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Made comments in headers for Python simple functions more python like (referring to numpy arrays etc)

This commit is contained in:
Joseph Lizier 2024-08-14 09:25:36 +10:00
parent 6b2cf5c69c
commit 1db1c3ac8c
9 changed files with 100 additions and 93 deletions
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2
course/Module01-Entropy/PythonSimpleFunctions/Module_1_notebook.ipynb
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@ -206,7 +206,7 @@
"Computes the Shannon entropy for a probability distribution p.\n",
"\n",
"Inputs:\n",
"- p - (array which much sum to 1) - a probability distribution to compute the Shannon info content for\n",
"- p - (numpy array or list which much sum to 1) - a probability distribution to compute the Shannon info content for\n",
"\n",
"Outputs:\n",
"- result - Shannon entropy of the probability distribution p\n",

32
course/Module01-Entropy/PythonSimpleFunctions/Module_2_notebook.ipynb
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@ -74,13 +74,13 @@
"X from samples x_n.\n",
"\n",
"Inputs:\n",
"- xn - samples of outcomes x.\n",
" xn is a column vector, e.g. xn = [0;0;1;0;1;0;1;1;1;0] for a binary variable.\n",
"- xn - samples of outcomes x as a numpy array or a list,\n",
" e.g. xn = [0,0,1,0,1,0,1,1,1,0] for a binary variable.\n",
"\n",
"Outputs:\n",
"- result - Shannon entropy over all outcomes\n",
"- symbols - list of unique samples\n",
"- probabilities - probabilities for each sample\n",
"- symbols - numpy array of unique samples\n",
"- probabilities - numpy array of probabilities for each sample\n",
"\n",
"Copyright (C) 2020-, Julio Correa, Joseph T. Lizier\n",
"Distributed under GNU General Public License v3\n",
@ -199,10 +199,11 @@
"\n",
"Inputs:\n",
"- p - probability distribution function over all outcome vectors x.\n",
" p is a matrix over all combinations of the sub-variables of x,\n",
"where p(1,3) gives the probability of the first symbol of sub-variable\n",
" p is a numpy matrix (or list of lists) over all combinations of the sub-variables of x,\n",
"where p[0,2] gives the probability of the first symbol of sub-variable\n",
"x1 co-occuring with the third symbol of sub-variable x2.\n",
" E.g. p = [0.2, 0.3; 0.1, 0.4]. The sum over p must be 1.\n",
" E.g. p = np.array([[0.2, 0.3], [0.1, 0.4]])\n",
" The sum over p must be 1.\n",
"\n",
"Outputs:\n",
"- result - joint Shannon entropy of the probability distribution p\n",
@ -275,7 +276,7 @@
"if they don't wish to join them outside of the call.\n",
"\n",
"Inputs:\n",
"- xn - matrix of samples of outcomes x. May be a 1D vector of samples\n",
"- xn - numpy matrix (or list of lists) of samples of outcomes x. May be a 1D vector of samples\n",
" (in which case yn is also supplied), or\n",
" a 2D matrix, where each row is a vector sample for a multivariate X\n",
" (in which case yn is not supplied).\n",
@ -284,8 +285,8 @@
"\n",
"Outputs:\n",
"- result - joint Shannon entropy over all samples\n",
"- symbols - list of unique joint vector samples\n",
"- probabilities - probabilities for each joint symbol\n",
"- symbols - numpy array of unique joint vector samples\n",
"- probabilities - numpy array of probabilities for each joint symbol\n",
"\n",
"Copyright (C) 2020-, Julio Correa, Joseph T. Lizier\n",
"Distributed under GNU General Public License v3\n",
@ -377,10 +378,11 @@
"\n",
"Inputs:\n",
"- p - 2D probability distribution function over all outcomes (x,y).\n",
" p is a matrix over all combinations of x and y,\n",
"where p(1,3) gives the probability of the first symbol of variable\n",
" p is a numpy matrix over all combinations of x and y,\n",
"where p[0, 2] gives the probability of the first symbol of variable\n",
"x co-occuring with the third symbol of variable y.\n",
" E.g. p = [0.2, 0.3; 0.1, 0.4]. The sum over p must be 1.\n",
" E.g. p = nump.array([[0.2, 0.3], [0.1, 0.4]]).\n",
" The sum over p must be 1.\n",
"\n",
"Outputs:\n",
"- result - conditional Shannon entropy of X given Y\n",
@ -476,9 +478,9 @@
"variable X, given samples yn of a random variable Y.\n",
"\n",
"Inputs:\n",
"- xn - matrix of samples of outcomes x. May be a 1D vector of samples, or\n",
"- xn - numpy matrix (or list of lists) of samples of outcomes x. May be a 1D vector of samples, or\n",
" a 2D matrix, where each row is a vector sample for a multivariate X.\n",
"- yn - matrix of samples of outcomes x. May be a 1D vector of samples, or\n",
"- yn - numpy matrix (or list of lists) of samples of outcomes x. May be a 1D vector of samples, or\n",
" a 2D matrix, where each row is a vector sample for a multivariate Y.\n",
" Must have the same number of rows as X.\n",
"\n",

