--Metaphorical expressions are abundant in Traditional Chinese Medicine (TCM), conveying complex disease mechanisms and holistic health concepts through culturally rich and often abstract terminology. Bridging these metaphors to anatomically driven Western medical (WM) concepts poses significant challenges for both automated language processing and real-world clinical practice. T o address this gap, we propose a novel multi-agent and chain-of-thought (CoT) framework designed to interpret TCM metaphors accurately and map them to WM pathophysiology. Specifically, our approach combines domain-specialized agents (TCM Expert, WM Expert) with a Coordinator Agent, leveraging stepwise chain-of-thought prompts to ensure transparent reasoning and conflict resolution. We detail a methodology for building a metaphor-rich TCM dataset, discuss strategies for effectively integrating multi-agent collaboration and CoT reasoning, and articulate the theoretical underpinnings that guide metaphor interpretation across distinct medical paradigms. We present a comprehensive system design and highlight both the potential benefits and limitations of our approach, while leaving placeholders for future experimental validation. Our work aims to support clinical decision-making, cross-system educational initiatives, and integrated healthcare research, ultimately offering a robust scaffold for reconciling TCM's symbolic language with the mechanistic focus of Western medicine.

In recent years, the ascendance of diffusion modeling as a state-of-the-art generative modeling approach has spurred significant interest in their use as priors in Bayesian inverse problems. However, it is unclear how to optimally integrate a diffusion model trained on the prior distribution with a given likelihood function to obtain posterior samples. While algorithms that have been developed for this purpose can produce high-quality, diverse point estimates of the unknown parameters of interest, they are often tested on problems where the prior distribution is analytically unknown, making it difficult to assess their performance in providing rigorous uncertainty quantification. In this work, we introduce a new framework, Bayesian Inverse Problem Solvers through Diffusion Annealing (BIPSDA), for diffusion model based posterior sampling. The framework unifies several recently proposed diffusion model based posterior sampling algorithms and contains novel algorithms that can be realized through flexible combinations of design choices. Algorithms within our framework were tested on model problems with a Gaussian mixture prior and likelihood functions inspired by problems in image inpainting, x-ray tomography, and phase retrieval. In this setting, approximate ground-truth posterior samples can be obtained, enabling principled evaluation of the performance of the algorithms. The results demonstrate that BIPSDA algorithms can provide strong performance on the image inpainting and x-ray tomography based problems, while the challenging phase retrieval problem, which is difficult to sample from even when the posterior density is known, remains outside the reach of the diffusion model based samplers.

Machine learning models have shown great success in predicting weather up to two weeks ahead, outperforming process-based benchmarks. However, existing approaches mostly focus on the prediction task, and do not incorporate the necessary data assimilation. Moreover, these models suffer from error accumulation in long roll-outs, limiting their applicability to seasonal predictions or climate projections. Here, we introduce Generative Assimilation and Prediction (GAP), a unified deep generative framework for assimilation and prediction of both weather and climate. By learning to quantify the probabilistic distribution of atmospheric states under observational, predictive, and external forcing constraints, GAP excels in a broad range of weather-climate related tasks, including data assimilation, seamless prediction, and climate simulation. In particular, GAP is competitive with state-of-the-art ensemble assimilation, probabilistic weather forecast and seasonal prediction, yields stable millennial simulations, and reproduces climate variability from daily to decadal time scales.

Motivated by the pursuit of safe, reliable, and weather-tolerant urban air mobility (UAM) solutions, this work proposes a generative modeling approach for characterizing microweather wind velocities. Microweather, or the weather conditions in highly localized areas, is particularly complex in urban environments owing to the chaotic and turbulent nature of wind flows. Furthermore, traditional means of assessing local wind fields are not generally viable solutions for UAM applications: 1) field measurements that would rely on permanent wind profiling systems in operational air space are not practical, 2) physics-based models that simulate fluid dynamics at a sufficiently high resolution are not computationally tractable, and 3) data-driven modeling approaches that are largely deterministic ignore the inherent variability in turbulent flows that dictates UAM reliability. Thus, advancements in predictive capabilities are needed to help mitigate the unique operational safety risks that microweather winds pose for smaller, lighter weight UAM aircraft. This work aims to model microweather wind velocities in a manner that is computationally-efficient, captures random variability, and would only require a temporary, rather than permanent, field measurement campaign. Inspired by recent breakthroughs in conditional generative AI such as text-to-image generation, the proposed approach learns a probabilistic macro-to-microweather mapping between regional weather forecasts and measured local wind velocities using generative modeling (denoising diffusion probabilistic models, flow matching, and Gaussian mixture models). A simple proof of concept was implemented using a dataset comprised of local (micro) measurements from a Sonic Detection and Ranging (SoDAR) wind profiler along with (macro) forecast data from a nearby weather station over the same time period.

Most reinforcement learning (RL) approaches for the decision-making of autonomous driving consider safety as a reward instead of a cost, which makes it hard to balance the tradeoff between safety and other objectives. Human risk preference has also rarely been incorporated, and the trained policy might be either conservative or aggressive for users. To this end, this study proposes a human-aligned safe RL approach for autonomous merging, in which the high-level decision problem is formulated as a constrained Markov decision process (CMDP) that incorporates users' risk preference into the safety constraints, followed by a model predictive control (MPC)-based low-level control. The safety level of RL policy can be adjusted by computing cost limits of CMDP's constraints based on risk preferences and traffic density using a fuzzy control method. To filter out unsafe or invalid actions, we design an action shielding mechanism that pre-executes RL actions using an MPC method and performs collision checks with surrounding agents. We also provide theoretical proof to validate the effectiveness of the shielding mechanism in enhancing RL's safety and sample efficiency. Simulation experiments in multiple levels of traffic densities show that our method can significantly reduce safety violations without sacrificing traffic efficiency. Furthermore, due to the use of risk preference-aware constraints in CMDP and action shielding, we can not only adjust the safety level of the final policy but also reduce safety violations during the training stage, proving a promising solution for online learning in real-world environments.

