Actually if A --> B --> C and I observe some function of (A, B, C) it’s just not generally the case that my beliefs about A and C are conditionally independent given my beliefs about B (e.g. suppose I observe A+C). This just makes it even easier to avoid the bad function in this case, but means I want to be more careful about the definition of the case to ensure that it’s actually difficult before concluding that this kid of conditional independence structure is potentially useful.
Sometimes we figure out the conditional in/dependence by looking at the data. It may not match common sense intuition, but if your model takes that into account and gives better results, then they just keep the conditional independence in there. You are only able to do with what you have. Lack of attributes may force you to rely on other dependencies for better predictions.
Actually if A --> B --> C and I observe some function of (A, B, C) it’s just not generally the case that my beliefs about A and C are conditionally independent given my beliefs about B (e.g. suppose I observe A+C). This just makes it even easier to avoid the bad function in this case, but means I want to be more careful about the definition of the case to ensure that it’s actually difficult before concluding that this kid of conditional independence structure is potentially useful.
Sometimes we figure out the conditional in/dependence by looking at the data. It may not match common sense intuition, but if your model takes that into account and gives better results, then they just keep the conditional independence in there. You are only able to do with what you have. Lack of attributes may force you to rely on other dependencies for better predictions.