Akira Horiguchi

Hengrui Luo, Akira Horiguchi, Li Ma

We proposed the tensor-input tree (TT) method for scalar-on-tensor and tensor-on-tensor regression problems. We first address scalar-on-tensor problem by proposing scalar-output regression tree models whose input variable are tensors (i.e., multi-way arrays). We devised and implemented fast randomized and deterministic algorithms for efficient fitting of scalar-on-tensor trees, making TT competitive against tensor-input GP models. Based on scalar-on-tensor tree models, we extend our method to tensor-on-tensor problems using additive tree ensemble approaches. Theoretical justification and extensive experiments on real and synthetic datasets are provided to illustrate the performance of TT.

Lingyou Pang, Lei Huang, Jianyu Lin et al.

Deploying black-box LLMs requires managing uncertainty in the absence of token-level probability or true labels. We propose introducing an unsupervised conformal inference framework for generation, which integrates: generative models, incorporating: (i) an LLM-compatible atypical score derived from response-embedding Gram matrix, (ii) UCP combined with a bootstrapping variant (BB-UCP) that aggregates residuals to refine quantile precision while maintaining distribution-free, finite-sample coverage, and (iii) conformal alignment, which calibrates a single strictness parameter $τ$ so a user predicate (e.g., factuality lift) holds on unseen batches with probability $\ge 1-α$. Across different benchmark datasets, our gates achieve close-to-nominal coverage and provide tighter, more stable thresholds than split UCP, while consistently reducing the severity of hallucination, outperforming lightweight per-response detectors with similar computational demands. The result is a label-free, API-compatible gate for test-time filtering that turns geometric signals into calibrated, goal-aligned decisions.

Akira Horiguchi, Thomas J. Santner, Ying Sun et al.

Techniques to reduce the energy burden of an industrial ecosystem often require solving a multiobjective optimization problem. However, collecting experimental data can often be either expensive or time-consuming. In such cases, statistical methods can be helpful. This article proposes Pareto Front (PF) and Pareto Set (PS) estimation methods using Bayesian Additive Regression Trees (BART), which is a non-parametric model whose assumptions are typically less restrictive than popular alternatives, such as Gaussian Processes (GPs). These less restrictive assumptions allow BART to handle scenarios (e.g. high-dimensional input spaces, nonsmooth responses, large datasets) that GPs find difficult. The performance of our BART-based method is compared to a GP-based method using analytic test functions, demonstrating convincing advantages. Finally, our BART-based methodology is applied to a motivating engineering problem. Supplementary materials, which include a theorem proof, algorithms, and R code, for this article are available online.