A colleague has built a Polynomial Regression model and suspects overfitting. What diagnostic tools and techniques would you recommend to confirm or deny this suspicion?
- Cross-validation and visual inspection of residuals
- Ignore the suspicion
- Increase polynomial degree
- Look at training data only
Cross-validation and visual inspection of residuals are common techniques to detect overfitting. They can help in assessing how well the model generalizes to new data, revealing any overfitting issues.
In LDA, what is meant by the term "between-class variance"?
- Variance among different classes
- Variance among similar classes
- Variance between individual data points
- Variance within individual classes
"Between-class variance" in LDA refers to the "variance among different classes." It quantifies how separated the means of different classes are from each other. Maximizing this variance enhances class separation.
Explain the role of eigenvalues and eigenvectors in PCA.
- Eigenvalues represent direction, eigenvectors variance
- Eigenvalues represent variance, eigenvectors direction
- Neither plays a role in PCA
- They are used in LDA, not PCA
In PCA, eigenvectors represent the directions in which the data varies the most, while the corresponding eigenvalues give the amount of variance in those directions. These are obtained from the covariance matrix of the original data, and the eigenvectors with the largest eigenvalues become the principal components that capture the most significant patterns in the data.
What is the mathematical relationship between Eigenvalues and Eigenvectors in PCA?
- Eigenvalues are scalar multiples of eigenvectors
- They are inversely related
- They are the same
- They are unrelated
In PCA, eigenvalues and eigenvectors have a mathematical relationship where the eigenvalues are scalar multiples of the eigenvectors. They form the eigenvalue-eigenvector equation for the covariance matrix.
What could be the possible consequence of choosing a very small value of K in the KNN algorithm?
- Increased efficiency
- Overfitting
- Reduced complexity
- Underfitting
Choosing a very small value of K in the KNN algorithm can lead to overfitting, where the model becomes too sensitive to noise in the training data.
Imagine you're using DBSCAN for spatial data clustering, but the clusters are not forming as expected. What steps would you take to analyze and fix the situation?
- All of the above
- Analyze feature scaling; Adjust Epsilon and MinPts
- Apply a linear transformation to the data
- Increase the dimensionality of the data
Clustering spatial data requires a careful analysis of the scale of the features, as well as appropriate tuning of Epsilon and MinPts. Feature scaling ensures that distances are comparable across dimensions. Adjusting Epsilon and MinPts tailors the algorithm to the specific density and size characteristics of the clusters in the spatial data.
In the context of model evaluation, Bootstrapping can be used to assess the _________ of a statistical estimator or a machine learning model.
- bias
- robustness
- stability
- variance
In the context of model evaluation, Bootstrapping can be used to assess the stability of a statistical estimator or a machine learning model. By repeatedly resampling with replacement and observing the changes in estimates, one can gain insights into the stability and reliability of the model or estimator.
You've applied PCA but the variance explained by the first few components is very low. What could be the underlying issue and how might you remedy it?
- The data has no variance, so PCA is not applicable
- The data is not centered, so you should center it before applying PCA
- The data is too complex for PCA, so you should switch algorithms
- The eigenvalues have been miscalculated and you should recalculate them
If the variance explained by the first few components is very low, it may be because the data is not centered. Centering the data by subtracting the mean is a necessary preprocessing step for PCA.
What are the main types of Machine Learning?
- Reinforcement, Unsupervised
- Supervised, Semi-supervised
- Supervised, Unsupervised
- Supervised, Unsupervised, Reinforcement
The main types of Machine Learning are Supervised Learning (learning with labeled data), Unsupervised Learning (learning without labeled data), and Reinforcement Learning (learning by interacting with an environment). These types facilitate different learning processes and are applied in various domains.
In classification, the ________ metric is often used to evaluate the balance between precision and recall.
- Accuracy
- F1 Score
- Mean Squared Error
- R-squared
The F1 Score is the harmonic mean of precision and recall, providing a single metric that balances the trade-off between these two important metrics.