'If we build it, they will come': Skövde, the tiny town powering up Sweden's video game boom It started with a goat. Now - via a degree for developers and an incubator for startups - the tiny city is churning out world-famous video game hits. What is the secret of its success? O n 26 March 2014, a trailer for a video game appeared on YouTube. The first thing the viewer sees is a closeup of a goat lying on the ground, its tongue out, its eyes open. Behind it is a man on fire, running backwards in slow motion towards a house.

Identifying and measuring biases associated with sensitive attributes is a crucial consideration in healthcare to prevent treatment disparities. One prominent issue is inaccurate pulse oximeter readings, which tend to overestimate oxygen saturation for dark-skinned patients and misrepresent supplemental oxygen needs. Most existing research has revealed statistical disparities linking device errors to patient outcomes in intensive care units (ICUs) without causal formalization. In contrast, this study causally investigates how racial discrepancies in oximetry measurements affect invasive ventilation in ICU settings. We employ a causal inference-based approach using path-specific effects to isolate the impact of bias by race on clinical decision-making. To estimate these effects, we leverage a doubly robust estimator, propose its self-normalized variant for improved sample efficiency, and provide novel finite-sample guarantees. Our methodology is validated on semi-synthetic data and applied to two large real-world health datasets: MIMIC-IV and eICU. Contrary to prior work, our analysis reveals minimal impact of racial discrepancies on invasive ventilation rates. However, path-specific effects mediated by oxygen saturation disparity are more pronounced on ventilation duration, and the severity differs by dataset. Our work provides a novel and practical pipeline for investigating potential disparities in the ICU and, more crucially, highlights the necessity of causal methods to robustly assess fairness in decision-making.

In this paper we propose Discretely Indexed flows (DIF) as a new tool for solving variational estimation problems. Roughly speaking, DIF are built as an extension of Normalizing Flows (NF), in which the deterministic transport becomes stochastic, and more precisely discretely indexed. Due to the discrete nature of the underlying additional latent variable, DIF inherit the good computational behavior of NF: they benefit from both a tractable density as well as a straightforward sampling scheme, and can thus be used for the dual problems of Variational Inference (VI) and of Variational density estimation (VDE). On the other hand, DIF can also be understood as an extension of mixture density models, in which the constant mixture weights are replaced by flexible functions. As a consequence, DIF are better suited for capturing distributions with discontinuities, sharp edges and fine details, which is a main advantage of this construction. Finally we propose a methodology for constructiong DIF in practice, and see that DIF can be sequentially cascaded, and cascaded with NF.

Causal estimation relies on separating the variation in the outcome due to the confounders from that due to the treatment. To achieve this separation, practitioners can use external sources of randomness that only influence the treatment called instrumental variables (IVs). Traditional IV-methods rely on structural assumptions that limit the effect that the confounders can have on both outcome and treatment. To relax these assumptions we develop a new estimator called the generalized control-function method (GCFN). GCFN's first stage called variational decoupling (VDE) recovers the residual variation in the treatment given the IV. In the second stage, GCFN regresses the outcome on the treatment and residual variation to compute the causal effect. We evaluate GCFN on simulated data and on recovering the causal effect of slave export on community trust. We show how VDE can help unify IV-estimators and non-IV-estimators.

We analyze the Kozachenko–Leonenko (KL) fixed k-nearest neighbor estimator for the differential entropy. We obtain the first uniform upper bound on its performance for any fixed k over H\"{o}lder balls on a torus without assuming any conditions on how close the density could be from zero. Accompanying a recent minimax lower bound over the H\"{o}lder ball, we show that the KL estimator for any fixed k is achieving the minimax rates up to logarithmic factors without cognizance of the smoothness parameter s of the H\"{o}lder ball for $s \in (0,2]$ and arbitrary dimension d, rendering it the first estimator that provably satisfies this property.

Often the analysis of time-dependent chemical and biophysical systems produces high-dimensional time-series data for which it can be difficult to interpret which individual features are most salient. While recent work from our group and others has demonstrated the utility of time-lagged co-variate models to study such systems, linearity assumptions can limit the compression of inherently nonlinear dynamics into just a few characteristic components. Recent work in the field of deep learning has led to the development of variational autoencoders (VAE), which are able to compress complex datasets into simpler manifolds. We present the use of a time-lagged VAE, or variational dynamics encoder (VDE), to reduce complex, nonlinear processes to a single embedding with high fidelity to the underlying dynamics. We demonstrate how the VDE is able to capture nontrivial dynamics in a variety of examples, including Brownian dynamics and atomistic protein folding. Additionally, we demonstrate a method for analyzing the VDE model, inspired by saliency mapping, to determine what features are selected by the VDE model to describe dynamics. The VDE presents an important step in applying techniques from deep learning to more accurately model and interpret complex biophysics.