MINTS: Minimalist Thompson Sampling

The Bayesian paradigm offers principled tools for sequential decision-making under uncertainty, but its reliance on a probabilistic model for all parameters can hinder the incorporation of complex structural constraints. We introduce a minimalist Bayesian framework that places a prior only on the location of the optimum, while eliminating nuisance parameters through profile likelihood. This yields a generalized posterior that naturally accommodates structural constraints. As a direct instantiation, we develop MINimalist Thompson Sampling (MINTS). For multi-armed bandits with mean constraints, we establish near-optimal non-asymptotic regret guarantees and sharp almost-sure asymptotic regret characterizations. In particular, MINTS attains the classical Lai--Robbins constant in the unstructured setting and automatically adapts to unimodal structure, achieving the sharp constant determined only by the immediate neighbors of the optimal arm.

Shape-Prior-Based Point Cloud Completion for Single-Stage Fully Sparse 3D Object Detection

Single-stage fully sparse 3D object detectors rely on point clouds data to detect objects in autonomous driving scenarios. However, the sparsity and incompleteness of point clouds significantly limit the performance of 3D object detection. To address this issue, this paper proposes a point clouds completion method specifically designed for single-stage fully sparse detectors. The entire shape-prior-based completion process consists of two consecutive steps. In the first step, we design a novel Instance Selection module, which is capable of identifying point clouds corresponding to foreground objects even when the baseline model does not generate proposals, while effectively ignoring the point clouds of background regions. In the second step, we introduce a novel Alignment-Based Point Completion module, which aligns the point clouds of foreground objects with prototypes in terms of both their centers and orientations. Subsequently, points are selected from the prototype to fill in the missing parts of the foreground object. We evaluated our method on two single-stage fully sparse detectors using the KITTI dataset. The experimental results demonstrate that the proposed method significantly improves the detection performance, confirming its effectiveness and generalizability.

Estimating Continuous Treatment Effects with Two-Stage Kernel Ridge Regression

We study the problem of estimating the effect function for a continuous treatment, which maps each treatment value to a population-averaged outcome. A central challenge in this setting is confounding: treatment assignment often depends on covariates, creating selection bias that makes direct regression of the response on treatment unreliable. To address this issue, we propose a two-stage kernel ridge regression method. In the first stage, we learn a model for the response as a function of both treatment and covariates; in the second stage, we use this model to construct pseudo-outcomes that correct for distribution shift, and then fit a second model to estimate the treatment effect. Although the response varies with both treatment and covariates, the induced effect function obtained by averaging over covariates is typically much simpler, and our estimator adapts to this structure. Furthermore, we introduce a fully data-driven model selection procedure that achieves provable adaptivity to both the unknown degree of overlap and the regularity (eigenvalue decay) of the underlying kernel.

SYN-DIGITS: A Synthetic Control Framework for Calibrated Digital Twin Simulation

AI-based persona simulation -- often referred to as digital twin simulation -- is increasingly used for market research, recommender systems, and social sciences. Despite their flexibility, large language models (LLMs) often exhibit systematic bias and miscalibration relative to real human behavior, limiting their reliability. Inspired by synthetic control methods from causal inference, we propose SYN-DIGITS (SYNthetic Control Framework for Calibrated DIGItal Twin Simulation), a principled and lightweight calibration framework that learns latent structure from digital-twin responses and transfers it to align predictions with human ground truth. SYN-DIGITS operates as a post-processing layer on top of any LLM-based simulator and thus is model-agnostic. We develop a latent factor model that formalizes when and why calibration succeeds through latent space alignment conditions, and we systematically evaluate ten calibration methods across thirteen persona constructions, three LLMs, and two datasets. SYN-DIGITS supports both individual-level and distributional simulation for previously unseen questions and unobserved populations, with provable error guarantees. Experiments show that SYN-DIGITS achieves up to 50% relative improvements in individual-level correlation and 50--90% relative reductions in distributional discrepancy compared to uncalibrated baselines.

Pseudo-Labeling for Unsupervised Domain Adaptation with Kernel GLMs

We propose a principled framework for unsupervised domain adaptation under covariate shift in kernel Generalized Linear Models (GLMs), encompassing kernelized linear, logistic, and Poisson regression with ridge regularization. Our goal is to minimize prediction error in the target domain by leveraging labeled source data and unlabeled target data, despite differences in covariate distributions. We partition the labeled source data into two batches: one for training a family of candidate models, and the other for building an imputation model. This imputation model generates pseudo-labels for the target data, enabling robust model selection. We establish non-asymptotic excess-risk bounds that characterize adaptation performance through an "effective labeled sample size", explicitly accounting for the unknown covariate shift. Experiments on synthetic and real datasets demonstrate consistent performance gains over source-only baselines.

