# Linear Generative Classification Algorithm

(Redirected from Linear Generative Classification)

A Linear Generative Classification Algorithm is a generative classification algorithm that uses a Linear Classification Model.

**Example(s):****Counter-Example(s):****See:**Generative Statistical Model ..

## References

### 2011

- http://en.wikipedia.org/wiki/Linear_classifier#Generative_models_vs._discriminative_models
- There are two broad classes of methods for determining the parameters of a linear classifier [math]\vec w[/math].
^{[1]}^{[2]}Methods of the first class model conditional density functions [math]P(\vec x|{\rm class})[/math]. Examples of such algorithms include:- Linear Discriminant Analysis (or Fisher's linear discriminant) (LDA) — assumes Gaussian conditional density models
- Naive Bayes classifier — assumes independent binomial conditional density models.

- There are two broad classes of methods for determining the parameters of a linear classifier [math]\vec w[/math].

### 2004

- (Bouchard & Triggs, 2004) ⇒ Guillaume Bouchard, and Bill Triggs. (2004). “The Trade-off Between Generative and Discriminative Classifiers.” In: Proceedings of COMPSTAT 2004.
- QUOTE: Well known generative-discriminative pairs include Linear Discriminant Analysis (LDA) vs. Linear logistic regression and naive Bayes vs. Generalized Additive Models (GAM). Many authors have already studied these models e.g. [5,6]. Under the assumption that the underlying distributions are Gaussian with equal covariances, it is known that LDA requires less data than its discriminative counterpart, linear logistic regression [3]. More generally, it is known that generative classifiers have a smaller variance than. … Conversely, the generative approach converges to the best model for the joint distribution [math]p(x,y)[/math] but the resulting conditional density is usually a biased classifier unless its [math]p_\theta(x)[/math] part is an accurate model for [math]p(x)[/math]. In real world problems the assumed generative model is rarely exact, and asymptotically, a discriminative classifier should typically be preferred [9,5].