Simulation-based science often requires a distribution over simulator parameters whose push-forward reproduces a set of real observations: this is the source distribution estimation (SDE) problem. Existing methods fit the source against a likelihood surrogate trained once from a fixed proposal prior. Their objective is therefore stated only in terms of the surrogate instead of the true simulator, which may fail for inaccurate areas in parameter space where the surrogate was never trained. We instead solve SDE by expectation maximization: an E-step trains an amortized posterior on fresh simulations from the current source estimate, and an M-step refits the source to the average of that posterior over the observed data. We give two parameterizations, (1) separate source and posterior flows and (2) a single shared conditional flow. We evaluate our method on three benchmark tasks under both broad and misspecified initial priors. Both improve on existing fixed surrogate approaches and on iterated variants of each, most clearly on Lotka--Volterra, where no baseline falls below 0.96 data-space C2ST while our methods reach 0.64-0.68 in three of four initial-prior settings.
Nawel Arab, Mohammed Nabil El Korso, Isabelle Vin +1astro-ph.IM cs.LG stat.ML
State--space models provide a flexible framework for analyzing dynamical systems, yet they often rely on Gaussian assumptions that fail to capture heavy-tailed or outlier-prone measurement noise. We propose a robust estimation scheme for linear state--space models subject to compound-Gaussian noise, as encountered for instance in radio interferometry affected by radio-frequency interference (RFI). The method relies on a Stochastic Approximation Expectation--Maximization (SAEM) algorithm in which the standard E-step is replaced by Monte Carlo sampling of the latent states and noise texture through closed-form Gibbs updates, enabling tractable inference despite the heavy-tailed likelihood. Numerical experiments show that the proposed method significantly improves reconstruction fidelity and robustness to RFI, outperforming a Gaussian EM algorithm and even an oracle RTS smoother. These results highlight the benefits of heavy-tailed state--space modeling and SAEM-based inference in interference-dominated imaging scenarios.
In this article we describe Cohort Organized Learning (CoOL), a method for clustering data without explicit distance or similarity computations. Herein, we will describe CoOL, derive the gradients determined by expectation maximization to train the networks, show how to monitor convergence during training and evaluate the clusters after training, and discuss a series of examples and use cases. We also discuss CoOL's limitations and future prospects on related tasks. Because CoOL uses neural networks to estimate the clusters, it can be used to cluster any data that can be made compatible and we illustrate this on vector data and images.
Neurosymbolic (NeSy) models integrate neural networks and symbolic reasoning for robust and interpretable AI. State-of-the-art NeSy models require that the symbolic component is expressed in a differentiable way, often complicating the use of approximate inference. We propose EM-NeSy which casts probabilistic NeSy learning as an instance of the Expectation-Maximization (EM) algorithm. In the expectation step, we compute the posterior over the neurally predicted symbols conditioned on the label via probabilistic inference. In the maximization step, we update the neural parameters based on this posterior using gradient descent only through the neural component. This formulation unlocks the full potential of the EM algorithm for NeSy learning. It allows NeSy to extend naturally to approximate reasoning without any additional modifications or differentiability requirements of the symbolic component. Furthermore, it recovers the standard end-to-end gradient-based NeSy setting under exact inference. Our experimental results demonstrate the scalability and computational efficiency of EM-NeSy.