Your regression model's MSE is high, but the MAE is relatively low. What might this indicate about the model's error distribution, and how would you investigate further?
- Model has consistent errors; needs more training
- Model has frequent large errors; needs regularization
- Model has many small errors, but some significant outliers; analyze residuals
- Model is perfect; no further investigation required
A high Mean Squared Error (MSE) with a relatively low Mean Absolute Error (MAE) indicates that the model likely has many small errors but also some significant outliers. The squaring in MSE amplifies the effect of these outliers. Analyzing the residuals (the differences between predicted and actual values) can help to understand the nature of these errors and possibly guide improvements in the model.
___________ is a popular method for dimensionality reduction that transforms the data into a new coordinate system where the variance is maximized.
- Feature Selection
- Linear Discriminant Analysis
- Principal Component Analysis
- t-SNE
Principal Component Analysis (PCA) is a method that transforms data into a new coordinate system where the variance is maximized. It's a popular technique for reducing dimensions while preserving as much information as possible in the reduced space.
Can you explain the concept of Semi-Supervised Learning and how it bridges the gap between supervised and unsupervised learning?
- Combines labeled & unlabeled data
- Uses only labeled data
- Uses only unlabeled data
- Uses rewards and penalties
Semi-Supervised Learning bridges the gap by combining both labeled and unlabeled data, utilizing strengths of both supervised and unsupervised.
Cross-Validation divides the dataset into "k" subsets, or _______, where one subset is used as the validation set, and the rest are used for training.
- clusters
- folds
- groups
- partitions
Cross-Validation involves dividing the dataset into "k" subsets, referred to as "folds." One fold is used as the validation set, while the remaining are used for training. This process is repeated k times, with each fold being used exactly once as the validation set.
How does Principal Component Analysis (PCA) work as a method of dimensionality reduction?
- By classifying features
- By maximizing variance
- By minimizing variance
- By selecting principal features
Principal Component Analysis (PCA) works by transforming the original features into a new set of uncorrelated features called principal components. It does so by maximizing the variance along these new axes, meaning that the first principal component explains the most variance, the second explains the second most, and so on.
What are some common challenges in high-dimensional data that dimensionality reduction aims to address?
- All of the above
- Computational efficiency
- Curse of dimensionality
- Overfitting
Dimensionality reduction aims to address several challenges in high-dimensional data, including the curse of dimensionality (where distance measures lose meaning), overfitting (where models fit noise), and computational efficiency (since fewer dimensions require less computing resources).
Interaction effects in Multiple Linear Regression can be represented by adding a ___________ term for the interacting variables.
- additive
- divided
- multiplied
- subtractive
Interaction effects are represented by adding a multiplied term for the interacting variables in the model. It captures the combined effect that is not simply additive and reflects how the response variable changes when both interacting variables change together.
In Polynomial Regression, a higher degree can lead to ________, where the model learns the noise in the data.
- accuracy
- overfitting
- stability
- underfitting
A higher degree in Polynomial Regression may cause the model to fit the noise in the data, leading to overfitting.
If you are facing multicollinearity in your regression model, how can dimensionality reduction techniques be employed to mitigate this issue?
- Increase the number of observations
- Apply PCA and use principal components
- Add interaction terms
- Use a non-linear regression model
Multicollinearity arises when features are highly correlated with each other, and it can be mitigated by applying PCA. By transforming the data into principal components, which are uncorrelated, the multicollinearity problem is resolved. Using the principal components in the regression model ensures that the feature relationships are captured without redundancy. Other options do not address the issue of multicollinearity directly.
Poor initialization of centroids in K-Means clustering may lead to __________, affecting the quality of the clustering.
- Convergence to global maxima
- Local minima
- Noise
- Overfitting
Poor initialization of centroids can lead the K-Means algorithm to converge to local minima, affecting the quality of the clustering. Local minima occur when the algorithm finds a suboptimal clustering solution.