Medical imaging is key in modern medicine. From magnetic resonance imaging (MRI) to microscopic imaging for blood cell detection, diagnostic medical imaging reveals vital insights into patient health. To predict diseases or provide individualized therapies, machine learning techniques like kernel methods have been widely used. Nevertheless, there are multiple challenges for implementing kernel methods. Medical image data often originates from various hospitals and cannot be combined due to privacy concerns, and the high dimensionality of image data presents another significant obstacle. While randomised encoding offers a promising direction, existing methods often struggle with a trade-off between accuracy and efficiency. Addressing the need for efficient privacy-preserving methods on distributed image data, we introduce OKRA (Orthonormal K-fRAmes), a novel randomized encoding-based approach for kernel-based machine learning. This technique, tailored for widely used kernel functions, significantly enhances scalability and speed compared to current state-of-the-art solutions. Through experiments conducted on various clinical image datasets, we evaluated model quality, computational performance, and resource overhead. Additionally, our method outperforms comparable approaches

We provide a rigorous analysis of implicit regularization in an overparametrized tensor factorization problem beyond the lazy training regime. For matrix factorization problems, this phenomenon has been studied in a number of works. A particular challenge has been to design universal initialization strategies which provably lead to implicit regularization in gradient-descent methods. At the same time, it has been argued by Cohen et. al. 2016 that more general classes of neural networks can be captured by considering tensor factorizations. However, in the tensor case, implicit regularization has only been rigorously established for gradient flow or in the lazy training regime. In this paper, we prove the first tensor result of its kind for gradient descent rather than gradient flow. We focus on the tubal tensor product and the associated notion of low tubal rank, encouraged by the relevance of this model for image data. We establish that gradient descent in an overparametrized tensor factorization model with a small random initialization exhibits an implicit bias towards solutions of low tubal rank. Our theoretical findings are illustrated in an extensive set of numerical simulations show-casing the dynamics predicted by our theory as well as the crucial role of using a small random initialization.

Identifying dynamical systems characterized by nonlinear parameters presents significant challenges in deriving mathematical models that enhance understanding of physics. Traditional methods, such as Sparse Identification of Nonlinear Dynamics (SINDy) and symbolic regression, can extract governing equations from observational data; however, they also come with distinct advantages and disadvantages. This paper introduces a novel method within the SINDy framework, termed ADAM-SINDy, which synthesizes the strengths of established approaches by employing the ADAM optimization algorithm. This facilitates the simultaneous optimization of nonlinear parameters and coefficients associated with nonlinear candidate functions, enabling precise parameter estimation without requiring prior knowledge of nonlinear characteristics such as trigonometric frequencies, exponential bandwidths, or polynomial exponents, thereby addressing a key limitation of SINDy. Through an integrated global optimization, ADAM-SINDy dynamically adjusts all unknown variables in response to data, resulting in an adaptive identification procedure that reduces the sensitivity to the library of candidate functions. The performance of the ADAM-SINDy methodology is demonstrated across a spectrum of dynamical systems, including benchmark coupled nonlinear ordinary differential equations such as oscillators, chaotic fluid flows, reaction kinetics, pharmacokinetics, as well as nonlinear partial differential equations (wildfire transport). The results demonstrate significant improvements in identifying parameterized dynamical systems and underscore the importance of concurrently optimizing all parameters, particularly those characterized by nonlinear parameters. These findings highlight the potential of ADAM-SINDy to extend the applicability of the SINDy framework in addressing more complex challenges in dynamical system identification.

Live comments, also known as Danmaku, are user-generated messages that are synchronized with video content. These comments overlay directly onto streaming videos, capturing viewer emotions and reactions in real-time. While prior work has leveraged live comments in affective analysis, its use has been limited due to the relative rarity of live comments across different video platforms. To address this, we first construct the Live Comment for Affective Analysis (LCAffect) dataset which contains live comments for English and Chinese videos spanning diverse genres that elicit a wide spectrum of emotions. Then, using this dataset, we use contrastive learning to train a video encoder to produce synthetic live comment features for enhanced multimodal affective content analysis. Through comprehensive experimentation on a wide range of affective analysis tasks (sentiment, emotion recognition, and sarcasm detection) in both English and Chinese, we demonstrate that these synthetic live comment features significantly improve performance over state-of-the-art methods.

The scarcity of high-quality, multimodal training data severely hinders the creation of lifelike avatar animations for conversational AI in virtual environments. Existing datasets often lack the intricate synchronization between speech, facial expressions, and body movements that characterize natural human communication. To address this critical gap, we introduce Allo-AVA, a large-scale dataset specifically designed for text and audio-driven avatar gesture animation in an allocentric (third person point-of-view) context. Allo-AVA consists of $\sim$1,250 hours of diverse video content, complete with audio, transcripts, and extracted keypoints. Allo-AVA uniquely maps these keypoints to precise timestamps, enabling accurate replication of human movements (body and facial gestures) in synchronization with speech. This comprehensive resource enables the development and evaluation of more natural, context-aware avatar animation models, potentially transforming applications ranging from virtual reality to digital assistants.