Set-based v.s. Distribution-based Representations of Epistemic Uncertainty: A Comparative Study

Epistemic uncertainty in neural networks is commonly modeled using two second-order paradigms: distribution-based representations, which rely on posterior parameter distributions, and set-based representations based on credal sets (convex sets of probability distributions). These frameworks are often regarded as fundamentally non-comparable due to differing semantics, assumptions, and evaluation practices, leaving their relative merits unclear. Empirical comparisons are further confounded by variations in the underlying predictive models. To clarify this issue, we present a controlled comparative study enabling principled, like-for-like evaluation of the two paradigms. Both representations are constructed from the same finite collection of predictive distributions generated by a shared neural network, isolating representational effects from predictive accuracy. Our study evaluates each representation through the lens of 3 uncertainty measures across 8 benchmarks, including selective prediction and out-of-distribution detection, spanning 6 underlying predictive models and 10 independent runs per configuration. Our results show that meaningful comparison between these seemingly non-comparable frameworks is both feasible and informative, providing insights into how second-order representation choices impact practical uncertainty-aware performance.

Learning Credal Ensembles via Distributionally Robust Optimization

Credal predictors are models that are aware of epistemic uncertainty and produce a convex set of probabilistic predictions. They offer a principled way to quantify predictive epistemic uncertainty (EU) and have been shown to improve model robustness in various settings. However, most state-of-the-art methods mainly define EU as disagreement caused by random training initializations, which mostly reflects sensitivity to optimization randomness rather than uncertainty from deeper sources. To address this, we define EU as disagreement among models trained with varying relaxations of the i.i.d. assumption between training and test data. Based on this idea, we propose CreDRO, which learns an ensemble of plausible models through distributionally robust optimization. As a result, CreDRO captures EU not only from training randomness but also from meaningful disagreement due to potential distribution shifts between training and test data. Empirical results show that CreDRO consistently outperforms existing credal methods on tasks such as out-of-distribution detection across multiple benchmarks and selective classification in medical applications.

The Nonstationarity-Complexity Tradeoff in Return Prediction

We investigate machine learning models for stock return prediction in non-stationary environments, revealing a fundamental nonstationarity-complexity tradeoff: complex models reduce misspecification error but require longer training windows that introduce stronger non-stationarity. We resolve this tension with a novel model selection method that jointly optimizes model class and training window size using a tournament procedure that adaptively evaluates candidates on non-stationary validation data. Our theoretical analysis demonstrates that this approach balances misspecification error, estimation variance, and non-stationarity, performing close to the best model in hindsight. Applying our method to 17 industry portfolio returns, we consistently outperform standard rolling-window benchmarks, improving out-of-sample $R^2$ by 14-23% on average. During NBER-designated recessions, improvements are substantial: our method achieves positive $R^2$ during the Gulf War recession while benchmarks are negative, and improves $R^2$ in absolute terms by at least 80bps during the 2001 recession as well as superior performance during the 2008 Financial Crisis. Economically, a trading strategy based on our selected model generates 31% higher cumulative returns averaged across the industries.

Credal Ensemble Distillation for Uncertainty Quantification

Deep ensembles (DE) have emerged as a powerful approach for quantifying predictive uncertainty and distinguishing its aleatoric and epistemic components, thereby enhancing model robustness and reliability. However, their high computational and memory costs during inference pose significant challenges for wide practical deployment. To overcome this issue, we propose credal ensemble distillation (CED), a novel framework that compresses a DE into a single model, CREDIT, for classification tasks. Instead of a single softmax probability distribution, CREDIT predicts class-wise probability intervals that define a credal set, a convex set of probability distributions, for uncertainty quantification. Empirical results on out-of-distribution detection benchmarks demonstrate that CED achieves superior or comparable uncertainty estimation compared to several existing baselines, while substantially reducing inference overhead compared to DE.

Epistemic Wrapping for Uncertainty Quantification

Uncertainty estimation is pivotal in machine learning, especially for classification tasks, as it improves the robustness and reliability of models. We introduce a novel `Epistemic Wrapping' methodology aimed at improving uncertainty estimation in classification. Our approach uses Bayesian Neural Networks (BNNs) as a baseline and transforms their outputs into belief function posteriors, effectively capturing epistemic uncertainty and offering an efficient and general methodology for uncertainty quantification. Comprehensive experiments employing a Bayesian Neural Network (BNN) baseline and an Interval Neural Network for inference on the MNIST, Fashion-MNIST, CIFAR-10 and CIFAR-100 datasets demonstrate that our Epistemic Wrapper significantly enhances generalisation and uncertainty quantification.