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Related Questions
- Can you explain the relationship between sampling complexity and the dimensionality of the search space?
- How do the curse of dimensionality and the increase in noise affect the accuracy of uncertainty sampling in high-dimensional spaces?
- Can you discuss the theoretical implications of using probabilistic embeddings to reduce dimensionality for uncertainty sampling?
- What are the potential benefits and limitations of using sparse or low-rank models to approximate high-dimensional probability distributions?
- Can you explain the interplay between data density, sampling efficiency, and optimization algorithms in uncertainty sampling for high-dimensional problems?
- How does the choice of uncertainty metric (e.g., variance, entropy, or expected information gain) impact the effectiveness of uncertainty sampling in high-dimensional spaces?
- Can you discuss the connections between uncertainty sampling and Bayesian optimization, particularly in high-dimensional spaces with expensive evaluations?
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