11
course/Module01-Entropy/PythonSimpleFunctions/Module_3_notebook.ipynb
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@ -100,10 +100,11 @@
"\n",
"Inputs:\n",
"- p - 2D probability distribution function over all outcomes (x,y).\n",
" p is a matrix over all combinations of x and y,\n",
"where p(1,3) gives the probability of the first symbol of variable\n",
" p is a numpy matrix (or list of lists) over all combinations of x and y,\n",
"where p[0,2] gives the probability of the first symbol of variable\n",
"x co-occuring with the third symbol of variable y.\n",
" E.g. p = [0.2, 0.3; 0.1, 0.4]. The sum over p must be 1.\n",
" E.g. p = np.array([[0.2, 0.3], [0.1, 0.4]]).\n",
" The sum over p must be 1.\n",
"\n",
"Outputs:\n",
"- result - mutual information of X with Y\n",
@ -210,9 +211,9 @@
"variable X with samples yn of a random variable Y.\n",
"\n",
"Inputs:\n",
"- xn - matrix of samples of outcomes x. May be a 1D vector of samples, or\n",
"- xn - numpy matrix of samples of outcomes x. May be a 1D vector of samples, or\n",
" a 2D matrix, where each row is a vector sample for a multivariate X.\n",
"- yn - matrix of samples of outcomes x. May be a 1D vector of samples, or\n",
"- yn - numpy matrix of samples of outcomes x. May be a 1D vector of samples, or\n",
" a 2D matrix, where each row is a vector sample for a multivariate Y.\n",
" Must have the same number of rows as X.\n",
"\n",

6
course/Module01-Entropy/PythonSimpleFunctions/Module_4_notebook.ipynb
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@ -75,12 +75,12 @@
"samples zn of a random variable Z.\n",
"\n",
"Inputs:\n",
"- xn - matrix of samples of outcomes x. May be a 1D vector of samples, or\n",
"- xn - numpy matrix of samples of outcomes x. May be a 1D vector of samples, or\n",
" a 2D matrix, where each row is a vector sample for a multivariate X.\n",
"- yn - matrix of samples of outcomes y. May be a 1D vector of samples, or\n",
"- yn - numpy matrix of samples of outcomes y. May be a 1D vector of samples, or\n",
" a 2D matrix, where each row is a vector sample for a multivariate Y.\n",
" Must have the same number of rows as X.\n",
"- zn - matrix of samples of outcomes z. May be a 1D vector of samples, or\n",
"- zn - numpy matrix of samples of outcomes z. May be a 1D vector of samples, or\n",
" a 2D matrix, where each row is a vector sample for a multivariate Z\n",
" which will be conditioned on.\n",
" Must have the same number of rows as X.\n",

