The recent development of foundation models for time series data has generated considerable interest in using such models across a variety of applications. Although foundation models achieve state-of-the-art predictive performance, their calibration properties remain relatively underexplored, despite the fact that calibration can be critical for many practical applications. In this paper, we investigate the calibration-related properties of five recent time series foundation models and two competitive baselines. We perform a series of systematic evaluations assessing model calibration (i.e., over- or under-confidence), effects of varying prediction heads, and calibration under long-term autoregressive forecasting. We find that time series foundation models are consistently better calibrated than baseline models and tend not to be either systematically over- or under-confident, in contrast to the overconfidence often seen in other deep learning models.

We address the problem of learning to assign prediction tasks to one agent from a set of available human or AI agents. In particular, we focus on the sequential learning of agent expertise and assignment policies where each agent is constrained to handle a fraction of tasks. We provide a general theoretical characterization of this problem in terms of agent capacities, differences in agent expertise, and task context. We then develop a framework of sequential explore-exploit policy-learning algorithms that seek to maximize overall performance. Experimental results over a variety of tabular, image, and text prediction tasks demonstrate systematic gains from our policy-learning algorithms relative to non-contextual baselines across different types of agents, including LLMs and humans.

Artificial intelligence (AI) is being increasingly integrated into human problem-solving, yet its effects on individual skill development remain unclear. We examine how both AI usage and informativeness can shape learning in the context of a controlled logical reasoning task with on-demand access to AI assistance. We find that greater AI usage is associated with weaker skill development: heavy AI users underperform relative to comparable peers, whereas light AI users perform similarly to matched users who do not use AI. We also find in our study that these patterns are mediated by AI informativeness. Low-information AI neither improves immediate performance nor preserves performance after AI assistance is removed, and is linked to weaker learning overall. On the other hand, high-information AI was found to improve short-run performance without reducing post-AI outcomes on average in our experiments, but with heterogeneous effects. Our findings in general suggest that AI can, depending on context, either complement human skill development by amplifying independent reasoning or can act as a substitute that undermines such reasoning, with the implication that regulating AI access and usage will be important for promoting skill development in the presence of AI assistance.

While AI assistance can improve human task performance in the short term, it may also undermine the development of skills in the longer term. We examine this tension in a controlled logic-puzzle experiment involving on-demand AI assistance, where participants complete tasks before, during, and after AI is available. By experimentally varying AI request costs, we find that lower-cost assistance induces more frequent AI use. We also find that participants who request AI assistance during the AI-access phase perform worse at the task after assistance is removed, and their subsequent unassisted performance is overestimated when predicted from earlier AI-assisted performance. We use a Bayesian latent ability model to separate initial ability, post-AI ability, and participant-specific skill change, while estimating how independent reasoning during the AI-access phase relates to skill development. The results show that greater independent problem-solving effort is associated with larger gains in latent ability, consistent with the interpretation that skill development is weaker when AI assistance substitutes for independent reasoning.

Humans increasingly turn to Language Models (LMs) in ways that shape beliefs and drive decisions, including discussing, rewriting, and summarizing information from scientific articles, news, and medical reports. However, in these domains, where how confidently a claim is expressed matters, little is known about whether LMs faithfully preserve it. In this work, we investigate certainty distortion in LMs, defined as meaningful changes in expressed certainty when semantic content is preserved. We propose an LM-based evaluation metric that is consistent with population-level judgments of certainty. Using this metric, we characterize certainty distortion across different sizes and families of models in the context of scientific and medical communication tasks. Our results show that certainty distortion affects up to 75% of LM outputs and is systematically asymmetric in rewriting tasks with most LMs being 1.5-2× more likely to increase the expressed certainty than to decrease it. These effects can compound over repeated paraphrasing: in the medical domain, claude-haiku-4-5 increases certainty of 20% examples after a single iteration, increasing to 40% after five iterations. Prompt-based interventions reduce overall certainty distortion but do not eliminate it. Together, these findings reveal a general bias toward inflating expressed certainty, with direct implications for users who rely on LMs in high-stakes domains.

Large ensembles of climate projections are essential for characterizing uncertainty in future climate and extreme weather events, yet computational constraints of numerical climate models limit ensemble sizes to a small number of realizations per model. We present a unified conditional diffusion model that dramatically reduces this computational barrier by learning shared distributional patterns across multiple Coupled Model Intercomparison Project phase 6 models and emission scenarios. Rather than training separate emulators for each model-scenario combination, our approach captures the common statistical structures underlying nine CMIP6 models, generating daily temperature maps with a global coverage for historical and future periods. This unified framework enables: (i) efficient probabilistic sampling for comprehensive uncertainty quantification across models and scenarios; (ii) rapid generation of large ensembles that would be computationally intractable with traditional climate models; (iii) variance-reduced treatment effect analysis via fixed-seed generation that disentangles forced climate responses from internal variability. Evaluations on held-out models demonstrate reliable generalization to unseen future climates, enabling rapid exploration of different emission pathways.

