The quality of probabilistic forecasts is crucial for decision-making under uncertainty. While proper scoring rules incentivize truthful reporting of precise forecasts, they fall short when forecasters face epistemic uncertainty about their beliefs, limiting their use in safety-critical domains where decision-makers (DMs) prioritize proper uncertainty management. To address this, we propose a framework for scoring imprecise forecasts -- forecasts given as a set of beliefs. Despite existing impossibility results for deterministic scoring rules, we enable truthful elicitation by drawing connection to social choice theory and introducing a two-way communication framework where DMs first share their aggregation rules (e.g., averaging or min-max) used in downstream decisions for resolving forecast ambiguity. This, in turn, helps forecasters resolve indecision during elicitation. We further show that truthful elicitation of imprecise forecasts is achievable using proper scoring rules randomized over the aggregation procedure. Our approach allows DM to elicit and integrate the forecaster's epistemic uncertainty into their decision-making process, thus improving credibility.

Decision Focused Learning has emerged as a critical paradigm for integrating machine learning with downstream optimisation. Despite its promise, existing methodologies predominantly rely on probabilistic models and focus narrowly on task objectives, overlooking the nuanced challenges posed by epistemic uncertainty, non-probabilistic modelling approaches, and the integration of uncertainty into optimisation constraints. This paper bridges these gaps by introducing innovative frameworks: (i) a non-probabilistic lens for epistemic uncertainty representation, leveraging intervals (the least informative uncertainty model), Contamination (hybrid model), and probability boxes (the most informative uncertainty model); (ii) methodologies to incorporate uncertainty into constraints, expanding Decision-Focused Learning's utility in constrained environments; (iii) the adoption of Imprecise Decision Theory for ambiguity-rich decision-making contexts; and (iv) strategies for addressing sparse data challenges. Empirical evaluations on benchmark optimisation problems demonstrate the efficacy of these approaches in improving decision quality and robustness and dealing with said gaps.

In zero-shot image recognition tasks, humans demonstrate remarkable flexibility in classifying unseen categories by composing known simpler concepts. However, existing vision-language models (VLMs), despite achieving significant progress through large-scale natural language supervision, often underperform in real-world applications because of sub-optimal prompt engineering and the inability to adapt effectively to target classes. To address these issues, we propose a Concept-guided Human-like Bayesian Reasoning (CHBR) framework. Grounded in Bayes' theorem, CHBR models the concept used in human image recognition as latent variables and formulates this task by summing across potential concepts, weighted by a prior distribution and a likelihood function. To tackle the intractable computation over an infinite concept space, we introduce an importance sampling algorithm that iteratively prompts large language models (LLMs) to generate discriminative concepts, emphasizing inter-class differences. We further propose three heuristic approaches involving Average Likelihood, Confidence Likelihood, and Test Time Augmentation (TTA) Likelihood, which dynamically refine the combination of concepts based on the test image. Extensive evaluations across fifteen datasets demonstrate that CHBR consistently outperforms existing state-of-the-art zero-shot generalization methods.

This paper introduces a novel plug-and-play (PnP) Langevin sampling methodology for Bayesian inference in low-photon Poisson imaging problems, a challenging class of problems with significant applications in astronomy, medicine, and biology. PnP Langevin sampling algorithms offer a powerful framework for Bayesian image restoration, enabling accurate point estimation as well as advanced inference tasks, including uncertainty quantification and visualization analyses, and empirical Bayesian inference for automatic model parameter tuning. However, existing PnP Langevin algorithms are not well-suited for low-photon Poisson imaging due to high solution uncertainty and poor regularity properties, such as exploding gradients and non-negativity constraints. To address these challenges, we propose two strategies for extending Langevin PnP sampling to Poisson imaging models: (i) an accelerated PnP Langevin method that incorporates boundary reflections and a Poisson likelihood approximation and (ii) a mirror sampling algorithm that leverages a Riemannian geometry to handle the constraints and the poor regularity of the likelihood without approximations. The effectiveness of these approaches is demonstrated through extensive numerical experiments and comparisons with state-of-the-art methods.

We propose TVineSynth, a vine copula based synthetic tabular data generator, which is designed to balance privacy and utility, using the vine tree structure and its truncation to do the trade-off. Contrary to synthetic data generators that achieve DP by globally adding noise, TVineSynth performs a controlled approximation of the estimated data generating distribution, so that it does not suffer from poor utility of the resulting synthetic data for downstream prediction tasks. TVineSynth introduces a targeted bias into the vine copula model that, combined with the specific tree structure of the vine, causes the model to zero out privacy-leaking dependencies while relying on those that are beneficial for utility. Privacy is here measured with membership (MIA) and attribute inference attacks (AIA). Further, we theoretically justify how the construction of TVineSynth ensures AIA privacy under a natural privacy measure for continuous sensitive attributes. When compared to competitor models, with and without DP, on simulated and on real-world data, TVineSynth achieves a superior privacy-utility balance.

