A central goal in nonparametric statistics is adaptation: the ability of an estimator to perform simultaneously and optimally across a wide variety of settings with little to no tuning. When inference is carried out over a class of functional spaces, it is desirable that the estimator automatically adapts to unknown features of these spaces, such as smoothness, geometry, sparsity or other finer structural properties. A large body of literature has focused on adaptation: Lepski's method Lepski ı [1990, 1991], thresholding Donoho et al. [1995] and model selection Barron et al. [1999] are amongst the most well-known nonBayesian approaches. Bayesian methods, on the other hand, have a natural ability to achieve adaptation, as we discuss in more detail below, by choosing prior distributions that are flexible enough to achieve this task (one possibility is for instance to draw certain prior parameters at random in a hierarchical Bayes fashion). Recently, motivated by the remarkable empirical success of deep learning methods, there has been a growing interest in understanding how neural networks can automatically learn structural parameters, such as smoothness of functions or'effective' dimensions, for instance in regression settings exhibiting a compositional structure as in Schmidt-Hieber [2020], Kohler and Langer [2021] or for data lying on geometric structures (e.g.

The growing popularity of vine copulas in multivariate statistical analysis is largely driven by their ability to capture complex dependence structures. However, this flexibility comes at a cost, as the number of possible vine models grows rapidly and becomes intractable even in moderately low-dimensional settings. These limitations affect the practical applicability of current Bayesian inference and model selection approaches, effectively restricting it to problems of relatively small-dimension due to their high computational cost. This paper addresses the still open challenge of efficient model selection and estimation in Bayesian vine methodology. We propose a novel framework for Bayesian vine copula model selection that combines loss-based model priors with the shotgun stochastic search strategy. The strength of the proposed approach is twofold: it promotes sparsity and enables fast and effective structure selection. Furthermore, our comprehensive framework jointly identifies the vine structure, selects the copula families, and estimates the model parameters. The power of the proposed approach is demonstrated via simulation studies and an application to a real dataset of EFT portfolio asset returns.

Communication is one of the effective means to improve the learning of cooperative policy in multi-agent systems. However, in most real-world scenarios, lossy communication is a prevalent issue. Existing multi-agent reinforcement learning with communication, due to their limited scalability and robustness, struggles to apply to complex and dynamic real-world environments. To address these challenges, we propose a generalized communication-constrained model to uniformly characterize communication conditions across different scenarios. Based on this, we utilize it as a learning prior to distinguish between lossy and lossless messages for specific scenarios. Additionally, we decouple the impact of lossy and lossless messages on distributed decision-making, drawing on a dual mutual information estimatior, and introduce a communication-constrained multi-agent reinforcement learning framework, quantifying the impact of communication messages into the global reward.

When building a world model, a common assumption is that the environment has a single, unchanging underlying causal rule, like applying Newton's laws to every situation. However, in truly open-ended environments, the apparent causal mechanism may drift over time because the agent continually encounters novel contexts and operates within a limited observational window. This brings about a problem that, when building a world model, even subtle shifts in policy or environment states can alter the very observed causal mechanisms. In this work, we introduce the Meta-Causal Graph as world models for open-ended environments, a minimal unified representation that efficiently encodes the transformation rules governing how causal structures shift across different latent world states. A single Meta-Causal Graph is composed of multiple causal subgraphs, each triggered by meta state, which is in the latent state space. Building on this representation, we introduce a Causality-Seeking Agent whose objectives are to (1) identify the meta states that trigger each subgraph, (2) discover the corresponding causal relationships by agent curiosity-driven intervention policy, and (3) iteratively refine the Meta-Causal Graph through ongoing curiosity-driven exploration and agent experiences. Experiments on both synthetic tasks and a challenging robot arm manipulation task demonstrate that our method robustly captures shifts in causal dynamics and generalizes effectively to previously unseen contexts.

We study offline policy optimization for infinite-horizon average-reward Markov decision processes (MDPs) with large or infinite state spaces. Specifically, we propose a pessimistic version of actor-critic methods using a computationally efficient linear function class for value function estimation. At the core of our method is a critic that computes a pessimistic estimate of the average reward under the current policy, as well as the corresponding policy gradient, by solving a fixedpoint Bellman equation, rather than solving a successive sequence of regression problems as in finite horizon settings. Due to the nature of our policy-based method, the critic only needs to solve a linear optimization problem with convex quadratic constraints. We show that a very mild data coverage requirement is sufficient for our algorithm to achieve O(ε 2) sample complexity for learning a near-optimal policy up to model misspecification errors. To our knowledge, this is the first result with optimal εdependence in the offline average reward setting.