Semantic control entails steering LM generations towards satisfying subtle non-lexical constraints, e.g., toxicity, sentiment, or politeness, attributes that can be captured by a sequence-level verifier. It can thus be viewed as sampling from the LM distribution conditioned on the target attribute, a computationally intractable problem due to the non-decomposable nature of the verifier. Existing approaches to LM control either only deal with syntactic constraints which cannot capture the aforementioned attributes, or rely on sampling to explore the conditional LM distribution, an ineffective estimator for low-probability events. In this work, we leverage a verifier's gradient information to efficiently reason over all generations that satisfy the target attribute, enabling precise steering of LM generations by reweighing the next-token distribution. Starting from an initial sample, we create a local LM distribution favoring semantically similar sentences. This approximation enables the tractable computation of an expected sentence embedding. We use this expected embedding, informed by the verifier's evaluation at the initial sample, to estimate the probability of satisfying the constraint, which directly informs the update to the next-token distribution. We evaluated the effectiveness of our approach in controlling the toxicity, sentiment, and topic-adherence of LMs yielding generations satisfying the constraint with high probability (>95

Systems of interacting continuous-time Markov chains are a powerful model class, but inference is typically intractable in high dimensional settings. Auxiliary information, such as noisy observations, is typically only available at discrete times, and incorporating it via a Doob's h-transform gives rise to an intractable posterior process that requires approximation. We introduce Latent Interacting Particle Systems, a model class parameterizing the generator of each Markov chain in the system. Our inference method involves estimating look-ahead functions (twist potentials) that anticipate future information, for which we introduce an efficient parameterization. We incorporate this approximation in a twisted Sequential Monte Carlo sampling scheme. We demonstrate the effectiveness of our approach on a challenging posterior inference task for a latent SIRS model on a graph, and on a neural model for wildfire spread dynamics trained on real data.

Uncertainty quantification is an important component of satellite-derived precipitation products, yet most current methodologies lack the ability to provide such estimates. Here we use a generative diffusion model to produce probabilistic ensembles of precipitation intensity maps at the 1-hour 5-km resolution, conditional on infrared and microwave radiometric measurements from the GOES and DMSP satellites. The model is trained with merged ground radar and gauge data over the southeastern United States. We show that the generated precipitation maps accurately reproduce the magnitude and location of precipitation features, and the spatial autocovariance and higher order statistics of the gauge-radar reference fields over a range of scales. The 128-member ensemble is evaluated to assess whether it provides an accurate estimate of the precipitation uncertainty. We show that on average, the spectral coherence between any two ensemble members is approximately the same as that between any ensemble member and the ground reference, attesting that the ensemble dispersion is a proper measure of the estimation uncertainty across a range of scales. We also evaluate the ensemble in terms of reproducing the probability of exceedance of any desired intensity threshold, at the 5-km resolution of the generation up to 80-km aggregation scale and show impressive agreement. Finally, generalization of the model to “unseen domains” is pursued by applying the trained model to the Western US and the challenges and opportunities in this generalization will be discussed.

As artificial intelligence systems, particularly large language models (LLMs), become increasingly integrated into decision-making processes, the ability to trust their outputs is crucial. To earn human trust, LLMs must be well calibrated such that they can accurately assess and communicate the likelihood of their predictions being correct. Whereas recent work has focused on LLMs’ internal confidence, less is understood about how effectively they convey uncertainty to users. Here we explore the calibration gap, which refers to the difference between human confidence in LLM-generated answers and the models’ actual confidence, and the discrimination gap, which reflects how well humans and models can distinguish between correct and incorrect answers. Our experiments with multiple-choice and short-answer questions reveal that users tend to overestimate the accuracy of LLM responses when provided with default explanations. Moreover, longer explanations increased user confidence, even when the extra length did not improve answer accuracy. By adjusting LLM explanations to better reflect the models’ internal confidence, both the calibration gap and the discrimination gap narrowed, significantly improving user perception of LLM accuracy. These findings underscore the importance of accurate uncertainty communication and highlight the effect of explanation length in influencing user trust in artificial-intelligence-assisted decision-making environments. Understanding how people perceive and interpret uncertainty from large language models (LLMs) is crucial, as users often overestimate LLM accuracy, especially with default explanations. Steyvers et al. show that aligning LLM explanations with their internal confidence improves user perception.

