Machine Learning and Neural Networks - page 70
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6.7 Code Example Implementing Decision Trees in Scikit-Learn (L06: Decision Trees)
6.7 Code Example Implementing Decision Trees in Scikit-Learn (L06: Decision Trees)
To conclude lecture six, we will now examine a code example using scikit-learn, specifically focusing on the decision tree algorithm. Scikit-learn is recommended for real-world machine learning projects due to its speed, efficiency, and robustness. While we will be using scikit-learn for this demonstration, it's worth mentioning that you will be implementing a decision tree from scratch for the homework assignment to enhance your understanding of the algorithm.
To begin, let's import the necessary packages, including the watermark package, which will help us track the versions of the software being used. This can be helpful in case any issues arise when running the code due to outdated software versions. Next, we load the iris dataset, a popular dataset often used for classification tasks. By using a well-known dataset like iris, we can focus more on understanding the code and its functionality rather than explaining the data.
We split the dataset into training and test sets, with 30% of the data allocated for testing. It's important to note that we won't be performing any tuning in this notebook. Although it's possible to tune the decision tree hyperparameters using techniques like grid search, we will keep it simple and skip tuning for now. Therefore, we don't need a separate validation set, as we will train the decision tree solely on the training set and evaluate its performance on the test set.
Moving on to plotting the decision regions, we initialize the decision tree classifier and set the hyperparameters. In this case, we choose the entropy criterion for information gain and set the maximum depth to two for educational purposes. Additionally, we fit the decision tree to the training data and plot the decision regions. By visualizing the decision regions, we can observe how the decision tree separates the data based on the selected features.
We explore different options and hyperparameters that can be set for the decision tree classifier. These include the splitter, which determines how the splits are made at each node, and parameters related to minimum samples required for splitting nodes and leaf nodes. There are also options for selecting the impurity measure and controlling the randomness of splits. These hyperparameters can be adjusted and tuned based on the specific problem and dataset.
Next, we proceed to visualize the decision tree using the graphviz library. We export the decision tree as a dot file, which represents the tree structure as a graph. We can customize the appearance of the nodes, edges, and labels in the graph. By using the graphviz library in conjunction with the pydotplus library, we can plot the decision tree directly without saving the dot file separately. This way, we can visualize the decision tree within the notebook itself.
To display the decision tree plot, we load the generated PNG file using the ipython display module. We import the image class from ipython display and use it to load the PNG file. This allows us to view the decision tree plot directly in the Jupyter Notebook. The decision tree plot shows the splits and decision boundaries as vertical and horizontal lines, respectively, based on the selected features.
In summary, this code example demonstrates how to implement and visualize a decision tree classifier using scikit-learn. The decision tree algorithm provides an interpretable model for classification tasks and can be tuned using various hyperparameters to improve performance. Visualizing the decision tree helps in understanding how the algorithm makes decisions based on the input features.
7.1 Intro to ensemble methods (L07: Ensemble Methods)
7.1 Intro to ensemble methods (L07: Ensemble Methods)
In this week's lecture, we will delve into ensemble methods, which are a crucial field in machine learning. These methods are widely used in applied machine learning research to achieve high performance in real-world applications. Solid methods, which are known for their effectiveness in practice, often yield the best results.
The lecture will also revisit decision trees, addressing some questions raised on Piazza about their relevance. Despite being a relatively old and familiar algorithm, decision trees remain highly relevant today. They are not only interpretable but are frequently employed in ensemble methods, where they exhibit exceptional performance. The lecture aims to explore this aspect as well.
Before delving into ensemble methods, it's important to recap where we stand in the semester. We are currently concluding part three, which focuses on tree-based methods. However, it's worth noting that some of these methods extend beyond decision trees and encompass other techniques, including solid methods applied to deep neural networks. Decision trees have been categorized under part three due to their close association with most ensemble methods.
After completing this section, we will take a deep dive into model evaluation before discussing unsupervised learning and, if time permits, Bayesian learning. Although the initial plan was to have the midterm exam and cover other methods earlier, the course progression took longer than anticipated. Nonetheless, the additional time spent setting up the Python environment and familiarizing everyone, particularly those without a strong Python background, was beneficial. It ensures that all participants are on the same page and prepared for the upcoming homework, which will involve implementing a CART (Classification and Regression Trees) decision tree without relying on pre-built libraries like scikit-learn.
The lecture is structured into seven parts. The first part provides an introduction and overview of ensemble methods. Subsequently, we will explore various internal methods, starting with majority voting, the simplest type of ensemble method. We will then delve into bagging, a technique that involves bootstrap sampling from the training set. This method's usefulness will be explained. Boosting, which involves boosting weak learners (such as short decision trees) into strong models, will also be covered. In particular, we will discuss gradient boosting, one of the most popular algorithms today, known for its success in Kaggle competitions. Random forests, another widely recognized ensemble method, will be introduced. These models are known for their ease of use, as they often yield excellent performance without extensive hyperparameter tuning. They are recommended for individuals seeking predictive models in various scientific fields, especially if they lack expertise in machine learning.
Support vector machines (SVM) will also be mentioned, particularly their popularity in the past due to their performance, especially with RBF (Radial Basis Function) kernels. However, random forests often deliver equally good or better results without the need for extensive tuning, making them preferable for practical applications. Lastly, stacking, another popular technique in applications, will be discussed.
To illustrate the significance of ensemble methods, a figure will be presented, showcasing an example involving random forests. This model is not limited to classification tasks and can compute feature importance easily. For instance, in the mentioned example, sulfur atoms were identified as the most important features for predicting the activity of molecules. Such insights can be valuable in practice.
Furthermore, ensemble methods, including random forests and gradient boosting, are among the most widely used non-deep learning machine learning models. Although deep learning is gaining prominence, ensembles are still highly relevant due to their outstanding performance and ease of implementation. The article mentioned the rise of extreme gradient boosting (XGBoost) as the "new queen" in machine learning algorithms. This underscores the significance of tree-based models, particularly gradient boosting, in various applications.
In summary, this week's lecture will provide a comprehensive understanding of ensemble methods. It will cover different types of ensemble techniques and their applications.