10
course/Module01-Entropy/PythonSimpleFunctions/completed/Module_1_notebook_solutions.ipynb
View File

@ -247,7 +247,7 @@
"Computes the Shannon entropy for a probability distribution p.\n",
"\n",
"Inputs:\n",
"- p - (array which much sum to 1) - a probability distribution to compute the Shannon info content for\n",
"- p - (numpy array or list which much sum to 1) - a probability distribution to compute the Shannon info content for\n",
"\n",
"Outputs:\n",
"- result - Shannon entropy of the probability distribution p\n",
@ -303,9 +303,9 @@
"name": "stderr",
"output_type": "stream",
"text": [
"/tmp/ipykernel_617811/3406804068.py:20: RuntimeWarning: divide by zero encountered in log2\n",
"/tmp/ipykernel_1348680/3406804068.py:20: RuntimeWarning: divide by zero encountered in log2\n",
" return -np.log2(p)\n",
"/tmp/ipykernel_617811/1887577405.py:28: RuntimeWarning: invalid value encountered in multiply\n",
"/tmp/ipykernel_1348680/253220426.py:28: RuntimeWarning: invalid value encountered in multiply\n",
" weightedShannonInfos = p*(infocontent(p))\n"
]
}
@ -349,9 +349,9 @@
"name": "stderr",
"output_type": "stream",
"text": [
"/tmp/ipykernel_617811/3406804068.py:20: RuntimeWarning: divide by zero encountered in log2\n",
"/tmp/ipykernel_1348680/3406804068.py:20: RuntimeWarning: divide by zero encountered in log2\n",
" return -np.log2(p)\n",
"/tmp/ipykernel_617811/1887577405.py:28: RuntimeWarning: invalid value encountered in multiply\n",
"/tmp/ipykernel_1348680/253220426.py:28: RuntimeWarning: invalid value encountered in multiply\n",
" weightedShannonInfos = p*(infocontent(p))\n"
]
},

