Practice
1. You implemented PCA but the variance explained by the first principal component is unexpectedly low. What is the most likely cause?
medium
Solution
Step 1: Identify the impact of centering data
Centering data is crucial for PCA as it ensures the covariance matrix reflects true variance.Step 2: Eliminate wrong options
Eigenvectors were not normalized. is incorrect because normalization affects direction, not variance. Covariance matrix was computed using rowvar=True. affects orientation, not variance. Too few principal components were selected. is irrelevant to the variance of the first component.Final Answer:
Option A -> Option AQuick Check:
Center data before PCA to capture variance. [OK]
Hint: Center data before PCA to capture variance. [OK]
Common Mistakes:
2. How can you optimize the computation of cosine similarity for a large dataset of vectors?
hard
Solution
Step 1: Identify computational bottlenecks
Looping over pairs is inefficient for large datasets.Step 2: Optimize using matrix operations
Precomputing norms and using matrix multiplication reduces redundant calculations.Final Answer:
Option C -> Option CQuick Check:
Matrix ops reduce redundancy. [OK]
Hint: Matrix ops reduce redundancy. [OK]
Common Mistakes:
3. How can you optimize the implementation of a learning rate scheduler to reduce computational overhead in a large-scale training setup?
hard
Solution
Step 1: Identify computational overhead sources
Frequent updates can increase overhead, especially in large-scale setups.Step 2: Optimize scheduler updates
Creating a custom scheduler that reduces the frequency of updates can minimize computational costs while maintaining performance.Final Answer:
Option D -> Option DQuick Check:
Custom schedulers can reduce update frequency. [OK]
Hint: Custom schedulers can reduce update frequency. [OK]
Common Mistakes:
4. How can you optimize a KD-Tree implementation for a KNN classifier to handle large datasets more efficiently?
hard
Solution
Step 1: Identify optimization strategies
Approximate nearest neighbors can significantly speed up queries in large datasets.Step 2: Evaluate other options
A: Balancing helps but isn't enough for large datasets. B: Increasing dimensions worsens performance. D: Reducing data points isn't always feasible.Final Answer:
Option B -> Option BQuick Check:
Approximate neighbors speed up KD-Tree [OK]
Hint: Approximate neighbors speed up KD-Tree [OK]
Common Mistakes:
5. How can you optimize the memory usage of the Adam optimizer in a large-scale deep learning model?
hard
Solution
Step 1: Identify memory-intensive components
Adam requires storing additional momentum and velocity arrays, which can be memory-intensive.Step 2: Optimize storage precision
Using half-precision floating points reduces memory usage significantly while maintaining sufficient precision for most deep learning tasks.Final Answer:
Option B -> Option BQuick Check:
Use half-precision to save memory in Adam [OK]
Hint: Use half-precision to save memory in Adam [OK]
Common Mistakes:
