Particle-based Bayesian inference methods by sampling from a partition-free target (posterior) distribution, e.g., Stein variational gradient descent (SVGD), have attracted significant attention. We propose a path-guided particle-based sampling~(PGPS) method based on a novel Log-weighted Shrinkage (LwS) density path linking an initial distribution to the target distribution. We propose to utilize a Neural network to learn a vector field motivated by the Fokker-Planck equation of the designed density path. Particles, initiated from the initial distribution, evolve according to the ordinary differential equation defined by the vector field. The distribution of these particles is guided along a density path from the initial distribution to the target distribution. The proposed LwS density path allows for an efficient search of modes of the target distribution while canonical methods fail. We theoretically analyze the Wasserstein distance of the distribution of the PGPS-generated samples and the target distribution due to approximation and discretization errors. Practically, the proposed PGPS-LwS method demonstrates higher Bayesian inference accuracy and better calibration ability in experiments conducted on both synthetic and real-world Bayesian learning tasks, compared to baselines, such as SVGD and Langevin dynamics, etc.

Relying on the representation power of neural networks, most recent works have often neglected several factors involved in haze degradation, such as transmission (the amount of light reaching an observer from a scene over distance) and atmospheric light. These factors are generally unknown, making dehazing problems ill-posed and creating inherent uncertainties. To account for such uncertainties and factors involved in haze degradation, we introduce a variational Bayesian framework for single image dehazing. We propose to take not only a clean image and but also transmission map as latent variables, the posterior distributions of which are parameterized by corresponding neural networks: dehazing and transmission networks, respectively. Based on a physical model for haze degradation, our variational Bayesian framework leads to a new objective function that encourages the cooperation between them, facilitating the joint training of and thereby boosting the performance of each other. In our framework, a dehazing network can estimate a clean image independently of a transmission map estimation during inference, introducing no overhead. Furthermore, our model-agnostic framework can be seamlessly incorporated with other existing dehazing networks, greatly enhancing the performance consistently across datasets and models.

Transformer-based architectures have achieved unprecedented success in time series analysis. However, facing the challenge of across-domain modeling, existing studies utilize statistical prior as prompt engineering fails under the huge distribution shift among various domains. In this paper, a Unified Time Series Diffusion (UTSD) model is established for the first time to model the multi-domain probability distribution, utilizing the powerful probability distribution modeling ability of Diffusion. Unlike the autoregressive models that capture the conditional probabilities of the prediction horizon to the historical sequence, we use a diffusion denoising process to model the mixture distribution of the cross-domain data and generate the prediction sequence for the target domain directly utilizing conditional sampling. The proposed UTSD contains three pivotal designs: (1) The condition network captures the multi-scale fluctuation patterns from the observation sequence, which are utilized as context representations to guide the denoising network to generate the prediction sequence; (2) Adapter-based fine-tuning strategy, the multi-domain universal representation learned in the pretraining stage is utilized for downstream tasks in target domains; (3) The diffusion and denoising process on the actual sequence space, combined with the improved classifier free guidance as the conditional generation strategy, greatly improves the stability and accuracy of the downstream task. We conduct extensive experiments on mainstream benchmarks, and the pre-trained UTSD outperforms existing foundation models on all data domains, exhibiting superior zero-shot generalization ability. After training from scratch, UTSD achieves comparable performance against domain-specific proprietary models. The empirical results validate the potential of UTSD as a time series foundational model.

