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With the modern software and online platforms to collect massive amount of data, there is an increasing demand of applying causal inference methods at large scale when randomized experimentation is not viable. Weighting methods that directly incorporate covariate balancing have recently gained popularity for estimating causal effects in observational studies. These methods reduce the manual efforts required by researchers to iterate between propensity score modeling and balance checking until a satisfied covariate balance result. However, conventional solvers for determining weights lack the scalability to apply such methods on large scale datasets in companies like Snap Inc. To address the limitations and improve computational efficiency, in this paper we present scalable algorithms, DistEB and DistMS, for two balancing approaches: entropy balancing and MicroSynth. The solvers have linear time complexity and can be conveniently implemented in distributed computing frameworks such as Spark, Hive, etc. We study the properties of balancing approaches at different scales up to 1 million treated units and 487 covariates. We find that with larger sample size, both bias and variance in the causal effect estimation are significantly reduced. The results emphasize the importance of applying balancing approaches on large scale datasets. We combine the balancing approach with a synthetic control framework and deploy an end-to-end system for causal impact estimation at Snap Inc., Comment: KDD '23: Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining

Strong electron correlations in rare earth hexaborides can give rise to a variety of interesting phenomena like ferromagnetism, Kondo hybridization, mixed valence, superconductivity and possibly topological characteristics. The theoretical prediction of topological properties in SmB$_{6}$ and YbB$_{6}$, has rekindled the scientific interest in the rare earth hexaborides, and high-resolution ARPES has been playing a major role in the debate. The electronic band structure of the hexaborides contains the key to understand the origin of the different phenomena observed, and much can be learned by comparing the experimental data from different rare earth hexaborides. We have performed high-resolution ARPES on the (001) surfaces of YbB$_{6}$, CeB$_{6}$ and SmB$_{6}$. On the most basic level, the data show that the differences in the valence of the rare earth element are reflected in the experimental electronic band structure primarily as a rigid shift of the energy position of the metal 5$\textit{d}$ states with respect to the Fermi level. Although the overall shape of the $\textit{d}$-derived Fermi surface contours remains the same, we report differences in the dimensionality of these states between the compounds studied. Moreover, the spectroscopic fingerprint of the 4$\textit{f}$ states also reveals considerable differences that are related to their coherence and the strength of the $\textit{d}$-$\textit{f}$ hybridization. For the SmB$_6$ case, we use ARPES in combination with STM imaging and electron diffraction to reveal time dependent changes in the structural symmetry of the highly debated SmB$_{6}$(001) surface. All in all, our study highlights the suitability of electron spectroscopies like high-resolution ARPES to provide links between electronic structure and function in complex and correlated materials such as the rare earth hexaborides., Comment: 10 pages, 5 figures

Topological insulators are a novel materials platform with high applications potential in fields ranging from spintronics to quantum computation. In the ongoing scientific effort to demonstrate controlled manipulation of their electronic structure by external means, stoichiometric variation and surface decoration are two effective approaches that have been followed. In ARPES experiments, both approaches are seen to lead to electronic band structure changes. Such approaches result in variations of the energy position of bulk and surface-related features and the creation of two-dimensional electron gases.The data presented here demonstrate that a third manipulation handle is accessible by utilizing the amount of illumination a topological insulator surface has been exposed to under typical experimental ARPES conditions. Our results show that this new, third, knob acts on an equal footing with stoichiometry and surface decoration as a modifier of the electronic band structure, and that it is in continuous competition with the latter. The data clearly point towards surface photovoltage and photo-induced desorption as the physical phenomena behind modifications of the electronic band structure under exposure to high-flux photons. We show that the interplay of these phenomena can minimize and even eliminate the adsorbate-related surface band bending on typical binary, ternary and quaternary Bi-based topological insulators. Including the influence of the sample temperature, these data set up a framework for the external control of the electronic band structure in topological insulator compounds in an ARPES setting. Four external knobs are available: bulk stoichiometry, surface decoration, temperature and photon exposure. These knobs can be used in conjunction to tune the band energies near the surface and consequently influence the topological properties of the relevant electronic states., Comment: 16 pages, 8 figures