In the evolving domains of Machine Learning and Data Analytics, existing dataset characterization methods such as statistical, structural, and model-based analyses often fail to deliver the deep understanding and insights essential for innovation and explainability. This work surveys the current state-of-the-art conventional data analytic techniques and examines their limitations, and discusses a variety of tensor-based methods and how these may provide a more robust alternative to traditional statistical, structural, and model-based dataset characterization techniques. Through examples, we illustrate how tensor methods unveil nuanced data characteristics, offering enhanced interpretability and actionable intelligence. We advocate for the adoption of tensor-based characterization, promising a leap forward in understanding complex datasets and paving the way for intelligent, explainable data-driven discoveries.

Diffusion models enable the synthesis of highly accurate samples from complex distributions and have become foundational in generative modeling. Recently, they have demonstrated significant potential for solving Bayesian inverse problems by serving as priors. This review offers a comprehensive overview of current methods that leverage \emph{pre-trained} diffusion models alongside Monte Carlo methods to address Bayesian inverse problems without requiring additional training. We show that these methods primarily employ a \emph{twisting} mechanism for the intermediate distributions within the diffusion process, guiding the simulations toward the posterior distribution. We describe how various Monte Carlo methods are then used to aid in sampling from these twisted distributions.

The study of X-ray spectra is crucial to understanding the physical nature of astrophysical sources. Machine learning methods can extract compact and informative representations of data from large datasets. The Chandra Source Catalog (CSC) provides a rich archive of X-ray spectral data, which remains largely underexplored in this context. This work aims to develop a compact and physically meaningful representation of Chandra X-ray spectra using deep learning. To verify that the learned representation captures relevant information, we evaluate it through classification, regression, and interpretability analyses. We use a transformer-based autoencoder to compress X-ray spectra. The input spectra, drawn from the CSC, include only high-significance detections. Astrophysical source types and physical summary statistics are compiled from external catalogs. We evaluate the learned representation in terms of spectral reconstruction accuracy, clustering performance on 8 known astrophysical source classes, and correlation with physical quantities such as hardness ratios and hydrogen column density ($N_H$). The autoencoder accurately reconstructs spectra with 8 latent variables. Clustering in the latent space yields a balanced classification accuracy of $\sim$40% across the 8 source classes, increasing to $\sim$69% when restricted to AGNs and stellar-mass compact objects exclusively. Moreover, latent features correlate with non-linear combinations of spectral fluxes, suggesting that the compressed representation encodes physically relevant information. The proposed autoencoder-based pipeline is a powerful tool for the representation and interpretation of X-ray spectra, providing a compact latent space that supports both classification and the estimation of physical properties. This work demonstrates the potential of deep learning for spectral studies and uncovering new patterns in X-ray data.

Recovering true signals from noisy measurements is a central challenge in inverse problems spanning medical imaging, geophysics, and signal processing. Current solutions balance prior assumptions regarding the true signal (regularization) with agreement to noisy measured data (data-fidelity). Conventional data-fidelity loss functions, such as mean-squared error (MSE) or negative log-likelihood, seek pointwise agreement with noisy measurements, often leading to overfitting to noise. In this work, we instead evaluate data-fidelity collectively by testing whether the observed measurements are statistically consistent with the noise distributions implied by the current estimate. We adopt this aggregated perspective and introduce distributional consistency (DC) loss, a data-fidelity objective that replaces pointwise matching with distribution-level calibration using model-based probability scores for each measurement. DC loss acts as a direct and practical plug-in replacement for standard data consistency terms: i) it is compatible with modern regularizers, ii) it is optimized in the same way as traditional losses, and iii) it avoids overfitting to measurement noise even without the use of priors. Its scope naturally fits many practical inverse problems where the measurement-noise distribution is known and where the measured dataset consists of many independent noisy values. We demonstrate efficacy in two key example application areas: i) in image denoising with deep image prior, using DC instead of MSE loss removes the need for early stopping and achieves higher PSNR; ii) in medical image reconstruction from Poisson-noisy data, DC loss reduces artifacts in highly-iterated reconstructions and enhances the efficacy of hand-crafted regularization. These results position DC loss as a statistically grounded, performance-enhancing alternative to conventional fidelity losses for inverse problems.

Label distribution learning (LDL) is a paradigm that each sample is associated with a label distribution. At present, the existing approaches are proposed for the single-view LDL problem with labeled data, while the multi-view LDL problem with labeled and unlabeled data has not been considered. In this paper, we put forward the multi-view semi-supervised label distribution learning with local structure complementarity (MVSS-LDL) approach, which exploits the local nearest neighbor structure of each view and emphasizes the complementarity of local nearest neighbor structures in multiple views. Specifically speaking, we first explore the local structure of view $v$ by computing the $k$-nearest neighbors. As a result, the $k$-nearest neighbor set of each sample $\boldsymbol{x}_i$ in view $v$ is attained. Nevertheless, this $k$-nearest neighbor set describes only a part of the nearest neighbor information of sample $\boldsymbol{x}_i$. In order to obtain a more comprehensive description of sample $\boldsymbol{x}_i$'s nearest neighbors, we complement the nearest neighbor set in view $v$ by incorporating sample $\boldsymbol{x}_i$'s nearest neighbors in other views. Lastly, based on the complemented nearest neighbor set in each view, a graph learning-based multi-view semi-supervised LDL model is constructed. By considering the complementarity of local nearest neighbor structures, different views can mutually provide the local structural information to complement each other. To the best of our knowledge, this is the first attempt at multi-view LDL. Numerical studies have demonstrated that MVSS-LDL attains explicitly better classification performance than the existing single-view LDL methods.

