What is spike and slab priors?

In statistics, spike-and-slab regression is a Bayesian variable selection technique that is particularly useful when the number of possible predictors is larger than the number of observations. Initially, the idea of the spike-and-slab model was proposed by Mitchell & Beauchamp (1988).

What is a spike prior?

A spike and slab prior for a random variable X is a generative model—i.e., a prior—in which X either attains some fixed value v, called the spike, or is drawn some other prior pslab(x), called the slab.

What is horseshoe prior?

The horseshoe prior is a member of the family of multivariate scale mixtures of normals, and is therefore closely related to widely used ap- proaches for sparse Bayesian learning, includ- ing, among others, Laplacian priors (e.g. the LASSO) and Student-t priors (e.g. the rel- evance vector machine).

What is Bayesian variable selection?

The Bayesian approach to variable selection is straightforward in principle. One quantifies the prior uncertainties via probabilities for each model under consideration, specifies a prior distribution for each of the parameters in each model, and then uses Bayes’ theorem to calculate posterior model probabilities.

What does a flat prior distribution mean?

The term “flat” in reference to a prior generally means f(θ)∝c over the support of θ. So a flat prior for p in a Bernoulli would usually be interpreted to mean U(0,1). A flat prior for μ in a normal is an improper prior where f(μ)∝c over the real line.

What does Lasso regression do?

Lasso regression is a regularization technique. It is used over regression methods for a more accurate prediction. This model uses shrinkage. Shrinkage is where data values are shrunk towards a central point as the mean.

What is Bayesian shrinkage?

In Bayesian analysis, shrinkage is defined in terms of priors. Shrinkage is where: “…the posterior estimate of the prior mean is shifted from the sample mean towards the prior mean” ~ Zhao et. Models that include prior distributions can result in a great improvement in the accuracy of a shrunk estimator.

What is L1 L2 regularization?

L1 regularization gives output in binary weights from 0 to 1 for the model’s features and is adopted for decreasing the number of features in a huge dimensional dataset. L2 regularization disperse the error terms in all the weights that leads to more accurate customized final models.

What is the prior in Bayes Theorem?

Understanding Bayes’ Theorem Prior probability, in Bayesian statistical inference, is the probability of an event before new data is collected. This is the best rational assessment of the probability of an outcome based on the current knowledge before an experiment is performed.

What makes a prior vague?

“Vague prior: A term used for the prior distribution in Bayesian inference in the situation when there is complete ignorance about the value of a parameter.”

Why does the lasso give zero coefficients?

The lasso performs shrinkage so that there are “corners” in the constraint, which in two dimensions corresponds to a diamond. If the sum of squares “hits” one of these corners, then the coefficient corresponding to the axis is shrunk to zero.

Which is better ridge or lasso?

Lasso tends to do well if there are a small number of significant parameters and the others are close to zero (ergo: when only a few predictors actually influence the response). Ridge works well if there are many large parameters of about the same value (ergo: when most predictors impact the response).