Probability
The Probability object provides methods for operating on univariate and bivariate probability distributions of discrete random variables X and Y. A probability distribution is specified by its probability mass functions (pmf) stored either as a "probability vector" for a univariate distribution or a "probability matrix" for a bivariate distribution. joint probability matrix: pxy(i, j) = P(X = x_i, Y = y_j) marginal probability vector: px(i) = P(X = x_i) conditional probability matrix: px_y(i, j) = P(X = x_i|Y = y_j) In addition to computing joint, marginal and conditional probabilities, methods for computing entropy and mutual information are also provided. Entropy provides a measure of disorder or randomness. If there is little randomness, entropy will close to 0, while when randomness is high, entropy will be close to, e.g., log2 (px.dim). Mutual information provides a robust measure of dependency between random variables (contrast with correlation).
Attributes
- Graph
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- Supertypes
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class Objecttrait Matchableclass Any
- Self type
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Probability.type
Members list
Value members
Concrete methods
Given probability vectors px and qx, compute the "cross entropy". May also pass in response vectors: y (actual) and yp (predicted).
Given probability vectors px and qx, compute the "cross entropy". May also pass in response vectors: y (actual) and yp (predicted).
Value parameters
- base_e
-
whether to use base e or base 2 logarithms (defaults to e)
- px
-
the first probability vector
- qx
-
the second probability vector (requires qx.dim >= px.dim)
Attributes
Given a joint probability matrix pxy, compute the "conditional probability" for random variable X given random variable Y, i.e, P(X = x_i|Y = y_j).
Given a joint probability matrix pxy, compute the "conditional probability" for random variable X given random variable Y, i.e, P(X = x_i|Y = y_j).
Value parameters
- pxy
-
the joint probability matrix
- py_
-
the marginal probability vector for Y
Attributes
Given a joint probability matrix pxy, compute the "conditional probability" for random variable Y given random variable X, i.e, P(Y = y_j|X = x_i).
Given a joint probability matrix pxy, compute the "conditional probability" for random variable Y given random variable X, i.e, P(Y = y_j|X = x_i).
Value parameters
- px_
-
the marginal probability vector for X
- pxy
-
the joint probability matrix
Attributes
Count the total number of occurrence in vector x of value vl, e.g., x is column 2 (Humidity), vl is 1 (High) matches 7 rows. This method works for vectors with integer or continuous values.
Count the total number of occurrence in vector x of value vl, e.g., x is column 2 (Humidity), vl is 1 (High) matches 7 rows. This method works for vectors with integer or continuous values.
Value parameters
- cont
-
whether feature/variable x is to be treated as continuous
- k
-
the maximum value of y + 1
- thres
-
the splitting threshold for features/variables treated as continuous
- vl
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one of the possible branch values for feature x (e.g., 1 (High))
- x
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the feature/column vector (e.g., column j of matrix)
- y
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the response/classification vector
Attributes
Given a probability vector px, compute the "entropy" of random variable X.
Given a probability vector px, compute the "entropy" of random variable X.
Value parameters
- px
-
the probability vector
Attributes
- See also
Given a frequency vector nu, compute the "entropy" of random variable X.
Given a frequency vector nu, compute the "entropy" of random variable X.
Value parameters
- nu
-
the frequency vector
Attributes
- See also
Given a probability vector px, compute the " base-k entropy" of random variable X.
Given a probability vector px, compute the " base-k entropy" of random variable X.
Value parameters
- b
-
the base for the logarithm
- px
-
the probability vector
Attributes
- See also
Given a joint probability matrix pxy, compute the "joint entropy" of random variables X and Y.
Given a joint probability matrix pxy, compute the "joint entropy" of random variables X and Y.
Value parameters
- pxy
-
the joint probability matrix
Attributes
Given a joint probability matrix pxy and a conditional probability matrix py_x, compute the "conditional entropy" of random variable X given random variable Y.
