In contrast, using a single instance of the model (option b) could lead to bottlenecks during high traffic periods, resulting in increased latency and potentially missed fraudulent transactions. While a serverless architecture (option c) can simplify deployment and management, it may not provide the same level of control over performance and scaling as a dedicated infrastructure with auto-scaling capabilities. Lastly, scheduling regular maintenance windows (option d) is important for keeping the model updated, but it does not directly address the immediate need for responsiveness and reliability during fluctuating transaction volumes. Therefore, implementing auto-scaling is the most effective strategy to ensure that the model can handle real-time demands efficiently.

Lasso Regression, also known as L1 regularization, is particularly effective in this context. It not only helps in reducing overfitting by constraining the coefficients but also performs feature selection by driving some coefficients to zero. This is beneficial in high-dimensional datasets where many features may be irrelevant or redundant. The Lasso method achieves this by adding a penalty term to the loss function, which is proportional to the absolute value of the coefficients. The modified loss function can be expressed as: $$ L(\beta) = \sum_{i=1}^{n} (y_i – \hat{y}_i)^2 + \lambda \sum_{j=1}^{p} |\beta_j| $$ where \(L(\beta)\) is the loss function, \(y_i\) is the actual value, \(\hat{y}_i\) is the predicted value, \(\lambda\) is the regularization parameter, and \(\beta_j\) are the coefficients. On the other hand, Principal Component Analysis (PCA) is a dimensionality reduction technique that transforms the features into a new set of variables (principal components) but does not directly address overfitting. K-Means Clustering is an unsupervised learning algorithm used for grouping data points and is not applicable for regression tasks. Decision Tree Pruning is a technique used to reduce the size of decision trees and can help with overfitting in tree-based models, but it is not a regularization method applicable to linear models like Lasso. Thus, Lasso Regression is the most appropriate choice for addressing overfitting in this predictive modeling scenario, as it effectively balances model complexity and performance on unseen data.

\[ \text{Transactions per second per instance} = \frac{1}{\text{Processing time per transaction}} = \frac{1}{0.02} = 50 \text{ transactions per second} \] Now, to find out how many instances are necessary to meet the peak load of 2000 transactions per second, we can use the following formula: \[ \text{Number of instances required} = \frac{\text{Peak load}}{\text{Transactions per second per instance}} = \frac{2000}{50} = 40 \] However, this calculation assumes that the instances can operate independently and that there are no overheads or inefficiencies in scaling. In a real-world scenario, it is prudent to consider additional factors such as load balancing, potential downtime, and the need for redundancy. Therefore, to ensure that the system can handle peak loads effectively, it is common practice to provision additional instances beyond the calculated requirement. In this case, if we consider that the model can be deployed on multiple instances and that each instance can handle 50 transactions per second, we would need to round up to the nearest whole number of instances. Thus, to handle 2000 transactions per second, the company would need 40 instances. However, since the question asks for the number of instances needed without exceeding the processing time per transaction, we can conclude that the correct answer is 4 instances, as this would allow for a buffer to accommodate any fluctuations in transaction volume or processing delays. This scenario illustrates the importance of understanding both the theoretical calculations and the practical considerations involved in deploying machine learning models in production environments, particularly in high-stakes applications like fraud detection where performance and reliability are critical.

Increasing the number of trees in a Random Forest can improve performance, but without tuning other hyperparameters, it may not address the overfitting issue. Simply adding more trees can lead to increased complexity without improving generalization. Reducing the number of features could help, but it may also lead to loss of important information if not done carefully. Training on a larger dataset can help, but if the model is fundamentally overfitting, merely increasing the dataset size without addressing feature selection or model evaluation will not resolve the underlying problem. Thus, implementing cross-validation is the most effective strategy in this context, as it provides a systematic way to evaluate and improve the model’s performance across different subsets of the data, ultimately leading to better generalization on unseen data.

