Distributional Robustness of K-class Estimators and the PULSE

Recently, in causal discovery, invariance properties such as the moment criterion which two-stage least square estimator leverage have been exploited for causal structure learning: e.g., in cases, where the causal parameter is not identifiable, some structure of the non-zero components may be identified, and coverage guarantees are available. Subsequently, anchor regression has been proposed to trade-off invariance and predictability. The resulting estimator is shown to have optimal predictive performance under bounded shift interventions. In this paper, we show that the concepts of anchor regression and K-class estimators are closely related. Establishing this connection comes with two benefits: (1) It enables us to prove robustness properties for existing K-class estimators when considering distributional shifts. And, (2), we propose a novel estimator in instrumental variable settings by minimizing the mean squared prediction error subject to the constraint that the estimator lies in an asymptotically valid confidence region of the causal parameter. We call this estimator PULSE (p-uncorrelated least squares estimator) and show that it can be computed efficiently, even though the underlying optimization problem is non-convex. We further prove that it is consistent. We perform simulation experiments illustrating that there are several settings including weak instrument settings, where PULSE outperforms other estimators and suffers from less variability.Comment: 85 pages, 15 figure

Tetraquark resonances computed with static lattice QCD potentials and scattering theory

We study tetraquark resonances with lattice QCD potentials computed for two static quarks and two dynamical quarks, the Born-Oppenheimer approximation and the emergent wave method of scattering theory. As a proof of concept we focus on systems with isospin $I = 0$, but consider different relative angular momenta $l$ of the heavy $b$ quarks. We compute the phase shifts and search for \mbox{S} and \mbox{T} matrix poles in the second Riemann sheet. We predict a new tetraquark resonance for $l = 1$, decaying into two $B$ mesons, with quantum numbers $I(J^P) = 0(1^-)$, mass $m = 10576_{-4}^{+4} \, \textrm{MeV}$ and decay width $\Gamma = 112_{-103}^{+90} \, \textrm{MeV}$.Comment: 7 pages, 6 figures, 1 table, Proceedings of the 35th International Symposium on Lattice Field Theory, Granada, Spai