supplement
The Sperm-Maxxing Bros Are Actually Onto Something
Wellness influencers have stumbled onto a huge issue when it comes male fertility, though not every solution they're pitching is good advice. Supplements are "like a religion" for Pachi Paris, a 29-year-old from Miami who works in finance. So when he and his wife started trying to conceive last year, it felt only natural that he started taking pills meant to boost his fertility, to the tune of $250 per month. Six months later, "we found it odd that she's not pregnant yet," Paris said. "We both got a workup done, and it turns out that I was one that had some health issues going on with my sperm."
Leveraging heterogeneity for identifiability: Bayesian order-based learning of multiple DAGs
Chang, Hyunwoong, Taskin, Fariha
We propose a joint order-based scoring framework for causal structure learning of directed acyclic graph (DAG) models under heterogeneous data settings. We show that leveraging heterogeneity improves the accuracy of causal ordering estimation. In the most favorable case, the causal ordering is identifiable up to two permutations. Building on this framework, we propose an order-based Bayesian method for Gaussian DAG models and establish its theoretical properties in the high-dimensional regime. For posterior inference over the space of orderings, we introduce a random-to-random (R2R) proposal neighborhood for the Metropolis-Hastings algorithm, which is theoretically motivated and exhibits efficient mixing behavior. Simulation studies confirm the strong empirical performance of the proposed method, and an application to single-nucleus RNA sequencing data from major depressive disorder demonstrates practical utility.
Supplement to " Uniform Concentration Bounds toward a Unified Framework for Robust Clustering "
For the theoretical exposition, we first establish the following Lemmas. Lemma A.1 proves that the derivative of the function φis bounded in the `2-norm when the domain is restricted to the support of P. Lemma A.1. Lemma A.3 proves that the function fΘ, as a function of Θ, is Lipschitz with respect to the k k norm. Joint first authors contributed equally Corresponding author 35th Conference on Neural Information Processing Systems (NeurIPS 2021). Thus, from equation (1), h φ(PC(θ)) φ(θ),x PC(θ)i 0. (2) We now observe that, dφ(x,θ) dφ(x,PC(θ)) dφ(PC(θ),θ) = h φ(PC(θ)) φ(θ),x PC(θ)i 0. Hence the result.