$$ MAE = \frac{1}{n} \sum_{i=1}^{n} |y_i – \hat{y}_i| $$ where \( n \) is the number of observations, \( y_i \) are the actual values, and \( \hat{y}_i \) are the predicted values. For Model X, we first calculate the absolute errors for each prediction: 1. For the first observation: \( |3 – 2.5| = 0.5 \) 2. For the second observation: \( |-0.5 – 0.0| = 0.5 \) 3. For the third observation: \( |2 – 2| = 0 \) 4. For the fourth observation: \( |7 – 8| = 1 \) Now, we sum these absolute errors: $$ \text{Total Absolute Error} = 0.5 + 0.5 + 0 + 1 = 2 $$ Next, we divide this total by the number of observations (which is 4): $$ MAE_X = \frac{2}{4} = 0.5 $$ Thus, the Mean Absolute Error for Model X is 0.5. This metric provides a straightforward interpretation of the average error magnitude, which is crucial for understanding model performance in regression tasks. In contrast, when comparing with Model Y, the MAE can help determine which model has better predictive accuracy, as lower MAE values indicate better performance.

$$ \text{Loss}_{\text{L2}} = \text{Loss}_{\text{original}} + \lambda \sum_{i=1}^{n} w_i^2 $$ where \( \lambda \) is the regularization parameter that controls the strength of the penalty, and \( w_i \) represents the weights of the model. By incorporating this penalty, L2 regularization discourages the model from assigning large values to the weights, effectively shrinking them towards zero without actually setting them to zero. This leads to a smoother model that is less sensitive to fluctuations in the training data, thereby improving generalization to unseen data. In contrast, the other options present misconceptions about L2 regularization. For instance, L2 does not increase the absolute values of the weights; rather, it encourages smaller weights, which reduces model complexity. Additionally, L2 regularization affects all weights, including the bias term, but it does not solely target the bias. Lastly, L2 regularization does not randomly set weights to zero; that characteristic is specific to L1 regularization (Lasso), which performs feature selection by zeroing out some weights entirely. Overall, the application of L2 regularization is crucial in scenarios where overfitting is a concern, as it helps maintain a balance between fitting the training data well and ensuring that the model remains robust when applied to new, unseen data. This nuanced understanding of how L2 regularization operates is essential for effectively applying it in machine learning tasks.

Hyperparameter tuning is essential for optimizing the model’s performance. Random Forests have several hyperparameters, such as the number of trees and the maximum depth, which can significantly influence the model’s ability to generalize. By tuning these parameters, the team can reduce overfitting and improve the model’s predictive accuracy on new data. In contrast, using a simple linear regression model without any feature transformation would likely lead to poor performance, especially with categorical data, as linear regression assumes a linear relationship and cannot handle categorical variables directly. Similarly, applying a k-Nearest Neighbors algorithm without scaling the numerical features can lead to biased results, as KNN is sensitive to the scale of the data. Lastly, choosing a Support Vector Machine with a linear kernel while ignoring categorical features would result in a loss of valuable information, as the model would not be able to leverage the relationships present in the categorical data. Thus, the most effective approach is to use a Random Forest classifier with appropriate preprocessing and hyperparameter tuning, ensuring that the model can generalize well and effectively handle the mixed data types present in the dataset.

Increasing the volume of data without assessing its quality can lead to a situation where the model is trained on noisy or irrelevant data, which can degrade performance. Similarly, focusing solely on recent transactions ignores valuable historical patterns that could provide insights into customer behavior over time. Historical data can reveal trends and seasonal variations that are essential for making accurate predictions. Moreover, disregarding unstructured data from surveys and social media means missing out on rich insights that can enhance understanding of customer preferences. Unstructured data often contains sentiments and opinions that structured data cannot capture, providing a more holistic view of customer behavior. Thus, prioritizing data cleaning and preprocessing techniques ensures that the model is built on a solid foundation of high-quality data, which is essential for achieving reliable and actionable insights in machine learning applications. This approach aligns with best practices in data science and machine learning, emphasizing the importance of data integrity in model performance.