Given a joint probability matrix pxy and a conditional probability matrix py_x, compute the "conditional entropy" of random variable X given random variable Y.
Value parameters
- px_y
-
the conditional probability matrix
- pxy
-
the joint probability matrix
Attributes
Compute the Joint Frequency Table (JFT) for vector x and vector y. Count the number of cases where x(i) = v and y(i) = c.
Compute the Joint Frequency Table (JFT) for vector x and vector y. Count the number of cases where x(i) = v and y(i) = c.
Value parameters
- k
-
the maximum value of y + 1 (number of classes)
- vc
-
the number of disctinct values in vector x (value count)
- x
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the variable/feature vector
- y
-
the response/classification vector
Attributes
Count the frequency of occurrence in vector x of value vl for each of y's classification values, e.g., x is column 2 (Humidity), vl is 1 (High)) and y can be 0 (no) or 1 (yes). Also, determine the fraction of training cases where the feature has this value (e.g., fraction where Humidity is High = 7/14).
Count the frequency of occurrence in vector x of value vl for each of y's classification values, e.g., x is column 2 (Humidity), vl is 1 (High)) and y can be 0 (no) or 1 (yes). Also, determine the fraction of training cases where the feature has this value (e.g., fraction where Humidity is High = 7/14).
Value parameters
- k
-
the maximum value of y + 1
- vl
-
one of the possible branch values for feature x (e.g., 1 (High))
- x
-
the feature/column vector (e.g., column j of matrix)
- y
-
the response/classification vector
Attributes
Count the frequency of occurrence in vector x of value vl for each of y's classification values, e.g., x is column 2 (Humidity), vl is 1 (High)) and y can be 0 (no) or 1 (yes). Also, determine the fraction of training cases where the feature has this value (e.g., fraction where Humidity is High = 7/14).
Count the frequency of occurrence in vector x of value vl for each of y's classification values, e.g., x is column 2 (Humidity), vl is 1 (High)) and y can be 0 (no) or 1 (yes). Also, determine the fraction of training cases where the feature has this value (e.g., fraction where Humidity is High = 7/14).
Value parameters
- idx_
-
the index positions within x (if null, use all index positions)
- k
-
the maximum value of y + 1
- vl
-
one of the possible branch values for feature x (e.g., 1 (High))
- x
-
the feature/column vector (e.g., column j of matrix)
- y
-
the response/classification vector
Attributes
Count the frequency of occurrence in vector x of value vl for each of y's classification values, e.g., x is column 2 (Humidity), vl is 1 (High)) and y can be 0 (no) or 1 (yes). Also, determine the fraction of training cases where the feature has this value (e.g., fraction where Humidity is High = 7/14). This method works for vectors with integer or continuous values.
Count the frequency of occurrence in vector x of value vl for each of y's classification values, e.g., x is column 2 (Humidity), vl is 1 (High)) and y can be 0 (no) or 1 (yes). Also, determine the fraction of training cases where the feature has this value (e.g., fraction where Humidity is High = 7/14). This method works for vectors with integer or continuous values.
Value parameters
- cont
-
whether feature/variable x is to be treated as continuous
- idx_
-
the index positions within x (if null, use all index positions)
- k
-
the maximum value of y + 1
- thres
-
the splitting threshold for features/variables treated as continuous
- vl
-
one of the possible branch values for feature x (e.g., 1 (High))
- x
-
the feature/column vector (e.g., column j of matrix)
- y
-
the response/classification vector
Attributes
Determine whether the vector px is a legitimate "probability vector". The elements of the vector must be non-negative and add to one.
Determine whether the vector px is a legitimate "probability vector". The elements of the vector must be non-negative and add to one.
Value parameters
- px
-
the probability vector
Attributes
Determine whether the matrix pxy is a legitimate joint "probability matrix". The elements of the matrix must be non-negative and add to one.
Determine whether the matrix pxy is a legitimate joint "probability matrix". The elements of the matrix must be non-negative and add to one.
