You are taking a timed online assessment with multiple-select and numeric-response questions. ## 1) Confusion-matrix metrics (multiple select) A binary classifier is evaluated on 200 examples. For each option below, the confusion matrix is given as `(TP, FP, FN, TN)`. Select all options where: - **Recall** \(= \frac{TP}{TP+FN}\) is **> 0.90**, and - **False Positive Rate (FPR)** \(= \frac{FP}{FP+TN}\) is **< 0.10**. Options: - **A:** (95, 8, 5, 92) - **B:** (92, 12, 8, 88) - **C:** (180, 18, 20, 182) - **D:** (45, 1, 5, 149) - **E:** (91, 9, 9, 91) --- ## 2) Ensemble learning for loan-default prediction (multiple select) You built an initial classifier to predict whether a customer will default on a loan, but its accuracy is only slightly better than chance. You consider using an ensemble method. Select all statements that are **true**: - (1) If the dataset contains both linear and non-linear relationships, ensemble learning can impair performance compared to most approaches. - (2) Modern ensemble learning techniques can improve overall model interpretability. - (3) Ensemble learning techniques can be time-intensive to train. - (4) Ensemble learning techniques typically create overfitted models. - (5) If the dataset contains both linear and non-linear relationships, ensemble learning can improve performance compared to most approaches. - (6) None of the above. --- ## 3) Decision-tree split criteria (multiple select) You are choosing an impurity measure to score candidate splits in a **classification** decision tree. Select all options that are valid impurity/split criteria: - Entropy - Classification Error - Gini index - Pruning - None of the above --- ## 4) Training loss increases every epoch (multiple select) You train a model to detect intrusion attempts. You notice that **training loss consistently increases every epoch**. Select all rationales that could plausibly cause this: - Regularization is too high - Step size (learning rate) is too large - Regularization is too low - Step size is too small - None of the above --- ## 5) Learning-curve diagnosis (multiple select) You are training a sentiment regressor that predicts a score in \([-1.0, +1.0]\) using **47 features**. You observe this pattern: - **Training error** decreases steadily and becomes very low. - **Validation error** decreases initially, then starts increasing and stays much higher than training error. Select all actions that best address the problem: - Reduce the size of the training data - Include a regularization component to your model - Increase the number of features included in your data - Increase the number of epochs used to train your model - Choose a more complex modeling technique - None of the above --- ## 6) Random Forest vs Gradient Boosting (training speed focus) (multiple select) You need a fast-to-train baseline fraud classifier. You are choosing between a **Random Forest** and a **Gradient Boosting Machine (GBM)**. Select all statements that are **true and relevant** to training speed: - (1) GBM fits trees sequentially rather than independently like Random Forest. - (2) GBM is harder to overfit than Random Forest. - (3) Random Forest is slower than GBM for real-time prediction. - (4) GBMs are typically more accurate than Random Forest for anomaly detection. - (5) Random Forest has fewer parameters than GBM. - (6) None of the above. --- ## 7) Manual forward pass in a small neural network (numeric) Compute the output of the following neural network. Assume: - All **biases are 0**. - Hidden activations \(f_1\) and \(f_2\) are **linear** (identity). - Output activation \(f_3\) is **sigmoid**: \(\sigma(z)=\frac{1}{1+e^{-z}}\). Inputs: - \(x_1 = 1.2\) - \(x_2 = -0.7\) Hidden layer (2 units): - \(h_1 = 0.5\,x_1 + (-1.0)\,x_2\) - \(h_2 = (-0.25)\,x_1 + 0.75\,x_2\) Output layer (1 unit): - \(z = 1.0\,h_1 + 0.5\,h_2\) - \(\hat{y} = \sigma(z)\) **Return \(\hat{y}\) rounded to the nearest thousandth (3 decimals).**