50
course/Module01-Entropy/PythonSimpleFunctions/completed/Module_2_notebook_solutions.ipynb
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@ -74,13 +74,13 @@
"X from samples x_n.\n",
"\n",
"Inputs:\n",
"- xn - samples of outcomes x.\n",
" xn is a column vector, e.g. xn = [0;0;1;0;1;0;1;1;1;0] for a binary variable.\n",
"- xn - samples of outcomes x as a numpy array or a list,\n",
" e.g. xn = [0,0,1,0,1,0,1,1,1,0] for a binary variable.\n",
"\n",
"Outputs:\n",
"- result - Shannon entropy over all outcomes\n",
"- symbols - list of unique samples\n",
"- probabilities - probabilities for each sample\n",
"- symbols - numpy array of unique samples\n",
"- probabilities - numpy array of probabilities for each sample\n",
"\n",
"Copyright (C) 2020-, Julio Correa, Joseph T. Lizier\n",
"Distributed under GNU General Public License v3\n",
@ -136,8 +136,7 @@
"name": "stdout",
"output_type": "stream",
"text": [
"1.0\n",
"2.0\n"
"1.0\n"
]
}
],
@ -146,8 +145,7 @@
"(result, symbols, probabilities) = entropyempirical([0,0,1,1])\n",
"print( result )\n",
"# Other cases:\n",
"(result, symbols, probabilities) = entropyempirical([0,0,1,1,2,2,3,3])\n",
"print( result )\n"
"(result, symbols, probabilities) = entropyempirical([0,0,1,1,2,2,3,3])\n"
]
},
{
@ -192,9 +190,9 @@
"name": "stdout",
"output_type": "stream",
"text": [
"1.0\n",
"0.9987271686073539\n",
"1.9969914126082884\n"
"0.9709505944546686\n",
"0.9999884584088952\n",
"1.999117638235098\n"
]
}
],
@ -244,10 +242,11 @@
"\n",
"Inputs:\n",
"- p - probability distribution function over all outcome vectors x.\n",
" p is a matrix over all combinations of the sub-variables of x,\n",
"where p(1,3) gives the probability of the first symbol of sub-variable\n",
" p is a numpy matrix (or list of lists) over all combinations of the sub-variables of x,\n",
"where p[0,2] gives the probability of the first symbol of sub-variable\n",
"x1 co-occuring with the third symbol of sub-variable x2.\n",
" E.g. p = [0.2, 0.3; 0.1, 0.4]. The sum over p must be 1.\n",
" E.g. p = np.array([[0.2, 0.3], [0.1, 0.4]])\n",
" The sum over p must be 1.\n",
"\n",
"Outputs:\n",
"- result - joint Shannon entropy of the probability distribution p\n",
@ -294,9 +293,9 @@
"name": "stderr",
"output_type": "stream",
"text": [
"/home/joseph/Dropbox/Work/Teaching/USyd/CSYS5030-InfoTheoryAndSelfOrg/Lectures/Module1-Entropy/PythonCode/completed/simpleinfotheory.py:23: RuntimeWarning: divide by zero encountered in log2\n",
"/home/joseph/JIDT/course/course/Module01-Entropy/PythonSimpleFunctions/completed/simpleinfotheory.py:23: RuntimeWarning: divide by zero encountered in log2\n",
" return -np.log2(p)\n",
"/home/joseph/Dropbox/Work/Teaching/USyd/CSYS5030-InfoTheoryAndSelfOrg/Lectures/Module1-Entropy/PythonCode/completed/simpleinfotheory.py:48: RuntimeWarning: invalid value encountered in multiply\n",
"/home/joseph/JIDT/course/course/Module01-Entropy/PythonSimpleFunctions/completed/simpleinfotheory.py:52: RuntimeWarning: invalid value encountered in multiply\n",
" weightedShannonInfos = p*(infocontent(p))\n"
]
}
@ -342,7 +341,7 @@
"if they don't wish to join them outside of the call.\n",
"\n",
"Inputs:\n",
"- xn - matrix of samples of outcomes x. May be a 1D vector of samples\n",
"- xn - numpy matrix (or list of lists) of samples of outcomes x. May be a 1D vector of samples\n",
" (in which case yn is also supplied), or\n",
" a 2D matrix, where each row is a vector sample for a multivariate X\n",
" (in which case yn is not supplied).\n",
@ -351,8 +350,8 @@
"\n",
"Outputs:\n",
"- result - joint Shannon entropy over all samples\n",
"- symbols - list of unique joint vector samples\n",
"- probabilities - probabilities for each joint symbol\n",
"- symbols - numpy array of unique joint vector samples\n",
"- probabilities - numpy array of probabilities for each joint symbol\n",
"\n",
"Copyright (C) 2020-, Julio Correa, Joseph T. Lizier\n",
"Distributed under GNU General Public License v3\n",
@ -407,7 +406,7 @@
"text": [
"2.0\n",
"1.0\n",
"2.997035867545411\n"
"2.996212691342311\n"
]
}
],
@ -459,10 +458,11 @@
"\n",
"Inputs:\n",
"- p - 2D probability distribution function over all outcomes (x,y).\n",
" p is a matrix over all combinations of x and y,\n",
"where p(1,3) gives the probability of the first symbol of variable\n",
" p is a numpy matrix over all combinations of x and y,\n",
"where p[0, 2] gives the probability of the first symbol of variable\n",
"x co-occuring with the third symbol of variable y.\n",
" E.g. p = [0.2, 0.3; 0.1, 0.4]. The sum over p must be 1.\n",
" E.g. p = nump.array([[0.2, 0.3], [0.1, 0.4]]).\n",
" The sum over p must be 1.\n",
"\n",
"Outputs:\n",
"- result - conditional Shannon entropy of X given Y\n",
@ -582,9 +582,9 @@
"variable X, given samples yn of a random variable Y.\n",
"\n",
"Inputs:\n",
"- xn - matrix of samples of outcomes x. May be a 1D vector of samples, or\n",
"- xn - numpy matrix (or list of lists) of samples of outcomes x. May be a 1D vector of samples, or\n",
" a 2D matrix, where each row is a vector sample for a multivariate X.\n",
"- yn - matrix of samples of outcomes x. May be a 1D vector of samples, or\n",
"- yn - numpy matrix (or list of lists) of samples of outcomes x. May be a 1D vector of samples, or\n",
" a 2D matrix, where each row is a vector sample for a multivariate Y.\n",
" Must have the same number of rows as X.\n",
"\n",