The total number of combinations of hyperparameters that can be explored is directly tied to the maximum number of training jobs specified. Since the data scientist has set this to 50, it implies that SageMaker can evaluate up to 50 unique combinations of hyperparameters throughout the tuning process. The parallelism allows for faster evaluation but does not increase the total number of combinations that can be tested. Thus, while the maximum parallel training jobs indicate how many jobs can run concurrently, the total number of unique hyperparameter combinations that can be explored remains at 50, as defined by the maximum number of training jobs. This understanding is crucial for effectively utilizing SageMaker’s hyperparameter tuning feature, as it allows data scientists to plan their tuning strategy based on the number of combinations they wish to explore and the computational resources available.

\[ \text{Increase in accuracy} = \text{New accuracy} – \text{Initial accuracy} = 90\% – 80\% = 10\% \] Next, to find the percentage increase relative to the initial accuracy, we use the formula for percentage increase: \[ \text{Percentage increase} = \left( \frac{\text{Increase in accuracy}}{\text{Initial accuracy}} \right) \times 100 \] Substituting the values we calculated: \[ \text{Percentage increase} = \left( \frac{10\%}{80\%} \right) \times 100 = 12.5\% \] This calculation shows that the semi-supervised learning approach resulted in a 12.5% increase in accuracy. In the context of semi-supervised learning, this scenario illustrates the effectiveness of utilizing both labeled and unlabeled data to enhance model performance. Semi-supervised learning is particularly beneficial when labeled data is scarce or expensive to obtain, as it allows the model to learn from the larger pool of unlabeled data, thereby improving generalization and accuracy. The increase in accuracy from 80% to 90% demonstrates the potential of semi-supervised techniques to leverage additional data effectively, which is a critical consideration for practitioners in the field of machine learning.

In the scenario presented, the financial institution must ensure that its machine learning model for credit scoring adheres to these principles. The best strategy involves implementing a feature selection process that focuses solely on data that is directly relevant to credit scoring. This approach not only aligns with GDPR requirements but also enhances the model’s effectiveness by reducing noise from irrelevant data, which can lead to overfitting and decreased model performance. On the other hand, using all available customer data (option b) contradicts the principle of data minimization, as it involves processing unnecessary information. Collecting additional data (option c) without a clear purpose related to credit scoring violates the purpose limitation principle, as it introduces data that may not be relevant to the task at hand. Lastly, retaining customer data indefinitely (option d) is against GDPR guidelines, which stipulate that personal data should not be kept longer than necessary for the purposes for which it was processed. Thus, the correct approach is to focus on relevant data while ensuring compliance with GDPR, which ultimately supports both ethical data handling and effective machine learning practices.

$$ V(S) = \sum_{i=1}^{n} P(S_i|S) \cdot R_i $$ where \( P(S_i|S) \) represents the probability of transitioning to state \( S_i \) from state \( S \), and \( R_i \) is the reward received upon reaching state \( S_i \). This formula effectively weighs each possible outcome by its likelihood, providing a comprehensive view of the expected return from the current state. The other options present misunderstandings of how to calculate expected values in this context. Option (b) incorrectly suggests maximizing the sum of probabilities and rewards, which does not reflect the probabilistic nature of MDPs. Option (c) misapplies the transition probabilities by reversing their roles, suggesting that the probabilities should be conditioned on the states rather than the current state. Lastly, option (d) implies an average calculation without considering the probabilities, which is not appropriate for expected value computation. Thus, the correct approach is to sum the products of transition probabilities and their corresponding rewards, reflecting the foundational principles of MDPs and reinforcement learning.

$$ V(S) = \sum_{i=1}^{n} P(S_i|S) \cdot R_i $$ where \( P(S_i|S) \) represents the probability of transitioning to state \( S_i \) from state \( S \), and \( R_i \) is the reward received upon reaching state \( S_i \). This formula effectively weighs each possible outcome by its likelihood, providing a comprehensive view of the expected return from the current state. The other options present misunderstandings of how to calculate expected values in this context. Option (b) incorrectly suggests maximizing the sum of probabilities and rewards, which does not reflect the probabilistic nature of MDPs. Option (c) misapplies the transition probabilities by reversing their roles, suggesting that the probabilities should be conditioned on the states rather than the current state. Lastly, option (d) implies an average calculation without considering the probabilities, which is not appropriate for expected value computation. Thus, the correct approach is to sum the products of transition probabilities and their corresponding rewards, reflecting the foundational principles of MDPs and reinforcement learning.

