Approach:\n", | |
"\n", | |
"The basic idea is borrowed from random forests. A random forest is an ensemble of decision trees, where each tree is built (A) on a bootstrapped sample of the training data and (B) using random feature sub-selection.\n", | |
"\n", | |
"In this case, we're going to use the same approach, however with linear regressors instead of trees. \n", | |
"\n", | |
"Naturally, this will result in a range of predictions from the models. You might think that some will over-predict and others will under-predict and therefore by taking the mean of predictions we can get a reasonable ensemble prediction. We'll see in a minute that it doesn't work that way, and we'll come up with a fix.\n", | |
"\n", | |
"## The Data\n", | |
"\n", | |
"I'm going to use this to predict on a data set that contains a fair amount of noise, and 40 features, of which only 10 are informative and the remainders are spurious. Also, I'm going to give the targets a slight sine-wave curvature, which is a challenge for any parametric regressor\n" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 1, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"import numpy as np\n", | |
"import matplotlib.pyplot as plt\n", | |
"from sklearn.base import RegressorMixin\n", | |
"from sklearn.linear_model import LinearRegression as LR\n", | |
"from sklearn.datasets import make_regression\n", | |
"from sklearn.model_selection import train_test_split as TTS" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 2, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"X, y = make_regression(1000, 40, n_informative = 10, noise = 40)\n", | |
"y = np.sin(y/500)\n", | |
"\n", | |
"X_train, X_test, y_train, y_test = TTS(X,y)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## The Regressor\n", | |
"\n", | |
"I'm going to build my model in the style of `sklearn` and inherit from the `RegressorMixin` to add some functionality.\n", | |
"\n", | |
"The `init` function takes two parameters:\n", | |
"* The number of estimators (i.e. the number of trees in the forest)\n", | |
"* The probability (0,1] of each feature being included in a given regressor.\n", | |
"\n", | |
"For example, if we have 40 features and use a `p = .2`, that means each feature has a 20% probability of being selected for use in each estimator. On average, each estimator will be built on $40 \\times .2 = 8$ features, more or less. Because each regressor contains fewer than the full set of features, we can think of these as *de-tuned* or regularized regressors -- however this regularization is by randomness, but by minimizing a cost function.\n", | |
"\n", | |
"In this first approach, the final prediction will be the mean of the predictions of all the individual predictors.\n", | |
"\n", | |
"The analysis of the code is left as an exercise for the reader. :)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 3, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"class LinearEnsemble0(RegressorMixin):\n", | |
" '''An ensemble of linear regressors \n", | |
" each built on a bootstrapped sample with random feature space subsampling\n", | |
" '''\n", | |
"\n", | |
" def __init__(self, n_estimators = 100, p_feature = .5):\n", | |
" self.n_estimators = n_estimators\n", | |
" self.p_feature = p_feature\n", | |
"\n", | |
" def fit(self, X, y):\n", | |
" self.estimators = []\n", | |
"\n", | |
" self.features = np.random.choice([True, False], p = [self.p_feature, 1-self.p_feature], size = (self.n_estimators, X.shape[1]))\n", | |
" self.features = self.features[self.features.any(axis=1)]\n", | |
"\n", | |
" indices = np.random.choice(range(len(X)), size=(len(self.features), len(X)), replace = True)\n", | |
"\n", | |
" for idx, feat in zip(indices, self.features):\n", | |
" data = X[idx][:,feat]\n", | |
" self.estimators.append(LR().fit(data, y[idx]))\n", | |
" \n", | |
" return self\n", | |
"\n", | |
"\n", | |
" def predict(self, X):\n", | |
" assert 'estimators' in dir(self), \"Must be fit before predict\"\n", | |
"\n", | |
" predictions = np.empty((X.shape[0], len(self.estimators)))\n", | |
"\n", | |
" for i, (feat, estimator) in enumerate(zip(self.features, self.estimators)):\n", | |
" data = X[:,feat]\n", | |
" predictions[:, i] = estimator.predict(data)\n", | |
"\n", | |
" return predictions.mean(axis=1)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 4, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": "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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"le = LinearEnsemble0(100, .1).fit(X_train, y_train)\n", | |
"plt.scatter(y_train, le.predict(X_train), label = 'Train')\n", | |
"plt.scatter(y_test, le.predict(X_test), label = 'Test')\n", | |
"plt.xlabel('Actual')\n", | |
"plt.ylabel('Predicted')\n", | |
"plt.legend();\n" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Right away, we can see that there is a good correlation between actuals and predictions. However, if we add in a line indicating ideal performance: (i.e, $actual \\equiv predicted$), we see that we miss the mark" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 5, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": "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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.scatter(y_train, le.predict(X_train), label = 'Train')\n", | |
"plt.scatter(y_test, le.predict(X_test), label = 'Test')\n", | |
"plt.plot([-1,1],[-1,1], label = 'Ideal')\n", | |
"plt.xlabel('Actual')\n", | |
