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Cross-study replicability is a powerful model evaluation criterion that emphasizes generalizability of predictions. When training cross-study replicable prediction models, it is critical to decide between merging and treating the studies separately. We study boosting algorithms in the presence of potential heterogeneity in predictor-outcome relationships across studies and compare two multi-study learning strategies: 1) merging all the studies and training a single model, and 2) multi-study ensembling, which involves training a separate model on each study and ensembling the resulting predictions. In the regression setting, we provide theoretical guidelines based on an analytical transition point to determine whether it is more beneficial to merge or to ensemble for boosting with linear learners. In addition, we characterize a bias-variance decomposition of estimation error for boosting with component-wise linear learners. We verify the theoretical transition point result in simulation and illustrate how it can guide the decision on merging vs. ensembling in an application to breast cancer gene expression data.

We investigate the power of censoring techniques, first developed for learning {\em fair representations}, to address domain generalization. We examine {\em adversarial} censoring techniques for learning invariant representations from multiple "studies" (or domains), where each study is drawn according to a distribution on domains. The mapping is used at test time to classify instances from a new domain. In many contexts, such as medical forecasting, domain generalization from studies in populous areas (where data are plentiful), to geographically remote populations (for which no training data exist) provides fairness of a different flavor, not anticipated in previous work on algorithmic fairness. We study an adversarial loss function for $k$ domains and precisely characterize its limiting behavior as $k$ grows, formalizing and proving the intuition, backed by experiments, that observing data from a larger number of domains helps. The limiting results are accompanied by non-asymptotic learning-theoretic bounds. Furthermore, we obtain sufficient conditions for good worst-case prediction performance of our algorithm on previously unseen domains. Finally, we decompose our mappings into two components and provide a complete characterization of invariance in terms of this decomposition. To our knowledge, our results provide the first formal guarantees of these kinds for adversarial invariant domain generalization.

A critical decision point when training predictors using multiple studies is whether these studies should be combined or treated separately. We compare two multi-study learning approaches in the presence of potential heterogeneity in predictor-outcome relationships across datasets. We consider 1) merging all of the datasets and training a single learner, and 2) multi-study ensembling, which involves training a separate learner on each dataset and combining the predictions resulting from each learner. In a linear regression setting, we show analytically and confirm via simulation that merging yields lower prediction error than ensembling when the predictor-outcome relationships are relatively homogeneous across studies. However, as cross-study heterogeneity increases, there exists a transition point beyond which ensembling outperforms merging. We provide analytic expressions for the transition point in various scenarios, study asymptotic properties, and illustrate how transition point theory can be used for deciding when studies should be combined with an application from metabolomics.

A novel series of benzo crown ether (dibenzo 18-crown-6 ether, benzo 18-crown-6 ether, and benzo 15-crown-5 ether) functionalized enamines derivatives from amino benzo crown ether (4-amino dibenzo 18-crown-6 ether, 4-amino benzo 18-crown-6 ether, 4-amino benzo 15-crown-5 ether) and substituted 3-(dimethylamino)-1-phenylprop-2-en-1-one compounds have been synthesized. All the synthesized compounds were characterized by infrared, 1H NMR, 13C NMR, distortionless enhancement polarization transfer, and mass and elemental analysis techniques. The cation recognition property for benzo crown ether enamine 8a was studied by absorption and fluorescence spectroscopy.