Since the debut of DPO, it has been shown that aligning a target LLM with human preferences via the KL-constrained RLHF loss is mathematically equivalent to a special kind of reward modeling task. Concretely, the task requires: 1) using the target LLM to parameterize the reward model, and 2) tuning the reward model so that it has a 1:1 linear relationship with the true reward. However, we identify a significant issue: the DPO loss might have multiple minimizers, of which only one satisfies the required linearity condition. The problem arises from a well-known issue of the underlying Bradley-Terry preference model: it does not always have a unique maximum likelihood estimator (MLE). Consequently,the minimizer of the RLHF loss might be unattainable because it is merely one among many minimizers of the DPO loss. As a better alternative, we propose an energy-based model (EBM) that always has a unique MLE, inherently satisfying the linearity requirement. To approximate the MLE in practice, we propose a contrastive loss named Energy Preference Alignment (EPA), wherein each positive sample is contrasted against one or more strong negatives as well as many free weak negatives. Theoretical properties of our EBM enable the approximation error of EPA to almost surely vanish when a sufficient number of negatives are used. Empirically, we demonstrate that EPA consistently delivers better performance on open benchmarks compared to DPO, thereby showing the superiority of our EBM.

Here, nodes from the two-cluster Stochastic Block Model (SBM) are coupled with feature vectors, which are derived from a Gaussian Mixture Model (GMM) that corresponds to their respective node labels. With only a subset of the CSBM node labels accessible for training, our primary objective becomes the accurate classification of the remaining nodes. Venturing into the transductive learning landscape, we, for the first time, pinpoint the information-theoretical threshold for the exact recovery of all test nodes in CSBM. Concurrently, we design an optimal spectral estimator inspired by Principal Component Analysis (PCA) with the training labels and essential data from both the adjacency matrix and feature vectors. We also evaluate the efficacy of graph ridge regression and Graph Convolutional Networks (GCN) on this synthetic dataset. Our findings underscore that graph ridge regression and GCN possess the ability to achieve the information threshold of exact recovery in a manner akin to the optimal estimator when using the optimal weighted self-loops. This highlights the potential role of feature learning in augmenting the proficiency of GCN, especially in the realm of semi-supervised learning.

Large language models (LLMs), trained on diverse data effectively acquire a breadth of information across various domains. However, their computational complexity, cost, and lack of transparency hinder their direct application for specialised tasks. In fields such as clinical research, acquiring expert annotations or prior knowledge about predictive models is often costly and time-consuming. This study proposes the use of LLMs to elicit expert prior distributions for predictive models. This approach also provides an alternative to in-context learning, where language models are tasked with making predictions directly. In this work, we compare LLM-elicited and uninformative priors, evaluate whether LLMs truthfully generate parameter distributions, and propose a model selection strategy for in-context learning and prior elicitation. Our findings show that LLM-elicited prior parameter distributions significantly reduce predictive error compared to uninformative priors in low-data settings. Applied to clinical problems, this translates to fewer required biological samples, lowering cost and resources. Prior elicitation also consistently outperforms and proves more reliable than in-context learning at a lower cost, making it a preferred alternative in our setting. We demonstrate the utility of this method across various use cases, including clinical applications. For infection prediction, using LLM-elicited priors reduced the number of required labels to achieve the same accuracy as an uninformative prior by 55%, 200 days earlier in the study.

This paper studies semiparametric Bayesian inference for the average treatment effect on the treated (ATT) within the difference-in-differences research design. We propose two new Bayesian methods with frequentist validity. The first one places a standard Gaussian process prior on the conditional mean function of the control group. We obtain asymptotic equivalence of our Bayesian estimator and an efficient frequentist estimator by establishing a semiparametric Bernstein-von Mises (BvM) theorem. The second method is a double robust Bayesian procedure that adjusts the prior distribution of the conditional mean function and subsequently corrects the posterior distribution of the resulting ATT. We establish a semiparametric BvM result under double robust smoothness conditions; i.e., the lack of smoothness of conditional mean functions can be compensated by high regularity of the propensity score, and vice versa. Monte Carlo simulations and an empirical application demonstrate that the proposed Bayesian DiD methods exhibit strong finite-sample performance compared to existing frequentist methods. Finally, we outline an extension to difference-in-differences with multiple periods and staggered entry.

We address the challenge of incorporating document-level metadata into topic modeling to improve topic mixture estimation. To overcome the computational complexity and lack of theoretical guarantees in existing Bayesian methods, we extend probabilistic latent semantic indexing (pLSI), a frequentist framework for topic modeling, by incorporating document-level covariates or known similarities between documents through a graph formalism. Modeling documents as nodes and edges denoting similarities, we propose a new estimator based on a fast graph-regularized iterative singular value decomposition (SVD) that encourages similar documents to share similar topic mixture proportions. We characterize the estimation error of our proposed method by deriving high-probability bounds and develop a specialized cross-validation method to optimize our regularization parameters. We validate our model through comprehensive experiments on synthetic datasets and three real-world corpora, demonstrating improved performance and faster inference compared to existing Bayesian methods.