Marked temporal point processes (MTPPs) model sequences of events occurring at irregular time intervals, with wide-ranging applications in fields such as healthcare, finance and social networks. We propose the _state-space point process_ (S2P2) model, a novel and performant model that leverages techniques derived for modern deep state-space models (SSMs) to overcome limitations of existing MTPP models, while simultaneously imbuing strong inductive biases for continuous-time event sequences that other discrete sequence models (i.e., RNNs, transformers) do not capture. Inspired by the classical linear Hawkes processes, we propose an architecture that interleaves stochastic jump differential equations with nonlinearities to create a highly expressive intensity-based MTPP model, without the need for restrictive parametric assumptions for the intensity. Our approach enables efficient training and inference with a parallel scan, bringing linear complexity and sublinear scaling while retaining expressivity to MTPPs. Empirically, S2P2 achieves state-of-the-art predictive likelihoods across eight real-world datasets, delivering an average improvement of 33% over the best existing approaches.

Stein variational gradient descent (SVGD) [Liu and Wang, 2016] performs approximate Bayesian inference by representing the posterior with a set of particles. However, SVGD suffers from variance collapse, i.e. poor predictions due to underestimating uncertainty [Ba et al., 2021], even for moderately-dimensional models such as small Bayesian neural networks (BNNs). To address this issue, we generalize SVGD by letting each particle parameterize a component distribution in a mixture model. Our method, Stein Mixture Inference (SMI), optimizes a lower bound to the evidence (ELBO) and introduces user-specified guides parameterized by particles. SMI extends the Nonlinear SVGD framework [Wang and Liu, 2019] to the case of variational Bayes. SMI effectively avoids variance collapse, judging by a previously described test developed for this purpose, and performs well on standard data sets. In addition, SMI requires considerably fewer particles than SVGD to accurately estimate uncertainty for small BNNs. The synergistic combination of NSVGD, ELBO optimization and user-specified guides establishes a promising approach towards variational Bayesian inference in the case of tall and wide data.

Applications of machine learning often involve making predictions based on both model outputs and the opinions of human experts. In this context, we investigate the problem of querying experts for class label predictions, using as few human queries as possible, and leveraging the class probability estimates of pre-trained classifiers. We develop a general Bayesian framework for this problem, modeling expert correlation via a joint latent representation, enabling simulation-based inference about the utility of additional expert queries, as well as inference of posterior distributions over unobserved expert labels. We apply our approach to two real-world medical classification problems, as well as to CIFAR-10H and ImageNet-16H, demonstrating substantial reductions relative to baselines in the cost of querying human experts while maintaining high prediction accuracy.

Conformal prediction provides machine learning models with prediction sets that offer theoretical guarantees, but the underlying assumption of exchangeability limits its applicability to time series data. Furthermore, existing approaches struggle to handle multi-step ahead prediction tasks, where uncertainty estimates across multiple future time points are crucial. We propose JANET (Joint Adaptive predictioN-region Estimation for Time-series), a novel framework for constructing conformal prediction regions that are valid for both univariate and multivariate time series. JANET generalises the inductive conformal framework and efficiently produces joint prediction regions with controlled K-familywise error rates, enabling flexible adaptation to specific application needs. Our empirical evaluation demonstrates JANET's superior performance in multi-step prediction tasks across diverse time series datasets, highlighting its potential for reliable and interpretable uncertainty quantification in sequential data.

Background. Large language models are increasingly used in settings where confident but incorrect answers can mislead users. Reliable uncertainty communication requires a form of metacognition: monitoring when one's own answers are likely to be correct. Yet models' stated confidence is often poorly aligned with answer correctness. We test whether supervised fine-tuning improves uncertainty communication and whether gains transfer across domains and task formats. Methods. We fine-tuned two models on general knowledge, mathematics, and open-ended trivia questions. We evaluated single-question confidence estimation, in which the model reports numeric confidence for one answer, and pairwise confidence comparison, in which it chooses which of two questions it is more likely to answer correctly. We tested held-out questions from training domains and new medical, legal, and truthfulness benchmarks. We assessed calibration, discrimination, and answer accuracy before and after fine-tuning. Results. Here we show that fine-tuning improves alignment between stated confidence and observed accuracy and increases the model's ability to assign higher confidence to correct than to incorrect answers. Gains occur within training domains and, to a lesser extent, in new domains. However, single-task training does not reliably transfer between single-question confidence estimation and pairwise confidence comparison. Multitask fine-tuning produces broader gains in the models and tasks studied here. Conclusions. Uncertainty communication in large language models is trainable, but transfer across metacognitive tasks is limited. Joint training on multiple confidence tasks may support broader generalization, although further tests across model families and metacognitive tasks are needed.