The t-Distributed Stochastic Neighbor Embedding (t-SNE) has emerged as a popular dimensionality reduction technique for visualizing high-dimensional data. It computes pairwise similarities between data points by default using an RBF kernel and random initialization (in low-dimensional space), which successfully captures the overall structure but may struggle to preserve the local structure efficiently. This research proposes a novel approach called the Modified Isolation Kernel (MIK) as an alternative to the Gaussian kernel, which is built upon the concept of the Isolation Kernel. MIK uses adaptive density estimation to capture local structures more accurately and integrates robustness measures. It also assigns higher similarity values to nearby points and lower values to distant points. Comparative research using the normal Gaussian kernel, the isolation kernel, and several initialization techniques, including random, PCA, and random walk initializations, are used to assess the proposed approach (MIK). Additionally, we compare the computational efficiency of all $3$ kernels with $3$ different initialization methods. Our experimental results demonstrate several advantages of the proposed kernel (MIK) and initialization method selection. It exhibits improved preservation of the local and global structure and enables better visualization of clusters and subclusters in the embedded space. These findings contribute to advancing dimensionality reduction techniques and provide researchers and practitioners with an effective tool for data exploration, visualization, and analysis in various domains.

Infectious diseases occur when pathogens from other individuals or animals infect a person, resulting in harm to both individuals and society as a whole. The outbreak of such diseases can pose a significant threat to human health. However, early detection and tracking of these outbreaks have the potential to reduce the mortality impact. To address these threats, public health authorities have endeavored to establish comprehensive mechanisms for collecting disease data. Many countries have implemented infectious disease surveillance systems, with the detection of epidemics being a primary objective. The clinical healthcare system, local/state health agencies, federal agencies, academic/professional groups, and collaborating governmental entities all play pivotal roles within this system. Moreover, nowadays, search engines and social media platforms can serve as valuable tools for monitoring disease trends. The Internet and social media have become significant platforms where users share information about their preferences and relationships. This real-time information can be harnessed to gauge the influence of ideas and societal opinions, making it highly useful across various domains and research areas, such as marketing campaigns, financial predictions, and public health, among others. This article provides a review of the existing standard methods developed by researchers for detecting outbreaks using time series data. These methods leverage various data sources, including conventional data sources and social media data or Internet data sources. The review particularly concentrates on works published within the timeframe of 2015 to 2022.

Time series analysis plays a critical role in numerous applications, supporting tasks such as forecasting, classification, anomaly detection, and imputation. In this work, we present the time series pattern machine (TSPM), a model designed to excel in a broad range of time series tasks through powerful representation and pattern extraction capabilities. Traditional time series models often struggle to capture universal patterns, limiting their effectiveness across diverse tasks. To address this, we define multiple scales in the time domain and various resolutions in the frequency domain, employing various mixing strategies to extract intricate, task-adaptive time series patterns. MRTI transforms multi-scale time series into multi-resolution time images, capturing patterns across both temporal and frequency domains. TID leverages dual-axis attention to extract seasonal and trend patterns, while MCM hierarchically aggregates these patterns across scales. Our work marks a promising step toward the next generation of TSPMs, paving the way for further advancements in time series analysis. Time series analysis is crucial for identifying and predicting temporal patterns across various domains, including weather forecasting (Bi et al., 2023), medical symptom classification (Kiyasseh et al., 2021), anomaly detection in spacecraft monitoring (Xu, 2021), and imputing missing data in wearable sensors (Wu et al., 2020). These diverse applications highlight the versatility and importance of time series analysis in addressing real-world challenges. A key advancement in this field is the development of time series pattern machines (TSPMs), which aim to create a unified model architecture capable of handling a broad range of time series tasks across domains (Zhou et al., 2023; Wu et al., 2023). At the core of TSPMs is their ability to recognize and generalize time series patterns inherent in time series data, enabling the model to uncover meaningful temporal structures and adapt to varying time series task scenarios.

Deep Reinforcement Learning (DRL) algorithms have achieved great success in solving many challenging tasks while their black-box nature hinders interpretability and real-world applicability, making it difficult for human experts to interpret and understand DRL policies. Existing works on interpretable reinforcement learning have shown promise in extracting decision tree (DT) based policies from DRL policies with most focus on the single-agent settings while prior attempts to introduce DT policies in multi-agent scenarios mainly focus on heuristic designs which do not provide any quantitative guarantees on the expected return. In this paper, we establish an upper bound on the return gap between the oracle expert policy and an optimal decision tree policy. This enables us to recast the DT extraction problem into a novel non-euclidean clustering problem over the local observation and action values space of each agent, with action values as cluster labels and the upper bound on the return gap as clustering loss. Both the algorithm and the upper bound are extended to multi-agent decentralized DT extractions by an iteratively-grow-DT procedure guided by an action-value function conditioned on the current DTs of other agents. Further, we propose the Return-Gap-Minimization Decision Tree (RGMDT) algorithm, which is a surprisingly simple design and is integrated with reinforcement learning through the utilization of a novel Regularized Information Maximization loss. Evaluations on tasks like D4RL show that RGMDT significantly outperforms heuristic DT-based baselines and can achieve nearly optimal returns under given DT complexity constraints (e.g., maximum number of DT nodes).

Conformal prediction has emerged as a powerful tool for building prediction intervals that are valid in a distribution-free way. However, its evaluation may be computationally costly, especially in the high-dimensional setting where the dimensionality and sample sizes are both large and of comparable magnitudes. To address this challenge in the context of generalized linear regression, we propose a novel algorithm based on Approximate Message Passing (AMP) to accelerate the computation of prediction intervals using full conformal prediction, by approximating the computation of conformity scores. Our work bridges a gap between modern uncertainty quantification techniques and tools for high-dimensional problems involving the AMP algorithm. We evaluate our method on both synthetic and real data, and show that it produces prediction intervals that are close to the baseline methods, while being orders of magnitude faster. Additionally, in the high-dimensional limit and under assumptions on the data distribution, the conformity scores computed by AMP converge to the one computed exactly, which allows theoretical study and benchmarking of conformal methods in high dimensions.