In this paper, we present a new classifier, which integrates significance testing results over different random subspaces to yield consensus p-values for quantifying the uncertainty of classification decision. The null hypothesis is that the test sample has no association with the target class on a randomly chosen subspace, and hence the classification problem can be formulated as a problem of testing for the conjunction of hypotheses. The proposed classifier can be easily deployed for the purpose of conformal prediction and selective classification with reject and refine options by simply thresholding the consensus p-values. The theoretical analysis on the generalization error bound of the proposed classifier is provided and empirical studies on real data sets are conducted as well to demonstrate its effectiveness.

The Kalman filter (KF) and its variants are among the most celebrated algorithms in signal processing. These methods are used for state estimation of dynamic systems by relying on mathematical representations in the form of simple state-space (SS) models, which may be crude and inaccurate descriptions of the underlying dynamics. Emerging data-centric artificial intelligence (AI) techniques tackle these tasks using deep neural networks (DNNs), which are model-agnostic. Recent developments illustrate the possibility of fusing DNNs with classic Kalman-type filtering, obtaining systems that learn to track in partially known dynamics. This article provides a tutorial-style overview of design approaches for incorporating AI in aiding KF-type algorithms. We review both generic and dedicated DNN architectures suitable for state estimation, and provide a systematic presentation of techniques for fusing AI tools with KFs and for leveraging partial SS modeling and data, categorizing design approaches into task-oriented and SS model-oriented. The usefulness of each approach in preserving the individual strengths of model-based KFs and data-driven DNNs is investigated in a qualitative and quantitative study, whose code is publicly available, illustrating the gains of hybrid model-based/data-driven designs. We also discuss existing challenges and future research directions that arise from fusing AI and Kalman-type algorithms.

Developing efficient traffic models is essential for optimizing transportation systems, yet current approaches remain time-intensive and susceptible to human errors due to their reliance on manual processes. Traditional workflows involve exhaustive literature reviews, formula optimization, and iterative testing, leading to inefficiencies in research. In response, we introduce the Traffic Research Agent (TR-Agent), an AI-driven system designed to autonomously develop and refine traffic models through an iterative, closed-loop process. Specifically, we divide the research pipeline into four key stages: idea generation, theory formulation, theory evaluation, and iterative optimization; and construct TR-Agent with four corresponding modules: Idea Generator, Code Generator, Evaluator, and Analyzer. Working in synergy, these modules retrieve knowledge from external resources, generate novel ideas, implement and debug models, and finally assess them on the evaluation datasets. Furthermore, the system continuously refines these models based on iterative feedback, enhancing research efficiency and model performance. Experimental results demonstrate that TR-Agent achieves significant performance improvements across multiple traffic models, including the Intelligent Driver Model (IDM) for car following, the MOBIL lane-changing model, and the Lighthill-Whitham-Richards (LWR) traffic flow model. Additionally, TR-Agent provides detailed explanations for its optimizations, allowing researchers to verify and build upon its improvements easily. This flexibility makes the framework a powerful tool for researchers in transportation and beyond. To further support research and collaboration, we have open-sourced both the code and data used in our experiments, facilitating broader access and enabling continued advancements in the field.

We propose a new method of independent component analysis (ICA) in order to extract appropriate features from high-dimensional data. In general, matrix factorization methods including ICA have a problem regarding the interpretability of extracted features. For the improvement of interpretability, it is considered that sparse constraint on a factorized matrix is helpful. With this background, we construct a new ICA method with sparsity. In our method, the L1-regularization term is added to the cost function of ICA, and minimization of the cost function is performed by difference of convex functions algorithm. For the validity of our proposed method, we apply it to synthetic data and real functional magnetic resonance imaging data.

This work considers large-data asymptotics for t-distributed stochastic neighbor embedding (tSNE), a widely-used non-linear dimension reduction algorithm. We identify an appropriate continuum limit of the tSNE objective function, which can be viewed as a combination of a kernel-based repulsion and an asymptotically-vanishing Laplacian-type regularizer. As a consequence, we show that embeddings of the original tSNE algorithm cannot have any consistent limit as $n \to \infty$. We propose a rescaled model which mitigates the asymptotic decay of the attractive energy, and which does have a consistent limit.

The computational cost for inference and prediction of statistical models based on Gaussian processes with Mat\'ern covariance functions scales cubicly with the number of observations, limiting their applicability to large data sets. The cost can be reduced in certain special cases, but there are currently no generally applicable exact methods with linear cost. Several approximate methods have been introduced to reduce the cost, but most of these lack theoretical guarantees for the accuracy. We consider Gaussian processes on bounded intervals with Mat\'ern covariance functions and for the first time develop a generally applicable method with linear cost and with a covariance error that decreases exponentially fast in the order $m$ of the proposed approximation. The method is based on an optimal rational approximation of the spectral density and results in an approximation that can be represented as a sum of $m$ independent Gaussian Markov processes, which facilitates easy usage in general software for statistical inference, enabling its efficient implementation in general statistical inference software packages. Besides the theoretical justifications, we demonstrate the accuracy empirically through carefully designed simulation studies which show that the method outperforms all state-of-the-art alternatives in terms of accuracy for a fixed computational cost in statistical tasks such as Gaussian process regression.