Information and free-energy maximization are physics principles that provide general rules for an agent to optimize actions in line with specific goals and policies. These principles are the building blocks for designing decision-making policies capable of efficient performance with only partial information. Notably, the information maximization principle has shown remarkable success in the classical bandit problem and has recently been shown to yield optimal algorithms for Gaussian and sub-Gaussian reward distributions. This article explores a broad extension of physics-based approaches to more complex and structured bandit problems. To this end, we cover three distinct types of bandit problems, where information maximization is adapted and leads to strong performance. Since the main challenge of information maximization lies in avoiding over-exploration, we highlight how information is tailored at various levels to mitigate this issue, paving the way for more efficient and robust decision-making strategies.

Despite the accelerating presence of exploratory causal analysis in modern science and medicine, the available non-experimental methods for validating causal models are not well characterized. One of the most popular methods is to evaluate the stability of model features after resampling the data, similar to resampling methods for estimating confidence intervals in statistics. Many aspects of this approach have received little to no attention, however, such as whether the choice of resampling method should depend on the sample size, algorithms being used, or algorithm tuning parameters. We present theoretical results proving that certain resampling methods closely emulate the assignment of specific values to algorithm tuning parameters. We also report the results of extensive simulation experiments, which verify the theoretical result and provide substantial data to aid researchers in further characterizing resampling in the context of causal discovery analysis. Together, the theoretical work and simulation results provide specific guidance on how resampling methods and tuning parameters should be selected in practice.

We present a novel preference learning framework to capture participant preferences efficiently within limited interaction rounds. It involves three main contributions. First, we develop a variational Bayesian approach to infer the participant's preference model by estimating posterior distributions and managing uncertainty from limited information. Second, we propose an adaptive questioning policy that maximizes cumulative uncertainty reduction, formulating questioning as a finite Markov decision process and using Monte Carlo Tree Search to prioritize promising question trajectories. By considering long-term effects and leveraging the efficiency of the Bayesian approach, the policy avoids shortsightedness. Third, we apply the framework to Multiple Criteria Decision Aiding, with pairwise comparison as the preference information and an additive value function as the preference model. We integrate the reparameterization trick to address high-variance issues, enhancing robustness and efficiency. Computational studies on real-world and synthetic datasets demonstrate the framework's practical usability, outperforming baselines in capturing preferences and achieving superior uncertainty reduction within limited interactions.

Language models usually use left-to-right (L2R) autoregressive factorization. However, L2R factorization may not always be the best inductive bias. Therefore, we investigate whether alternative factorizations of the text distribution could be beneficial in some tasks. We investigate right-to-left (R2L) training as a compelling alternative, focusing on multiple-choice questions (MCQs) as a test bed for knowledge extraction and reasoning. Through extensive experiments across various model sizes (2B-8B parameters) and training datasets, we find that R2L models can significantly outperform L2R models on several MCQ benchmarks, including logical reasoning, commonsense understanding, and truthfulness assessment tasks. Our analysis reveals that this performance difference may be fundamentally linked to multiple factors including calibration, computability and directional conditional entropy. We ablate the impact of these factors through controlled simulation studies using arithmetic tasks, where the impacting factors can be better disentangled. Our work demonstrates that exploring alternative factorizations of the text distribution can lead to improvements in LLM capabilities and provides theoretical insights into optimal factorization towards approximating human language distribution, and when each reasoning order might be more advantageous.

This paper studies how AI-assisted programming and large language models (LLM) improve software developers' ability via AI tools (LLM agents) like Github Copilot and Amazon CodeWhisperer, while integrating human feedback to enhance reinforcement learning (RLHF) with crowd-sourced computation to enhance text-to-code generation. Additionally, we demonstrate that our Bayesian optimization framework supports AI alignment in code generation by distributing the feedback collection burden, highlighting the value of collecting human feedback of good quality. Our empirical evaluations demonstrate the efficacy of this approach, showcasing how LLM agents can be effectively trained for improved text-to-code generation. Our Bayesian optimization framework can be designed for general domain-specific languages, promoting the alignment of large language model capabilities with human feedback in AI-assisted programming for code generation.