It is increasingly important to evaluate how text generation systems based on large language models (LLMs) behave, such as their tendency to produce harmful output or their sensitivity to adversarial inputs. Such evaluations often rely on a curated benchmark set of input prompts provided to the LLM, where the output for each prompt may be assessed in a binary fashion (e.g., harmful/non-harmful or does not leak/leaks sensitive information), and the aggregation of binary scores is used to evaluate the LLM. However, existing approaches to evaluation often neglect statistical uncertainty quantification. With an applied statistics audience in mind, we provide background on LLM text generation and evaluation, and then describe a Bayesian approach for quantifying uncertainty in binary evaluation metrics. We focus in particular on uncertainty that is induced by the probabilistic text generation strategies typically deployed in LLM-based systems. We present two case studies applying this approach: 1) evaluating refusal rates on a benchmark of adversarial inputs designed to elicit harmful responses, and 2) evaluating pairwise preferences of one LLM over another on a benchmark of open-ended interactive dialogue examples. We demonstrate how the Bayesian approach can provide useful uncertainty quantification about the behavior of LLM-based systems.

While gender bias in large language models (LLMs) has been extensively studied in many domains, uses of LLMs in e-commerce remain largely unexamined and may reveal novel forms of algorithmic bias and harm. Our work investigates this space, developing data-driven taxonomic categories of gender bias in the context of product description generation, which we situate with respect to existing general purpose harms taxonomies. We illustrate how AI-generated product descriptions can uniquely surface gender biases in ways that require specialized detection and mitigation approaches. Further, we quantitatively analyze issues corresponding to our taxonomic categories in two models used for this task -- GPT-3.5 and an e-commerce-specific LLM -- demonstrating that these forms of bias commonly occur in practice. Our results illuminate unique, under-explored dimensions of gender bias, such as assumptions about clothing size, stereotypical bias in which features of a product are advertised, and differences in the use of persuasive language. These insights contribute to our understanding of three types of AI harms identified by current frameworks: exclusionary norms, stereotyping, and performance disparities, particularly for the context of e-commerce.

A generative diffusion model is used to produce probabilistic ensembles of precipitation intensity maps at the 1-hour 5-km resolution. The generation is conditioned on infrared and microwave radiometric measurements from the GOES and DMSP satellites and is trained with merged ground radar and gauge data over southeastern United States. The generated precipitation maps reproduce the spatial autocovariance and other multiscale statistical properties of the gauge-radar reference fields on average. Conditioning the generation on the satellite measurements allows us to constrain the magnitude and location of each generated precipitation feature. The mean of the 128- member ensemble shows high spatial coherence with the reference fields with 0.82 linear correlation between the two. On average, the coherence between any two ensemble members is approximately the same as the coherence between any ensemble member and the ground reference, attesting that the ensemble dispersion is a proper measure of the estimation uncertainty. From the generated ensembles we can easily derive the probability of the precipitation intensity exceeding any given intensity threshold, at the 5-km resolution of the generation or at any desired aggregated resolution.

Continuous-time event sequences, in which events occur at irregular intervals, are ubiquitous across a wide range of industrial and scientific domains. The contemporary modeling paradigm is to treat such data as realizations of a temporal point process, and in machine learning it is common to model temporal point processes in an autoregressive fashion using a neural network. While autoregressive models are successful in predicting the time of a single subsequent event, their performance can degrade when forecasting longer horizons due to cascading errors and myopic predictions. We propose EventFlow, a non-autoregressive generative model for temporal point processes. The model builds on the flow matching framework in order to directly learn joint distributions over event times, side-stepping the autoregressive process. EventFlow is simple to implement and achieves a 20

We study the geometry of conditional optimal transport (COT) and prove a dynamic formulation which generalizes the Benamou-Brenier Theorem. Equipped with these tools, we propose a simulation-free flow-based method for conditional generative modeling. Our method couples an arbitrary source distribution to a specified target distribution through a triangular COT plan, and a conditional generative model is obtained by approximating the geodesic path of measures induced by this COT plan. Our theory and methods are applicable in infinite-dimensional settings, making them well suited for a wide class of Bayesian inverse problems. Empirically, we demonstrate that our method is competitive on several challenging conditional generation tasks, including an infinite-dimensional inverse problem.