Discrete diffusion models have recently gained significant attention due to their ability to process complex discrete structures for language modeling. However, fine-tuning these models with policy gradient methods, as is commonly done in Reinforcement Learning from Human Feedback (RLHF), remains a challenging task. We propose an efficient, broadly applicable, and theoretically justified policy gradient algorithm, called Score Entropy Policy Optimization (SEPO), for finetuning discrete diffusion models over non-differentiable rewards. Our numerical experiments across several discrete generative tasks demonstrate the scalability and efficiency of our method. Our code is available at https://github.com/ozekri/SEPO.

Recurrent neural networks (RNNs) provide a powerful approach in neuroscience to infer latent dynamics in neural populations and to generate hypotheses about the neural computations underlying behavior. However, past work has focused on relatively simple, input-driven, and largely deterministic behaviors - little is known about the mechanisms that would allow RNNs to generate the richer, spontaneous, and potentially stochastic behaviors observed in natural settings. Modeling with Hidden Markov Models (HMMs) has revealed a segmentation of natural behaviors into discrete latent states with stochastic transitions between them, a type of dynamics that may appear at odds with the continuous state spaces implemented by RNNs. Here we first show that RNNs can replicate HMM emission statistics and then reverse-engineer the trained networks to uncover the mechanisms they implement. In the absence of inputs, the activity of trained RNNs collapses towards a single fixed point.

In domain adaption (DA), joint maximum mean discrepancy (JMMD), as a famous distribution-distance metric, aims to measure joint probability distribution difference between the source domain and target domain, while it is still not fully explored and especially hard to be applied into a subspace-learning framework as its empirical estimation involves a tensor-product operator whose partial derivative is difficult to obtain. To solve this issue, we deduce a concise JMMD based on the Representer theorem that avoids the tensor-product operator and obtains two essential findings. First, we reveal the uniformity of JMMD by proving that previous marginal, class conditional, and weighted class conditional probability distribution distances are three special cases of JMMD with different label reproducing kernels. Second, inspired by graph embedding, we observe that the similarity weights, which strengthen the intra-class compactness in the graph of Hilbert Schmidt independence criterion (HSIC), take opposite signs in the graph of JMMD, revealing why JMMD degrades the feature discrimination. This motivates us to propose a novel loss JMMD-HSIC by jointly considering JMMD and HSIC to promote discrimination of JMMD. Extensive experiments on several cross-domain datasets could demonstrate the validity of our revealed theoretical results and the effectiveness of our proposed JMMD-HSIC.

We study a sequential decision-making problem on a n-node graph G where each node has an unknown label from a finite set Ω, drawn from a joint distribution P that is Markov with respect to G. At each step, selecting a node reveals its label and yields a label-dependent reward. The goal is to adaptively choose nodes to maximize expected accumulated discounted rewards. We impose a frontier exploration constraint, where actions are limited to neighbors of previously selected nodes, reflecting practical constraints in settings such as contact tracing and robotic exploration. We design a Gittins index-based policy that applies to general graphs and is provably optimal when G is a forest.

Concept-based models are an emerging paradigm in deep learning that constrains the inference process to operate through human-interpretable variables, facilitating explainability and human interaction. However, these architectures, on par with popular opaque neural models, fail to account for the true causal mechanisms underlying the target phenomena represented in the data. This hampers their ability to support causal reasoning tasks, limits out-of-distribution generalization, and hinders the implementation of fairness constraints. To overcome these issues, we propose Causally reliable Concept Bottleneck Models (C2BMs), a class of concept-based architectures that enforce reasoning through a bottleneck of concepts structured according to a model of the real-world causal mechanisms. We also introduce a pipeline to automatically learn this structure from observational data and unstructured background knowledge (e.g., scientific literature). Experimental evidence suggests that C2BMs are more interpretable, causally reliable, and improve responsiveness to interventions w.r.t.