generative response modeling

This work proposes a probabilistic inference framework that integrates inductive biases to address the challenges of uncertainty quantification in deep sequential models. While traditional Bayesian approaches struggle with prior specification and inference accuracy in large-scale networks, the proposed method establishes a theoretical connection between Transformer attention mechanisms and sparse Gaussian processes, enabling scalable approximate Bayesian inference. It introduces cross-domain inducing points derived from HiPPO operators to support long-range historical modeling in online learning settings. Furthermore, self-supervised signals are leveraged to enrich the probabilistic structure of latent variables in sequence generation. The resulting approach significantly enhances the uncertainty quantification capability, probabilistic expressiveness, and scalability of deep sequential models, all while maintaining competitive predictive performance.

This paper addresses the problem of predicting the distribution of future events in human action sequences—emphasizing the composition of likely outcomes rather than precise temporal ordering—a task critical for applications in retail, finance, healthcare, and recommender systems. To overcome the limitations of dominant autoregressive paradigms—namely, their strong sequential dependency and tendency toward category-mode collapse—we propose a non-autoregressive distributional prediction framework. Our approach introduces KL divergence to quantify temporal distributional drift, identifies distributional imbalance as the primary cause of mode collapse, and incorporates three key components: an explicit distribution-aware learning objective, locally order-invariant representations, and multi-token parallel prediction. Experiments across multiple real-world datasets demonstrate substantial improvements over state-of-the-art baselines. The framework offers both interpretability and practicality, providing a principled alternative for behavioral sequence modeling with clear design rationales and deployable mechanisms.

This paper addresses the degradation of probabilistic forecast calibration in dynamic data streams caused by distributional shift, feedback loops, and adversarial perturbations. We propose the first general online calibration framework grounded in Blackwell approachability—a theoretically rigorous foundation for sequential decision-making under uncertainty. Our method provides strong calibration guarantees in compact output spaces (e.g., classification and bounded regression) and enables lossless post-hoc recalibration of arbitrary pre-trained predictors. Technically, it unifies insights from Blackwell approachability theory, online optimization, and gradient-based updates, and introduces task-specific efficient algorithms for both classification and regression. Empirical evaluation demonstrates substantial improvements in calibration quality for energy system forecasting, with marked gains in robustness and practical utility for downstream decision-making tasks.

This paper addresses the challenge of identifying heterogeneous individual-level choice behaviors from macro-level aggregate selection data. To this end, it establishes, for the first time, a systematic theoretical linkage between ordered probit choice models and copula theory, mapping individual heterogeneity onto the structural form of copula functions. The authors propose an analytically tractable representation based on extreme-value theory, enabling unique and unbiased identification of both heterogeneity types and their mixing weights. Methodologically, the approach integrates copula modeling, extreme-value function analysis, and structural identification theory to derive a general closed-form extreme-value representation. This framework overcomes key limitations of conventional aggregate modeling—such as loss of behavioral granularity and identifiability constraints—thereby substantially improving the accuracy, interpretability, and structural fidelity of micro-behavioral inference. It introduces a novel paradigm for discrete choice analysis, behavioral econometrics, and multivariate dependence modeling.

This paper addresses the challenge of modeling nonlinear and asymmetric dynamic relationships among macroeconomic and financial variables. We propose the first scenario-analysis-oriented, dynamic nonparametric multivariate Bayesian machine learning framework. Methodologically, we adapt classical econometric tools—including conditional forecasting and generalized impulse response analysis—to high-dimensional Bayesian nonparametric models, integrating dynamic factor extensions and Monte Carlo simulation to enable asymmetric shock response estimation and conditional scenario inference. Our key contribution is the first systematic integration of traditional scenario-analysis tools with nonlinear Bayesian machine learning, explicitly capturing structural asymmetry. The framework is validated across three empirical domains: financial stress testing, macroeconomic risk assessment, and cross-border spillover analysis. Results demonstrate substantial improvements in risk measurement accuracy and cross-jurisdictional early-warning capability, offering a novel paradigm for prudential regulation and policy evaluation.

This study addresses the challenge of modeling predictive distributions for nonlinear, multivariate time series by proposing a general generative representation framework grounded in measure-theoretic probability, which is, to the authors’ knowledge, the first to be integrated with conditional generative adversarial networks (CGANs). Under a mild temporal dependence assumption, the method establishes estimation consistency in the Hausdorff metric and enables efficient simulation and computation of conditional means, variances, and risk measures. Empirical results demonstrate that the model achieves strong predictive performance on tasks involving stock returns, realized variances, and covariances, delivering high accuracy with remarkable computational efficiency—requiring only about one minute for a single training run.

This work proposes a unified mathematical framework grounded in dynamic information flow for constructing structurally rigorous models of future prediction. By integrating filtering theory, regular conditional probabilities, Markov semigroups, infinitesimal generators, and multiple information geometries—including Hilbert, Fisher–Rao, and Wasserstein—the approach conceptualizes prediction as the construction of conditional distributions governed by informational, geometric, and modeling constraints. The framework elucidates deep connections among classical results such as the tower property and semigroup laws, as well as Itô’s formula and backward equations. Explicit transition laws, spectral decompositions, term structures, and asymptotic behaviors are derived within canonical models like Ornstein–Uhlenbeck and Cox–Ingersoll–Ross, thereby establishing a compact mathematical mapping from idealized theoretical constructs to empirical forecasting.