In the realm of data analysis and bioinformatics, representing time series data in a manner akin to biological sequences offers a novel approach to leverage sequence analysis techniques. Transforming time series signals into molecular sequence-type representations allows us to enhance pattern recognition by applying sophisticated sequence analysis techniques (e.g. $k$-mers based representation) developed in bioinformatics, uncovering hidden patterns and relationships in complex, non-linear time series data. This paper proposes a method to transform time series signals into biological/molecular sequence-type representations using a unique alphabetic mapping technique. By generating 26 ranges corresponding to the 26 letters of the English alphabet, each value within the time series is mapped to a specific character based on its range. This conversion facilitates the application of sequence analysis algorithms, typically used in bioinformatics, to analyze time series data. We demonstrate the effectiveness of this approach by converting real-world time series signals into character sequences and performing sequence classification. The resulting sequences can be utilized for various sequence-based analysis techniques, offering a new perspective on time series data representation and analysis.

Quinn et al propose challenge datasets in their work called ``Kryptonite-N". These datasets aim to counter the universal function approximation argument of machine learning, breaking the notation that machine learning can ``approximate any continuous function" \cite{original_paper}. Our work refutes this claim and shows that universal function approximations can be applied successfully; the Kryptonite datasets are constructed predictably, allowing logistic regression with sufficient polynomial expansion and L1 regularization to solve for any dimension N.

Time series, as one of the most fundamental representations of sequential data, has been extensively studied across diverse disciplines, including computer science, biology, geology, astronomy, and environmental sciences. The advent of advanced sensing, storage, and networking technologies has resulted in high-dimensional time-series data, however, posing significant challenges for analyzing latent structures over extended temporal scales. Time-series clustering, an established unsupervised learning strategy that groups similar time series together, helps unveil hidden patterns in these complex datasets. In this survey, we trace the evolution of time-series clustering methods from classical approaches to recent advances in neural networks. While previous surveys have focused on specific methodological categories, we bridge the gap between traditional clustering methods and emerging deep learning-based algorithms, presenting a comprehensive, unified taxonomy for this research area. This survey highlights key developments and provides insights to guide future research in time-series clustering.

Distance measures have been recognized as one of the fundamental building blocks in time-series analysis tasks, e.g., querying, indexing, classification, clustering, anomaly detection, and similarity search. The vast proliferation of time-series data across a wide range of fields has increased the relevance of evaluating the effectiveness and efficiency of these distance measures. To provide a comprehensive view of this field, this work considers over 100 state-of-the-art distance measures, classified into 7 categories: lock-step measures, sliding measures, elastic measures, kernel measures, feature-based measures, model-based measures, and embedding measures. Beyond providing comprehensive mathematical frameworks, this work also delves into the distinctions and applications across these categories for both univariate and multivariate cases. By providing comprehensive collections and insights, this study paves the way for the future development of innovative time-series distance measures.

Machine learning (ML) and artificial intelligence (AI) can provide powerful tools for the scientific community, as demonstrated by the recent Nobel Prize in Chemistry. Reversely, insights from traditional physics theories also contribute to a deeper understanding of the mechanism of learning. Ref. [1] contains a broad overview of the successful cross-fertilisation between ML and the physical sciences, covering a number of domains. One way to mitigate against possible scepticism with regard to using ML as a "black box" is by unveiling the dynamics of training (or learning) and explaining how the relevant information is engraved in the model during the training stage. To further develop this programme, we study here the dynamics of first-order stochastic gradient descent as applied to weight matrices, reporting and expanding on the work presented in Ref. [2]. When training ML models, weight matrices are commonly updated by one of the variants of the stochastic gradient descent algorithm. The dynamics can then be decomposed into a drift and a fluctuating term, and such a system can be described by a discrete Langevin equation. The dynamics of stochastic matrix updates is richer than the dynamics for vector or scalar quantities, as captured by Dyson Brownian motion and random matrix theory (RMT), with the appearance of universal features for the eigenvalues [3-9]. Earlier descriptions of the statistical properties of weight matrices in terms of RMT can be found in e.g.

Multiple signal modalities, such as vision and sounds, are naturally present in real-world phenomena. Recently, there has been growing interest in learning generative models, in particular variational autoencoder (VAE), to for multimodal representation learning especially in the case of missing modalities. The primary goal of these models is to learn a modality-invariant and modality-specific representation that characterizes information across multiple modalities. Previous attempts at multimodal VAEs approach this mainly through the lens of experts, aggregating unimodal inference distributions with a product of experts (PoE), a mixture of experts (MoE), or a combination of both. In this paper, we provide an alternative generic and theoretical formulation of multimodal VAE through the lens of barycenter. We first show that PoE and MoE are specific instances of barycenters, derived by minimizing the asymmetric weighted KL divergence to unimodal inference distributions. Our novel formulation extends these two barycenters to a more flexible choice by considering different types of divergences. In particular, we explore the Wasserstein barycenter defined by the 2-Wasserstein distance, which better preserves the geometry of unimodal distributions by capturing both modality-specific and modality-invariant representations compared to KL divergence. Empirical studies on three multimodal benchmarks demonstrated the effectiveness of the proposed method.