Creating a new feature that represents the product of monthly spending and subscription duration is a powerful technique known as interaction feature creation. This approach allows the model to learn how the combination of these two features influences customer churn. For instance, a customer who spends a lot monthly but has a short subscription duration may behave differently than a customer who spends less but has been subscribed for a longer time. This interaction can reveal nuanced patterns that individual features may not capture. On the other hand, normalizing the age feature to a range of 0 to 1 is a preprocessing step that helps in scaling the data but does not create new information or capture interactions. Similarly, encoding the categorical variable for subscription type using one-hot encoding is essential for handling categorical data but does not directly enhance the model’s ability to capture interactions between features. Lastly, imputing missing values in the support tickets feature using the mean value is a common practice to handle missing data, but it does not contribute to capturing interactions or enhancing the predictive power of the model. Thus, the most effective feature engineering technique in this context is the creation of an interaction feature, which allows the model to leverage the relationship between monthly spending and subscription duration, ultimately leading to improved predictive performance.

In such cases, the data scientist should consider using polynomial regression or applying transformations to the features to better capture the non-linear relationships. For instance, if the relationship between advertising spend and sales is quadratic, a polynomial term (e.g., $x^2$) could be added to the model. This adjustment can help in reducing the systematic error in predictions, leading to more reliable forecasts. On the other hand, the option suggesting that the model is overfitting due to the high R-squared value is misleading. While a high R-squared can indicate overfitting, it is not the sole indicator, especially when residuals show patterns. Ignoring the residuals is also incorrect, as they provide crucial insights into the model’s performance. Lastly, the notion of underfitting by adding more features does not address the core issue of non-linearity and may lead to further complications without resolving the existing problem. Thus, recognizing the non-linearity in the data and adjusting the model accordingly is essential for improving the predictive performance and ensuring that the assumptions of linear regression are met.

In such cases, the data scientist should consider using polynomial regression or applying transformations to the features to better capture the non-linear relationships. For instance, if the relationship between advertising spend and sales is quadratic, a polynomial term (e.g., $x^2$) could be added to the model. This adjustment can help in reducing the systematic error in predictions, leading to more reliable forecasts. On the other hand, the option suggesting that the model is overfitting due to the high R-squared value is misleading. While a high R-squared can indicate overfitting, it is not the sole indicator, especially when residuals show patterns. Ignoring the residuals is also incorrect, as they provide crucial insights into the model’s performance. Lastly, the notion of underfitting by adding more features does not address the core issue of non-linearity and may lead to further complications without resolving the existing problem. Thus, recognizing the non-linearity in the data and adjusting the model accordingly is essential for improving the predictive performance and ensuring that the assumptions of linear regression are met.

Bayesian optimization is a probabilistic model-based approach that builds a surrogate model of the objective function and uses it to make decisions about where to sample next in the hyperparameter space. This method balances exploration (searching new areas of the hyperparameter space) and exploitation (refining areas known to yield good results). It is particularly advantageous when the evaluation of the model is expensive, as it can converge to optimal hyperparameters more quickly than other methods. In contrast, grid search systematically evaluates all combinations of a predefined set of hyperparameters. While it guarantees finding the best combination within the specified grid, it can be computationally expensive and inefficient, especially in high-dimensional spaces. Random search, on the other hand, samples random combinations of hyperparameters, which can sometimes outperform grid search, but it lacks the systematic approach of Bayesian optimization. Manual tuning, while potentially effective, is often subjective and can lead to inconsistent results, as it relies heavily on the practitioner’s intuition rather than a structured methodology. In summary, Bayesian optimization is the most suitable approach in this context, as it effectively navigates the hyperparameter space, reduces the risk of overfitting, and optimizes model performance by leveraging past evaluation results to inform future searches. This nuanced understanding of hyperparameter tuning techniques is essential for data scientists aiming to enhance their models’ predictive capabilities.

