Vincent Guan

Joseph Janssen, Vincent Guan, Elina Robeva

Scientists frequently prioritize learning from data rather than training the best possible model; however, research in machine learning often prioritizes the latter. Marginal contribution feature importance (MCI) was developed to break this trend by providing a useful framework for quantifying the relationships in data. In this work, we aim to improve upon the theoretical properties, performance, and runtime of MCI by introducing ultra-marginal feature importance (UMFI), which uses dependence removal techniques from the AI fairness literature as its foundation. We first propose axioms for feature importance methods that seek to explain the causal and associative relationships in data, and we prove that UMFI satisfies these axioms under basic assumptions. We then show on real and simulated data that UMFI performs better than MCI, especially in the presence of correlated interactions and unrelated features, while partially learning the structure of the causal graph and reducing the exponential runtime of MCI to super-linear.

Vincent Guan, Lazar Atanackovic, Kirill Neklyudov

The population dynamics of molecules, cells, and organisms are governed by a number of unknown forces. In the last decade, population dynamics have predominantly been modeled with Wasserstein gradient flows. However, since gradient flows minimize free energy, they fail to capture important dynamical properties, such as periodicity. In this work, we propose a change in perspective by considering dynamics that minimize a population-level action under a damped Wasserstein Lagrangian. By deriving the corresponding Hamiltonian equations of motion, we formalize Wasserstein Lagrangian Mechanics, a structured class of second-order dynamics that encompasses classical mechanics, quantum mechanics, and gradient flows. We then propose WLM as the first algorithm that learns these second-order dynamics from observed marginals, without specifying the Lagrangian. By directly learning the population mechanics, WLM can both forecast and interpolate unseen marginals, and outperforms existing gradient flow and flow matching methods across a wide range of dynamics, including vortex dynamics, embryonic development, and flocking.

Vincent Guan, Joseph Janssen, Hossein Rahmani et al.

Stochastic differential equations (SDEs) are a fundamental tool for modelling dynamic processes, including gene regulatory networks (GRNs), contaminant transport, financial markets, and image generation. However, learning the underlying SDE from data is a challenging task, especially if individual trajectories are not observable. Motivated by burgeoning research in single-cell datasets, we present the first comprehensive approach for jointly identifying the drift and diffusion of an SDE from its temporal marginals. Assuming linear drift and additive diffusion, we prove that these parameters are identifiable from marginals if and only if the initial distribution lacks any generalized rotational symmetries. We further prove that the causal graph of any SDE with additive diffusion can be recovered from the SDE parameters. To complement this theory, we adapt entropy-regularized optimal transport to handle anisotropic diffusion, and introduce APPEX (Alternating Projection Parameter Estimation from $X_0$), an iterative algorithm designed to estimate the drift, diffusion, and causal graph of an additive noise SDE, solely from temporal marginals. We show that APPEX iteratively decreases Kullback-Leibler divergence to the true solution, and demonstrate its effectiveness on simulated data from linear additive noise SDEs.

Vincent Guan, Florent Guépin, Ana-Maria Cretu et al.

Location data is frequently collected from populations and shared in aggregate form to guide policy and decision making. However, the prevalence of aggregated data also raises the privacy concern of membership inference attacks (MIAs). MIAs infer whether an individual's data contributed to the aggregate release. Although effective MIAs have been developed for aggregate location data, these require access to an extensive auxiliary dataset of individual traces over the same locations, which are collected from a similar population. This assumption is often impractical given common privacy practices surrounding location data. To measure the risk of an MIA performed by a realistic adversary, we develop the first Zero Auxiliary Knowledge (ZK) MIA on aggregate location data, which eliminates the need for an auxiliary dataset of real individual traces. Instead, we develop a novel synthetic approach, such that suitable synthetic traces are generated from the released aggregate. We also develop methods to correct for bias and noise, to show that our synthetic-based attack is still applicable when privacy mechanisms are applied prior to release. Using two large-scale location datasets, we demonstrate that our ZK MIA matches the state-of-the-art Knock-Knock (KK) MIA across a wide range of settings, including popular implementations of differential privacy (DP) and suppression of small counts. Furthermore, we show that ZK MIA remains highly effective even when the adversary only knows a small fraction (10%) of their target's location history. This demonstrates that effective MIAs can be performed by realistic adversaries, highlighting the need for strong DP protection.