15
course/Module01-Entropy/PythonSimpleFunctions/completed/Module_3_notebook_solutions.ipynb
View File

@ -100,10 +100,11 @@
"\n",
"Inputs:\n",
"- p - 2D probability distribution function over all outcomes (x,y).\n",
" p is a matrix over all combinations of x and y,\n",
"where p(1,3) gives the probability of the first symbol of variable\n",
" p is a numpy matrix (or list of lists) over all combinations of x and y,\n",
"where p[0,2] gives the probability of the first symbol of variable\n",
"x co-occuring with the third symbol of variable y.\n",
" E.g. p = [0.2, 0.3; 0.1, 0.4]. The sum over p must be 1.\n",
" E.g. p = np.array([[0.2, 0.3], [0.1, 0.4]]).\n",
" The sum over p must be 1.\n",
"\n",
"Outputs:\n",
"- result - mutual information of X with Y\n",
@ -172,9 +173,9 @@
"name": "stderr",
"output_type": "stream",
"text": [
"/home/joseph/Dropbox/Work/Teaching/USyd/CSYS5030-InfoTheoryAndSelfOrg/Lectures/Module1-Entropy/PythonCode/completed/simpleinfotheory.py:23: RuntimeWarning: divide by zero encountered in log2\n",
"/home/joseph/JIDT/course/course/Module01-Entropy/PythonSimpleFunctions/completed/simpleinfotheory.py:23: RuntimeWarning: divide by zero encountered in log2\n",
" return -np.log2(p)\n",
"/home/joseph/Dropbox/Work/Teaching/USyd/CSYS5030-InfoTheoryAndSelfOrg/Lectures/Module1-Entropy/PythonCode/completed/simpleinfotheory.py:48: RuntimeWarning: invalid value encountered in multiply\n",
"/home/joseph/JIDT/course/course/Module01-Entropy/PythonSimpleFunctions/completed/simpleinfotheory.py:52: RuntimeWarning: invalid value encountered in multiply\n",
" weightedShannonInfos = p*(infocontent(p))\n"
]
}
@ -255,9 +256,9 @@
"variable X with samples yn of a random variable Y.\n",
"\n",
"Inputs:\n",
"- xn - matrix of samples of outcomes x. May be a 1D vector of samples, or\n",
"- xn - numpy matrix of samples of outcomes x. May be a 1D vector of samples, or\n",
" a 2D matrix, where each row is a vector sample for a multivariate X.\n",
"- yn - matrix of samples of outcomes x. May be a 1D vector of samples, or\n",
"- yn - numpy matrix of samples of outcomes x. May be a 1D vector of samples, or\n",
" a 2D matrix, where each row is a vector sample for a multivariate Y.\n",
" Must have the same number of rows as X.\n",
"\n",

14
course/Module01-Entropy/PythonSimpleFunctions/completed/Module_4_notebook_solutions.ipynb
View File