Complex networked systems driven by latent inputs are common in fields like neuroscience, finance, and engineering. A key inference problem here is to learn edge connectivity from node outputs (potentials). We focus on systems governed by steady-state linear conservation laws: $X_t = {L^{\ast}}Y_{t}$, where $X_t, Y_t \in \mathbb{R}^p$ denote inputs and potentials, respectively, and the sparsity pattern of the $p \times p$ Laplacian $L^{\ast}$ encodes the edge structure. Assuming $X_t$ to be a wide-sense stationary stochastic process with a known spectral density matrix, we learn the support of $L^{\ast}$ from temporally correlated samples of $Y_t$ via an $\ell_1$-regularized Whittle's maximum likelihood estimator (MLE). The regularization is particularly useful for learning large-scale networks in the high-dimensional setting where the network size $p$ significantly exceeds the number of samples $n$. We show that the MLE problem is strictly convex, admitting a unique solution. Under a novel mutual incoherence condition and certain sufficient conditions on $(n, p, d)$, we show that the ML estimate recovers the sparsity pattern of $L^\ast$ with high probability, where $d$ is the maximum degree of the graph underlying $L^{\ast}$. We provide recovery guarantees for $L^\ast$ in element-wise maximum, Frobenius, and operator norms. Finally, we complement our theoretical results with several simulation studies on synthetic and benchmark datasets, including engineered systems (power and water networks), and real-world datasets from neural systems (such as the human brain).

Tensor decompositions play a crucial role in numerous applications related to multi-way data analysis. By employing a Bayesian framework with sparsity-inducing priors, Bayesian Tensor Ring (BTR) factorization offers probabilistic estimates and an effective approach for automatically adapting the tensor ring rank during the learning process. However, previous BTR method employs an Automatic Relevance Determination (ARD) prior, which can lead to sub-optimal solutions. Besides, it solely focuses on continuous data, whereas many applications involve discrete data. More importantly, it relies on the Coordinate-Ascent Variational Inference (CAVI) algorithm, which is inadequate for handling large tensors with extensive observations. These limitations greatly limit its application scales and scopes, making it suitable only for small-scale problems, such as image/video completion. To address these issues, we propose a novel BTR model that incorporates a nonparametric Multiplicative Gamma Process (MGP) prior, known for its superior accuracy in identifying latent structures. To handle discrete data, we introduce the P\'olya-Gamma augmentation for closed-form updates. Furthermore, we develop an efficient Gibbs sampler for consistent posterior simulation, which reduces the computational complexity of previous VI algorithm by two orders, and an online EM algorithm that is scalable to extremely large tensors. To showcase the advantages of our model, we conduct extensive experiments on both simulation data and real-world applications.

Advancements in artificial intelligence, machine learning, and deep learning have catalyzed the transformation of big data analytics and management into pivotal domains for research and application. This work explores the theoretical foundations, methodological advancements, and practical implementations of these technologies, emphasizing their role in uncovering actionable insights from massive, high-dimensional datasets. The study presents a systematic overview of data preprocessing techniques, including data cleaning, normalization, integration, and dimensionality reduction, to prepare raw data for analysis. Core analytics methodologies such as classification, clustering, regression, and anomaly detection are examined, with a focus on algorithmic innovation and scalability. Furthermore, the text delves into state-of-the-art frameworks for data mining and predictive modeling, highlighting the role of neural networks, support vector machines, and ensemble methods in tackling complex analytical challenges. Special emphasis is placed on the convergence of big data with distributed computing paradigms, including cloud and edge computing, to address challenges in storage, computation, and real-time analytics. The integration of ethical considerations, including data privacy and compliance with global standards, ensures a holistic perspective on data management. Practical applications across healthcare, finance, marketing, and policy-making illustrate the real-world impact of these technologies. Through comprehensive case studies and Python-based implementations, this work equips researchers, practitioners, and data enthusiasts with the tools to navigate the complexities of modern data analytics. It bridges the gap between theory and practice, fostering the development of innovative solutions for managing and leveraging data in the era of artificial intelligence.

