Causal discovery aims to learn causal relationships between variables from targeted data, making it a fundamental task in machine learning. However, causal discovery algorithms often rely on unverifiable causal assumptions, which are usually difficult to satisfy in real-world data, thereby limiting the broad application of causal discovery in practical scenarios. Inspired by these considerations, this work extensively benchmarks the empirical performance of various mainstream causal discovery algorithms, which assume i.i.d. data, under eight model assumption violations. Our experimental results show that differentiable causal discovery methods exhibit robustness under the metrics of Structural Hamming Distance and Structural Intervention Distance of the inferred graphs in commonly used challenging scenarios, except for scale variation. We also provide the theoretical explanations for the performance of differentiable causal discovery methods. Finally, our work aims to comprehensively benchmark the performance of recent differentiable causal discovery methods under model assumption violations, and provide the standard for reasonable evaluation of causal discovery, as well as to further promote its application in real-world scenarios.

PAC generalization bounds on the risk, when expressed in terms of the expected loss, are often insufficient to capture imbalances between subgroups in the data. To overcome this limitation, we introduce a new family of risk measures, called constrained f-entropic risk measures, which enable finer control over distributional shifts and subgroup imbalances via f-divergences, and include the Conditional Value at Risk (CVaR), a well-known risk measure. We derive both classical and disintegrated PAC-Bayesian generalization bounds for this family of risks, providing the first disintegratedPAC-Bayesian guarantees beyond standard risks. Building on this theory, we design a self-bounding algorithm that minimizes our bounds directly, yielding models with guarantees at the subgroup level. Finally, we empirically demonstrate the usefulness of our approach.

Derivative-free Bayesian inversion is an important task in many science and engineering applications, particularly when computing the forward model derivative is computationally and practically challenging. In this paper, we introduce Blade, which can produce accurate and well-calibrated posteriors for Bayesian inversion using an ensemble of interacting particles. Blade leverages powerful data-driven priors based on diffusion models, and can handle nonlinear forward models that permit only black-box access (i.e., derivative-free). Theoretically, we establish a non-asymptotic convergence analysis to characterize the effects of forward model and prior estimation errors. Empirically, Blade achieves superior performance compared to existing derivative-free Bayesian inversion methods on various inverse problems, including challenging highly nonlinear fluid dynamics.

Anemia, a condition marked by insufficient levels of red blood cells or hemoglobin, remains a widespread health issue affecting millions of individuals globally. Accurate and timely diagnosis is essential for effective management and treatment of anemia. In recent years, there has been a growing interest in the use of artificial intelligence techniques, i.e., machine learning (ML) and deep learning (DL) for the detection, classification, and diagnosis of anemia. This paper provides a systematic review of the recent advancements in this field, with a focus on various models applied to anemia detection. The review also compares these models based on several performance metrics, including accuracy, sensitivity, specificity, and precision. By analyzing these metrics, the paper evaluates the strengths and limitation of discussed models in detecting and classifying anemia, emphasizing the importance of addressing these factors to improve diagnostic accuracy.

Deploying reinforcement learning (RL) in robotics, industry, and health care is blocked by two obstacles: the difficulty of specifying accurate rewards and the risk of unsafe, data-hungry exploration. We address this by proposing a two-stage framework that first learns a safe initial policy from a reward-free dataset of expert demonstrations, then fine-tunes it online using preference-based human feedback. We provide the first principled analysis of this offline-to-online approach and introduce BRIDGE, a unified algorithm that integrates both signals via an uncertainty-weighted objective. We derive regret bounds that shrink with the number of offline demonstrations, explicitly connecting the quantity of offline data to online sample efficiency. We validate BRIDGE in discrete and continuous control MuJoCo environments, showing it achieves lower regret than both standalone behavioral cloning and online preference-based RL. Our work establishes a theoretical foundation for designing more sample-efficient interactive agents.

Personalized Bayesian federated learning (PBFL) handles non-i.i.d. client data and quantifies uncertainty by combining personalization with Bayesian inference. However, existing PBFL methods face two limitations: restrictive parametric assumptions in client posterior inference and naive parameter averaging for server aggregation. To overcome these issues, we propose FedWBA, a novel PBFL method that enhances both local inference and global aggregation. At the client level, we use particle-based variational inference for nonparametric posterior representation. At the server level, we introduce particle-based Wasserstein barycenter aggregation, offering a more geometrically meaningful approach. Theoretically, we provide local and global convergence guarantees for FedWBA. Locally, we prove a KL divergence decrease lower bound per iteration for variational inference convergence. Globally, we show that the Wasserstein barycenter converges to the true parameter as the client data size increases. Empirically, experiments show that FedWBA outperforms baselines in prediction accuracy, uncertainty calibration, and convergence rate, with ablation studies confirming its robustness.

