Explanation

You should treat this as a classic binary classification problem in a low‑dimensional space. Start by visualizing the points to get an intuition about whether a linear boundary will separate the yes and no classes. That visual check guides your choice of model family: if the classes look linearly separable, a simple logistic regression (with feature scaling) is often enough; if the boundary looks curved or irregular, tree‑based models, kernel SVMs, or adding polynomial features can capture the non‑linearity. Regardless of the model, you’ll want to set up a robust training pipeline: split the data (or use k‑fold cross‑validation) to estimate out‑of‑sample performance, pick appropriate metrics (accuracy, precision/recall, ROC‑AUC), and tune hyperparameters (regularization strength, tree depth, kernel parameters) with grid or random search. Finally, after selecting the best model, retrain on the full training set, evaluate on a held‑out test set, and package the preprocessing steps (scaling, feature engineering) together with the model for deployment.

Naive Response

I would just feed the raw x and y coordinates into a logistic regression model and use its predictions for new points.

Good Response

First, I would plot the 2‑D points to see whether the yes and no classes appear linearly separable. If the scatter plot suggests a straight‑line boundary, I would start with a logistic regression model, scaling the x and y features to zero mean and unit variance so that the coefficients are well‑behaved. If the boundary looks curved or there are clusters, I would consider a decision tree or a kernel SVM, or I would augment the data with polynomial features (e.g., x², xy, y²) to let a linear model capture non‑linear patterns. I would then set up a training pipeline that uses k‑fold cross‑validation (e.g., 5‑fold) to estimate performance reliably and to tune hyperparameters: the regularization strength C for logistic regression, max_depth and min_samples_leaf for the tree, or the kernel type and gamma for the SVM. I would evaluate models using accuracy, but also look at precision, recall, and ROC‑AUC, especially if the yes/no classes are imbalanced. After selecting the best‑performing model, I would retrain it on the entire training set, verify that the preprocessing steps (scaling, polynomial expansion) are included in the pipeline, and finally test on a held‑out test set to confirm generalization. I would also document the pipeline and consider saving the model with its preprocessing steps for easy deployment.

Assessment

The naive answer shows the right idea of using a model but stops at “logistic regression on raw coordinates,” missing critical steps such as data exploration, feature scaling, handling non‑linear decision boundaries, proper validation, and hyperparameter tuning. The good answer walks through the full end‑to‑end workflow: visual inspection to inform model choice, appropriate preprocessing, robust cross‑validation, thoughtful metric selection, systematic hyperparameter search, and final training and deployment considerations. This depth demonstrates both technical competence and the interviewer's expectation that you think about the whole modeling pipeline, not just the algorithm.

98. Classify 2D Points

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