This paper proposes the DnD Filter, a differentiable filter that utilizes diffusion models for state estimation of dynamic systems. Unlike conventional differentiable filters, which often impose restrictive assumptions on process noise (e.g., Gaussianity), DnD Filter enables a nonlinear state update without such constraints by conditioning a diffusion model on both the predicted state and observational data, capitalizing on its ability to approximate complex distributions. We validate its effectiveness on both a simulated task and a real-world visual odometry task, where DnD Filter consistently outperforms existing baselines. Specifically, it achieves a 25\% improvement in estimation accuracy on the visual odometry task compared to state-of-the-art differentiable filters, and even surpasses differentiable smoothers that utilize future measurements. To the best of our knowledge, DnD Filter represents the first successful attempt to leverage diffusion models for state estimation, offering a flexible and powerful framework for nonlinear estimation under noisy measurements.

Posterior sampling with the spike-and-slab prior [MB88], a popular multimodal distribution used to model uncertainty in variable selection, is considered the theoretical gold standard method for Bayesian sparse linear regression [CPS09, Roc18]. However, designing provable algorithms for performing this sampling task is notoriously challenging. Existing posterior samplers for Bayesian sparse variable selection tasks either require strong assumptions about the signal-to-noise ratio (SNR) [YWJ16], only work when the measurement count grows at least linearly in the dimension [MW24], or rely on heuristic approximations to the posterior. We give the first provable algorithms for spike-and-slab posterior sampling that apply for any SNR, and use a measurement count sublinear in the problem dimension. Concretely, assume we are given a measurement matrix $\mathbf{X} \in \mathbb{R}^{n\times d}$ and noisy observations $\mathbf{y} = \mathbf{X}\mathbf{\theta}^\star + \mathbf{\xi}$ of a signal $\mathbf{\theta}^\star$ drawn from a spike-and-slab prior $\pi$ with a Gaussian diffuse density and expected sparsity k, where $\mathbf{\xi} \sim \mathcal{N}(\mathbb{0}_n, \sigma^2\mathbf{I}_n)$. We give a polynomial-time high-accuracy sampler for the posterior $\pi(\cdot \mid \mathbf{X}, \mathbf{y})$, for any SNR $\sigma^{-1}$ > 0, as long as $n \geq k^3 \cdot \text{polylog}(d)$ and $X$ is drawn from a matrix ensemble satisfying the restricted isometry property. We further give a sampler that runs in near-linear time $\approx nd$ in the same setting, as long as $n \geq k^5 \cdot \text{polylog}(d)$. To demonstrate the flexibility of our framework, we extend our result to spike-and-slab posterior sampling with Laplace diffuse densities, achieving similar guarantees when $\sigma = O(\frac{1}{k})$ is bounded.

Gaussian Process (GP) models are widely utilized as surrogate models in scientific and engineering fields. However, standard GP models are limited to continuous variables due to the difficulties in establishing correlation structures for categorical variables. To overcome this limitati on, we introduce WEighted Euclidean distance matrices Gaussian Process (WEGP). WEGP constructs the kernel function for each categorical input by estimating the Euclidean distance matrix (EDM) among all categorical choices of this input. The EDM is represented as a linear combination of several predefined base EDMs, each scaled by a positive weight. The weights, along with other kernel hyperparameters, are inferred using a fully Bayesian framework. We analyze the predictive performance of WEGP theoretically. Numerical experiments validate the accuracy of our GP model, and by WEGP, into Bayesian Optimization (BO), we achieve superior performance on both synthetic and real-world optimization problems.

In many practical applications of machine learning, a discrepancy often arises between a source distribution from which labeled training examples are drawn and a target distribution for which only unlabeled data is observed. Traditionally, two main scenarios have been considered to address this issue: covariate shift (CS), where only the marginal distribution of features changes, and label shift (LS), which involves a change in the class variable's prior distribution. However, these frameworks do not encompass all forms of distributional shift. This paper introduces a new setting, Conditional Probability Shift (CPS), which captures the case when the conditional distribution of the class variable given some specific features changes while the distribution of remaining features given the specific features and the class is preserved. For this scenario we present the Conditional Probability Shift Model (CPSM) based on modeling the class variable's conditional probabilities using multinomial regression. Since the class variable is not observed for the target data, the parameters of the multinomial model for its distribution are estimated using the Expectation-Maximization algorithm. The proposed method is generic and can be combined with any probabilistic classifier. The effectiveness of CPSM is demonstrated through experiments on synthetic datasets and a case study using the MIMIC medical database, revealing its superior balanced classification accuracy on the target data compared to existing methods, particularly in situations situations of conditional distribution shift and no apriori distribution shift, which are not detected by LS-based methods.

Rigorous statistical evaluations of large language models (LLMs), including valid error bars and significance testing, are essential for meaningful and reliable performance assessment. Currently, when such statistical measures are reported, they typically rely on the Central Limit Theorem (CLT). In this position paper, we argue that while CLT-based methods for uncertainty quantification are appropriate when benchmarks consist of thousands of examples, they fail to provide adequate uncertainty estimates for LLM evaluations that rely on smaller, highly specialized benchmarks. In these small-data settings, we demonstrate that CLT-based methods perform very poorly, usually dramatically underestimating uncertainty (i.e. producing error bars that are too small). We give recommendations for alternative frequentist and Bayesian methods that are both easy to implement and more appropriate in these increasingly common scenarios. We provide a simple Python library for these Bayesian methods at https://github.com/sambowyer/bayes_evals .