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This is conditioning in the sense of conditional probability. The idea is that the authors have some "standard physically-inspired features". They are splitting the data up into bins based on the values of these features, and then training a model for each bin. They are then examining the differences between the models. Usually this is done to learn ...

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Perhaps the shortest answer to this question is that Bayes' Theorem itself allows us to easily change the direction of a conditional probability: $$P(A|B) = \frac{P(B|A)P(A)}{P(B)}$$ So if you have $P(B|A)$, $P(A)$, and $P(B)$, we can determine $P(A|B)$, and similarly you can determine $P(B|A)$ from $P(A|B)$, $P(B)$ and $P(A)$. Just by looking at $P(B|A)$...

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But the conditional probability is clearly not symmetric and captures directed relationships. One needs to consider the kinds of directed relationships that is captured by conditional probability. It surely does capture some kind of association or dependence which could be directed. At the same time, it is not right to say that it surely captures the causal ...

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A probability distribution in ML is the same as a probability distribution elsewhere. A probability distribution (or probability function, or probability mass function, or probability density function) is any function that accepts as input elements of some specific set $x \in X$, and produces as output, real-valued numbers between 0 and 1 (inclusive), such ...

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This is the definition of conditional probability + Total probability decomposition formula: $p(y|x) = \frac{p(y,x}{p(x)} = \frac{p(x,y)}{\sum_{y'}p(x,y')}$. The idea is to use some unsupervised learning algorithm to learn the distribution $p(x,y)$ for every possible value of $y$, and by using the previous formula you can find $p(y|x)$.

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Random variables You do not necessarily need to understand the concept of a random variable (r.v.) to understand the concept of a probability distribution, but the concept of a random variable is strictly connected to the concept of a probability distribution (given that each random variable has an associated probability distribution), so, before proceeding,...

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