Archives AI News

arXiv:2411.15189v4 Announce Type: replace-cross Abstract: Clustering is a popular machine learning technique for data mining that can process and analyze datasets to automatically reveal sample distribution patterns. Since the ubiquitous categorical data naturally lack a well-defined metric space such as the Euclidean distance space of numerical data, the distribution of categorical data is usually under-represented, and thus valuable information can be easily twisted in clustering. This paper, therefore, introduces a novel order distance metric learning approach to intuitively represent categorical attribute values by learning their optimal order relationship and quantifying their distance in a line similar to that of the numerical attributes. Since subjectively created qualitative categorical values involve ambiguity and fuzziness, the order distance metric is learned in the context of clustering. Accordingly, a new joint learning paradigm is developed to alternatively perform clustering and order distance metric learning with low time complexity and a guarantee of convergence. Due to the clustering-friendly order learning mechanism and the homogeneous ordinal nature of the order distance and Euclidean distance, the proposed method achieves superior clustering accuracy on categorical and mixed datasets. More importantly, the learned order distance metric greatly reduces the difficulty of understanding and managing the non-intuitive categorical data. Experiments with ablation studies, significance tests, case studies, etc., have validated the efficacy of the proposed method. The source code is available at https://github.com/DAJ0612/OCL_Source_Code.

arXiv:2508.20618v1 Announce Type: cross Abstract: We develop a stochastic algorithm for independent component analysis that incorporates multi-trial supervision, which is available in many scientific contexts. The method blends a proximal gradient-type algorithm in the space of invertible matrices with joint learning of a prediction model through backpropagation. We illustrate the proposed algorithm on synthetic and real data experiments. In particular, owing to the additional supervision, we observe an increased success rate of the non-convex optimization and the improved interpretability of the independent components.

arXiv:2105.02597v2 Announce Type: replace-cross Abstract: The study of the dynamics of natural and artificial systems has provided several examples of deviations from Brownian behavior, generally defined as anomalous diffusion. The investigation of these dynamics can provide a better understanding of diffusing objects and their surrounding media, but a quantitative characterization from individual trajectories is often challenging. Efforts devoted to improving anomalous diffusion detection using classical statistics and machine learning have produced several new methods. Recently, the anomalous diffusion challenge (AnDi, www.andi-challenge.org) was launched to objectively assess these approaches on a common dataset, focusing on three aspects of anomalous diffusion: the inference of the anomalous diffusion exponent; the classification of the diffusion model; and the segmentation of trajectories. In this article, I describe a simple approach to tackle the tasks of the AnDi challenge by combining extreme learning machine and feature engineering (AnDi-ELM). The method reaches satisfactory performance while offering a straightforward implementation and fast training time with limited computing resources, making it a suitable tool for fast preliminary screening of anomalous diffusion.

arXiv:2508.20886v1 Announce Type: new Abstract: Operator learning (OL) has emerged as a powerful tool in scientific machine learning (SciML) for approximating mappings between infinite-dimensional functional spaces. One of its main applications is learning the solution operator of partial differential equations (PDEs). While much of the progress in this area has been driven by deep neural network-based approaches such as Deep Operator Networks (DeepONet) and Fourier Neural Operator (FNO), recent work has begun to explore traditional machine learning methods for OL. In this work, we introduce polynomial chaos expansion (PCE) as an OL method. PCE has been widely used for uncertainty quantification (UQ) and has recently gained attention in the context of SciML. For OL, we establish a mathematical framework that enables PCE to approximate operators in both purely data-driven and physics-informed settings. The proposed framework reduces the task of learning the operator to solving a system of equations for the PCE coefficients. Moreover, the framework provides UQ by simply post-processing the PCE coefficients, without any additional computational cost. We apply the proposed method to a diverse set of PDE problems to demonstrate its capabilities. Numerical results demonstrate the strong performance of the proposed method in both OL and UQ tasks, achieving excellent numerical accuracy and computational efficiency.

arXiv:2508.20942v1 Announce Type: new Abstract: In this paper, we extend the transfer learning classification framework from regression function-based methods to decision rules. We propose a novel methodology for modeling posterior drift through Bayes decision rules. By exploiting the geometric transformation of the Bayes decision boundary, our method reformulates the problem as a low-dimensional empirical risk minimization problem. Under mild regularity conditions, we establish the consistency of our estimators and derive the risk bounds. Moreover, we illustrate the broad applicability of our method by adapting it to the estimation of optimal individualized treatment rules. Extensive simulation studies and analyses of real-world data further demonstrate both superior performance and robustness of our approach.