7.2 Majority Voting (L07: Ensemble Methods)
7.2 Majority Voting (L07: Ensemble Methods)
In this video, we will explore one of the fundamental cases of model ensembles known as majority voting. Through a toy example, we will examine the benefits of majority voting compared to using a single classifier in isolation.
To begin, let's consider a scenario where we have a binary classification problem. We have a dataset consisting of several observations, each associated with a set of features and a corresponding class label. Our goal is to build a classifier that can accurately predict the class labels for new, unseen instances.
To demonstrate the concept of majority voting, we start by training three individual classifiers on our dataset. Each classifier utilizes a different algorithm or model to make predictions. For simplicity, let's assume these classifiers are decision trees.
Once we have trained our three decision tree classifiers, we can now make predictions on new instances. However, instead of relying on the prediction of a single classifier, we employ the majority voting principle. In majority voting, each classifier in the ensemble casts a vote for its predicted class label. The class label that receives the most votes is considered the final prediction of the ensemble.
Now, let's see why majority voting can be more effective than using a single classifier alone. Consider a scenario where each individual decision tree classifier has some degree of error due to the inherent noise or variability in the dataset. These errors can lead to incorrect predictions, reducing the overall accuracy of a single classifier.
However, by combining the predictions of multiple classifiers through majority voting, we can potentially mitigate the impact of individual errors. Even if one or two decision tree classifiers make incorrect predictions, the majority voting process can compensate for these errors. The class label that receives the majority of votes is more likely to be correct, resulting in improved accuracy compared to using a single classifier.
To illustrate this, let's imagine a situation where two decision tree classifiers predict the correct class label, while one classifier makes an erroneous prediction. In this case, the correct class label will receive two votes, whereas the erroneous prediction will only receive one vote. As a result, the ensemble's majority voting process will correctly identify the class label with the most votes as the final prediction, overriding the incorrect prediction of the individual classifier.
This example demonstrates the power of ensemble methods, specifically majority voting, in enhancing prediction accuracy. By combining the predictions of multiple classifiers, we can leverage the strengths of each classifier and minimize the impact of their individual weaknesses or errors.
In conclusion, this video highlights the importance of majority voting as a basic form of model ensembles. Through a toy example, we have seen how majority voting can outperform using a single classifier alone, particularly when individual classifiers exhibit errors or variability. Ensemble methods, such as majority voting, offer a powerful approach to improve prediction accuracy and are widely used in practical machine learning applications.
7.3 Bagging (L07: Ensemble Methods)
7.3 Bagging (L07: Ensemble Methods)
After thoroughly discussing the concept of majority voting in the previous video, the upcoming video will delve into another fundamental method known as bagging, which stands for bootstrap aggregating. The term "bagging" is derived from the combination of the initials "B" and "ag G" and is closely related to the concept of bootstrapping. This technique was originally proposed by Leo Breiman, a prominent figure in the field of decision trees, specifically classification and regression trees (CART). We will explore Breiman's contributions in more detail in a future lecture focused on random forests.
To begin, let's outline the algorithm for bagging. Although it may seem complex at first glance, it is actually quite simple and consists of only six lines of code, or five if we exclude the blank line. The algorithm operates as follows: Let's assume we have a total of n bootstrap samples or rounds. For each round i, we draw a bootstrap sample of size m from the training set. Here, m represents the size of the training set. It's important to note that the usage of single letters for variables may seem unconventional, but it was necessary due to the limitations imposed by the choice of letters. In the previous video, we used n to represent the number of bootstrap samples, which corresponds to the number of classifiers in the ensemble voting classifiers we discussed.
For each bootstrap sample, we train a classifier and apply majority voting. This process is quite similar to the ensemble voting classifier we covered earlier, with the only difference being that instead of training each classifier on the entire training set, we train each base classifier on a bootstrap sample extracted from the training set.
Before we proceed, let's briefly recap the concept of bootstrap sampling. Consider a dataset with a size of m. Each bootstrap sample drawn from this dataset will also have a size of m, based on the aforementioned algorithm. Bootstrap sampling involves randomly selecting data points from the dataset with replacement. For example, if we have ten data points labeled from one to ten, and we perform sampling with replacement, some of the data points will be duplicated in the bootstrap dataset. This duplication occurs because each position is independently drawn from the training set. Consequently, some data points may appear multiple times, while others may not appear at all, resulting in what we refer to as out-of-bag (OOB) samples. These OOB samples are the data points that are not included in the bootstrap sample for a particular round.
To gain a better understanding of the probability associated with not selecting a specific item in a bootstrap sample, let's examine the probability of not selecting a particular data point for a single position. The probability of choosing a specific data point for a given position is 1/m, since there are m examples in the training set. Therefore, the probability of not selecting that particular data point is 1 - 1/m. Since we have m choices, the probability of not choosing a specific example in the entire bootstrap sample is (1 - 1/m)^n. As m becomes sufficiently large, approximately 36.8% of the points will not be included in the bootstrap sample. Consequently, 63.2% of the data points will be unique in the bootstrap sample, while the remaining points will be duplicates.
Visualizing bootstrap sampling within the bagging procedure can aid in further comprehension of the concept. Multiple rounds of bootstrap sampling are conducted, each resulting in a new bootstrap sample. A classifier is then trained independently on each bootstrap sample. This process facilitates model parallelism since there is no dependency between the bootstrap rounds. Consequently, each round can be executed simultaneously, enhancing the potential for parallel processing.
The flowchart of the bagging classifier provides an overview of the steps involved. Similar to the voting classifier, the bagging classifier begins with a training set. However, in bagging, we reuse the training set to create multiple bootstrap samples. Each bootstrap sample is used to train a classifier, resulting in a total of m classifiers. Each classifier generates predictions, and the final prediction is determined through majority voting. This approach aids in reducing overfitting and improving the stability and generalization of the model.
Bagging offers several advantages:
Despite its advantages, bagging also has some limitations:
In this section, we will delve deeper into the concepts discussed earlier. When predictions from a model exhibit significant variations, it indicates high variance. For instance, let's consider a complex decision tree for the orange case. The predictions from this model will differ significantly from the predictions of the blue model. Similarly, the green case will have its own set of different predictions. These varying predictions illustrate the concept of high variance.
