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Formally, an "ordinary" classifier is some rule, or function, that assigns to a sample x a class label ŷ: ^ = The samples come from some set X (e.g., the set of all documents, or the set of all images), while the class labels form a finite set Y defined prior to training.
Collective classification problems are defined in terms of networks of random variables, where the network structure determines the relationship between the random variables. Inference is performed on multiple random variables simultaneously, typically by propagating information between nodes in the network to perform approximate inference.
A given instruction set can be implemented in a variety of ways. All ways of implementing a particular instruction set provide the same programming model, and all implementations of that instruction set are able to run the same executables. The various ways of implementing an instruction set give different tradeoffs between cost, performance ...
When classification is performed by a computer, statistical methods are normally used to develop the algorithm. Often, the individual observations are analyzed into a set of quantifiable properties, known variously as explanatory variables or features. These properties may variously be categorical (e.g.
In theoretical terms, a classifier is a measurable function : {,, …,}, with the interpretation that C classifies the point x to the class C(x). The probability of misclassification, or risk , of a classifier C is defined as R ( C ) = P { C ( X ) ≠ Y } . {\displaystyle {\mathcal {R}}(C)=\operatorname {P} \{C(X)\neq Y\}.}
In general, any two sets of nodes are conditionally independent given a third set if a criterion called d-separation holds in the graph. Local independences and global independences are equivalent in Bayesian networks. This type of graphical model is known as a directed graphical model, Bayesian network, or belief network.
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. [1] The term 'random variable' in its mathematical definition refers to neither randomness nor variability [ 2 ] but instead is a mathematical function in which
A chart showing a uniform distribution. In probability theory and statistics, a collection of random variables is independent and identically distributed (i.i.d., iid, or IID) if each random variable has the same probability distribution as the others and all are mutually independent. [1]