.. currentmodule:: pmlearn.linear_model
The following are a set of methods intended for regression in which the target value is expected to be a linear combination of the input variables. In mathematical notion, if \hat{y} is the predicted value.
\hat{y}(\beta, x) = \beta_0 + \beta_1 x_1 + ... + \beta_p x_p
Where \beta = (\beta_1, ..., \beta_p) are the coefficients and \beta_0 is the y-intercept.
To perform classification with generalized linear models, see :ref:`bayesian_logistic_regression`.
To obtain a fully probabilistic model, the output y is assumed to be Gaussian distributed around X w:
p(y|X,w,\alpha) = \mathcal{N}(y|X w,\alpha)
Alpha is again treated as a random variable that is to be estimated from the data.
References
- A good introduction to Bayesian methods is given in C. Bishop: Pattern Recognition and Machine learning
- Original Algorithm is detailed in the book Bayesian learning for neural networks by Radford M. Neal
Bayesian Logistic regression, despite its name, is a linear model for classification rather than regression. Logistic regression is also known in the literature as logit regression, maximum-entropy classification (MaxEnt) or the log-linear classifier. In this model, the probabilities describing the possible outcomes of a single trial are modeled using a logistic function.
The implementation of logistic regression in pymc-learn can be accessed from class :class:`LogisticRegression`.