The central objective of empirical asset pricing is to identify firm-level signals that explain the cross-section of expected stock returns--whether through exposure to risk factors or persistent mispricing. The dominant paradigm, grounded in the assumption of self-predictability, asserts that a firm's own characteristics forecast its own returns (see, e.g., Cochrane (2011); Harvey et al. (2016)). Complementing this view is a growing literature on cross-predictability--the idea that the characteristics or returns of one asset can help forecast the returns of others (see, e.g., Lo and MacKinlay (1990); Hou (2007); Cohen and Frazzini (2008); Cohen and Lou (2012); Huang et al. (2021, 2022)). A key mechanism underpinning this phenomenon is the presence of lead-lag effects, whereby price movements or information from one firm precede and predict those of related firms. Such effects can stem from staggered information diffusion, peer influence within industries, supply chain linkages, or correlated trading by institutional investors that induces price pressure across related assets. Despite recent methodological advances in modeling cross-stock predictability, several foundational questions remain unresolved. Chief among them is how a mean-variance investor can analytically integrate multiple predictive signals when returns are interconnected across assets. Equally crucial is developing a framework that jointly captures both the relevance of individual signals and the structure of return spillovers--enhancing portfolio performance while preserving interpretability .

We study the optimization of functions with $n>2$ arguments that have a representation as a sum of several functions that have only $2$ of the $n$ arguments each, termed sums of bivariates, on finite domains. The complexity of optimizing sums of bivariates is shown to be NP-equivalent and it is shown that there exists free lunch in the optimization of sums of bivariates. Based on measure-valued extensions of the objective function, so-called relaxations, $\ell^2$-approximation, and entropy-regularization, we derive several tractable problem formulations solvable with linear programming, coordinate ascent as well as with closed-form solutions. The limits of applying tractable versions of such relaxations to sums of bivariates are investigated using general results for reconstructing measures from their bivariate marginals. Experiments in which the derived algorithms are applied to random functions, vertex coloring, and signal reconstruction problems provide insights into qualitatively different function classes that can be modeled as sums of bivariates.

Scientists have developed hundreds of techniques to measure the interactions between pairs of processes in complex systems. But these computational methods, from correlation coefficients to causal inference, rely on distinct quantitative theories that remain largely disconnected. Here we introduce a library of 237 statistics of pairwise interactions and assess their behavior on 1053 multivariate time series from a wide range of real-world and model-generated systems. Our analysis highlights new commonalities between different mathematical formulations, providing a unified picture of a rich interdisciplinary literature. Using three real-world case studies, we then show that simultaneously leveraging diverse methods from across science can uncover those most suitable for addressing a given problem, yielding interpretable understanding of the conceptual formulations of pairwise dependence that drive successful performance. Our framework is provided in extendable open software, enabling comprehensive data-driven analysis by integrating decades of methodological advances.

Even for a medical discipline steeped in a tradition of randomized trials, the evidence basis for only a few guidelines is based on randomized trials (Tricoci et al., 2009). In part this is due to continued development of treatments, in part to enormous expense of clinical trials, and in large part to the hundreds of treatments and their nuances involved in real-world, heterogeneous clinical practice. Thus, many therapeutic decisions are based on observational studies. However, comparative treatment effectiveness studies of observational data suffer from two major problems: only partial overlap of treatments and selection bias. Each treatment is to a degree bounded within constraints of indication and appropriateness. Thus, transplantation is constrained by variables such as age, a mitral valve procedure is constrained by presence of mitral valve regurgitation. However, these boundaries overlap widely, and the same patient may be treated differently by different physicians or different hospitals, often without explicit or evident reasons. Thus, a fundamental hurdle in observational studies evaluating comparative effectiveness of treatment options is to address the resulting selection bias or confounding. Naively evaluating differences in outcomes without doing so leads to biased results and flawed scientific conclusions.