Question

Read the example in the Appendix to learn how to import and flatten the images in the digit dataset. Pick a number. We want to train a binary classification model to determine if the given hand-written digit is this number or not.

(a) Split the dataset (80/20), and use LogisticRegressionGD() to train the logistic regression model . Next, test your model on the test data set.
(b) Use scikit-learn to train the logistic regression model with l2-norm regularization and find the best parameter.
(c) Fit a Linear SVM and find the best parameters.
(d) Fit Nonlinear SVMs (with 3 different kernels) and find the best parameters.

Answer 1

The student's question touches on topics of logistic regression, support vector machines, and statistical analysis in the context of machine learning and data analysis. It involves visualizing data, calculating regression lines and correlation coefficients, and optimizing machine learning models for classification tasks.

Step-by-step explanation:

The student's question involves several aspects of data analysis and machine learning, particularly focusing on logistic regression, support vector machines (SVMs), and the recognition and application of probability distributions. When handling the task of classifying handwritten digits, the following steps are crucial:

• Deciding on independent and dependent variables for your analysis.
• Constructing scatter plots and histograms to visualize data relationships and distributions.
• Calculating the least-squares regression line and the correlation coefficient to assess the strength of linear relationships.
• Applying various algorithms, such as logistic regression and SVM, to classify data and optimize their parameters for the best predictive performance.
• Utilizing regularization techniques like l2-norm to manage overfitting in logistic regression models.
• Experimenting with different SVM kernels to capture non-linear patterns in the data.

The question encompasses elements of both supervised learning models (e.g., logistic regression, linear and nonlinear SVMs) and statistical analysis (e.g., calculating the least-squares line, correlation coefficient, and recognizing various probability distributions). Moreover, selecting the appropriate type of regression analysis and the best parameters for each model is essential to develop accurate and reliable predictive models.