Recovering from Biased Data: Can Fairness Constraints Improve Accuracy?

Multiple fairness constraints have been proposed in the literature, motivated by a range of concerns about how demographic groups might be treated unfairly by machine learning classifiers. In this work we consider a different motivation; learning from biased training data. We posit several ways in which training data may be biased, including having a more noisy or negatively biased labeling process on members of a disadvantaged group, or a decreased prevalence of positive or negative examples from the disadvantaged group, or both. Given such biased training data, Empirical Risk Minimization (ERM) may produce a classifier that not only is biased but also has suboptimal accuracy on the true data distribution. We examine the ability of fairness-constrained ERM to correct this problem. In particular, we find that the Equal Opportunity fairness constraint [Hardt et al., 2016] combined with ERM will provably recover the Bayes optimal classifier under a range of bias models. We also consider other recovery methods including re-weighting the training data, Equalized Odds, and Demographic Parity, and Calibration. These theoretical results provide additional motivation for considering fairness interventions even if an actor cares primarily about accuracy

Direct and indirect signals of natural composite Higgs models

We present a comprehensive numerical analysis of a four-dimensional model with the Higgs as a composite pseudo-Nambu-Goldstone boson that features a calculable Higgs potential and protective custodial and flavour symmetries to reduce electroweak fine-tuning. We employ a novel numerical technique that allows us for the first time to study constraints from radiative electroweak symmetry breaking, Higgs physics, electroweak precision tests, flavour physics, and direct LHC bounds on fermion and vector boson resonances in a single framework. We consider four different flavour symmetries in the composite sector, one of which we show to not be viable anymore in view of strong precision constraints. In the other cases, all constraints can be passed with a sub-percent electroweak fine-tuning. The models can explain the excesses recently observed in $WW$, $WZ$, $Wh$ and $\ell^+\ell^-$ resonance searches by ATLAS and CMS and the anomalies in angular observables and branching ratios of rare semi-leptonic $B$ decays observed by LHCb. Solving the $B$ physics anomalies predicts the presence of a dijet or $t\bar t$ resonance around 1 TeV just below the sensitivity of LHC run 1. We discuss the prospects to probe the models at run 2 of the LHC. As a side product, we identify several gaps in the searches for vector-like quarks at hadron colliders, that could be closed by reanalyzing existing LHC data.Comment: 74 pages, 21 figures. v2: references added, discussion in 3.2.6 extende

Electroweak symmetry breaking and collider signatures in the next-to-minimal composite Higgs model

We conduct a detailed numerical analysis of the composite pseudo-Nambu-Goldstone Higgs model based on the next-to-minimal coset $\text{SO}(6)/\text{SO}(5)\cong\text{SU}(4)/\text{Sp}(4)$, featuring an additional SM singlet scalar in the spectrum, which we allow to mix with the Higgs boson. We identify regions in parameter space compatible with all current experimental constraints, including radiative electroweak symmetry breaking, flavour physics, and direct searches at colliders. We find the additional scalar, with a mass predicted to be below a TeV, to be virtually unconstrained by current LHC data, but potentially in reach of run 2 searches. Promising indirect searches include rare semi-leptonic $B$ decays, CP violation in $B_s$ mixing, and the electric dipole moment of the neutron.Comment: 32 pages + appendices, 9 figures. v2: minor clarifications, matches the JHEP versio

Violation of lepton flavour universality in composite Higgs models

We investigate whether the $2.6\sigma$ deviation from lepton flavour universality in $B^+\to K^+\ell^+\ell^-$ decays recently observed at the LHCb experiment can be explained in minimal composite Higgs models. We show that a visible departure from universality is indeed possible if left-handed muons have a sizable degree of compositeness. Constraints from $Z$-pole observables are avoided by a custodial protection of the muon coupling. The deficit in the invisible $Z$ width at LEP is explained in the same region of parameters.Comment: 5 pages, 2 figures. v4: discussion of invisible Z width adde

Celebrating 70: An Interview with Don Berry

Donald (Don) Arthur Berry, born May 26, 1940 in Southbridge, Massachusetts, earned his A.B. degree in mathematics from Dartmouth College and his M.A. and Ph.D. in statistics from Yale University. He served first on the faculty at the University of Minnesota and subsequently held endowed chair positions at Duke University and The University of Texas M.D. Anderson Center. At the time of the interview he served as Head of the Division of Quantitative Sciences, and Chairman and Professor of the Department of Biostatistics at UT M.D. Anderson Center.Comment: Published in at http://dx.doi.org/10.1214/11-STS366 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Status of the B→K∗μ+μ−B\to K^*\mu^+\mu^- anomaly after Moriond 2017

Motivated by recent results by the ATLAS and CMS collaborations on the angular distribution of the $B \to K^* \mu^+\mu^-$ decay, we perform a state-of-the-art analysis of rare $B$ meson decays based on the $b \to s \mu \mu$ transition. Using standard estimates of hadronic uncertainties, we confirm the presence of a sizable discrepancy between data and SM predictions. We do not find evidence for a $q^2$ or helicity dependence of the discrepancy. The data can be consistently described by new physics in the form of a four-fermion contact interaction $(\bar s \gamma_\alpha P_L b)(\bar \mu \gamma^\alpha \mu)$. Assuming that the new physics affects decays with muons but not with electrons, we make predictions for a variety of theoretically clean observables sensitive to violation of lepton flavour universality.Comment: 20 pages, 8 figures, 3 tables. v3: numerics updated using v2 of arXiv:1606.04731. Conclusions unchanged. Matches published version. Example script available at https://github.com/DavidMStraub/paper-bkstarmumu-ans