To gain a better understanding of the impact of high variance, let's examine the actual decision trees fitted on these datasets. Despite their variations, the high variance case still manages to provide a good average prediction. It's important to note that even though I haven't explicitly shown the average prediction here, averaging the predictions from the three models (model one, two, and three) fitted on different training sets will result in a prediction that closely approximates the true function. In contrast, high bias models, as shown earlier, are only accurate at specific positions where the lines intersect with the true function. In all other cases, they perform poorly due to their high bias.
However, by employing a high variance model and averaging the predictions from multiple models, we can still achieve accurate predictions. This concept forms the basis of bagging, which involves using different training sets generated through bootstrap sampling. In bagging, each bootstrap sample is used to fit a decision tree, resulting in multiple high variance models. These models are then averaged using ensemble voting, either by considering class labels in classification tasks or regression outputs in regression tasks. This averaging process helps in obtaining highly accurate predictions by reducing the variance.
By averaging the predictions of the three decision trees fitted on different training sets, we would obtain an average prediction that closely approximates the true function. This averaging is similar to the concept of bagging, where each training set acts as a bootstrap data set. Secondly, it's important to note that decision trees cannot interpolate values. They can only predict target values that exist in the training set or their averages. Thus, the stepwise function shown in the figure is an approximation of an unpruned decision tree.
To conclude, bagging is an effective technique for reducing variance by averaging predictions from high variance models. By employing parallelization, bagging can accelerate model fitting by utilizing multiple CPUs. However, some Windows computers may face issues with multiprocessing in Python, limiting the usage of multiple jobs. It's also worth mentioning that bagging classifiers can compute the out-of-bag accuracy, which involves using the data points that are not included in the bootstrap sample to evaluate model performance. This provides a useful metric for assessing the model's generalization ability. In the code example using scikit-learn, the bagging classifier can be imported from the ensemble submodule.
The base estimator, which is the decision tree in this case, is initialized with the maximum depth set to None to create an unpruned decision tree. The number of estimators determines the number of bootstrap rounds, and parallelization can be achieved by setting the n_jobs parameter accordingly. Additionally, the oob_score parameter enables computation of the out-of-bag score. After training the bagging classifier, the out-of-bag score and test set accuracy can be evaluated.
Overall, bagging offers an effective approach to mitigate high variance and improve prediction accuracy by combining multiple high variance models. In summary, bagging is a powerful ensemble method that combines multiple classifiers trained on different bootstrap samples to improve prediction accuracy and reduce variance. It is particularly useful when dealing with complex datasets and can enhance the stability and generalization of the model. However, it also has some limitations, including reduced interpretability and increased computational complexity.
7.4 Boosting and AdaBoost (L07: Ensemble Methods)
7.4 Boosting and AdaBoost (L07: Ensemble Methods)
In the previous video, we discussed the concept of high variance and low bias models, focusing specifically on unpruned decision trees. We also learned about a technique called bagging, which helps improve the performance of high variance models by reducing variance through averaging.
In this lecture, we will shift our attention to boosting, which operates in the opposite direction. Boosting involves using high bias models with low variance, such as simple decision tree stumps, and boosting them to enhance the overall model's performance. This first video will provide an overview of boosting concepts and introduce boosting in general, while the next video will delve into a popular type of boosting called gradient boosting.
Boosting can be broadly categorized into two main types: adaptive boosting (e.g., adaboost) and gradient boosting. Historically, gradient boosting was less widely used due to its computational complexity. However, recent advancements, such as the introduction of XGBoost in 2016, have significantly improved the performance of gradient boosting. Nowadays, even better variants like LightGBM have emerged, which we will discuss in the next video. While gradient boosting has gained popularity, it is essential to understand the general boosting procedure through adaptive boosting.
The boosting procedure follows a specific outline, which differs from the bagging procedure. One notable distinction is the presence of dependencies between rounds. The boosting procedure involves multiple classifiers, denoted as classifier one, classifier two, and so on, up to classifier M. Initially, we start with a regular training dataset and fit classifier one. Based on the predictions of classifier one, we weight the training samples using a specific weighting method, which we will discuss in more detail later. Then, the second classifier uses this weighted training dataset, and the process continues. The weighting depends on the predictions of the previous classifiers, making it difficult to parallelize boosting. Unlike bagging, where classifiers can be trained simultaneously, boosting requires waiting until the previous classifier has made predictions before updating the dataset for the next classifier. When making final predictions, boosting employs a weighted combination of the classifiers, unlike ensemble voting or averaging used in bagging. The weighted combination is determined based on the sign function, which assigns weights to each classifier's prediction. For binary classification, the sign function returns 1 for positive results and -1 for negative results. This weighted prediction results in a final prediction of either -1 or 1. The process can be extended to handle arbitrary numbers of classes using indicator functions.
To further understand the general boosting procedure, let's outline the steps involved. Firstly, we initialize a weight vector with uniform weights for each training example. These weights represent the importance of each training example. Then, we enter a loop that iterates over the different classifiers or rounds of the boosting procedure. In each round, we apply a weak learner, which is a classifier slightly better than random guessing, to the weighted training examples. We can assign higher weights to specific examples or draw bootstrap samples with weighted probabilities. After training the weak learner, we increase the weight for misclassified examples, enabling the next classifier to focus on these misclassified examples. This loop is repeated multiple times, and finally, a weighted majority voting is performed on the trained classifiers to obtain the final predictions.
Now let's focus on the adaboost algorithm, which closely aligns with the general boosting procedure discussed earlier. Adaboost is similar to the general boosting outline, where classifiers are fitted on weighted training examples. The algorithm begins by initializing the weights for each training data point. Then, the main for loop, comprising the adaboost rounds, begins. In each round, the weights are normalized to ensure they sum up to one. Next, a weak learner is trained on the weighted training set, and the weighted prediction errors are computed. The prediction errors are weighted by the training set weights and indicate the misclassifications. The prediction errors are then used to calculate the contribution of the weak learner to the final prediction. The contribution is determined by the weak learner's accuracy, with more accurate learners having a higher contribution. The contribution is then used to update the weights of the training examples. The weights of the misclassified examples are increased, while the weights of the correctly classified examples are decreased. This adjustment emphasizes the importance of the misclassified examples in subsequent rounds.