"plt.ylabel('Predicted')\n", | |
"plt.legend();" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"So what's going on here? \n", | |
"We have created a variety of linear regressors of various quality. The best of them, trained only on the most informative feature and unaffected by the spurious features, yield predictions very near to the actual values.\n", | |
"The low quality regressors, not having the benefit of any useful features to predict on, will simply predict the mean value of the training dataset. \n", | |
"So, if we average these regressors of various quality together, and weight them all equally, we will find that all of our predictions fall someowhere between the target value and the sample mean. \n", | |
"\n", | |
"To fix this problem, we have to recognize that not all of our de-tuned regressors are of equal quality. When we take our averaging to get the final results, we should weight the high-quality regressors higher than the low quality regressors. But how shall we know which regressors are high quality and which are low quality and how much to weight each one?\n", | |
"\n", | |
"An easy way to do this is to pass the results through another linear regressor. After all, a linear regressor is nothing more than a weighted sum of various factors. In this case the factors are the predictions of our de-tuned regressors." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 6, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"class LinearEnsemble(RegressorMixin):\n", | |
" '''An ensemble of linear regressors \n", | |
" each built on a bootstrapped sample with random feature space subsampling\n", | |
" '''\n", | |
"\n", | |
" def __init__(self, n_estimators = 100, p_feature = .5):\n", | |
" self.n_estimators = n_estimators\n", | |
" self.p_feature = p_feature\n", | |
"\n", | |
" def fit(self, X, y):\n", | |
" self.estimators = []\n", | |
"\n", | |
" self.features = np.random.choice([True, False], p = [self.p_feature, 1-self.p_feature], size = (self.n_estimators, X.shape[1]))\n", | |
" self.features = self.features[self.features.any(axis=1)] #Avoid sitatution where no features are selected\n", | |
"\n", | |
" indices = np.random.choice(range(len(X)), size=(len(self.features), len(X)), replace = True)\n", | |
"\n", | |
" prelim = np.empty((X.shape[0], len(self.features)))\n", | |
"\n", | |
" for i, (idx, feat) in enumerate(zip(indices, self.features)):\n", | |
" data = X[idx][:,feat]\n", | |
" self.estimators.append(LR().fit(data, y[idx]))\n", | |
"\n", | |
" prelim[:,i]= self.estimators[-1].predict(X[:,feat])\n", | |
"\n", | |
" self.ensemble = LR().fit(prelim, y)\n", | |
"\n", | |
" \n", | |
" return self\n", | |
"\n", | |
"\n", | |
" def predict(self, X):\n", | |
" assert 'estimators' in dir(self), \"Must be fit before predict\"\n", | |
"\n", | |
" predictions = np.empty((X.shape[0], len(self.estimators)))\n", | |
"\n", | |
" for i, (feat, estimator) in enumerate(zip(self.features, self.estimators)):\n", | |
" data = X[:,feat]\n", | |
" predictions[:, i] = estimator.predict(data)\n", | |
"\n", | |
" return self.ensemble.predict(predictions)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Now our `LinearEnsebmle` regressor contains a list of de-tuned regressors (`self.estimators`) and a final regressor (`self.ensemble`) that produces the final output.\n", | |
"\n", | |
"Let's see how it works, in comparison to a conventional Linear Regressor:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 7, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": "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\n", | |
"text/plain": [ | |
"<Figure size 720x360 with 2 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"le = LinearEnsemble(100, .1)\n", | |
"\n", | |
"models = [l.fit(X_train,y_train) for l in [le, LR()]]\n", | |
"\n", | |
"titles = [f'Predictions from {le.n_estimators} ensemble', 'Conventional Linear Regression']\n", | |
"\n", | |
"fig, axs = plt.subplots(1,2, figsize = (10,5))\n", | |
"\n", | |
"for l, ax, title in zip(models, axs, titles):\n", | |
"\n", | |
" ax.scatter(y_train, l.predict(X_train), label = 'Train')\n", | |
" ax.scatter(y_test, l.predict(X_test), label = 'Test')\n", | |
" ax.set_xlabel('Actual')\n", | |
" ax.set_ylabel('Predictions')\n", | |
" ax.plot([y_train.min(), y_train.max()], [y_train.min(), y_train.max()], label = 'Ideal')\n", | |
"\n", | |
" ax.set_title(f'{title}\\n Train score: {l.score(X_train, y_train):.2f} \\n Test score: {l.score(X_test, y_test):.2f}')\n", | |
"\n", | |
" ax.legend()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"These results are pretty much indistinguishable from conventional linear regression. That may explain why I've never seen this appraoch before.\n", | |
"\n", | |
"However, considering that Linear Regrssion is a venerable technique, I would say matching that performance is nothing to be ashamed of.\n", | |
"\n", | |
"## Comparing the Estimators\n", | |
"\n", | |
"The synthetic dataset had 40 features, only 10 of which are informative and we don't know which those are. Using `p=.1`, let us see how many features were included in each of our de-tuned regressors:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 8, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": "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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.hist(le.features.sum(axis = 1));\n", | |