@ -75,12 +75,12 @@
"samples zn of a random variable Z.\n",
"\n",
"Inputs:\n",
"- xn - matrix of samples of outcomes x. May be a 1D vector of samples, or\n",
"- xn - numpy matrix of samples of outcomes x. May be a 1D vector of samples, or\n",
" a 2D matrix, where each row is a vector sample for a multivariate X.\n",
"- yn - matrix of samples of outcomes y. May be a 1D vector of samples, or\n",
"- yn - numpy matrix of samples of outcomes y. May be a 1D vector of samples, or\n",
" a 2D matrix, where each row is a vector sample for a multivariate Y.\n",
" Must have the same number of rows as X.\n",
"- zn - matrix of samples of outcomes z. May be a 1D vector of samples, or\n",
"- zn - numpy matrix of samples of outcomes z. May be a 1D vector of samples, or\n",
" a 2D matrix, where each row is a vector sample for a multivariate Z\n",
" which will be conditioned on.\n",
" Must have the same number of rows as X.\n",
@ -151,10 +151,10 @@
"0.0\n",
"1.0\n",
"1.0\n",
"I(X;Y) = 0.0004 bits\n",
"I(Z;Y) = 0.0004 bits\n",
"I(X;Y|Z) = 0.9995 bits\n",
"I(Z;Y|X) = 0.9995 bits\n"
"I(X;Y) = 0.0001 bits\n",
"I(Z;Y) = 0.0013 bits\n",
"I(X;Y|Z) = 0.9987 bits\n",
"I(Z;Y|X) = 0.9998 bits\n"
]
}
],

53
course/Module01-Entropy/PythonSimpleFunctions/completed/simpleinfotheory.py
View File

