Research task (AI & ML):
Write an explanatory article comparing and contrasting Support Vector Machine and Logistic Regression.

Evaluation rubric:
criterion: The response contains at least four explicit sentences or bullets describing similarities shared by Support Vector Machine (SVM) and Logistic Regression (e.g. both are supervised learning algorithms for classification, both are linear classifiers, can handle non-linear data, uses regularization).
weight: 4
axis: Synthesis of Information

criterion: The response contains at least four explicit sentences or bullets describing differences between Support Vector Machine (SVM) and Logistic Regression (e.g. SVM maximizes margin while Logistic Regression maximizes likelihood, SVM is geometric while Logistic Regression is statistical, SVM is robust to outliers while Logistic Regression is more sensitive).
weight: 5
axis: Synthesis of Information

criterion: The response includes executable code snippets as examples of how to use Support Vector Machine or Logistic Regression (e.g. setup codes, library imports, example usage).
weight: -2
axis: Implicit Criteria

criterion: The response correctly states that Support Vector Machine constructs a decision boundary or hyperplane that maximizes the margin between classes, and how support vectors define the SVM model.
weight: 4
axis: Explicit Criteria

criterion: The response correctly states that Logistic Regression models class probability with the logistic sigmoid function or log-odds formulation.
weight: 4
axis: Explicit Criteria

criterion: The response correctly states that Support Vector Machines can handle non-linear relationships by using kernel functions (e.g. linear kernel, Radial Basis Function(RBF), polynomial, sigmoid).
weight: 3
axis: Implicit Criteria

criterion: The response correctly explains the difference between hard-margin and soft-margin Support Vector Machines (e.g. hard-margin SVM requires perfect separation with no errors; soft-margin SVM allows some misclassifications to improve generalization).
weight: 3
axis: Implicit Criteria

criterion: The response correctly states that the standard Logistic Regression assumes a linear decision boundary in the feature space unless features are transformed.
weight: 2
axis: Implicit Criteria

criterion: The response correctly states that Support Vector Machine produces label predictions, not probabilities by default.
weight: 2
axis: Implicit Criteria

criterion: The response explains the derivation of the objective function for Support Vector Machine, which includes hinge loss and regularization parameters.
weight: 2
axis: Implicit Criteria

criterion: The response explains the derivation of the Logistic Regression from Gaussian Naive Bayes.
weight: 2
axis: Implicit Criteria

criterion: The response mentions that Support Vector Machine is a quadratic programming problem.
weight: 1
axis: Implicit Criteria

criterion: The response contains the formula for Support Vector Machine's dual formulation.
weight: 1
axis: Implicit Criteria

criterion: The response discusses at least five distinct dimensions of comparison for Support Vector Machine and Logistic Regression (e.g. mathematical objective, decision boundary shape, interpretability, computational complexity, robustness to outliers, scalability, regularization, typical data‐set size/shape).
weight: 4
axis: Explicit Criteria

criterion: The response provides at least one practical scenario where Support Vector Machine is preferable, justified by its attributes (e.g. effective in high-dimensional spaces, robust to overfitting/outlier, applicable to small dataset).
weight: 2
axis: Implicit Criteria

criterion: The response provides at least one practical scenario where Logistic Regression is preferable, justified by its attributes (e.g. simplicity, computationally efficient, effective for binary classification).
weight: 2
axis: Implicit Criteria

criterion: The response describes practical use-case scenarios for Support Vector Machine based on its properties (e.g. bioinformatics, handwriting recognition, face recognition).
weight: 1
axis: Implicit Criteria

criterion: The response describes practical use-case scenarios for Logistic Regression based on its properties (e.g. fraud detection, spam detection, loan approval, disease prediction).
weight: 1
axis: Implicit Criteria

criterion: The response contains a summary of Support Vector Machine and Logistic Regression's comparison (e.g. synthesizing key similarities, differences, take-home messages).
weight: 1
axis: Communication Quality

criterion: The response compares Support Vector Machine and Logistic Regression's convexity properties in optimization problems.
weight: 1
axis: Implicit Criteria

criterion: The response explains the geometric intuition of the margin in Support Vector Machine.
weight: 3
axis: Implicit Criteria

criterion: The response discusses regularization techniques (e.g. the L1/L2 for Logistic Regression, C parameter in Support Vector Machine).
weight: 1
axis: Implicit Criteria

criterion: The response explains how gradient descent or related optimization methods are used to optimize loss functions for both Support Vector Machine and Logistic Regression.
weight: 2
axis: Implicit Criteria

criterion: The response includes a chart or table that compares Support Vector Machine and Logistic Regression across multiple dimensions in a condensed form (e.g. dimension, dataset size, computational efficiency, robustness to outliers).
weight: 3
axis: Communication Quality

criterion: The response incorporates a historical or theoretical context behind Logistic Regression and Support Vector Machine (e.g. origins of SVM in Vapnik-Chervonenkis theory, Logistic Regression in statistics).
weight: 1
axis: References & Citation Quality

criterion: The response compares model outputs in multi-class scenarios by introducing extensions like One-vs-All or Multinomial Logistic Regression.
weight: 2
axis: Implicit Criteria

criterion: The response explains how Support Vector Machine and Logistic Regression behave on imbalanced datasets (e.g. decision boundary skewing, loss function bias, probability threshold issues) and their mitigation techniques (e.g. class weights, sampling strategies).
weight: 3
axis: Implicit Criteria

criterion: The response discusses the impact of feature scaling on the Support Vector Machine and Logistic Regression (e.g. distance metrics, hyperplane skewing, gradient descent convergence, regularization impact).
weight: 1
axis: Implicit Criteria

criterion: Mathematical equations are displayed in clear mathematical notation like LaTex format.
weight: 2
axis: Communication Quality

criterion: The response discusses other alternative algorithms for classification (e.g. decision trees, k-nearest neighbors).
weight: -3
axis: Synthesis of Information