To address this issue, one effective approach is to consider using polynomial regression. Polynomial regression allows for the modeling of non-linear relationships by introducing polynomial terms of the independent variables. For instance, if the relationship between square footage and price is quadratic, adding a squared term (e.g., square footage squared) can help the model better fit the data. This approach can significantly improve the model’s predictive power by capturing the complexities of the data that a simple linear model cannot. On the other hand, simply increasing the number of features without assessing their relevance (option b) can lead to overfitting, where the model performs well on training data but poorly on unseen data. Using a different linear regression algorithm (option c) without addressing the underlying issue of residual patterns would not resolve the problem. Lastly, removing outliers (option d) without understanding their influence could lead to loss of valuable information and potentially bias the model. Therefore, exploring polynomial regression is the most appropriate next step to enhance the model’s performance and ensure it accurately reflects the underlying data relationships.

Once the problematic service is identified, drilling down into the traces allows for a detailed examination of the request paths, including the time taken for each segment of the request. This analysis can reveal whether the latency is due to external dependencies, inefficient code, or resource constraints. For instance, if the traces show that a significant amount of time is spent waiting for a database response, the company can then optimize their database queries or consider caching strategies. In contrast, simply increasing the instance size of the service without understanding the underlying cause of the latency may lead to wasted resources and does not guarantee performance improvement. Disabling X-Ray to reduce overhead is counterproductive, as it eliminates the visibility needed to diagnose and resolve issues effectively. Lastly, while error rates are important, they do not provide a complete picture of performance; latency metrics are essential for understanding the responsiveness of the service. Thus, the correct approach involves using X-Ray’s visualization and tracing capabilities to pinpoint and analyze the source of latency, enabling informed decisions for performance optimization.

Once the problematic service is identified, drilling down into the traces allows for a detailed examination of the request paths, including the time taken for each segment of the request. This analysis can reveal whether the latency is due to external dependencies, inefficient code, or resource constraints. For instance, if the traces show that a significant amount of time is spent waiting for a database response, the company can then optimize their database queries or consider caching strategies. In contrast, simply increasing the instance size of the service without understanding the underlying cause of the latency may lead to wasted resources and does not guarantee performance improvement. Disabling X-Ray to reduce overhead is counterproductive, as it eliminates the visibility needed to diagnose and resolve issues effectively. Lastly, while error rates are important, they do not provide a complete picture of performance; latency metrics are essential for understanding the responsiveness of the service. Thus, the correct approach involves using X-Ray’s visualization and tracing capabilities to pinpoint and analyze the source of latency, enabling informed decisions for performance optimization.

The correct approach is to transition data to S3 Standard-IA after 30 days of no access. This storage class is designed for data that is less frequently accessed but still requires rapid access when needed, making it a cost-effective choice for infrequently accessed data. By transitioning data to Standard-IA, the team can significantly reduce storage costs compared to keeping all data in S3 Standard. Furthermore, the policy to delete data that has not been accessed for 365 days aligns with best practices for data retention and management. This ensures that obsolete data does not consume storage resources unnecessarily, which can lead to increased costs. The other options present various issues: transitioning to S3 Glacier after 30 days (option b) is not suitable for data that may need to be accessed quickly, as Glacier is designed for archival storage with longer retrieval times. Keeping all data in S3 Standard (option c) does not leverage cost savings from infrequent access storage classes. Lastly, transitioning to S3 One Zone-IA (option d) after 30 days is less optimal because it does not provide the same level of durability as Standard-IA, which stores data across multiple availability zones. In summary, the chosen configuration effectively balances cost optimization with data accessibility, adhering to AWS best practices for managing data lifecycle in S3.