Drug repurposing identifies new therapeutic uses for existing drugs, reducing the time and costs compared to traditional de novo drug discovery. Most existing drug repurposing studies using real-world patient data often treat the entire population as homogeneous, ignoring the heterogeneity of treatment responses across patient subgroups. This approach may overlook promising drugs that benefit specific subgroups but lack notable treatment effects across the entire population, potentially limiting the number of repurposable candidates identified. To address this, we introduce STEDR, a novel drug repurposing framework that integrates subgroup analysis with treatment effect estimation. Our approach first identifies repurposing candidates by emulating multiple clinical trials on real-world patient data and then characterizes patient subgroups by learning subgroup-specific treatment effects. We deploy \model to Alzheimer's Disease (AD), a condition with few approved drugs and known heterogeneity in treatment responses. We emulate trials for over one thousand medications on a large-scale real-world database covering over 8 million patients, identifying 14 drug candidates with beneficial effects to AD in characterized subgroups. Experiments demonstrate STEDR's superior capability in identifying repurposing candidates compared to existing approaches. Additionally, our method can characterize clinically relevant patient subgroups associated with important AD-related risk factors, paving the way for precision drug repurposing.

Graph Neural Networks (GNNs) have recently gained widespread attention as a successful tool for analyzing graph-structured data. However, imperfect graph structure with noisy links lacks enough robustness and may damage graph representations, therefore limiting the GNNs' performance in practical tasks. Moreover, existing generative architectures fail to fit discriminative graph-related tasks. To tackle these issues, we introduce an unsupervised method based on a joint of generative training and discriminative training to learn graph structure and representation, aiming to improve the discriminative performance of generative models. We propose an Energy-based Contrastive Learning (ECL) guided Graph Structure Refinement (GSR) framework, denoted as ECL-GSR. To our knowledge, this is the first work to combine energy-based models with contrastive learning for GSR. Specifically, we leverage ECL to approximate the joint distribution of sample pairs, which increases the similarity between representations of positive pairs while reducing the similarity between negative ones. Refined structure is produced by augmenting and removing edges according to the similarity metrics among node representations. Extensive experiments demonstrate that ECL-GSR outperforms the state-of-the-art on eight benchmark datasets in node classification. ECL-GSR achieves faster training with fewer samples and memories against the leading baseline, highlighting its simplicity and efficiency in downstream tasks.

Most active learning research has focused on methods which perform well when many labels are available, but can be dramatically worse than random selection when label budgets are small. Other methods have focused on the low-budget regime, but do poorly as label budgets increase. As the line between "low" and "high" budgets varies by problem, this is a serious issue in practice. We propose uncertainty coverage, an objective which generalizes a variety of low- and high-budget objectives, as well as natural, hyperparameter-light methods to smoothly interpolate between low- and high-budget regimes. We call greedy optimization of the estimate Uncertainty Herding; this simple method is computationally fast, and we prove that it nearly optimizes the distribution-level coverage. In experimental validation across a variety of active learning tasks, our proposal matches or beats state-of-the-art performance in essentially all cases; it is the only method of which we are aware that reliably works well in both low- and high-budget settings.

We consider a minimax problem motivated by distributionally robust optimization (DRO) when the worst-case distribution is continuous, leading to significant computational challenges due to the infinite-dimensional nature of the optimization problem. Recent research has explored learning the worst-case distribution using neural network-based generative models to address these computational challenges but lacks algorithmic convergence guarantees. This paper bridges this theoretical gap by presenting an iterative algorithm to solve such a minimax problem, achieving global convergence under mild assumptions and leveraging technical tools from vector space minimax optimization and convex analysis in the space of continuous probability densities. In particular, leveraging Brenier's theorem, we represent the worst-case distribution as a transport map applied to a continuous reference measure and reformulate the regularized discrepancy-based DRO as a minimax problem in the Wasserstein space. Furthermore, we demonstrate that the worst-case distribution can be efficiently computed using a modified Jordan-Kinderlehrer-Otto (JKO) scheme with sufficiently large regularization parameters for commonly used discrepancy functions, linked to the radius of the ambiguity set. Additionally, we derive the global convergence rate and quantify the total number of subgradient and inexact modified JKO iterations required to obtain approximate stationary points. These results are potentially applicable to nonconvex and nonsmooth scenarios, with broad relevance to modern machine learning applications.