What is the “oracle” that serves as input to a constraint based search algorithm?
Answer: the oracle typically refers to a black-box function that provides answers to queries made by the algorithm.
Critique: this answer still doesn’t make much sense, I can create algorithms that can do anything with such an oracle.
How does the PC algorithm work?
Answer: PC algorithm performs a 3-step operations
- Connect all variables to construct a complete undirected graph
- Remove edges using conditional independence tests
- Orient edges based on certain rules and patterns
The last two steps are where “constraints” are used: conditional independence and edge orientation rules.
How do constraint based searches compare to the Bayesian approach to causal discovery and the scoring approach (e.g., Bayesian information criterion)?
Answer: I read the ChatGPT’s answer. But I don’t fully understand that. It’s no need to fully understand for now.
How is conditional independence statistically tested?
Answer: this uses the general hypothesis testing framework where null hypothesis and alternative hypothesis are specified and tests are performed to determine whether the observed outcomes are due to random chances or effects of variables (statistical significance).
Conditional independence are tests with different methods for different kinds of data. For example,
- Correlation Coefficients: For continuous data.
- Chi-Square Tests: For categorical data.
What does it mean for a statistical test to be powerful?
Answer: It means the probability the test correctly rejects a false null hypothesis. Power is influenced by sample size, variability within the data, significance level and effect size.
What is the problem of multiple testing?
Answer: it arises when multiple hypotheses are tested simultaneously.
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