After updating the weights, the process moves to the next round, where the weak learner is trained on the updated weighted training set. This iterative process continues for the specified number of rounds or until a certain criterion is met. Once all the rounds are completed, the final prediction is made by combining the predictions of all the weak learners. The weight of each weak learner's prediction is determined by its contribution to the overall accuracy during training.
The adaboost algorithm effectively combines the weak learners' predictions to create a strong ensemble model. The weights assigned to each weak learner's prediction reflect its performance in classifying the training examples. By iteratively adjusting the weights and focusing on the misclassified examples, adaboost is able to improve the model's accuracy over time.
It is important to note that adaboost is sensitive to outliers and noise in the data. Outliers can have a significant impact on the weight updates, potentially leading to overfitting. Therefore, preprocessing the data to handle outliers and noisy samples is recommended. Additionally, adaboost can be prone to overfitting if the weak learners are too complex or if the number of rounds is too high. Regularization techniques such as limiting the depth of decision trees or using early stopping can help mitigate overfitting.
If we were to roughly sketch the concept, it would look like this: we have an arrow on the x-axis, representing the alpha value. The alpha value determines the importance of each classifier in the final prediction. When we use the alpha value to weight the estimate and prediction, we find that if a classifier has a large error, the alpha value will be relatively small. This means that a classifier with a high error is not as important for the final prediction. On the other hand, classifiers with small errors will have a higher weight because we trust them more when computing the majority voting.
We use the alpha value in two ways: first, we use it to weight the estimate and prediction, and second, we use it to update the weights for the next round. If the prediction is correct, the weight assigned to that training example will be small. This means that if we make a correct prediction, we don't give much attention to that training example in the next round. It is considered an easy example. On the other hand, if we make a mistake, the weight assigned to that example will be larger. This means that we pay more attention to the misclassified examples in the next round. The smaller the alpha value, the larger the weight assigned to the misclassified examples.
To illustrate this concept, let's consider a two-dimensional case. We have a toy example with two features, x1 and x2. We fit a decision tree stump, which is a decision tree with only one split. The decision tree stump correctly classifies some points but makes mistakes on others. In the first round of AdaBoost, we give higher weights to the misclassified examples and lower weights to the correctly classified examples. Then we fit another decision tree stump, focusing on the misclassified examples from the previous round. This process continues, with each new classifier learning from the mistakes of the previous classifier and paying more attention to the misclassified examples. Finally, when we combine all the classifiers using majority voting, we may end up with a classifier that correctly classifies all the examples.
AdaBoost can be a bit complicated to understand, but there are resources available to help. The original paper on AdaBoost provides an in-depth explanation, but for a more accessible introduction, the tutorial paper by Manwani is recommended. Before moving on to code examples, it's worth mentioning a modification of the AdaBoost algorithm for multi-class classification called AdaBoost.M2 or SAMME. It introduces a small modification to the original algorithm to handle multiple classes. There is also a real number version called SAMME.R. If you're interested, you can explore these variations in the respective papers.
In scikit-learn, AdaBoost is implemented as a boosting classifier. It uses decision tree stumps as weak classifiers and adjusts the weights of training examples based on their classification results. By boosting these weak classifiers, AdaBoost improves the overall performance. Comparing the accuracy of an unpruned decision tree and a decision tree stump on the iris dataset, AdaBoost with decision tree stumps achieves a higher accuracy. The training process involves updating the sample weights, so there is no parallelization option like in bagging. AdaBoost in scikit-learn provides an effective way to boost weak classifiers and achieve better classification results.
Next, we will delve into gradient boosting, another popular variant of boosting. Gradient boosting builds upon the concepts of AdaBoost but introduces additional enhancements.
Gradient boosting is a popular variation of the boosting algorithm that aims to further enhance the performance of weak classifiers by iteratively improving upon their weaknesses. It is based on the concept of gradient descent, which is commonly used in optimization problems. In gradient boosting, the weak classifiers are sequentially trained and combined to create a strong classifier.
The basic idea behind gradient boosting is to iteratively train weak classifiers and then adjust the weights of training examples based on the errors made by the ensemble of classifiers. This adjustment is done by computing the gradients of the loss function with respect to the ensemble's predictions. By minimizing the loss function, the ensemble gradually improves its performance.
To illustrate the concept, let's consider a simple example. Suppose we have a binary classification problem where we want to classify data points as either positive or negative. We start by training an initial weak classifier, such as a decision tree stump, on the training data. This classifier will make some mistakes, and we compute the errors or residuals by comparing its predictions to the true labels of the training examples.
In the next iteration, we train a new weak classifier to predict the residuals of the previous classifier. This new classifier focuses on correcting the errors made by the previous one. We compute the residuals by subtracting the predicted values from the true residuals. Again, this new classifier will make some mistakes, and we compute the residuals.
We repeat this process, sequentially training new weak classifiers to predict the residuals of the ensemble, and updating the residuals based on the errors made by the current ensemble. Each weak classifier is trained to minimize the loss function with respect to the current residuals. The final ensemble is obtained by combining all the weak classifiers, with each classifier contributing a weighted vote based on its performance.
The weights of the weak classifiers are determined by the learning rate, which controls the contribution of each classifier to the final prediction. A smaller learning rate leads to a slower convergence but can result in better generalization. A larger learning rate can lead to faster convergence but may also lead to overfitting.
Gradient boosting has proven to be a powerful technique for a wide range of machine learning tasks, including regression, classification, and ranking problems. It has been successfully applied in various domains, such as computer vision, natural language processing, and bioinformatics.
In practice, there are several implementations of gradient boosting available, including XGBoost, LightGBM, and CatBoost, which offer efficient and optimized algorithms for gradient boosting. These implementations provide additional features, such as parallelization, regularization techniques, and handling missing values, to further improve the performance and flexibility of gradient boosting models.
That concludes the introduction to boosting and the overview of the adaboost algorithm. In the next video, we will explore gradient boosting in more detail, including the concepts of gradient descent, loss functions, and the specific algorithms that have been developed to enhance the gradient boosting process.
