I'm reading this article and I'm not sure to understand this equation: $b=Pr(y|h)$ where $y$ is, according to the article, "a 52-dimension one-hot vector encoding [the player $y$] cards" (page 5, Problem Setup). I guess the authors mean $y$ is a vector of 52 elements with 13 of them are 1 and the others are 0.
$h$ is a 52x2 matrix. I'm not sure what is $b$.
According to my knowledge, $b$ is the probability distribution over a vector with $\binom{52}{13}$ possible combinations so $b$ should have $\binom{52}{13}$ elements.
But, later in the article (page 5, Model Architecture), I can read that we can add $b$ to $x$ ($x$ is a 52 dimension vector). So I guess now $b$ is also a 52 dimension vector with xn is $P(y_{n} = 1)$.
My questions are: do I misunderstand the equation? Or the authors of the article wanted to simplify the probability distribution? What is $b$?
Note: I don't want to know what $b$ represents but I want to know how $b$ is mathematically represented.
Note 2: The point of the article is to use a POMDP to create a bridge bidding system. So, $b$ is the belief of the player, $y$ is the unobserved environment state and $h$ is the history of the bids.