Science is inherently inductive and thus involves uncertainties. They are commonly categorized as aleatoric uncertainty (AU), which refers to inherent variability, and epistemic uncertainty (EU), arising from limited information such as finite data or model assumptions (Hora, 1996). These uncertainties often overlap, as scientists may be epistemically uncertain about the aleatoric variation in their inquiry. Distinguishing and acknowledging them is crucial for the safe and trustworthy deployment of intelligent systems (Kendall and Gal, 2017; Hüllermeier and Waegeman, 2021), as they lead to different down-stream decisions. For example, experimental design aims to reduce EU (Nguyen et al., 2019; Chau et al., 2021b; Adachi et al., 2024), while risk management uses hedging strategy to address AU (Mashrur et al., 2020) While AU is often modelled using probability distributions, modelling EU--particularly in states of epistemic ignorance, also known as partial ignorance or incomplete knowledge (Dubois et al., 1996)--poses greater challenges. For instance, a scientist analysing insulin levels in Germany may have data from multiple hospitals, each representing aleatoric variation as a probability distribution. However, these distributions are merely proxies for the population-level insulin distribution, which is difficult to infer due to data collection limitations. A Bayesian approach could aggregate the data based on a prior if the representativeness of each source is known, but in many cases, scientists operate under partial ignorance, lacking such prior information (Bromberger, 1971). Assigning a uniform prior by following the principle of indifference (Keynes, 1921) and maximum entropy principle (Jaynes, 1957), or applying Jeffrey's prior by following the principle of transformation groups (Jaynes, 1968) only reflects indifference, not epistemic ignorance.

Transformers exhibit In-Context Learning (ICL), where these models solve new tasks by using examples in the prompt without additional training. In our work, we identify and analyze two key components of ICL: (1) context-scaling, where model performance improves as the number of in-context examples increases and (2) task-scaling, where model performance improves as the number of pre-training tasks increases. While transformers are capable of both context-scaling and task-scaling, we empirically show that standard Multi-Layer Perceptrons (MLPs) with vectorized input are only capable of task-scaling. To understand how transformers are capable of context-scaling, we first propose a significantly simplified transformer architecture without key, query, value weights. We show that it performs ICL comparably to the original GPT-2 model in various statistical learning tasks including linear regression, teacher-student settings. Furthermore, a single block of our simplified transformer can be viewed as data dependent feature map followed by an MLP. This feature map on its own is a powerful predictor that is capable of context-scaling but is not capable of task-scaling. We show empirically that concatenating the output of this feature map with vectorized data as an input to MLPs enables both context-scaling and task-scaling. This finding provides a simple setting to study context and task-scaling for ICL.

Adversarial training can be used to learn models that are robust against perturbations. For linear models, it can be formulated as a convex optimization problem. Compared to methods proposed in the context of deep learning, leveraging the optimization structure allows significantly faster convergence rates. Still, the use of generic convex solvers can be inefficient for large-scale problems. Here, we propose tailored optimization algorithms for the adversarial training of linear models, which render large-scale regression and classification problems more tractable. For regression problems, we propose a family of solvers based on iterative ridge regression and, for classification, a family of solvers based on projected gradient descent. The methods are based on extended variable reformulations of the original problem. We illustrate their efficiency in numerical examples.

Adversarial attacks, characterized by subtle data perturbations that destabilize neural network predictions, have been a topic of significant interest for over a decade [48, 16, 32, 5]. These attacks have evolved into various forms, depending on the knowledge of the model's architecture (white-box, gray-box, black-box) [49], the type of data being targeted (graphs, images, text, etc.) [12, 47, 16, 57], and the specific adversarial objectives (targeted, untargeted, defense-oriented) [55, 29]. While numerous defense strategies aim to broadly stabilize models against adversarial attacks, independent of the specific attack mechanism [7, 14, 15, 41], the most effective and widely-used defenses focus on adversarial training, where the model is trained to withstand particular attacks [29, 50]. Adversarial training is known for producing robust models efficiently, but its effectiveness hinges on the availability of adversarial attacks that are both potent in degrading model accuracy and efficient in terms of computational resources. However, the most aggressive attacks often require significant computational resources, making them less practical for adversarial training. The projected gradient descent (PGD) attack [29] is popular in adversarial training due to its balance between aggressiveness and computational efficiency. In this work, we observe that in many cases the perturbations generated by PGD predominantly affect the lower part of the singular value spectrum of input images, indicating that these perturbations are approximately low-rank. Additionally, we find that the size of PGD-generated attacks differs significantly between standard and adversarially trained models when measured by their nuclear norm, which sums the singular values of the attack. This metric provides insight into the frequency profile of the attack when analyzed using the singular value decomposition (SVD) transform, aligning with known frequency profiles observed under discrete Fourier transform (DFT) and discrete cosine transform (DCT) analyses of PGD attacks [54, 31].