arXiv:2508.20588v1 Announce Type: cross Abstract: Current methods for stochastic hyperparameter learning in Gaussian Processes (GPs) rely on approximations, such as computing biased stochastic gradients or using inducing points in stochastic variational inference. However, when using such methods we are not guaranteed to converge to a stationary point of the true marginal likelihood. In this work, we propose algorithms for exact stochastic inference of GPs with kernels that induce a Reproducing Kernel Hilbert Space (RKHS) of moderate finite dimension. Our approach can also be extended to infinite dimensional RKHSs at the cost of forgoing exactness. Both for finite and infinite dimensional RKHSs, our method achieves better experimental results than existing methods when memory resources limit the feasible batch size and the possible number of inducing points.

arXiv:2508.20327v1 Announce Type: cross Abstract: Electronic health records (EHR) contain valuable longitudinal patient-level information, yet most statistical methods reduce the irregular timing of EHR codes into simple counts, thereby discarding rich temporal structure. Existing temporal models often impose restrictive parametric assumptions or are tailored to code level rather than patient-level tasks. We propose the latent factor point process model, which represents code occurrences as a high-dimensional point process whose conditional intensity is driven by a low dimensional latent Poisson process. This low-rank structure reflects the clinical reality that thousands of codes are governed by a small number of underlying disease processes, while enabling statistically efficient estimation in high dimensions. Building on this model, we introduce the Fourier-Eigen embedding, a patient representation constructed from the spectral density matrix of the observed process. We establish theoretical guarantees showing that these embeddings efficiently capture subgroup-specific temporal patterns for downstream classification and clustering. Simulations and an application to an Alzheimer's disease EHR cohort demonstrate the practical advantages of our approach in uncovering clinically meaningful heterogeneity.

arXiv:2412.03414v2 Announce Type: replace-cross Abstract: Locally stationary (LSPs) constitute an essential modeling paradigm for capturing the nuanced dynamics inherent in time series data whose statistical characteristics, including mean and variance, evolve smoothly across time. In this paper, we introduce a novel conditional probability distribution estimator specifically tailored for LSPs, employing the Nadaraya-Watson (NW) kernel smoothing methodology. The NW estimator, a prominent local averaging technique, leverages kernel smoothing to approximate the conditional distribution of a response variable given its covariates. We rigorously establish convergence rates for the NW-based conditional probability estimator in the univariate setting under the Wasserstein metric, providing explicit bounds and conditions that guarantee optimal performance. Extending this theoretical framework, we subsequently generalize our analysis to the multivariate scenario using the sliced Wasserstein distance, an approach particularly advantageous in circumventing the computational and analytical challenges typically associated with high-dimensional settings. To corroborate our theoretical contributions, we conduct extensive numerical simulations on synthetic datasets and provide empirical validations using real-world data, highlighting the estimator's practical relevance and effectiveness in capturing intricate temporal dependencies and underscoring its relevance for analyzing complex nonstationary phenomena.

arXiv:2508.20616v1 Announce Type: cross Abstract: Assessing whether a sample survey credibly represents the population is a critical question for ensuring the validity of downstream research. Generally, this problem reduces to estimating the distance between two high-dimensional distributions, which typically requires a number of samples that grows exponentially with the dimension. However, depending on the model used for data analysis, the conclusions drawn from the data may remain consistent across different underlying distributions. In this context, we propose a task-based approach to assess the credibility of sampled surveys. Specifically, we introduce a model-specific distance metric to quantify this notion of credibility. We also design an algorithm to verify the credibility of survey data in the context of regression models. Notably, the sample complexity of our algorithm is independent of the data dimension. This efficiency stems from the fact that the algorithm focuses on verifying the credibility of the survey data rather than reconstructing the underlying regression model. Furthermore, we show that if one attempts to verify credibility by reconstructing the regression model, the sample complexity scales linearly with the dimensionality of the data. We prove the theoretical correctness of our algorithm and numerically demonstrate our algorithm's performance.

arXiv:2506.05200v2 Announce Type: replace-cross Abstract: Large language models are capable of in-context learning, the ability to perform new tasks at test time using a handful of input-output examples, without parameter updates. We develop a universal approximation theory to elucidate how transformers enable in-context learning. For a general class of functions (each representing a distinct task), we demonstrate how to construct a transformer that, without any further weight updates, can predict based on a few noisy in-context examples with vanishingly small risk. Unlike prior work that frames transformers as approximators of optimization algorithms (e.g., gradient descent) for statistical learning tasks, we integrate Barron's universal function approximation theory with the algorithm approximator viewpoint. Our approach yields approximation guarantees that are not constrained by the effectiveness of the optimization algorithms being mimicked, extending far beyond convex problems like linear regression. The key is to show that (i) any target function can be nearly linearly represented, with small $ell_1$-norm, over a set of universal features, and (ii) a transformer can be constructed to find the linear representation -- akin to solving Lasso -- at test time.