Notation of a probability distribution over a vector
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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.
probability-distributions vectors
asked Dec 30 '18 at 9:11
PierrePierre
1108
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add a comment |
$begingroup$
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.
probability-distributions vectors
asked Dec 30 '18 at 9:11
PierrePierre
1108
$endgroup$
$begingroup$
Vectors have a length, but not a dimension.
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– Wuestenfux
Dec 30 '18 at 9:15
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@Wuestenfux I'm surprised because it's written, about the $y$ vector: "is a 52-dimension one-hot vector encoding the 13 cards [of the player y]".
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– Pierre
Dec 30 '18 at 9:19
3
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@Wuestenfux Saying "an $n$-dimensional vector" is absolutely standard.
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– Clement C.
Dec 30 '18 at 9:19
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Thanks. I think it might help to cite some equations or page numbers in the article so that readers can find the relevant passages a little more quickly.
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– littleO
Dec 30 '18 at 10:39
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@littleO It's done.
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– Pierre
Dec 30 '18 at 10:49
add a comment |
$begingroup$
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.
probability-distributions vectors
asked Dec 30 '18 at 9:11
PierrePierre
1108
$endgroup$
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.
probability-distributions vectors
probability-distributions vectors
asked Dec 30 '18 at 9:11
PierrePierre
1108
asked Dec 30 '18 at 9:11
PierrePierre
1108
edited Dec 30 '18 at 11:50
Pierre
asked Dec 30 '18 at 9:11
PierrePierre
1108
asked Dec 30 '18 at 9:11
PierrePierre
1108
asked Dec 30 '18 at 9:11
PierrePierre
1108
1108
$begingroup$
Vectors have a length, but not a dimension.
$endgroup$
– Wuestenfux
Dec 30 '18 at 9:15
$begingroup$
@Wuestenfux I'm surprised because it's written, about the $y$ vector: "is a 52-dimension one-hot vector encoding the 13 cards [of the player y]".
$endgroup$
– Pierre
Dec 30 '18 at 9:19
3
$begingroup$
@Wuestenfux Saying "an $n$-dimensional vector" is absolutely standard.
$endgroup$
– Clement C.
Dec 30 '18 at 9:19
$begingroup$
Thanks. I think it might help to cite some equations or page numbers in the article so that readers can find the relevant passages a little more quickly.
$endgroup$
– littleO
Dec 30 '18 at 10:39
$begingroup$
@littleO It's done.
$endgroup$
– Pierre
Dec 30 '18 at 10:49
add a comment |
$begingroup$
Vectors have a length, but not a dimension.
$endgroup$
– Wuestenfux
Dec 30 '18 at 9:15
$begingroup$
@Wuestenfux I'm surprised because it's written, about the $y$ vector: "is a 52-dimension one-hot vector encoding the 13 cards [of the player y]".
$endgroup$
– Pierre
Dec 30 '18 at 9:19
3
$begingroup$
@Wuestenfux Saying "an $n$-dimensional vector" is absolutely standard.
$endgroup$
– Clement C.
Dec 30 '18 at 9:19
$begingroup$
Thanks. I think it might help to cite some equations or page numbers in the article so that readers can find the relevant passages a little more quickly.
$endgroup$
– littleO
Dec 30 '18 at 10:39
$begingroup$
@littleO It's done.
$endgroup$
– Pierre
Dec 30 '18 at 10:49
$begingroup$
Vectors have a length, but not a dimension.
$endgroup$
– Wuestenfux
Dec 30 '18 at 9:15
$begingroup$
Vectors have a length, but not a dimension.
$endgroup$
– Wuestenfux
Dec 30 '18 at 9:15
$begingroup$
@Wuestenfux I'm surprised because it's written, about the $y$ vector: "is a 52-dimension one-hot vector encoding the 13 cards [of the player y]".
$endgroup$
– Pierre
Dec 30 '18 at 9:19
$begingroup$
@Wuestenfux I'm surprised because it's written, about the $y$ vector: "is a 52-dimension one-hot vector encoding the 13 cards [of the player y]".
$endgroup$
– Pierre
Dec 30 '18 at 9:19
3
3
$begingroup$
@Wuestenfux Saying "an $n$-dimensional vector" is absolutely standard.
$endgroup$
– Clement C.
Dec 30 '18 at 9:19
$begingroup$
@Wuestenfux Saying "an $n$-dimensional vector" is absolutely standard.
$endgroup$
– Clement C.
Dec 30 '18 at 9:19
$begingroup$
Thanks. I think it might help to cite some equations or page numbers in the article so that readers can find the relevant passages a little more quickly.
$endgroup$
– littleO
Dec 30 '18 at 10:39
$begingroup$
Thanks. I think it might help to cite some equations or page numbers in the article so that readers can find the relevant passages a little more quickly.
$endgroup$
– littleO
Dec 30 '18 at 10:39
$begingroup$
@littleO It's done.
$endgroup$
– Pierre
Dec 30 '18 at 10:49
$begingroup$
@littleO It's done.
$endgroup$
– Pierre
Dec 30 '18 at 10:49
add a comment |
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$begingroup$
Vectors have a length, but not a dimension.
$endgroup$
– Wuestenfux
Dec 30 '18 at 9:15
$begingroup$
@Wuestenfux I'm surprised because it's written, about the $y$ vector: "is a 52-dimension one-hot vector encoding the 13 cards [of the player y]".
$endgroup$
– Pierre
Dec 30 '18 at 9:19
3
$begingroup$
@Wuestenfux Saying "an $n$-dimensional vector" is absolutely standard.
$endgroup$
– Clement C.
Dec 30 '18 at 9:19
$begingroup$
Thanks. I think it might help to cite some equations or page numbers in the article so that readers can find the relevant passages a little more quickly.
$endgroup$
– littleO
Dec 30 '18 at 10:39
$begingroup$
@littleO It's done.
$endgroup$
– Pierre
Dec 30 '18 at 10:49