Deep learning has generated diverse perspectives in astronomy, with ongoing discussions between proponents and skeptics motivating this review. We examine how neural networks complement classical statistics, extending our data analytical toolkit for modern surveys. Astronomy offers unique opportunities through encoding physical symmetries, conservation laws, and differential equations directly into architectures, creating models that generalize beyond training data. Yet challenges persist as unlabeled observations number in billions while confirmed examples with known properties remain scarce and expensive. This review demonstrates how deep learning incorporates domain knowledge through architectural design, with built-in assumptions guiding models toward physically meaningful solutions. We evaluate where these methods offer genuine advances versus claims requiring careful scrutiny. - Neural architectures overcome trade-offs between scalability, expressivity, and data efficiency by encoding physical symmetries and conservation laws into network structure, enabling learning from limited labeled data. - Simulation-based inference and anomaly detection extract information from complex, non-Gaussian distributions where analytical likelihoods fail, enabling field-level cosmological analysis and systematic discovery of rare phenomena. - Multi-scale neural modeling bridges resolution gaps in astronomical simulations, learning effective subgrid physics from expensive high-fidelity runs to enhance large-volume calculations where direct computation remains prohibitive. - Emerging paradigms-reinforcement learning for telescope operations, foundation models learning from minimal examples, and large language model agents for research automation-show promise though are still developing in astronomical applications.

Belief systems are rarely globally consistent, yet effective reasoning often persists locally. We propose a novel graph-theoretic framework that cleanly separates credibility--external, a priori trust in sources--from confidence--an internal, emergent valuation induced by network structure. Beliefs are nodes in a directed, signed, weighted graph whose edges encode support and contradiction. Confidence is obtained by a contractive propagation process that mixes a stated prior with structure-aware influence and guarantees a unique, stable solution. Within this dynamics, we define reasoning zones: high-confidence, structurally balanced subgraphs on which classical inference is safe despite global contradictions. We provide a near-linear procedure that seeds zones by confidence, tests balance using a parity-based coloring, and applies a greedy, locality-preserving repair with Jaccard de-duplication to build a compact atlas. To model belief change, we introduce shock updates that locally downscale support and elevate targeted contradictions while preserving contractivity via a simple backtracking rule. Re-propagation yields localized reconfiguration-zones may shrink, split, or collapse--without destabilizing the entire graph. We outline an empirical protocol on synthetic signed graphs with planted zones, reporting zone recovery, stability under shocks, and runtime. The result is a principled foundation for contradiction-tolerant reasoning that activates classical logic precisely where structure supports it.

Diffusion Posterior Sampling (DPS) provides a principled Bayesian approach to inverse problems by sampling from $p(x_0 \mid y)$. However, in practice, the goal of inverse problem solving is not to cover the posterior but to recover the most accurate reconstruction, where optimization-based diffusion solvers often excel despite lacking a clear probabilistic foundation. We introduce Local MAP Sampling (LMAPS), a new inference framework that iteratively solving local MAP subproblems along the diffusion trajectory. This perspective clarifies their connection to global MAP estimation and DPS, offering a unified probabilistic interpretation for optimization-based methods. Building on this foundation, we develop practical algorithms with a probabilistically interpretable covariance approximation, a reformulated objective for stability and interpretability, and a gradient approximation for non-differentiable operators. Across a broad set of image restoration and scientific tasks, LMAPS achieves state-of-the-art performance, including $\geq 2$ dB gains on motion deblurring, JPEG restoration, and quantization, and $>1.5$ dB improvements on inverse scattering benchmarks.

Conditional sampling is a fundamental task in Bayesian statistics and generative modeling. Consider the problem of sampling from the posterior distribution $P_{X|Y=y^*}$ for some observation $y^*$, where the likelihood $P_{Y|X}$ is known, and we are given $n$ i.i.d. samples $D=\{X_i\}_{i=1}^n$ drawn from an unknown prior distribution $π_X$. Suppose that $f(\hatπ_{X^n})$ is the distribution of a posterior sample generated by an algorithm (e.g. a conditional generative model or the Bayes rule) when $\hatπ_{X^n}$ is the empirical distribution of the training data. Although averaging over the randomness of the training data $D$, we have $\mathbb{E}_D\left(\hatπ_{X^n}\right)= π_X$, we do not have $\mathbb{E}_D\left\{f(\hatπ_{X^n})\right\}= f(π_X)$ due to the nonlinearity of $f$, leading to a bias. In this paper we propose a black-box debiasing scheme that improves the accuracy of such a naive plug-in approach. For any integer $k$ and under boundedness of the likelihood and smoothness of $f$, we generate samples $\hat{X}^{(1)},\dots,\hat{X}^{(k)}$ and weights $w_1,\dots,w_k$ such that $\sum_{i=1}^kw_iP_{\hat{X}^{(i)}}$ is a $k$-th order approximation of $f(π_X)$, where the generation process treats $f$ as a black-box. Our generation process achieves higher accuracy when averaged over the randomness of the training data, without degrading the variance, which can be interpreted as improving memorization without compromising generalization in generative models.