7.5 Gradient Boosting (L07: Ensemble Methods)
7.5 Gradient Boosting (L07: Ensemble Methods)
The concept of gradient boosting is introduced as a modern version of boosting that utilizes decision trees and a differentiable loss function. While similar to AdaBoost, gradient boosting differs in how decision trees are fitted. In gradient boosting, deeper trees are used, and there are no weights assigned to training examples or classifiers. The key idea behind gradient boosting is the use of gradients from the loss function to improve the model, resulting in better performance on tabular datasets. This algorithm has gained popularity, especially in machine learning competitions.
In the context of regression, gradient boosting starts with constructing a base tree. For example, in a house price prediction problem, the initial base tree consists of only the root node. The target is predicted based on the average value at that node, which in this case is the average price of the four houses in the training set. Then, the next tree is built based on the prediction error of the previous tree. This predicted error is used to fit a new tree. The trees from the first and second steps are combined, and this process is repeated multiple times, with each subsequent tree being fitted on the errors of the previous trees. By combining the simple decision tree with the new one based on residuals, the model can make better and more accurate predictions.
The concept of gradient boosting as an additive model is discussed, where the predictions of all the trees are combined consecutively by adding them up. The learning rate or step size is also introduced, which determines the weight or contribution of each tree to the final prediction. Gradient boosting is executed by repeating the process of fitting trees on the errors of the previous prediction, gradually building up the model with a small step size to prevent overfitting. This process continues until a predetermined number of trees, based on hyperparameter settings, have been completed.
The speaker explains the gradient boosting algorithm, which is used for both regression and classification problems. The algorithm involves initializing the model as a root node and then fitting multiple trees and creating terminal nodes. Predictions are made at each node, and the loss is computed. The algorithm can be repeated until the desired number of trees is reached, with the overall goal of minimizing the loss.
To compute the current model, the previous model and new prediction step are combined, weighted by the learning rate or step size, to determine the updated model. This process is repeated until the desired number of trees, denoted as T, is reached. Pseudo residuals are computed, followed by the computation of the derivative of the loss based on the true labels and predictions of the previous round's model. Residuals are then computed, and the prediction value that minimizes the loss at the specific node is determined. The model is updated accordingly, and this process is repeated until T models are reached. Although differentiable loss functions like negative log-likelihood loss can be used for classification, the focus in this class is on sum squared error or mean squared error.
The video discusses the steps involved in gradient boosting and its practical application. The first step involves minimizing the loss for all training examples at a given node by finding the prediction that minimizes the expression. In the second step, a loop is used for T trees, and the prediction at each leaf node is computed by averaging the examples at that node. The average prediction is combined with the previous model, and the predictions for each tree are added up. The learning rate is used to decrease the pseudo residuals and prevent overfitting. The video also briefly touches on other interesting aspects of gradient boosting used in practice.
The video highlights the potential downsides of boosting as a sequential algorithm, as it cannot fully utilize multiple processes or computing nodes. However, there is an implementation called xgBoost that incorporates several tricks to make the gradient boosting process more efficient. In fact, among the 29 Challenge Winning Solutions published on Kaggle from 2015 to 2017, 17 of them used xgBoost. Eight of those solutions solely relied on xgBoost for training the model, while others combined xgBoost with neural networks or utilized stacking, a popular ensemble voting technique. The video presents two tables from a paper that compare different boosting implementations, demonstrating the unique features of xgBoost that contribute to its effectiveness.
The video discusses Extra Boost, a variant of gradient boosting that offers several advantages, such as approximate global, out-of-core learning, sparsity awareness, and parallelism. Extra Boost incorporates approximation methods to find the best split by utilizing summary statistics of distributed data subsets. The video compares the performance of Extra Boost with other gradient boosting implementations using the exact greedy method and demonstrates that Extra Boost achieves identical performance to one implementation but with significantly reduced time per tree, making it more appealing for hyperparameter tuning.
Furthermore, the video explains the various improvements offered by Extra Boost, such as regularization techniques, handling missing features through imputation, and caching. These improvements help reduce overfitting and improve the overall performance of Extra Boost. Additionally, Extra Boost utilizes column and row-based subsampling, which randomly selects subsets of features and training examples, enhancing both computational efficiency and the reduction of overfitting. The video suggests referring to the paper on Extra Boost for a more detailed explanation of its techniques.
The video provides an overview of Extra Boost, a newer implementation of gradient boosting machines. Extra Boost aims to reduce overfitting and improve prediction accuracy. The video discusses different techniques for finding splits, including the exact greedy algorithm and histogram-based split finding. The latter approach involves binning a continuous feature into a discrete histogram, which can enhance training speed and reduce memory usage. The video also compares Extra Boost to Light GBM, another implementation that is even faster and more accurate. Light GBM utilizes histogram-based split finding and offers lower memory usage and higher prediction accuracy compared to Extra Boost.
The video discusses the implementation of gradient boosting classifiers in scikit-learn and introduces a new gradient boosting classifier that was added in a recent version of the library. The new classifier utilizes histogram-based splitting inspired by LightGBM, making it faster than the previous classifier. The video suggests using both gradient boosting classifiers and comparing them with XGBoost to determine which one performs the best. Code examples are provided to serve as templates for class projects or general use, including implementing the gradient boosting classifier in scikit-learn and utilizing the new histogram gradient boosting classifier.
The presenter discusses gradient boosting using the XGBoost and LightGBM libraries. The XGBoost library is similar, but a bit more involved than scikit-learn. It requires converting NumPy arrays into the DMatrix format, and instead of using the fit method, the train method is used to train the model. Predictions can be made by calling the predict method to obtain class membership probabilities. On the other hand, the Microsoft LightGBM library has an API that is similar to scikit-learn. Hyperparameters need to be set before fitting the gradient boosting machine, and the score method can be used to compute accuracy. In the presented case, the model exhibits 100% training accuracy without tuning hyperparameters.
The video concludes by emphasizing the effectiveness of gradient boosting techniques, particularly through the utilization of libraries like XGBoost and LightGBM. These libraries provide powerful tools for implementing gradient boosting models and offer various optimizations to enhance performance and accuracy.
Additionally, the presenter acknowledges the importance of hyperparameter tuning in gradient boosting. Different hyperparameters, such as the learning rate, number of trees, and depth of trees, can significantly impact the performance of the model. Therefore, it is recommended to experiment with different hyperparameter configurations to find the optimal settings for a specific problem.