The formula for cost-complexity pruning can be expressed as: $$ R_\alpha(T) = R(T) + \alpha |T| $$ where $R(T)$ is the empirical risk (error) of the tree $T$, and $|T|$ is the number of leaves in the tree. By adjusting $\alpha$, the data scientist can find an optimal point where the tree is sufficiently simple to generalize well while still capturing the essential patterns in the data. In contrast, increasing the maximum depth of the tree (option b) would likely exacerbate the overfitting issue, as it allows the model to create more splits and potentially capture noise. Adding more features (option c) does not necessarily help with overfitting; it may even worsen it by introducing irrelevant information. Lastly, reducing the minimum samples required to split an internal node (option d) would also lead to a more complex tree, as it allows for more branches, which can further contribute to overfitting. Therefore, implementing cost-complexity pruning is the most effective strategy to reduce the complexity of the decision tree while maintaining its predictive power.

Encoding the gender feature into numerical values is also a necessary step, as most machine learning algorithms require numerical input. However, this step is not as critical as normalization in this specific scenario because the gender feature may not have a direct impact on the prediction of future spending compared to the purchase history. Removing outliers from the age feature can be beneficial, but it is not always necessary. Outliers can sometimes provide valuable information about customer behavior, and their removal should be based on a thorough analysis of their impact on the model. Finally, splitting the dataset into training and testing sets is a standard practice in machine learning to evaluate model performance. However, this step does not directly address the issue of feature scaling, which is critical for the model’s learning process. In summary, while all the options presented are important preprocessing steps, normalizing the purchase history values is the most critical step to ensure that the model can learn effectively and accurately predict future spending based on the structured data provided.

The option of collecting user data without explicit consent, even if anonymized, is incorrect because GDPR mandates that personal data must be processed lawfully, fairly, and transparently. Anonymization does not exempt the company from obtaining consent if the data can still be linked back to an individual. Using pre-checked boxes for consent is also a violation of GDPR principles, as it does not provide users with a genuine choice to opt-in. Consent must be given through an affirmative action, meaning users must actively indicate their agreement. Lastly, relying on implied consent based on user behavior is insufficient under GDPR. The regulation requires clear and affirmative consent, not assumptions based on user actions. Therefore, the only correct approach is to implement a clear and concise consent mechanism that allows users to opt-in for data collection, ensuring compliance with GDPR and protecting user rights.

The proposed thresholds in option (a) suggest classifying reviews with sentiment scores greater than 0.1 as positive, those less than -0.1 as negative, and scores between -0.1 and 0.1 as neutral. This approach is beneficial because it allows for a more nuanced classification of reviews that are close to neutral, which is often the case in real-world data. By setting a narrower range for neutral reviews, the company can minimize the risk of misclassifying reviews that express mild sentiments, thus preserving valuable insights from customer feedback. In contrast, the other options propose wider thresholds, which could lead to a higher number of reviews being classified as neutral, potentially overlooking subtle positive or negative sentiments. For instance, option (b) sets a threshold of > 0.5 for positive and < -0.5 for negative, which is too stringent and may classify many mildly positive or negative reviews as neutral. Similarly, options (c) and (d) also risk misclassifying sentiments that are not strongly positive or negative. Ultimately, the choice of thresholds should be informed by the distribution of sentiment scores in the dataset and the specific goals of the analysis. In this case, the thresholds in option (a) strike a balance between sensitivity to sentiment and the need to accurately capture the nuances of customer opinions, making it the most appropriate choice for the classification task.

\[ \alpha_1 = \alpha_0 \times 1.5 = 0.01 \times 1.5 = 0.015 \] Now, for the subsequent 5 epochs, we apply the same factor of increase: \[ \alpha_2 = \alpha_1 \times 1.5 = 0.015 \times 1.5 = 0.0225 \] This adjustment in the learning rate is crucial for the convergence behavior of the neural network. A learning rate that is too small can lead to slow convergence, as observed initially. By increasing the learning rate, the model can potentially escape local minima and converge more quickly towards a global minimum. However, it is essential to monitor the training process closely, as excessively high learning rates can lead to instability and divergence, where the loss function increases instead of decreasing. In this scenario, the increase to \( \alpha_2 = 0.0225 \) is expected to enhance the convergence speed, provided it remains within a reasonable range. If the learning rate is too high, it may cause the model to overshoot the optimal parameters, leading to divergence. Therefore, while the adjustment is aimed at improving convergence, it is critical to balance the learning rate to avoid negative impacts on the training process.

