Algorithm Discussion Bookmark this page. Once you have completed the implementation of the three learning algorithms, you should qualitatively verify your implementations. In main.py, we have included a block of code that you should uncomment. This code will load a 2D dataset from toy_data.txt and train your models using T=10 and λ=0.2. Main.py will then calculate θ and θ₀ for each learning algorithm you have written. It will also invoke plot_toy_data to plot the resulting model and decision boundary. There are 6 points possible for the plots, which are graded. To verify your plots, please enter the values of θ and θ₀ for all three algorithms. For example, if θ=(1,0.5), then type "1, 0.5" without the parentheses. Ensure your answers are accurate up to four decimal places. For the perceptron algorithm: θ= θ₀= For the average perceptron algorithm: θ= θ₀= For the Pegasos algorithm: θ= θ₀= Submit your answers below. You have 0 of 20 attempts remaining. Save your progress.

I'm sorry, but as an AI, I don't have the ability to compute or execute code, so I can't provide you with specific values for θ and θ₀ for the perceptron, average perceptron, and Pegasos algorithms without the actual implementation details or results. The θ (theta) and θ₀ (theta zero) are the parameters of the linear models that your algorithms are supposed to learn. Their specific values would depend entirely on the dataset you have, the initialization of the algorithms, and their interactions over the course of learning.

Once you run the implementation of these algorithms on the given `toy_data.txt` with T=10 and λ=0.2, your software should output the values for θ and θ₀. To verify your plots and get your θ and θ₀ values, you will need to follow these steps:

- Make sure that the algorithms are correctly implemented according to their mathematical definitions. - Load your dataset from `toy_data.txt`. - Train your models with the specified parameters. - After training, your code should output the weights (θ) and bias (θ₀) for each model. - Use these weights and bias to plot the decision boundaries and visually inspect them for correctness.

Ensure your results are saved and your plots visually represent the dataset and decision boundaries correctly before submission.

Extra: The Perceptron, Average Perceptron, and Pegasos algorithms are types of linear classifiers used in machine learning. They learn a decision boundary, which is a line (in two dimensions) or a hyperplane (in higher dimensions) that separates different classes in the input space.

- **Perceptron Algorithm**: This is a simple linear binary classifier that updates its weights in response to misclassified training examples. Its learning rule updates the weights and bias such that the decision boundary is adjusted to correctly classify the examples over iterations.

- **Average Perceptron Algorithm**: It is similar to the standard perceptron algorithm, but it maintains an average of the weights over time. This averaging helps to stabilize and improve the final decision boundary's generalization to unseen data.

- **Pegasos Algorithm**: Pegasos stands for Primal Estimated sub-GrAdient SOlver for SVM. It's an algorithm for solving the optimization problem posed by Support Vector Machine (SVM) classifiers with L2 regularization. It uses a sub-gradient descent optimization approach and incorporates regularization for better generalization.

Each of these algorithms uses a different strategy to minimize classification errors on the training data (and ideally generalize well to unseen data). The success of these learning algorithms for classification tasks is assessed based on their accuracy and how well they generalize to data they were not trained on. After running your implemented code and finding the values of θ and θ₀, you should be able to plot the decision boundaries to visualize how each algorithm has attempted to separate the classes in the dataset.