Feature selection approaches are often grouped into three categories: "filter", "wrapper" and "embedded" approaches. Filter methods tend to assess the inclusion of an attribute based on some scoring metric, rather than in-situ. This has the advantage of being relatively computationally inexpensive, and easily human-interpretable.
Filter methods are often univariate, considering each attribute individually - for example by its mutual information or ANOVA f-score with the label. This has the disadvantage of not taking into account the interaction between features.
Do any multivariate filter methods exist, that take the interaction of features into account? If so - they would appear to have the advantages of filter methods, without the disadvantage. Are there any other pros or cons for them?