Large transformer-based foundation models have been commonly used as pre-trained models that can be adapted to different challenging datasets and settings with state-of-the-art generalization performance.

While synthetic data hold great promise for privacy protection, their statistical analysis poses significant challenges that necessitate innovative solutions.

These Q values are often objectives that offline algorithms aim to approximate.

This paper advances temporal reasoning within dynamically changing high-dimensional noisy observations, focusing on a latent space that characterizes the nonlinear dynamics of objects in their environment.

We draw parallels between the behavior of LLMs and the evolution of human culture, as the latter has been extensively studied by cognitive scientists for decades.

Thus, we propose a novel Bayesian approach to DPS.

Training machine learning and statistical models often involves optimizing a data-driven risk criterion.

Normalizing flows with a Gaussian base provide a computationally efficient way to approximate posterior distributions in Bayesian inference, but they often struggle to capture complex posteriors with multimodality and heavy tails. We propose a stick-breaking mixture base with component-wise tail adaptation (StiCTAF) for posterior approximation. The method first learns a flexible mixture base to mitigate the mode-seeking bias of reverse KL divergence through a weighted average of component-wise ELBOs. It then estimates local tail indices of unnormalized densities and finally refines each mixture component using a shared backbone combined with component-specific tail transforms calibrated by the estimated indices. This design enables accurate mode coverage and anisotropic tail modeling while retaining exact density evaluation and stable optimization. Experiments on synthetic posteriors demonstrate improved tail recovery and better coverage of multiple modes compared to benchmark models. We also present a real-data analysis illustrating the practical benefits of our approach for posterior inference.

We propose to perform mean-field variational inference (MFVI) in a rotated coordinate system that reduces correlations between variables. The rotation is determined by principal component analysis (PCA) of a cross-covariance matrix involving the target's score function. Compared with standard MFVI along the original axes, MFVI in this rotated system often yields substantially more accurate approximations with negligible additional cost. MFVI in a rotated coordinate system defines a rotation and a coordinatewise map that together move the target closer to Gaussian. Iterating this procedure yields a sequence of transformations that progressively transforms the target toward Gaussian. The resulting algorithm provides a computationally efficient way to construct flow-like transport maps: it requires only MFVI subproblems, avoids large-scale optimization, and yields transformations that are easy to invert and evaluate. In Bayesian inference tasks, we demonstrate that the proposed method achieves higher accuracy than standard MFVI, while maintaining much lower computational cost than conventional normalizing flows.