nclm {fairml}

Nonconvex Optimization for Regression with Fairness Constraints

Description

Fair regression model based on nonconvex optimization from Komiyama et al. (2018).

Usage

nclm(response, predictors, sensitive, unfairness, covfun, lambda = 0,
  save.auxiliary = FALSE)

Arguments

response

a numeric vector, the response variable.

predictors

a numeric matrix or a data frame containing numeric and factor columns; the predictors.

sensitive

a numeric matrix or a data frame containing numeric and factor columns; the sensitive attributes.

unfairness

a positive number in [0, 1], how unfair is the model allowed to be. A value of 0 means the model is completely fair, while a value of 1 means the model is not constrained to be fair at all.

covfun

a function computing covariance matrices. It defaults to the cov() function from the stats package.

lambda

a non-negative number, a ridge-regression penalty coefficient. It defaults to zero.

save.auxiliary

a logical value, whether to save the fitted values and the residuals of the auxiliary model that constructs the decorrelated predictors. The default value is FALSE.

Details

nclm() defines fairness as statistical parity. The model bounds the proportion of the variance that is explained by the sensitive attributes over the total explained variance.

The algorithm proposed by Komiyama et al. (2018) works like this:

1. regresses the predictors against the sensitive attributes;

2. constructs a new set of predictors that are decorrelated from the sensitive attributes using the residuals of this regression;

3. regresses the response against the decorrelated predictors and the sensitive attributes, while

4. bounding the proportion of variance the sensitive attributes can explain with respect to the overall explained variance of the model.

Both sensitive and predictors are standardized internally before estimating the regression coefficients, which are then rescaled back to match the original scales of the variables. response is only standardized if it has a variance smaller than 1, as that seems to improve the stability of the solutions provided by the optimizer (as far as the data included in fairml are concerned).

The covfun argument makes it possible to specify a custom function to compute the covariance matrices used in the constrained optimization. Some examples are the kernel estimators described in Komiyama et al. (2018) and the shrinkage estimators in the corpcor package.

Value

nclm() returns an object of class c("nclm", "fair.model").

Author(s)

Marco Scutari

References

Komiyama J, Takeda A, Honda J, Shimao H (2018). "Nonconvex Optimization for Regression with Fairness Constraints". Proceedints of the 35th International Conference on Machine Learning (ICML), PMLR 80:2737–2746.
http://proceedings.mlr.press/v80/komiyama18a/komiyama18a.pdf

See Also

frrm, zlm