# Discriminative Classification Model Instance

A Discriminative Classification Model Instance is a classification function that...

**AKA:**Fitted Discriminative Classification Function.**Context:**- It can be produced by Discriminative Classification System (that implements a Discriminative Classification algorithm).
- It can be based on a Discriminative Model Family.
- …

**Example(s):****Counter-Example(s):****See:**Class Conditional Probability Function.

## References

### 2004

- (Bouchard & Triggs, 2004) ⇒ Guillaume Bouchard, and Bill Triggs. (2004). “The Trade-off Between Generative and Discriminative Classifiers.” In: Proceedings of COMPSTAT 2004.
- QUOTE: … if the overall goal is to find the classification rule with the smallest error rate, this depends only on the conditional density [math]\displaystyle{ p(y \vert x) }[/math]. Discriminative methods directly model the conditional distribution, without assuming anything about the input distribution p(x). 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

*p*(*x*,*y*) but the resulting conditional density is usually a biased classifier unless its*p*_{θ}(x*) part is an accurate model for*p*(*x*). In real world problems the assumed generative model is rarely exact, and asymptotically, a '*discriminative classifier should typically be preferred [9, 5]. The key argument is that the discriminative estimator converges to the conditional density that minimizes the negative log-likelihood classification loss against the true density p(x, y) [2]. For finite sample sizes, there is a bias-variance tradeoff and it is less obvious how to choose between generative and discriminative classifiers.

- QUOTE: … if the overall goal is to find the classification rule with the smallest error rate, this depends only on the conditional density [math]\displaystyle{ p(y \vert x) }[/math]. Discriminative methods directly model the conditional distribution, without assuming anything about the input distribution p(x). 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.