To further explore gradient boosting, the video suggests referring to research papers and documentation on XGBoost, LightGBM, and other relevant implementations. These resources provide in-depth explanations of the algorithms, techniques, and advanced features of gradient boosting.
In summary, the video provides a comprehensive overview of gradient boosting, its concepts, and its practical implementations using libraries like XGBoost and LightGBM. It highlights the advantages of gradient boosting, such as its ability to handle complex tabular datasets, its effectiveness in competitions, and its potential for improving prediction accuracy. By understanding the principles and techniques behind gradient boosting, practitioners can leverage this powerful algorithm to tackle various regression and classification problems.
7.6 Random Forests (L07: Ensemble Methods)
7.6 Random Forests (L07: Ensemble Methods)
Great! We have finally reached the last part of Lecture 5, which happens to be the most interesting one: sacred learn pipelines. Sacred learn pipelines are objects or classes that combine various data processing and prediction steps, making them extremely useful in real-world applications. To help you understand how pipelines work, let's take a look at an outline flowchart. I won't delve into all the intricacies right now, but we'll revisit it shortly after I provide an example of a pipeline.
In essence, a pipeline can be thought of as an estimator and transformer API. Similar to an estimator, a pipeline has a fit method that can be used on the training set. Internally, multiple fit and transform steps are performed, followed by a final fit step. Depending on the components included in the pipeline, you can define a sequence of operations such as data scaling (e.g., standardization or min-max scaling) or dimensionality reduction, followed by training a learning algorithm. The pipeline then returns a predictive model that can be used on the test set.
During the prediction phase, when you call the predict method on the test set, the pipeline internally uses transform to apply the same scaling that was carried out on the training set. It also applies the final prediction step, such as returning class labels in the case of a classifier. Let's examine a simple code example of a pipeline to illustrate this concept.
Here, I'm creating a pipeline using the make_pipeline function from sacred learn's scikit-learn.dot.pipeline submodule. Although there are different ways to create pipelines, this method is quite convenient. In this example, I'm constructing a simple pipeline consisting of a classifier and a standard scaler. The standard scaler, as discussed in the previous video, standardizes the data to have zero mean and unit variance. After creating the pipeline, we can use the fit method to train the pipeline on the training data. We can then use the predict method to make predictions on the test set.
Now, let's dive deeper into how the fit method works within the pipeline. When fit is called, the standard scaler is applied first. It learns the mean and standard deviation from the training data and uses them to scale the data. This process involves a fit and transform step, where the standard scaler calculates the scaled data and passes it to the next step. In this case, the next step is the K nearest neighbor classifier. The K nearest neighbor classifier receives the standardized data, effectively combining these four steps into one. By calling pipe.fit, all these steps are performed automatically, saving us the trouble of executing them individually.
During the prediction phase, the same process occurs, except that there is no fit step. Instead, the pipeline reuses the training set parameters to scale the test data, ensuring consistency. It then passes the scaled test data to the classifier for prediction.
To better visualize this process, let's revisit the flowchart. As a user, you only need to use the fit and predict methods. By calling fit, the pipeline automatically invokes the transform step. It's important to note that the convention in pipelines is to have the last step as the classifier. Only the last step calls fit, while all the preceding steps call fit and transform. Consequently, a pipeline can have multiple transformers, such as the standard scaler or even dimensionality reduction techniques like principal component analysis (PCA). However, it can only have one classifier as the last step. This design ensures the pipeline's compatibility and functionality.
To illustrate the pipeline in action, let's explore a simple model selection scenario using the holdout method. Please note that this is just a basic demonstration, and we'll cover more advanced model selection methods like K-fold cross-validation in later lectures.
The holdout method involves splitting the data into two subsets: a training set and a validation set. The training set is used to train the pipeline, while the validation set is used to evaluate its performance and select the best model.
Here's an example of how you can implement the holdout method with a pipeline:
Next, we create a pipeline using make_pipeline and pass in the desired steps. In this case, we include a StandardScaler to standardize the data and a KNeighborsClassifier with n_neighbors=3 as the classifier.
We train the pipeline by calling the fit method on the training data (X_train and y_train).
After training, we use the pipeline to make predictions on the validation set (X_val) by calling the predict method.
Finally, we evaluate the pipeline's accuracy by comparing the predicted labels (y_pred) with the true labels (y_val) using the accuracy_score function.
This is a basic example of using a pipeline with the holdout method for model selection. Keep in mind that there are more advanced techniques, such as cross-validation, that can provide more robust evaluations of pipeline performance.
7.7 Stacking (L07: Ensemble Methods)
7.7 Stacking (L07: Ensemble Methods)
Yeah, it has been a long, long lecture seven. And finally, we are arriving at the last video to talk about stacking.
Throughout this lecture, we have covered a lot of ground. We discussed majority voting and bagging, where we fit decision trees on bootstrap samples. We also covered boosting, where we fit deep learners based on the mistakes or errors of previous learners, as well as residuals and gradient boosting. Additionally, we explored random forests, which improve performance over regular bagging by using random feature subsets at each node. And now, we are finally going to talk about stacking.
Stacking is similar to majority voting, but with a meta classifier combining the predictions of other classifiers instead of just doing majority voting. Let's dive into the details of stacking.
Before we proceed, let me remind you of the topic of this video: stacking. I apologize for the unnecessary slide, but let's focus on the basics of the stacking algorithm proposed by David H. Wolpert in his paper titled 'Stacked Generalization' published in 1992. Although it's an old paper, the notation used in a more recent book I'm referencing makes it easier to understand. So, let's begin with this basic version of stacking.
In this algorithm, we define the input and output, which sets up the problem. We are working with a training dataset of size 'n.' Each feature vector, denoted as 'x_i,' is an 'm'-dimensional vector. Similarly, the class labels corresponding to the training examples are denoted as 'y_i.' The output of this algorithm is an ensemble classifier, which we will call the second classifier.
Now, let's focus on the steps involved in stacking. Step one is to learn first-level classifiers. We use a loop from one to 't' to fit these classifiers. So, we have a collection of classifiers, denoted as 'h_1' to 'h_t,' which are trained on the input data 'X' and class labels 'Y.'