@ -26,7 +26,7 @@ def infocontent(p):
Computes the Shannon entropy for a probability distribution p.
Inputs:
- p - (array which much sum to 1) - a probability distribution to compute the Shannon info content for
- p - (numpy array or list which much sum to 1) - a probability distribution to compute the Shannon info content for
Outputs:
- result - Shannon entropy of the probability distribution p
@ -62,13 +62,13 @@ Computes the Shannon entropy over all outcomes x of a random variable
X from samples x_n.
Inputs:
- xn - samples of outcomes x.
xn is a column vector, e.g. xn = [0;0;1;0;1;0;1;1;1;0] for a binary variable.
- xn - samples of outcomes x as a numpy array or a list,
e.g. xn = [0,0,1,0,1,0,1,1,1,0] for a binary variable.
Outputs:
- result - Shannon entropy over all outcomes
- symbols - list of unique samples
- probabilities - probabilities for each sample
- symbols - numpy array of unique samples
- probabilities - numpy array of probabilities for each sample
Copyright (C) 2020-, Julio Correa, Joseph T. Lizier
Distributed under GNU General Public License v3
@ -116,10 +116,11 @@ vector x.
Inputs:
- p - probability distribution function over all outcome vectors x.
p is a matrix over all combinations of the sub-variables of x,
where p(1,3) gives the probability of the first symbol of sub-variable
p is a numpy matrix (or list of lists) over all combinations of the sub-variables of x,
where p[0,2] gives the probability of the first symbol of sub-variable
x1 co-occuring with the third symbol of sub-variable x2.
E.g. p = [0.2, 0.3; 0.1, 0.4]. The sum over p must be 1.
E.g. p = np.array([[0.2, 0.3], [0.1, 0.4]])
The sum over p must be 1.
Outputs:
- result - joint Shannon entropy of the probability distribution p
@ -146,7 +147,7 @@ variable X from sample vectors x_n. User can call with two such arguments
if they don't wish to join them outside of the call.
Inputs:
- xn - matrix of samples of outcomes x. May be a 1D vector of samples
- xn - numpy matrix (or list of lists) of samples of outcomes x. May be a 1D vector of samples
(in which case yn is also supplied), or
a 2D matrix, where each row is a vector sample for a multivariate X
(in which case yn is not supplied).
@ -155,8 +156,8 @@ Inputs:
Outputs:
- result - joint Shannon entropy over all samples
- symbols - list of unique joint vector samples
- probabilities - probabilities for each joint symbol
- symbols - numpy array of unique joint vector samples
- probabilities - numpy array of probabilities for each joint symbol
Copyright (C) 2020-, Julio Correa, Joseph T. Lizier
Distributed under GNU General Public License v3
@ -201,10 +202,11 @@ Probability matrix p(x,y) is given for each candidate outcome
Inputs:
- p - 2D probability distribution function over all outcomes (x,y).
p is a matrix over all combinations of x and y,
where p(1,3) gives the probability of the first symbol of variable
p is a numpy matrix over all combinations of x and y,
where p[0, 2] gives the probability of the first symbol of variable
x co-occuring with the third symbol of variable y.
E.g. p = [0.2, 0.3; 0.1, 0.4]. The sum over p must be 1.
E.g. p = nump.array([[0.2, 0.3], [0.1, 0.4]]).
The sum over p must be 1.
Outputs:
- result - conditional Shannon entropy of X given Y
@ -241,9 +243,9 @@ Computes the conditional Shannon entropy over all samples xn of a random
variable X, given samples yn of a random variable Y.
Inputs:
- xn - matrix of samples of outcomes x. May be a 1D vector of samples, or
- xn - numpy matrix (or list of lists) of samples of outcomes x. May be a 1D vector of samples, or
a 2D matrix, where each row is a vector sample for a multivariate X.
- yn - matrix of samples of outcomes x. May be a 1D vector of samples, or
- yn - numpy matrix (or list of lists) of samples of outcomes x. May be a 1D vector of samples, or
a 2D matrix, where each row is a vector sample for a multivariate Y.
Must have the same number of rows as X.
@ -291,10 +293,11 @@ Probability matrix p(x,y) is given for each candidate outcome
Inputs:
- p - 2D probability distribution function over all outcomes (x,y).
p is a matrix over all combinations of x and y,
where p(1,3) gives the probability of the first symbol of variable
p is a numpy matrix (or list of lists) over all combinations of x and y,
where p[0,2] gives the probability of the first symbol of variable
x co-occuring with the third symbol of variable y.
E.g. p = [0.2, 0.3; 0.1, 0.4]. The sum over p must be 1.
E.g. p = np.array([[0.2, 0.3], [0.1, 0.4]]).
The sum over p must be 1.
Outputs:
- result - mutual information of X with Y
@ -338,13 +341,13 @@ Computes the mutual information over all samples xn of a random
variable X with samples yn of a random variable Y.
Inputs:
- xn - matrix of samples of outcomes x. May be a 1D vector of samples, or
- xn - numpy matrix of samples of outcomes x. May be a 1D vector of samples, or
a 2D matrix, where each row is a vector sample for a multivariate X.
- yn - matrix of samples of outcomes x. May be a 1D vector of samples, or
- yn - numpy matrix of samples of outcomes x. May be a 1D vector of samples, or
a 2D matrix, where each row is a vector sample for a multivariate Y.
Must have the same number of rows as X.
Outputs:
Outputs: (There are additional outputs here in comparison to the solution notebook)
- result - mutual information of X with Y
- xySymbols - list of unique joint vector samples
- xyProbs - probabilities for each joint symbol
@ -463,12 +466,12 @@ variable X with samples yn of a random variable Y, conditioning on
samples zn of a random variable Z.
Inputs:
- xn - matrix of samples of outcomes x. May be a 1D vector of samples, or
- xn - numpy matrix of samples of outcomes x. May be a 1D vector of samples, or
a 2D matrix, where each row is a vector sample for a multivariate X.
- yn - matrix of samples of outcomes y. May be a 1D vector of samples, or
- yn - numpy matrix of samples of outcomes y. May be a 1D vector of samples, or
a 2D matrix, where each row is a vector sample for a multivariate Y.
Must have the same number of rows as X.
- zn - matrix of samples of outcomes z. May be a 1D vector of samples, or
- zn - numpy matrix of samples of outcomes z. May be a 1D vector of samples, or
a 2D matrix, where each row is a vector sample for a multivariate Z
which will be conditioned on.
Must have the same number of rows as X.