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Example of a naive Bayes classifier depicted as a Bayesian Network. In statistics, naive Bayes classifiers are a family of linear "probabilistic classifiers" which assumes that the features are conditionally independent, given the target class. The strength (naivety) of this assumption is what gives the classifier its name.
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For the following definitions, two examples will be used. The first is the problem of character recognition given an array of bits encoding a binary-valued image. The other example is the problem of finding an interval that will correctly classify points within the interval as positive and the points outside of the range as negative.
The transition model () and the observation model () are both specified using Gaussian laws with means that are linear functions of the conditioning variables. With these hypotheses and by using the recursive formula, it is possible to solve the inference problem analytically to answer the usual P ( S T ∣ O 0 ∧ ⋯ ∧ O T ∧ π ...
In statistical classification, the Bayes classifier is the classifier having the smallest probability of misclassification of all classifiers using the same set of features. [ 1 ] Definition
However, this loss function is non-convex and non-smooth, and solving for the optimal solution is an NP-hard combinatorial optimization problem. [4] As a result, it is better to substitute loss function surrogates which are tractable for commonly used learning algorithms, as they have convenient properties such as being convex and smooth.
Discriminative models, also referred to as conditional models, are a class of models frequently used for classification.They are typically used to solve binary classification problems, i.e. assign labels, such as pass/fail, win/lose, alive/dead or healthy/sick, to existing datapoints.
For example, naive Bayes and linear discriminant analysis are joint probability models, whereas logistic regression is a conditional probability model. There are two basic approaches to choosing f {\displaystyle f} or g {\displaystyle g} : empirical risk minimization and structural risk minimization . [ 6 ]