"plt.title('Number of Features in Each Regressor');" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Here we see that the probability that any one tree was built on all the informative features is vanishingly small. Therefore, the fact that we were able to match the performance of a model trained on all features indicates that this method does effectively combine the best value of multiple de-tuned regressors.\n", | |
"\n", | |
"It is interesting to observe the relative weighting of the de-tuned regressors. We should expect that we have some good ones that are weighted highly and other poor predictors that should be ignored and therefore weighted about zero. However, I was surprised to see that there are a fair number that cary a negative weight. That is to say, their predicitve value is so poor (at least when combined with other predictors), that the best thing to do with them is the opposite of what they say." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 9, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": "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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.hist(le.ensemble.coef_, bins = 50)\n", | |
"plt.axvline(0, color = 'red')\n", | |
"plt.title('The relative weighting of the de-tuned regressors');" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Regularization\n", | |
"\n", | |
"Using this appraoch, we have built two types of predictors:\n", | |
"* Those with equal weighting that tend to predict between the sample mean and the target (high bias, low variance)\n", | |
"* Those with tuned weighting that tend to predict exactly like an un-regularized linear regression. (high variance, low bias)\n", | |
"\n", | |
"This suggests the possiblily to introduce regularization.\n", | |
"\n", | |
"This can be achieved by adjusting the intercept and coefficient of the final ensemble predictor. If the intercept is 0 and the coefficients are all 1/len(coefficients), it is the equal-weighted (regularized) model. If the intercept and coefficients are allowed to take on their calculated values, it is unregularized. Intermediate values of can be achived through the use of a parameter `r`." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 10, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"class RegLinearEnsemble(RegressorMixin):\n", | |
" '''An ensemble of linear regressors \n", | |
" each built on a bootstrapped sample with random feature space subsampling\n", | |
" '''\n", | |
"\n", | |
" def __init__(self, n_estimators = 100, p_feature = .5, r = .5):\n", | |
" self.n_estimators = n_estimators\n", | |
" self.p_feature = p_feature\n", | |
" self.r = r\n", | |
"\n", | |
" def fit(self, X, y):\n", | |
" self.estimators = []\n", | |
"\n", | |
" self.features = np.random.choice([True, False], p = [self.p_feature, 1-self.p_feature], size = (self.n_estimators, X.shape[1]))\n", | |
" self.features = self.features[self.features.any(axis=1)] #Avoid sitatution where no features are selected\n", | |
"\n", | |
" indices = np.random.choice(range(len(X)), size=(len(self.features), len(X)), replace = True)\n", | |
"\n", | |
" prelim = np.empty((X.shape[0], len(self.features)))\n", | |
"\n", | |
" for i, (idx, feat) in enumerate(zip(indices, self.features)):\n", | |
" data = X[idx][:,feat]\n", | |
" self.estimators.append(LR().fit(data, y[idx]))\n", | |
"\n", | |
" prelim[:,i]= self.estimators[-1].predict(X[:,feat])\n", | |
"\n", | |
" self.ensemble = LR().fit(prelim, y)\n", | |
" \n", | |
" self.ensemble.intercept_ *= (1-self.r)\n", | |
" self.ensemble.coef_ = (self.r)/len(self.ensemble.coef_) + (1-self.r)*self.ensemble.coef_\n", | |
"\n", | |
" \n", | |
" return self\n", | |
"\n", | |
"\n", | |
" def predict(self, X):\n", | |
" assert 'estimators' in dir(self), \"Must be fit before predict\"\n", | |
"\n", | |
" predictions = np.empty((X.shape[0], len(self.estimators)))\n", | |
"\n", | |
" for i, (feat, estimator) in enumerate(zip(self.features, self.estimators)):\n", | |
" data = X[:,feat]\n", | |
" predictions[:, i] = estimator.predict(data)\n", | |
"\n", | |
" return self.ensemble.predict(predictions)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 11, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": "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\n", | |
"text/plain": [ | |
"<Figure size 1440x360 with 5 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"reg_le = [RegLinearEnsemble(20, .5, i) for i in np.linspace(0,1, 5)]\n", | |
"\n", | |
"models = [l.fit(X_train,y_train) for l in reg_le]\n", | |
"\n", | |
"\n", | |
"fig, axs = plt.subplots(1,len(reg_le), figsize = (20,5), sharey=True)\n", | |
"\n", | |
"for l, ax, in zip(models, axs):\n", | |
"\n", | |
" ax.scatter(y_train, l.predict(X_train), label = 'Train')\n", | |
" ax.scatter(y_test, l.predict(X_test), label = 'Test')\n", | |
" ax.set_xlabel('Actual')\n", | |
" ax.set_ylabel('Predictions')\n", | |
" ax.plot([y_train.min(), y_train.max()], [y_train.min(), y_train.max()], label = 'Ideal')\n", | |
"\n", | |
" ax.set_title(f'Regularization: {l.r}')\n", | |
" ax.legend()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"The exploration of the utility of this regularization parameter, especially as compared to LASSO, Ridge and Elastic Net, is left as an exercise for the reader." | |
] | |
} | |
], | |
"metadata": { | |
"kernelspec": { | |
"display_name": "Python 3", | |
"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": "3.8.5" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 4 | |
} |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment