We propose a data-driven Fourier-trained neural-network method for estimating fixed-horizon probability densities from empirical characteristic-function (CF) information. The estimator is a positive Gaussian--Laplace mixture with closed-form CF, so training can be performed directly in Fourier space while preserving nonnegativity and unit mass. We consider two sampling settings. In the direct i.i.d. sampling setting, the method is trained against an empirical CF constructed from i.i.d. samples. In the resampling-based pseudo-sampling setting, it is trained against an empirical pseudo-CF constructed from dependent data by resampling. For the direct i.i.d. case, we derive an expected $L_2$ error bound that separates Fourier truncation, empirical training error, discretization, and CF sampling error. For the pseudo-sampling case, we obtain a conditional analogue with two additional pseudo-law discrepancy terms. We develop a multidimensional extension of the framework and analyze its computational complexity. Numerical experiments show competitive performance relative to Expectation--Maximization on Gaussian-mixture benchmarks, clear gains on heavy-tailed targets, $L_2$ error decay consistent with the theory in a well-specified setting, and effective estimation of one-year Australian equity return law from resampled dependent data.

Modern data analysis increasingly requires flexible conditional inference P(X_B | X_A) where (X_A, X_B) is an arbitrary partition of observed variable X. Existing conditional inference methods lack this flexibility as they are tied to a fixed conditioning structure and cannot perform new conditional inference once trained. To solve this, we propose a Bayesian generative modeling (BGM) approach for arbitrary conditional inference without retraining. BGM learns a generative model of X through an iterative Bayesian updating algorithm where model parameters and latent variables are updated until convergence. Once trained, any conditional distribution can be obtained without retraining. Empirically, BGM achieves superior prediction performance with well calibrated predictive intervals, demonstrating that a single learned model can serve as a universal engine for conditional prediction with uncertainty quantification. We provide theoretical guarantees for the convergence of the stochastic iterative algorithm, statistical consistency and conditional-risk bounds. The proposed BGM framework leverages the power of AI to capture complex relationships among variables while adhering to Bayesian principles, emerging as a promising framework for advancing various applications in modern data science. The code for BGM is freely available at https://github.com/liuq-lab/bayesgm.

Short video platforms like YouTube Shorts and TikTok face significant copyright compliance challenges, as infringers frequently embed arbitrary background music (BGM) to obscure original soundtracks (OST) and evade content originality detection. To tackle this issue, we propose a novel pipeline that integrates Music Source Separation (MSS) and cross-modal video-music retrieval (CMVMR). Our approach effectively separates arbitrary BGM from the original OST, enabling the restoration of authentic video audio tracks. To support this work, we introduce two domain-specific datasets: OASD-20K for audio separation and OSVAR-160 for pipeline evaluation. OASD-20K contains 20,000 audio clips featuring mixed BGM and OST pairs, while OSVAR-160 is a unique benchmark dataset comprising 1,121 video and mixed-audio pairs, specifically designed for short video restoration tasks. Experimental results demonstrate that our pipeline not only removes arbitrary BGM with high accuracy but also restores OSTs, ensuring content integrity. This approach provides an ethical and scalable solution to copyright challenges in user-generated content on short video platforms.

We propose BGM2Pose, a non-invasive 3D human pose estimation method using arbitrary music (e.g., background music) as active sensing signals. Unlike existing approaches that significantly limit practicality by employing intrusive chirp signals within the audible range, our method utilizes natural music that causes minimal discomfort to humans. Estimating human poses from standard music presents significant challenges. In contrast to sound sources specifically designed for measurement, regular music varies in both volume and pitch. These dynamic changes in signals caused by music are inevitably mixed with alterations in the sound field resulting from human motion, making it hard to extract reliable cues for pose estimation. To address these challenges, BGM2Pose introduces a Contrastive Pose Extraction Module that employs contrastive learning and hard negative sampling to eliminate musical components from the recorded data, isolating the pose information. Additionally, we propose a Frequency-wise Attention Module that enables the model to focus on subtle acoustic variations attributable to human movement by dynamically computing attention across frequency bands. Experiments suggest that our method outperforms the existing methods, demonstrating substantial potential for real-world applications. Our datasets and code will be made publicly available.

The rising use of machine learning in various fields requires robust methods to create synthetic tabular data. Data should preserve key characteristics while addressing data scarcity challenges. Current approaches based on Generative Adversarial Networks, such as the state-of-the-art CTGAN model, struggle with the complex structures inherent in tabular data. These data often contain both continuous and discrete features with non-Gaussian distributions. Therefore, we propose a novel Variational Autoencoder (VAE)-based model that addresses these limitations. Inspired by the TVAE model, our approach incorporates a Bayesian Gaussian Mixture model (BGM) within the VAE architecture. This avoids the limitations imposed by assuming a strictly Gaussian latent space, allowing for a more accurate representation of the underlying data distribution during data generation. Furthermore, our model offers enhanced flexibility by allowing the use of various differentiable distributions for individual features, making it possible to handle both continuous and discrete data types. We thoroughly validate our model on three real-world datasets with mixed data types, including two medically relevant ones, based on their resemblance and utility. This evaluation demonstrates significant outperformance against CTGAN and TVAE, establishing its potential as a valuable tool for generating synthetic tabular data in various domains, particularly in healthcare.

Large Language Models (LLMs) have demonstrated superior results across a wide range of tasks, while retrieval has long been established as an effective means of obtaining task-relevant information for humans. Retrieval-augmented Generation (RAG) are known for their effectiveness in knowledge-intensive tasks by locating relevant information and placing it within the context window of the LLM. However, the relationship between retrievers and LLMs is still under-investigated. Most existing work treats the retriever and the LLM as independent components and leaves a gap between retrieving human-friendly information and assembling a LLM-friendly context. In this work, we examine a novel bridge model, validate the ranking and selection assumptions in retrievers in the context of RAG, and propose a training framework that chains together supervised and reinforcement learning to learn a bridge model. Empirical results demonstrate the effectiveness of our method in both question-answering and personalized generation tasks.

We study counterfactual identifiability in causal models with bijective generation mechanisms (BGM), a class that generalizes several widely-used causal models in the literature. We establish their counterfactual identifiability for three common causal structures with unobserved confounding, and propose a practical learning method that casts learning a BGM as structured generative modeling. Learned BGMs enable efficient counterfactual estimation and can be obtained using a variety of deep conditional generative models. We evaluate our techniques in a visual task and demonstrate its application in a real-world video streaming simulation task.