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Work in machine learning and statistics commonly focuses on building models that capture the vast majority of data, possibly ignoring a segment of the population as outliers. However, there may not exist a good, simple model for the distribution, so we seek to find a small subset where there exists such a model. We give a computationally efficient algorithm with theoretical analysis for the conditional linear regression task, which is the joint task of identifying a significant portion of the data distribution, described by a k-DNF, along with a linear predictor on that portion with a small loss. In contrast to work in robust statistics on small subsets, our loss bounds do not feature a dependence on the density of the portion we fit, and compared to previous work on conditional linear regression, our algorithm’s running time scales polynomially with the sparsity of the linear predictor. We also demonstrate empirically that our algorithm can leverage this advantage to obtain a k-DNF with a better linear predictor in practice. 

Abstract There is significant interest in approaches to the treatment of bacterial infections that block virulence without creating selective pressures that lead to resistance. Here, we report the development of an “anti‐virulence” strategy that exploits the activity of potent synthetic inhibitors of quorum sensing (QS) inStaphylococcus aureus. We identify peptide‐based inhibitors of QS that are resistant to sequestration or degradation by components of murine tissue and demonstrate that encapsulation of a lead inhibitor in degradable polymer microparticles provides materials that substantially inhibit QSin vitro. Using a murine abscess model, we show that this inhibitor attenuates methicillin‐resistantS. aureus(MRSA) skin infectionsin vivo, and that sustained release of the inhibitor from microparticles significantly improved outcomes compared to mice that received a single‐dose bolus. Our results present an effective and modular approach to controlling bacterial virulencein vivoand could advance the development of new strategies for skin infection control.