Moving on to step two, we construct new datasets from the training set. For each training example 'x_i,' we create a new dataset containing the modified feature vector 'x_i prime.' The modified feature vector, 'x_i prime,' contains the predictions of the first-level classifiers. These predictions can be the class labels or even the class membership probabilities. By using these predictions, we can perform majority voting, similar to what we discussed earlier. However, we don't stop there; we proceed to step three.
In step three, instead of performing majority voting, we learn a second-level classifier based on the predictions from the first-level classifiers. 'x_i prime' represents a modified design matrix, where each column contains the predictions from the classifiers 'h_1' to 'h_t.' We can fit a classifier on these predictions, taking into account either the class labels or the class membership probabilities. This second-level classifier will be trained on these predictions.
One weakness of the basic stacking procedure is its susceptibility to overfitting. If any of the first-level classifiers overfit the training set, it could negatively impact the performance of the meta classifier and lead to an overall overfitting of the system. To address this, we can improve the stacking procedure by incorporating cross-validation.
Cross-validation is a technique where we split the dataset into multiple subsets and train the model on different combinations of these subsets. This helps in reducing overfitting and obtaining a more reliable performance estimate. One commonly used variant is k-fold cross-validation, where the dataset is split into 'k' subsets or folds. We train the model on 'k-1' folds and evaluate its performance on the remaining fold. This process is repeated 'k' times, each time using a different fold as the validation set. The performance results from each fold can then be averaged to obtain a more robust estimate of the model's performance.
In the context of stacking, we can use cross-validation to improve the training of the first-level classifiers. Instead of training them on the entire training set, we divide the data into 'k' folds. For each fold, we train the first-level classifiers on the remaining 'k-1' folds and use them to make predictions on the fold that was left out. This process is repeated for each fold, resulting in predictions for the entire training set.
Once we have the predictions from the first-level classifiers for the entire training set, we can proceed to step three of the stacking algorithm, where we train the second-level classifier on these predictions. By incorporating cross-validation, we ensure that the second-level classifier is trained on diverse and reliable predictions from the first-level classifiers, reducing the risk of overfitting.
After training the second-level classifier, we can use it to make predictions on new, unseen data. The predictions are typically obtained by feeding the input through the first-level classifiers to obtain their predictions and then using these predictions as inputs for the second-level classifier. The output of the second-level classifier represents the final prediction of the stacking ensemble.
Stacking is a powerful ensemble learning technique that leverages the strengths of multiple classifiers to improve overall performance. By combining the predictions of multiple classifiers, stacking can capture different aspects of the data and make more accurate predictions. It is a flexible and versatile technique that can be adapted to different problem domains and classifier types.
In conclusion, stacking is an ensemble learning method that goes beyond simple majority voting. It combines the predictions of multiple classifiers through a second-level meta classifier, allowing for more sophisticated decision-making. By incorporating cross-validation, we can enhance the robustness and generalization ability of the stacking algorithm. Stacking is a valuable tool in machine learning and has been widely used in various applications to boost prediction performance.
8.1 Intro to overfitting and underfitting (L08: Model Evaluation Part 1)
8.1 Intro to overfitting and underfitting (L08: Model Evaluation Part 1)
Good day, everyone! I hope you're all doing well. I have some exciting news to share with you today, so let's dive right in.
First and foremost, I have finished grading your project proposals, and I must say, I am truly delighted by the ideas and plans I have seen. It's evident that each one of you has put a great deal of thought into your projects and has a clear vision for the upcoming weeks until the project presentations and reports are due in mid-December. I am genuinely impressed by the level of detail and thoughtfulness that went into your proposals.
However, if any of you feel the need for additional feedback or clarification, or if you would like some guidance on exploring additional techniques, please don't hesitate to reach out to me. I am more than happy to provide you with further assistance and support in any way I can. Simply send me an email, or schedule a meeting, and I'll be there to help.
Moving on to more good news, we have successfully concluded the ensemble methods lecture, which means it's time to embark on a new and exciting topic. In the upcoming series of lectures, we will be focusing on model evaluation. Unlike the previous lectures where we introduced various machine learning classifiers and algorithms, this time we will be exploring how to assess the performance of these algorithms fairly.
Throughout this new series, we will cover a range of topics. We will begin by understanding the concepts of underfitting and overfitting and how they relate to bias and variance decomposition of a loss function. We will then delve into cross-validation methods that allow us to compare models effectively. Additionally, we will discuss techniques for comparing different machine learning algorithms to determine their performance on specific datasets. It's essential to differentiate between model selection and algorithm selection, and we will explore this distinction in more detail.
Without further ado, let's get started with the introduction to model evaluation and dive deeper into the world of overfitting and underfitting. In this lecture (lecture eight), we will discuss the bias and variance decomposition and its relationship with overfitting and underfitting. We will analyze the bias and variance decomposition of both squared error loss (relevant to regression) and 01 loss (relevant to classification) to gain a comprehensive understanding of these concepts. Furthermore, we will touch upon different types of biases in machine learning, going beyond the statistical bias covered in the decomposition.
Before we delve into the lecture material, let's take a step back and briefly recap where we are in the course. We have covered the introduction, computational aspects such as Python, NumPy, and scikit-learn, as well as tree-based methods. We have also discussed the relevance of tree-based methods and the popularity of ensemble methods, specifically boosting and random forests, in the industry. Now, with model evaluation as our focus, we will explore various subtopics, including confidence intervals, cross-validation, model selection, algorithm selection, and performance metrics. Towards the end, we will touch upon dimensionality reduction and unsupervised learning.
I want to assure you that this lecture will be shorter than the previous one on ensemble methods, as it is relatively concise. Nevertheless, it covers crucial concepts that will help us understand model evaluation better. So, let's dive into the six subtopics that make up lecture eight: overfitting, underfitting, bias and variance decomposition, relationship with overfitting and underfitting, bias and variance decomposition of 01 loss, and an overview of different types of biases in machine learning.
Throughout this lecture, I encourage you to pause and reflect on the questions I pose, beyond the quizzes. It's always helpful to pause and formulate your own thoughts before considering my perspective on the matter. Engaging with the material in this manner will enhance your learning experience.
Overfitting can be caused by models that are too complex and have too many parameters relative to the amount of training data available. This leads to the model fitting the noise in the training data instead of the true underlying patterns. Underfitting, on the other hand, occurs when the model is not complex enough to capture the patterns in the data.