Spatiotemporal data imputation plays a crucial role in various fields such as traffic flow monitoring, air quality assessment, and climate prediction. However, spatiotemporal data collected by sensors often suffer from temporal incompleteness, and the sparse and uneven distribution of sensors leads to missing data in the spatial dimension. Among existing methods, autoregressive approaches are prone to error accumulation, while simple conditional diffusion models fail to adequately capture the spatiotemporal relationships between observed and missing data. To address these issues, we propose a novel two-stage Refined Diffusion Probability Impuation (RDPI) framework based on an initial network and a conditional diffusion model. In the initial stage, deterministic imputation methods are used to generate preliminary estimates of the missing data. In the refinement stage, residuals are treated as the diffusion target, and observed values are innovatively incorporated into the forward process. This results in a conditional diffusion model better suited for spatiotemporal data imputation, bridging the gap between the preliminary estimates and the true values. Experiments on multiple datasets demonstrate that RDPI not only achieves state-of-the-art imputation accuracy but also significantly reduces sampling computational costs.

In this work, we address the problem of controlling a classifier's accuracy at any user-specified level through selective classification, regardless of the problem's inherent difficulty. Traditional classification frameworks are designed to approximate the Bayes optimal error rate as closely as possible. However, with the growing deployment of artificial intelligence (AI) systems in automated, high-stakes decision-making, it has become critical to ensure reliable control over a classifier's accuracy and to guarantee accurate predictions for all individuals. When the underlying problem is truly difficult, as indicated by the distance between the true distributions for each decision class, achieving control over the error rate of an automated decisionmaking system may be impossible. This is particularly true when the number of potential classes is large or when the distributions of these classes are close enough, significantly increasing the difficulty of the problem. This phenomenon is illustrated in Figure 1, where the task is to classify various observations as High-Risk or Low-Risk, while maintaining an error rate below 5%. In this example, the High-Risk and Low-Risk classes are modeled as mixtures of two normal distributions with means of 2 and 1, respectively, and a shared variance of 1. The Bayes classifier is represented by the dotted line in the leftmost plot of Figure 1. In this scenario, the Bayes optimal error rate is 15.9%, significantly exceeding our target classification error of 5%.

Parametric Bayesian modeling offers a powerful and flexible toolbox for scientific data analysis. Yet the model, however detailed, may still be wrong, and this can make inferences untrustworthy. In this paper we study nonparametrically perturbed parametric (NPP) Bayesian models, in which a parametric Bayesian model is relaxed via a distortion of its likelihood. We analyze the properties of NPP models when the target of inference is the true data distribution or some functional of it, such as in causal inference. We show that NPP models can offer the robustness of nonparametric models while retaining the data efficiency of parametric models, achieving fast convergence when the parametric model is close to true. To efficiently analyze data with an NPP model, we develop a generalized Bayes procedure to approximate its posterior. We demonstrate our method by estimating causal effects of gene expression from single cell RNA sequencing data. NPP modeling offers an efficient approach to robust Bayesian inference and can be used to robustify any parametric Bayesian model.

Recent techniques in deep generative modeling have leveraged Markov generative processes to learn complex, high-dimensional probability distributions in a more structured and flexible manner [17]. By integrating Markov chain methods with deep neural architectures, these approaches aim to exploit the representational power of deep networks while maintaining a tractable and theoretically grounded training procedure. In contrast to early generative models that relied heavily on direct maximum likelihood estimation or adversarial objectives, this class of methods employs iterative stochastic transformations--often expressed as Markovian updates--to gradually refine initial noise samples into samples drawn from the desired target distribution. Diffusion and flow matching models represent two prominent classes of generative approaches that construct data samples through a sequence of continuous transformations. Diffusion models [6, 13] introduce a forward-noising and reverse-denoising process, progressively refining a simple noise distribution into a complex target distribution by learning to undo incremental noise corruption at each step.

In this paper, we study learning and knowledge acquisition (LKA) of an agent about a proposition that is either true or false. We use a Bayesian approach, where the agent receives data to update his beliefs about the proposition according to a posterior distribution. The LKA is formulated in terms of active information, with data representing external or exogenous information that modifies the agent's beliefs. It is assumed that data provide details about a number of features that are relevant to the proposition. We show that this leads to a Gibbs distribution posterior, which is in maximum entropy relative to the prior, conditioned on the side constraints that the data provide in terms of the features. We demonstrate that full learning is sometimes not possible and full knowledge acquisition is never possible when the number of extracted features is too small. We also distinguish between primary learning (receiving data about features of relevance for the proposition) and secondary learning (receiving data about the learning of another agent). We argue that this type of secondary learning does not represent true knowledge acquisition. Our results have implications for statistical learning algorithms, and we claim that such algorithms do not always generate true knowledge. The theory is illustrated with several examples.