Understanding how galaxies form and evolve is at the heart of modern astronomy. With the advent of large-scale surveys and simulations, remarkable progress has been made in the last few decades. Despite this, the physical processes behind the phenomena, and particularly their importance, remain far from known, as correlations have primarily been established rather than the underlying causality. We address this challenge by applying the causal inference framework. Specifically, we tackle the fundamental open question of whether galaxy formation and evolution depends more on nature (i.e., internal processes) or nurture (i.e., external processes), by estimating the causal effect of environment on star-formation rate in the IllustrisTNG simulations. To do so, we develop a comprehensive causal model and employ cutting-edge techniques from epidemiology to overcome the long-standing problem of disentangling nature and nurture. We find that the causal effect is negative and substantial, with environment suppressing the SFR by a maximal factor of $\sim100$. While the overall effect at $z=0$ is negative, in the early universe, environment is discovered to have a positive impact, boosting star formation by a factor of $\sim10$ at $z\sim1$ and by even greater amounts at higher redshifts. Furthermore, we show that: (i) nature also plays an important role, as ignoring it underestimates the causal effect in intermediate-density environments by a factor of $\sim2$, (ii) controlling for the stellar mass at a snapshot in time, as is common in the literature, is not only insufficient to disentangle nature and nurture but actually has an adverse effect, though (iii) stellar mass is an adequate proxy of the effects of nature. Finally, this work may prove a useful blueprint for extracting causal insights in other fields that deal with dynamical systems with closed feedback loops, such as the Earth's climate.

Diabetic Retinopathy is one of the most familiar diseases and is a diabetes complication that affects eyes. Initially, diabetic retinopathy may cause no symptoms or only mild vision problems. Eventually, it can cause blindness. So early detection of symptoms could help to avoid blindness. In this paper, we present some experiments on some features of diabetic retinopathy, like properties of exudates, properties of blood vessels and properties of microaneurysm. Using the features, we can classify healthy, mild non-proliferative, moderate non-proliferative, severe non-proliferative and proliferative stages of DR. Support Vector Machine, Random Forest and Naive Bayes classifiers are used to classify the stages. Finally, Random Forest is found to be the best for higher accuracy, sensitivity and specificity of 76.5%, 77.2% and 93.3% respectively.

The rapid advancements in machine learning have made its application to anomalous diffusion analysis both essential and inevitable. This review systematically introduces the integration of machine learning techniques for enhanced analysis of anomalous diffusion, focusing on two pivotal aspects: single trajectory characterization via machine learning and representation learning of anomalous diffusion. We extensively compare various machine learning methods, including both classical machine learning and deep learning, used for the inference of diffusion parameters and trajectory segmentation. Additionally, platforms such as the Anomalous Diffusion Challenge that serve as benchmarks for evaluating these methods are highlighted. On the other hand, we outline three primary strategies for representing anomalous diffusion: the combination of predefined features, the feature vector from the penultimate layer of neural network, and the latent representation from the autoencoder, analyzing their applicability across various scenarios. This investigation paves the way for future research, offering valuable perspectives that can further enrich the study of anomalous diffusion and advance the application of artificial intelligence in statistical physics and biophysics.

The AI safety literature is full of examples of powerful AI agents that, in blindly pursuing a specific and usually narrow objective, ends up with unacceptable and even catastrophic collateral damage to others. In this paper, we consider the problem of social harms that can result from actions taken by learning and utility-maximising agents in a multi-agent environment. The problem of measuring social harms or impacts in such multi-agent settings, especially when the agents are artificial generally intelligent (AGI) agents, was listed as an open problem in Everitt et al, 2018. We attempt a partial answer to that open problem in the form of market-based mechanisms to quantify and control the cost of such social harms. The proposed setup captures many well-studied special cases and is more general than existing formulations of multi-agent reinforcement learning with mechanism design in two ways: (i) the underlying environment is a history-based general reinforcement learning environment like in AIXI; (ii) the reinforcement-learning agents participating in the environment can have different learning strategies and planning horizons. To demonstrate the practicality of the proposed setup, we survey some key classes of learning algorithms and present a few applications, including a discussion of the Paperclips problem and pollution control with a cap-and-trade system.