Bias and variance can be decomposed mathematically. The expected squared error of a model can be decomposed into the squared bias, the variance, and the irreducible error. The squared bias measures the average difference between the predictions of the model and the true values. The variance measures the variability of the model's predictions for a given input. The irreducible error represents the inherent noise in the data that cannot be reduced by any model.
Underfitting, on the other hand, is associated with high bias and low variance. The model is too simple and cannot capture the underlying patterns in the data, resulting in poor performance on both the training and test data.
The bias-variance decomposition of the 01 loss is similar to that of the squared error loss, but it involves more complex mathematics. The squared bias measures the expected difference in the misclassification rate between the model's predictions and the true labels. The variance measures the variability in the misclassification rate for a given input.
Understanding these different types of biases is crucial for building fair and reliable machine learning models.
That concludes the main topics covered in lecture eight. As you can see, overfitting, underfitting, bias, and variance are interconnected concepts that play a crucial role in model evaluation. It's important to strike a balance between complexity and generalizability to avoid overfitting or underfitting your models. Additionally, being aware of different types of biases can help address fairness and ethical considerations in machine learning.
8.2 Intuition behind bias and variance (L08: Model Evaluation Part 1)
8.2 Intuition behind bias and variance (L08: Model Evaluation Part 1)
Hello, everyone! I hope you're doing well. I have some exciting news to share with you all. Firstly, I have completed the task of grading your project proposals. Let me express my delight in reading all your brilliant ideas and plans for the remainder of the semester. It's truly impressive to see that each one of you has a well-defined roadmap for the upcoming weeks leading to the project presentations and reports.
If any of you feel the need for additional feedback or require clarification on any aspect, don't hesitate to reach out to me via email or any other means. I am more than happy to provide you with further guidance and pointers to additional techniques that might be relevant to your projects.
Now, let's move on to the next piece of good news. We have successfully concluded the ensemble methods lecture, and it's time to dive into a new and exciting topic. In the upcoming series of lectures, we will explore the subject of model evaluation. Unlike the previous lectures, where we introduced various machine learning classifiers and algorithms, this time we will focus on assessing those algorithms fairly.
The lectures on model evaluation will cover several aspects. We will start by understanding the concepts of underfitting and overfitting and their relationship with bias and variance decomposition in a loss function. Then, we will explore cross-validation methods that allow us to compare models effectively. Later on, we will discuss techniques to compare different machine learning algorithms and their performance on specific datasets.
It's important to note that model selection, which involves choosing a well-fitted algorithm, will also be discussed in more detail. We will examine how it differs from model evaluation. So, let's begin our journey with an introduction to model evaluation and continue building our knowledge from there.
Before we delve into the new topic, let's take a moment to recap our progress in this course. We began with an introduction and covered important computational aspects such as Python, NumPy, and scikit-learn. We also explored tree-based methods, which sparked some interesting discussions about their relevance in the industry.
Now, as we enter the model evaluation phase, we will explore several subtopics related to underfitting and overfitting. In this particular lecture (Lecture Eight), we will focus on the bias and variance decomposition and its connection to overfitting and underfitting. We will examine how the bias and variance components impact the generalization performance of a model.
Additionally, we will explore the bias and variance decomposition of the 0-1 loss, which is more relevant to classification problems. This analysis will provide us with a deeper understanding of overfitting and underfitting in the context of classification tasks.
To wrap up this lecture, we will briefly touch upon different types of biases in machine learning beyond the statistical bias discussed earlier.
Now, let's shift our attention to the main concepts of overfitting and underfitting. In machine learning, our ultimate goal is to develop models (regression or classification) that demonstrate good generalization performance. This means the models should perform well on unseen data, which usually comes from the test set. While we also consider performance on the test set, it serves as an estimate of the generalization performance on unseen data.
In the absence of fitting or training the model, we expect the training error to be similar to the test error. However, when we fit the model to the training set, we often observe that the training error is lower than the test error. This is a result of overfitting, where the model becomes too closely tailored to the training data, including noise, leading to an optimistic estimate of performance.
Conversely, underfitting occurs when the model fails to capture the underlying patterns in the data, resulting in both the training and test errors being high. In this case, the model lacks.
sufficient complexity to represent the true relationship between the features and the target variable.
To understand overfitting and underfitting better, let's consider the bias-variance trade-off. Bias refers to the error introduced by approximating a real-world problem with a simplified model. A high bias model tends to oversimplify the underlying patterns in the data and may result in underfitting. On the other hand, variance refers to the error introduced by the model's sensitivity to fluctuations in the training data. A high variance model captures noise and random variations in the training data, leading to overfitting.
The bias-variance trade-off can be illustrated by decomposing the expected test error into three components: the irreducible error, the bias term, and the variance term. The irreducible error represents the inherent noise in the data that cannot be reduced by any model. The bias term measures the error introduced by approximating a real-world problem with a simplified model, and the variance term measures the error caused by the model's sensitivity to fluctuations in the training data.
Mathematically, we can express the expected test error as follows:
Expected Test Error = Irreducible Error + Bias^2 + Variance
Ideally, we want to find a balance between bias and variance that minimizes the expected test error. However, reducing one component often leads to an increase in the other. This trade-off is crucial in model selection and evaluation.
In the context of classification problems, we can also examine the bias-variance decomposition of the 0-1 loss, which is a common loss function used in classification tasks. The 0-1 loss measures the error as the proportion of misclassified instances. The bias-variance decomposition of the 0-1 loss provides insights into the sources of error in classification models.
Beyond the statistical bias, there are other types of biases that can affect machine learning models. These biases can arise from various sources, including sampling bias, measurement bias, and algorithmic bias. Understanding these biases is essential for building fair and reliable machine learning systems.
In the next lecture, we will dive deeper into cross-validation, a powerful technique for estimating the generalization performance of a model. Cross-validation allows us to assess how well a model will perform on unseen data by simulating the process of training and testing on different subsets of the data. We will explore different types of cross-validation methods, such as k-fold cross-validation and stratified cross-validation, and discuss their advantages and limitations.
That's all for today's lecture. I encourage you to review the material covered and come prepared with any questions you may have for our next session. Thank you, and have a great day!