Microwell microfluidics has been utilized for single-cell analysis to reveal heterogeneity in gene expression, signaling pathways, and phenotypic responses for identifying rare cell types, understanding disease progression, and developing more precise therapeutic strategies. However, designing microwell microfluidics is a considerably complex task, requiring knowledge, experience, and CAD software, as well as manual intervention, which often fails initial designs, demanding multiple costly and time-consuming iterations. In this study, we establish an autonomous large language model (LLM)-driven microwell design framework to generate code-based computer-aided design (CAD) scripts, that enables the rapid and reproducible creation of microwells with diverse geometries and imaging-based analysis. We propose a multimodal large language model (MLLM)-logistic regression framework based on integrating high-level semantic descriptions generated by MLLMs with image embeddings for image classification tasks, aiming to identify microwell occupancy and microwell shape. The fused multimodal representation is input to a logistic regression model, which is both interpretable and computationally efficient. We achieved significant improvements, exceeding 0.92 for occupancy classification and 0.99 for shape classification, across all evaluated MLLMs, compared with 0.50 and 0.55, respectively, when relying solely on direct classification. The MLLM-logistic regression framework is a scalable, efficient solution for high-throughput microwell image analysis. Our study demonstrates an autonomous design microwell platform by translating natural language prompts into optimized device geometries, CAD scripts and image analysis, facilitating the development of next-generation digital discovery by integration of literature mining, autonomous design and experimental data analysis.

Healthcare research and development face significant obstacles due to data scarcity and stringent privacy regulations, such as HIPAA and the GDPR, restricting access to essential real-world medical data. These limitations impede innovation, delay robust AI model creation, and hinder advancements in patient-centered care. Synthetic data generation offers a transformative solution by producing artificial datasets that emulate real data statistics while safeguarding patient privacy. We introduce a novel hybrid framework for high-fidelity healthcare data synthesis integrating five augmentation methods: noise injection, interpolation, Gaussian Mixture Model (GMM) sampling, Conditional Variational Autoencoder (CVAE) sampling, and SMOTE, combined via a reinforcement learning-based dynamic weight selection mechanism. Its key innovations include advanced calibration techniques -- moment matching, full histogram matching, soft and adaptive soft histogram matching, and iterative refinement -- that align marginal distributions and preserve joint feature dependencies. Evaluated on the Breast Cancer Wisconsin (UCI Repository) and Khulna Medical College cardiology datasets, our calibrated hybrid achieves Wasserstein distances as low as 0.001 and Kolmogorov-Smirnov statistics around 0.01, demonstrating near-zero marginal discrepancy. Pairwise trend scores surpass 90%, and Nearest Neighbor Adversarial Accuracy approaches 50%, confirming robust privacy protection. Downstream classifiers trained on synthetic data achieve up to 94% accuracy and F1 scores above 93%, comparable to models trained on real data. This scalable, privacy-preserving approach matches state-of-the-art methods, sets new benchmarks for joint-distribution fidelity in healthcare, and supports sensitive AI applications.

Many video workflows benefit from a mixture of user controls with varying granularity, from exact 4D object trajectories and camera paths to coarse text prompts, while existing video generative models are typically trained for fixed input formats. We develop Ctrl-VI, a video synthesis method that addresses this need and generates samples with high controllability for specified elements while maintaining diversity for under-specified ones. We cast the task as variational inference to approximate a composed distribution, leveraging multiple video generation backbones to account for all task constraints collectively. To address the optimization challenge, we break down the problem into step-wise KL divergence minimization over an annealed sequence of distributions, and further propose a context-conditioned factorization technique that reduces modes in the solution space to circumvent local optima. Experiments suggest that our method produces samples with improved controllability, diversity, and 3D consistency compared to prior works.

Samples of brain signals collected by EEG sensors have inherent anti-correlations that are well modeled by negative edges in a finite graph. To differentiate epilepsy patients from healthy subjects using collected EEG signals, we build lightweight and interpretable transformer-like neural nets by unrolling a spectral denoising algorithm for signals on a balanced signed graph -- graph with no cycles of odd number of negative edges. A balanced signed graph has well-defined frequencies that map to a corresponding positive graph via similarity transform of the graph Laplacian matrices. We implement an ideal low-pass filter efficiently on the mapped positive graph via Lanczos approximation, where the optimal cutoff frequency is learned from data. Given that two balanced signed graph denoisers learn posterior probabilities of two different signal classes during training, we evaluate their reconstruction errors for binary classification of EEG signals. Experiments show that our method achieves classification performance comparable to representative deep learning schemes, while employing dramatically fewer parameters.

Pretraining a policy on offline data followed by fine-tuning through online interactions, known as Offline-to-Online Reinforcement Learning (O2O RL), has emerged as a promising paradigm for real-world RL deployment. However, both offline datasets and online interactions in practical environments are often noisy or even maliciously corrupted, severely degrading the performance of O2O RL. Existing works primarily focus on mitigating the conservatism of offline policies via online exploration, while the robustness of O2O RL under data corruption, including states, actions, rewards, and dynamics, is still unexplored. In this work, we observe that data corruption induces heavy-tailed behavior in the policy, thereby substantially degrading the efficiency of online exploration. To address this issue, we incorporate Inverse Probability Weighted (IPW) into the online exploration policy to alleviate heavy-tailedness, and propose a novel, simple yet effective method termed $\textbf{RPEX}$: $\textbf{R}$obust $\textbf{P}$olicy $\textbf{EX}$pansion. Extensive experimental results on D4RL datasets demonstrate that RPEX achieves SOTA O2O performance across a wide range of data corruption scenarios. Code is available at $\href{https://github.com/felix-thu/RPEX}{https://github.com/felix-thu/RPEX}$.