Value parameters
- pxy
-
the probability matrix
Attributes
Given two independent random variables X and Y, compute their "joint probability", which is the outer product of their probability vectors px and py, i.e., P(X = x_i, Y = y_j).
Given two independent random variables X and Y, compute their "joint probability", which is the outer product of their probability vectors px and py, i.e., P(X = x_i, Y = y_j).
Attributes
Compute the Joint Probability Table (JPT) for vector x and vector y. Count the number of cases where x(i) = v and y(i) = c and divide by the number of instances/datapoints.
Compute the Joint Probability Table (JPT) for vector x and vector y. Count the number of cases where x(i) = v and y(i) = c and divide by the number of instances/datapoints.
Value parameters
- k
-
the maximum value of y + 1 (number of classes)
- vc
-
the number of disctinct values in vector x (value count)
- x
-
the variable/feature vector
- y
-
the response/classification vector
Attributes
Given a joint probability matrix pxy, compute the "marginal probability" for random variable X, i.e, P(X = x_i).
Given a joint probability matrix pxy, compute the "marginal probability" for random variable X, i.e, P(X = x_i).
Value parameters
- pxy
-
the probability matrix
Attributes
Given a joint probability matrix pxy, compute the "marginal probability" for random variable Y, i.e, P(Y = y_j).
Given a joint probability matrix pxy, compute the "marginal probability" for random variable Y, i.e, P(Y = y_j).
Value parameters
- pxy
-
the probability matrix
Attributes
Given a joint probability matrix pxy, compute the mutual information for random variables X and Y.
Given a joint probability matrix pxy, compute the mutual information for random variables X and Y.
Value parameters
- px
-
the marginal probability vector for X
- pxy
-
the probability matrix
- py
-
the marginal probability vector for Y
Attributes
Given a joint probability matrix pxy, compute the mutual information for random variables X and Y.
Given a joint probability matrix pxy, compute the mutual information for random variables X and Y.
Value parameters
- pxy
-
the probability matrix
Attributes
Given a probability vector px, compute the "normalized entropy" of random variable X.
Given a probability vector px, compute the "normalized entropy" of random variable X.
Value parameters
- px
-
the probability vector
Attributes
- See also
Given a probability p, compute the "positive log-probability". Requires the probability to be non-zero.
Given a probability p, compute the "positive log-probability". Requires the probability to be non-zero.
Value parameters
- p
-
the given probability
Attributes
Given a probability vector px, compute the "positive log-probability". Requires each probability to be non-zero.
Given a probability vector px, compute the "positive log-probability". Requires each probability to be non-zero.
Value parameters
- px
-
the probability vector
Attributes
Return the probability of discrete random variable y taking on any of k values
Return the probability of discrete random variable y taking on any of k values
Value parameters
- k
-
the maximum value of y + 1, e.g., { 0, 1, 2} => k = 3
- y
-
the feature/column vector of integer values whose frequency counts are sought
Attributes
Given probability vectors px and qx, compute the "relative entropy".
Given probability vectors px and qx, compute the "relative entropy".
Value parameters
- px
-
the first probability vector
- qx
-
the second probability vector (requires qx.dim >= px.dim)
Attributes
Given a frequency vector, convert it to a probability vector.
Given a frequency vector, convert it to a probability vector.
Value parameters
- nu
-
the frequency vector
Attributes
Given a frequency vector, convert it to a probability vector.
Given a frequency vector, convert it to a probability vector.
Value parameters
- n
-
the total number of instances/trials collected
- nu
-
the frequency vector
Attributes
Given a frequency matrix, convert it to a probability matrix.
Given a frequency matrix, convert it to a probability matrix.
Value parameters
- nu
-
the frequency matrix
Attributes
Given a frequency matrix, convert it to a probability matrix.
Given a frequency matrix, convert it to a probability matrix.
Value parameters
- n
-
the total number of instances/trials collected
- nu
-
the frequency matrix