Existing distribution compression methods, like Kernel Herding (KH), were originally developed for unlabelled data.

Neural processes (NPs) are a class of models that learn stochastic processes directly from data and can be used for inference, sampling and conditional sampling. We introduce a new NP model based on flow matching, a generative modeling paradigm that has demonstrated strong performance on various data modalities. Following the NP training framework, the model provides amortized predictions of conditional distributions over any arbitrary points in the data. Compared to previous NP models, our model is simple to implement and can be used to sample from conditional distributions using an ODE solver, without requiring auxiliary conditioning methods. In addition, the model provides a controllable tradeoff between accuracy and running time via the number of steps in the ODE solver. We show that our model outperforms previous state-of-the-art neural process methods on various benchmarks including synthetic 1DGaussian processes data, 2D images, and real-world weather data.

This position paper argues that post-deployment monitoring in clinical AI is underdeveloped and proposes statistically valid and label-efficient testing frameworks as a principled foundation for ensuring reliability and safety in real-world deployment. A recent review found that only 9% of FDA-registered AI-based healthcare tools include a post-deployment surveillance plan [1]. Existing monitoring approaches are often manual, sporadic, and reactive, making them ill-suited for the dynamic environments in which clinical models operate. We contend that post-deployment monitoring should be grounded in label-efficient and statistically valid testing frameworks, offering a principled alternative to current practices. We use the term "statistically valid" to refer to methods that provide explicit guarantees on error rates (e.g., Type I/II error), enable formal inference under pre-defined assumptions, and support reproducibility--features that align with regulatory requirements. Specifically, we propose that the detection of changes in the data and model performance degradation should be framed as distinct statistical hypothesis testing problems. Grounding monitoring in statistical rigor ensures a reproducible and scientifically sound basis for maintaining the reliability of clinical AI systems. Importantly, it also opens new research directions for the technical community--spanning theory, methods, and tools for statistically principled detection, attribution, and mitigation of post-deployment model failures in real-world settings.

We study the complexity of learning real-valued Multi-Index Models (MIMs) under the Gaussian distribution. AK-MIM is a function f: Rd R that depends only on the projection of its input onto a K-dimensional subspace. We give a general algorithm for PAC learning a broad class of MIMs with respect to the square loss, even in the presence of adversarial label noise. Moreover, we establish a nearly matching Statistical Query (SQ) lower bound, providing evidence that the complexity of our algorithm is qualitatively optimal as a function of the dimension. Specifically, we consider the class of bounded variation MIMs with the property that degree at most m distinguishing moments exist with respect to projections onto any subspace. In the presence of adversarial label noise, the complexity of our learning algorithm is dO(m)2poly(K/ϵ).

Modeling hierarchical latent dynamics behind time series data is critical for capturing temporal dependencies across multiple levels of abstraction in real-world tasks. However, existing temporal causal representation learning methods fail to capture such dynamics, as they fail to recover the joint distribution of hierarchical latent variables from single-timestep observed variables. Interestingly, we find that the joint distribution of hierarchical latent variables can be uniquely determined using three conditionally independent observations. Building on this insight, we propose a Causally Hierarchical Latent Dynamic (CHiLD) identification framework. Our approach first employs temporal contextual observed variables to identify the joint distribution of multi-layer latent variables. Sequentially, we exploit the natural sparsity of the hierarchical structure among latent variables to identify latent variables within each layer. Guided by the theoretical results, we develop a time series generative model grounded in variational inference. This model incorporates a contextual encoder to reconstruct multi-layer latent variables and normalize flowbased hierarchical prior networks to impose the independent noise condition of hierarchical latent dynamics. Empirical evaluations on both synthetic and realworld datasets validate our theoretical claims and demonstrate the effectiveness of CHiLD in modeling hierarchical latent dynamics.

Modeling hierarchical latent dynamics behind time series data is critical for capturing temporal dependencies across multiple levels of abstraction in real-world tasks. However, existing temporal causal representation learning methods fail to capture such dynamics, as they fail to recover the joint distribution of hierarchical latent variables from \textit{single-timestep observed variables}. Interestingly, we find that the joint distribution of hierarchical latent variables can be uniquely determined using three conditionally independent observations. Building on this insight, we propose a Causally Hierarchical Latent Dynamic (CHiLD) identification framework. Our approach first employs temporal contextual observed variables to identify the joint distribution of multi-layer latent variables. Sequentially, we exploit the natural sparsity of the hierarchical structure among latent variables to identify latent variables within each layer. Guided by the theoretical results, we develop a time series generative model grounded in variational inference. This model incorporates a contextual encoder to reconstruct multi-layer latent variables and normalize flow-based hierarchical prior networks to impose the independent noise condition of hierarchical latent dynamics. Empirical evaluations on both synthetic and real-world datasets validate our theoretical claims and demonstrate the effectiveness of CHiLD in modeling hierarchical latent dynamics.

Many decision in clinical science and epidemiology -- estimating probability of technical success for a clinical trial, assessing comparative effectiveness of two therapies, imputing a placebo effect onto natural history data -- rely on combining sources of information about a clinical cohort that comes from different kinds of studies. Specifically we contrast patient-level sources that provide granular pictures of individual disease course (clinical trial, registries, or electronic health records) with aggregate sources such as published clinical trial results and the TFLs (tables figures and listings). One strategy for combining aggregate with patient-level data sources is to bring each into a common format for a unified analysis. If one wants to maintain the analytic flexibility of patient-level data, then a natural solution is to convert the aggregate data information into a simulated patient-level dataset that recapitulate those aggregate statistics. This is an under-determined inverse problem in that there are many such datasets, and it cannot be well specified without further constraints. FRESH(Fusion of Recent Evidence with Subject Histories) provides a well-defined method for solving this problem, and therefore providing maximal analytic flexibility.

Models that rely solely on pairwise relationships often fail to capture the complete statistical structure of the complex multivariate data found in diverse domains, such as socio-economic, ecological, or biomedical systems. Non-trivial dependencies between groups of more than two variables can play a significant role in the analysis and modelling of such systems, yet extracting such high-order interactions from data remains challenging. Here, we introduce a hierarchy of d-order interaction measures, increasingly inclusive of possible factorisations of the joint probability distribution, and define non-parametric, kernel-based tests to establish systematically the statistical significance of d-order interactions. We also establish mathematical links with lattice theory, which elucidate the derivation of the interaction measures and their composite permutation tests; clarify the connection of simplicial complexes with kernel matrix centring; and provide a means to enhance computational efficiency. We illustrate our results numerically with validations on synthetic data, and through an application to neuroimaging data.