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1. Should We Learn Most Likely Functions or Parameters?

   Qiu, S; Rudner, T; Kapoor, S; Wilson, AG (December 2023, Advances in Neural Information Processing Systems)

   Standard regularized training procedures correspond to maximizing a posterior distribution over parameters, known as maximum a posteriori (MAP) estimation. However, model parameters are of interest only insomuch as they combine with the functional form of a model to provide a function that can make good predictions. Moreover, the most likely parameters under the parameter posterior do not generally correspond to the most likely function induced by the parameter posterior. In fact, we can re-parametrize a model such that any setting of parameters can maximize the parameter posterior. As an alternative, we investigate the benefits and drawbacks of directly estimating the most likely function implied by the model and the data. We show that this procedure leads to pathological solutions when using neural networks and prove conditions under which the procedure is well-behaved, as well as a scalable approximation. Under these conditions, we find that function-space MAP estimation can lead to flatter minima, better generalization, and improved robustness to overfitting 

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2. Inverse Modeling of Hydrologic Parameters in CLM4 via Generalized Polynomial Chaos in the Bayesian Framework

   https://doi.org/10.3390/computation10050072  

   Karagiannis, Georgios; Hou, Zhangshuan; Huang, Maoyi; Lin, Guang (May 2022, Computation)

   In this work, generalized polynomial chaos (gPC) expansion for land surface model parameter estimation is evaluated. We perform inverse modeling and compute the posterior distribution of the critical hydrological parameters that are subject to great uncertainty in the Community Land Model (CLM) for a given value of the output LH. The unknown parameters include those that have been identified as the most influential factors on the simulations of surface and subsurface runoff, latent and sensible heat fluxes, and soil moisture in CLM4.0. We set up the inversion problem in the Bayesian framework in two steps: (i) building a surrogate model expressing the input–output mapping, and (ii) performing inverse modeling and computing the posterior distributions of the input parameters using observation data for a given value of the output LH. The development of the surrogate model is carried out with a Bayesian procedure based on the variable selection methods that use gPC expansions. Our approach accounts for bases selection uncertainty and quantifies the importance of the gPC terms, and, hence, all of the input parameters, via the associated posterior probabilities. 

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3. Bayesian semiparametric causal inference: Targeted doubly robust estimation of treatment effects

   Sert, Gözde; Chakrabortty, Abhishek; Bhattacharya, Anirban (November 2025, arXiv.org)

   We propose a semiparametric Bayesian methodology for estimating the average treatment effect (ATE) within the potential outcomes framework using observational data with high-dimensional nuisance parameters. Our method introduces a Bayesian debiasing procedure that corrects for bias arising from nuisance estimation and employs a targeted modeling strategy based on summary statistics rather than the full data. These summary statistics are identified in a debiased manner, enabling the estimation of nuisance bias via weighted observables and facilitating hierarchical learning of the ATE. By combining debiasing with sample splitting, our approach separates nuisance estimation from inference on the target parameter, reducing sensitivity to nuisance model specification. We establish that, under mild conditions, the marginal posterior for the ATE satisfies a Bernstein-von Mises theorem when both nuisance models are correctly specified and remains consistent and robust when only one is correct, achieving Bayesian double robustness. This ensures asymptotic efficiency and frequentist validity. Extensive simulations confirm the theoretical results, demonstrating accurate point estimation and credible intervals with nominal coverage, even in high-dimensional settings. The proposed framework can also be extended to other causal estimands, and its key principles offer a general foundation for advancing Bayesian semiparametric inference more broadly. 

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4. Performance Bounds for Model and Policy Transfer in Hidden-parameter MDPs

   Fu, H; Yao, J; Gottesman, O; Doshi-Velez, F; Konidaris, GD (May 2023, Proceedings of the Eleventh International Conference on Learning Representations)

   In the Hidden-Parameter MDP (HiP-MDP) framework, a family of reinforcement learning tasks is generated by varying hidden parameters specifying the dynamics and reward function for each individual task. The HiP-MDP is a natural model for families of tasks in which meta- and lifelong-reinforcement learning approaches can succeed. Given a learned context encoder that infers the hidden parameters from previous experience, most existing algorithms fall into two categories: model transfer and policy transfer, depending on which function the hidden parameters are used to parameterize. We characterize the robustness of model and policy transfer algorithms with respect to hidden parameter estimation error. We first show that the value function of HiP-MDPs is Lipschitz continuous under certain conditions. We then derive regret bounds for both settings through the lens of Lipschitz continuity. Finally, we empirically corroborate our theoretical analysis by varying the hyper-parameters governing the Lipschitz constants of two continuous control problems; the resulting performance is consistent with our theoretical results. 

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5. Two‐Phase Content‐Balancing CD‐CAT Online Item Calibration

   https://doi.org/10.1111/jedm.70012  

   Huang, Jing; Zhang, Yuxiao; Morphew, Jason W; Nissen, Jayson M; Van_Dusen, Ben; Chang, Hua Hua (October 2025, Journal of Educational Measurement)

   Abstract Online calibration estimates new item parameters alongside previously calibrated items, supporting efficient item replenishment. However, most existing online calibration procedures for Cognitive Diagnostic Computerized Adaptive Testing (CD‐CAT) lack mechanisms to ensure content balance during live testing. This limitation can lead to uneven content coverage, potentially undermining the alignment with instructional goals. This research extends the current calibration framework by integrating a two‐phase test design with a content‐balancing item selection method into the online calibration procedure. Simulation studies evaluated item parameter recovery and attribute profile estimation accuracy under the proposed procedure. Results indicated that the developed procedure yielded more accurate new item parameter estimates. The procedure also maintained content representativeness under both balanced and unbalanced constraints. Attribute profile estimation was sensitive to item parameter values. Accuracy declined when items had larger parameter values. Calibration improved with larger sample sizes and smaller parameter values. Longer test lengths contributed more to profile estimation than to new item calibration. These findings highlight design trade‐offs in adaptive item replenishment and suggest new directions for hybrid calibration methods. 

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