This paper introduces posterior mean matching (PMM), a new method for generative modeling that is grounded in Bayesian inference. PMM uses conjugate pairs of distributions to model complex data of various modalities like images and text, offering a flexible alternative to existing methods like diffusion models. PMM models iteratively refine noisy approximations of the target distribution using updates from online Bayesian inference. PMM is flexible because its mechanics are based on general Bayesian models. We demonstrate this flexibility by developing specialized examples: a generative PMM model of real-valued data using the Normal-Normal model, a generative PMM model of count data using a Gamma-Poisson model, and a generative PMM model of discrete data using a Dirichlet-Categorical model. For the Normal-Normal PMM model, we establish a direct connection to diffusion models by showing that its continuous-time formulation converges to a stochastic differential equation (SDE). Additionally, for the Gamma-Poisson PMM, we derive a novel SDE driven by a Cox process, which is a significant departure from traditional Brownian motion-based generative models. PMMs achieve performance that is competitive with generative models for language modeling and image generation.

Many inverse problems are ill-posed and need to be complemented by prior information that restricts the class of admissible models. Bayesian approaches encode this information as prior distributions that impose generic properties on the model such as sparsity, non-negativity or smoothness. However, in case of complex structured models such as images, graphs or three-dimensional (3D) objects,generic prior distributions tend to favor models that differ largely from those observed in the real world. Here we explore the use of diffusion models as priors that are combined with experimental data within a Bayesian framework. We use 3D point clouds to represent 3D objects such as household items or biomolecular complexes formed from proteins and nucleic acids. We train diffusion models that generate coarse-grained 3D structures at a medium resolution and integrate these with incomplete and noisy experimental data. To demonstrate the power of our approach, we focus on the reconstruction of biomolecular assemblies from cryo-electron microscopy (cryo-EM) images, which is an important inverse problem in structural biology. We find that posterior sampling with diffusion model priors allows for 3D reconstruction from very sparse, low-resolution and partial observations.

Inspection of infrastructure using static sensor nodes has become a well established approach in recent decades. In this work, we present an experimental setup to address a binary inspection task using mobile sensor nodes. The objective is to identify the predominant tile type in a 1mx1m tiled surface composed of vibrating and non-vibrating tiles. A swarm of miniaturized robots, equipped with onboard IMUs for sensing and IR sensors for collision avoidance, performs the inspection. The decision-making approach leverages a Bayesian algorithm, updating robots' belief using inference. The original algorithm uses one of two information sharing strategies. We introduce a novel information sharing strategy, aiming to accelerate the decision-making. To optimize the algorithm parameters, we develop a simulation framework calibrated to our real-world setup in the high-fidelity Webots robotic simulator. We evaluate the three information sharing strategies through simulations and real-world experiments. Moreover, we test the effectiveness of our optimization by placing swarms with optimized and non-optimized parameters in increasingly complex environments with varied spatial correlation and fill ratios. Results show that our proposed information sharing strategy consistently outperforms previously established information-sharing strategies in decision time. Additionally, optimized parameters yield robust performance across different environments. Conversely, non-optimized parameters perform well in simpler scenarios but show reduced accuracy in complex settings.

Active Inference is a closed-loop computational theoretical basis for understanding behaviour, based on agents with internal probabilistic generative models that encode their beliefs about how hidden states in their environment cause their sensations. We review Active Inference and how it could be applied to model the human-computer interaction loop. Active Inference provides a coherent framework for managing generative models of humans, their environments, sensors and interface components. It informs off-line design and supports real-time, online adaptation. It provides model-based explanations for behaviours observed in HCI, and new tools to measure important concepts such as agency and engagement. We discuss how Active Inference offers a new basis for a theory of interaction in HCI, tools for design of modern, complex sensor-based systems, and integration of artificial intelligence technologies, enabling it to cope with diversity in human users and contexts. We discuss the practical challenges in implementing such Active Inference-based systems.

Dealing with missing data poses significant challenges in predictive analysis, often leading to biased conclusions when oversimplified assumptions about the missing data process are made. In cases where the data are missing not at random (MNAR), jointly modeling the data and missing data indicators is essential. Motivated by a real data application with partially missing multivariate outcomes related to leaf photosynthetic traits and several environmental covariates, we propose two methods under a selection model framework for handling data with missingness in the response variables suitable for recovering various missingness mechanisms. Both approaches use a multivariate extension of Bayesian additive regression trees (BART) to flexibly model the outcomes. The first approach simultaneously uses a probit regression model to jointly model the missingness. In scenarios where the relationship between the missingness and the data is more complex or non-linear, we propose a second approach using a probit BART model to characterize the missing data process, thereby employing two BART models simultaneously. Both models also effectively handle ignorable covariate missingness. The efficacy of both models compared to existing missing data approaches is demonstrated through extensive simulations, in both univariate and multivariate settings, and through the aforementioned application to the leaf photosynthetic trait data.

Transfer learning aims to transfer knowledge or information from a source domain to a relevant target domain. In this paper, we understand transfer learning from the perspectives of knowledge transferability and trustworthiness. This involves two research questions: How is knowledge transferability quantitatively measured and enhanced across domains? Can we trust the transferred knowledge in the transfer learning process? To answer these questions, this paper provides a comprehensive review of trustworthy transfer learning from various aspects, including problem definitions, theoretical analysis, empirical algorithms, and real-world applications. Specifically, we summarize recent theories and algorithms for understanding knowledge transferability under (within-domain) IID and non-IID assumptions. In addition to knowledge transferability, we review the impact of trustworthiness on transfer learning, e.g., whether the transferred knowledge is adversarially robust or algorithmically fair, how to transfer the knowledge under privacy-preserving constraints, etc. Beyond discussing the current advancements, we highlight the open questions and future directions for understanding transfer learning in a reliable and trustworthy manner.

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.