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Simpsons paradox, or Yule-Simpson effect, arises when a trend appears in different subsets of data but disappears or reverses when these subsets are combined. We describe here seven cases of this phenomenon for chemo-kinematical relations believed to constrain the Milky Way disk formation and evolution. We show that interpreting trends in relations, such as the radial and vertical chemical abundance gradients, the age-metallicity relation, and the metallicity-rotational velocity relation (MVR), can lead to conflicting conclusions about the Galaxy past if analyses marginalize over stellar age and/or birth radius. It is demonstrated that the MVR in RAVE giants is consistent with being always strongly negative, when narrow bins of [Mg/Fe] are considered. This is directly related to the negative radial metallicity gradients of stars grouped by common age (mono-age populations) due to the inside out disk formation. The effect of the asymmetric drift can then give rise to a positive MVR trend in high-[alpha/Fe] stars, with a slope dependent on a given surveys selection function and observational uncertainties. We also study the variation of lithium abundance, A(Li), with [Fe/H] of AMBRE:HARPS dwarfs. A strong reversal in the positive A(Li)-[Fe/H] trend of the total sample is found for mono-age populations, flattening for younger groups of stars. Dissecting by birth radius shows strengthening in the positive A(Li)-[Fe/H] trend, shifting to higher [Fe/H] with decreasing birth radius; these observational results suggest new constraints on chemical evolution models. This work highlights the necessity for precise age estimates for large stellar samples covering wide spatial regions.
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I present an overview of the science goals and achievements of ongoing spectroscopic surveys of individual stars in the nearby Universe. I include a brief discussion of the development of the field of Galactic Archaeology - using the fossil record in old stars nearby to infer how our Galaxy evolved and place the Milky Way in cosmological context.
Chemical tagging of stellar debris from disrupted open clusters and associations underpins the science cases for next-generation multi-object spectroscopic surveys. As part of the Galactic Archaeology project TraCD (Tracking Cluster Debris), a preliminary attempt at reconstructing the birth clouds of now phase-mixed thin disk debris is undertaken using a parametric minimum spanning tree (MST) approach. Empirically-motivated chemical abundance pattern uncertainties (for a 10-dimensional chemistry-space) are applied to NBODY6-realised stellar associations dissolved into a background sea of field stars, all evolving in a Milky Way potential. We demonstrate that significant population reconstruction degeneracies appear when the abundance uncertainties approach 0.1 dex and the parameterised MST approach is employed; more sophisticated methodologies will be required to ameliorate these degeneracies.
We describe a data-driven discovery method that leverages Simpsons paradox to uncover interesting patterns in behavioral data. Our method systematically disaggregates data to identify subgroups within a population whose behavior deviates significantly from the rest of the population. Given an outcome of interest and a set of covariates, the method follows three steps. First, it disaggregates data into subgroups, by conditioning on a particular covariate, so as minimize the variation of the outcome within the subgroups. Next, it models the outcome as a linear function of another covariate, both in the subgroups and in the aggregate data. Finally, it compares trends to identify disaggregations that produce subgroups with different behaviors from the aggregate. We illustrate the method by applying it to three real-world behavioral datasets, including Q&A site Stack Exchange and online learning platforms Khan Academy and Duolingo.
Recommendation systems are often evaluated based on users interactions that were collected from an existing, already deployed recommendation system. In this situation, users only provide feedback on the exposed items and they may not leave feedback on other items since they have not been exposed to them by the deployed system. As a result, the collected feedback dataset that is used to evaluate a new model is influenced by the deployed system, as a form of closed loop feedback. In this paper, we show that the typical offline evaluation of recommender systems suffers from the so-called Simpsons paradox. Simpsons paradox is the name given to a phenomenon observed when a significant trend appears in several different sub-populations of observational data but disappears or is even reversed when these sub-populations are combined together. Our in-depth experiments based on stratified sampling reveal that a very small minority of items that are frequently exposed by the deployed system plays a confounding factor in the offline evaluation of recommendation systems. In addition, we propose a novel evaluation methodology that takes into account the confounder, i.e the deployed systems characteristics. Using the relative comparison of many recommendation models as in the typical offline evaluation of recommender systems, and based on the Kendall rank correlation coefficient, we show that our proposed evaluation methodology exhibits statistically significant improvements of 14% and 40% on the examined open loop datasets (Yahoo! and Coat), respectively, in reflecting the true ranking of systems with an open loop (randomised) evaluation in comparison to the standard evaluation.
The next decade affords tremendous opportunity to achieve the goals of Galactic archaeology. That is, to reconstruct the evolutionary narrative of the Milky Way, based on the empirical data that describes its current morphological, dynamical, temporal and chemical structures. Here, we describe a path to achieving this goal. The critical observational objective is a Galaxy-scale, contiguous, comprehensive mapping of the disks phase space, tracing where the majority of the stellar mass resides. An ensemble of recent, ongoing, and imminent surveys are working to deliver such a transformative stellar map. Once this empirical description of the dust-obscured disk is assembled, we will no longer be operationally limited by the observational data. The primary and significant challenge within stellar astronomy and Galactic archaeology will then be in fully utilizing these data. We outline the next-decade framework for obtaining and then realizing the potential of the data to chart the Galactic disk via its stars. One way to support the investment in the massive data assemblage will be to establish a Galactic Archaeology Consortium across the ensemble of stellar missions. This would reflect a long-term commitment to build and support a network of personnel in a dedicated effort to aggregate, engineer, and transform stellar measurements into a comprehensive perspective of our Galaxy.
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