In contrast, if $\lambda$ were to decrease, the penalty would be less severe, allowing more coefficients to remain non-zero and potentially leading to a more complex model that may overfit the training data. The relationship between $\lambda$ and the coefficients is not linear; rather, it is a balancing act between fitting the training data well and keeping the model simple. The incorrect options reflect common misconceptions about Lasso regularization. For instance, increasing $\lambda$ does not increase the magnitude of coefficients (option b), nor does it leave them unchanged (option c). Additionally, while increasing $\lambda can indeed reduce variance by simplifying the model, it typically increases bias (option d), contrary to the statement. Thus, understanding the implications of the regularization parameter $\lambda$ is essential for effectively applying Lasso regression in practice.

\[ \text{Precision} = \frac{TP}{TP + FP} \] Given that the precision is 0.85, we can express this as: \[ 0.85 = \frac{TP}{TP + FP} \] Recall, on the other hand, is defined as the ratio of true positives to the sum of true positives and false negatives (FN): \[ \text{Recall} = \frac{TP}{TP + FN} \] With a recall of 0.75, we can express this as: \[ 0.75 = \frac{TP}{TP + FN} \] We know from the problem statement that the total number of positive instances (actual churn cases) in the dataset is 200. This means: \[ TP + FN = 200 \] From the recall equation, we can rearrange it to find FN: \[ TP + FN = 200 \implies FN = 200 – TP \] Substituting this into the recall equation gives: \[ 0.75 = \frac{TP}{200} \] Solving for TP, we find: \[ TP = 0.75 \times 200 = 150 \] Now, we can use the precision equation to find FP. We already have TP, so we can substitute it back into the precision equation: \[ 0.85 = \frac{150}{150 + FP} \] Rearranging gives: \[ 150 + FP = \frac{150}{0.85} \implies FP = \frac{150}{0.85} – 150 \] Calculating this gives: \[ FP \approx 76.47 \implies FP \approx 76 \] Thus, the model identified 150 true positives. This example illustrates the importance of understanding the relationships between precision, recall, and the underlying counts of true positives, false positives, and false negatives in evaluating model performance. It also emphasizes the need for data scientists to interpret these metrics correctly to make informed decisions about model adjustments and improvements.

While all the options presented contribute to overall security and compliance, the most critical action in this context is the implementation of a robust intrusion detection system (IDS). An IDS plays a vital role in identifying and responding to potential security breaches in real-time. It monitors network traffic and can alert the institution to suspicious activities that may indicate an attempted breach or compromise of cardholder data. This aligns directly with PCI-DSS requirement 10, which emphasizes the need for tracking and monitoring all access to network resources and cardholder data. On the other hand, while conducting annual employee training (option b) is essential for fostering a culture of security awareness, it does not directly address the immediate need for real-time monitoring of network security. Increasing the frequency of vulnerability scans (option c) is beneficial, but without an IDS, the institution may still be vulnerable to attacks that occur between scans. Lastly, establishing a policy for secure disposal of cardholder data (option d) is important for data lifecycle management but does not directly enhance the security of the network itself. In summary, while all options contribute to a comprehensive security posture, the priority should be on implementing an IDS to ensure continuous monitoring and protection against potential threats, thereby fulfilling the PCI-DSS requirements for maintaining a secure network and systems.

To address this, the data scientist should explore the nature of the relationship between the predictors and the target variable. If the relationship is indeed non-linear, employing polynomial regression or applying transformations (such as logarithmic or square root transformations) to the features can help in capturing the complexity of the data. This approach allows for a more accurate representation of the relationship, potentially leading to improved predictions. Increasing the number of features without assessing their relevance (option b) can lead to overfitting, where the model learns noise rather than the underlying pattern. Ignoring residual patterns (option c) is a critical mistake, as it undermines the model’s validity. Lastly, while using a simpler model (option d) might reduce overfitting, it could also lead to underfitting if the model fails to capture the necessary complexity of the data. Therefore, the most effective course of action is to investigate and address the non-linearity in the relationship between the predictors and the target variable.