Regression
A Losses Table 3 lists the losses used for training
Table 3 lists the losses used for training. T able 3: Base loss functions used for experiments. Comparison of logistic regression models trained with individual losses for the Fashion-MNIST dataset.Model / Metric Zero-one Hinge Cross-entropy AUC Zero-one 0.1603 - - - (std) ( 0 . As baselines, we train with just one loss at a time and compare the ALMO performance to this per-loss optimal performance.
R1: Comparison with inexact methods Aligning with prior exact papers [10, 18], we focus on comparisons with exact
We thank all five reviewers for their detailed and incisive feedback. We tested AustereMH [16], an inexact method, on robust linear regression in Section 5.1 with We added this to the Appendix. This does not affect the properties of TunaMH. Our theorem doesn't have this assumption; it suggests that for MHSubLhd with given user-specified The impact is 3-fold: it (1) provides an upper bound on performance for algorithms of Algorithm 1's TunaMH); (3) suggests directions for developing new algorithms. To be significantly faster than TunaMH, we either need more assumptions about the problem or new stateful algorithms.
Common Question Q1: The covariate shift assumption
We thank the reviewers for insightful and constructive comments. We have submitted code and detailed Appdendix . TransCal, it is inadvertently omitted by us while writing. Common Question Q2: Will TransCal have a lower accuracy while achieving a better calibration? TransCal maintains the same accuracy with that before calibration, while achieving a lower ECE (Figure 1(b)).
Fair Regression via Plug-In Estimator and Recalibration
We study the problem of learning an optimal regression function subject to a fairness constraint. It requires that, conditionally on the sensitive feature, the distribution of the function output remains the same. This constraint naturally extends the notion of demographic parity, often used in classification, to the regression setting. We tackle this problem by leveraging on a proxy-discretized version, for which we derive an explicit expression of the optimal fair predictor. This result naturally suggests a two stage approach, in which we first estimate the (unconstrained) regression function from a set of labeled data and then we recalibrate it with another set of unlabeled data.