Distributionally Robust Linear Regression With Block Lewis Weights

Machine learning algorithms and their training datasets have grown substantially in both size and complexity over the past decade. This increased model complexity has made it challenging to interpret and predict their behavior in unobserved scenarios. Hence, many applications that involve societal decisions still rely on simple, interpretable models like linear regression, often after feature engineering. Examples of such applications include predicting national housing prices, estimating wages across industries, forecasting loan amounts across banks, predicting life insurance premiums across groups, and projecting energy consumption across communities [CGKMN24]. A shared safety and sometimes legal concern across the above applications is the potential for wildly different model qualities for different distributions, i.e., outputting a notably worse model for some source data distributions [Dat14; BS16; HPS16; VVB18; SBFVV19; BHJKR21; CGNSG23; Cho16; KLMR18; ADW19; CGKMN24; SVWZ24].