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It is possible to have multiple independent variables or multiple dependent variables. For instance, in multivariable calculus, one often encounters functions of the form z = f(x,y), where z is a dependent variable and x and y are independent variables. [8] Functions with multiple outputs are often referred to as vector-valued functions.
One class depends on another if the independent class is a parameter variable or local variable of a method of the dependent class. Sometimes the relationship between two classes is very weak. They are not implemented with member variables at all. Rather they might be implemented as member function arguments.
Abstractly, naive Bayes is a conditional probability model: it assigns probabilities (, …,) for each of the K possible outcomes or classes given a problem instance to be classified, represented by a vector = (, …,) encoding some n features (independent variables).
In object-oriented programming, a class defines the shared aspects of objects created from the class. The capabilities of a class differ between programming languages, but generally the shared aspects consist of state and behavior that are each either associated with a particular object or with all objects of that class.
Simple mediation model. The independent variable causes the mediator variable; the mediator variable causes the dependent variable. In statistics, a mediation model seeks to identify and explain the mechanism or process that underlies an observed relationship between an independent variable and a dependent variable via the inclusion of a third hypothetical variable, known as a mediator ...
For example, consider the ordinary differential equation ′ = + The Euler method for solving this equation uses the finite difference quotient (+) ′ to approximate the differential equation by first substituting it for u'(x) then applying a little algebra (multiplying both sides by h, and then adding u(x) to both sides) to get (+) + (() +).
For each independent variable ,, …, a separate pass is therefore necessary in which the derivative with respect to that independent variable is set to one (=) and of all others to zero (= = =). In contrast, reverse accumulation requires the evaluated partial functions for the partial derivatives.
The observations on the dependent variable are stacked into a column vector y; the observations on each independent variable are also stacked into column vectors, and these latter column vectors are combined into a design matrix X (not denoting a random vector in this context) of observations on the independent variables. Then the following ...