In recent years, the intersection of tensor data analysis and non-parametric modeling (Guhaniyogi et al., 2017; Papadogeorgou et al., 2021; Wang and Xu, 2024) has garnered considerable interest among mathematicians and statisticians. Non-parametric tensor models have the potential to handle complex multi-dimensional data (Bi et al., 2021) and represent spatial correlation between entries of data. This paper addresses both scalar-on-tensor (i.e., to predict a scalar response based on a tensor input) and tensor-on-tensor (i.e., both the input and output are tensors) non-linear regression problems using recursive partitioning methods, often referred to as tree(-based) models. Supervised learning on tensor data, such as tensor regression, has significant relevance due to the proliferation of multi-dimensional data in modern applications. Tensor data naturally arises in various fields such as imaging (Wang and Xu, 2024), neuroscience (Li et al., 2018), and computer vision (Luo and Ma, 2023), where observations often take the form of multi-way arrays. Traditional regression models typically handle vector inputs and outputs, and thus can fail to capture the structural information embedded within tensor data.

We investigate the use of derivative information for Batch Active Learning in Gaussian Process regression models. The proposed approach employs the predictive covariance matrix for selection of data batches to exploit full correlation of samples. We theoretically analyse our proposed algorithm taking different optimality criteria into consideration and provide empirical comparisons highlighting the advantage of incorporating derivatives information. Our results show the effectiveness of our approach across diverse applications.

Sparse estimation has been studied extensively over the past 20 ye ars to handle modern high-dimensional data with [ 40 ] as a starting point. Because the advancement of computer tech nology has made it possible to collect very high dimensional data efficiently, sparse estimation will continue to be an important and effective method for high dimensional data an alysis in the future. In this study, we focus on the estimation of coefficients in sparse linear reg ression.

Knowing accurate joint positions is crucial for safe and precise control of laparoscopic surgical robots, especially for the automation of surgical sub-tasks. These robots have often been designed with cable-driven arms and tools because cables allow for larger motors to be placed at the base of the robot, further from the operating area where space is at a premium. However, by connecting the joint to its motor with a cable, any stretch in the cable can lead to errors in kinematic estimation from encoders at the motor, which can result in difficulties for accurate control of the surgical tool. In this work, we propose an efficient data-driven calibration of positioning joints of such robots, in this case the RAVEN-II surgical robotics research platform. While the calibration takes only 8-21 minutes, the accuracy of the calibrated joints remains high during a 6-hour heavily loaded operation, suggesting desirable feasibility in real practice. The calibration models take original robot states as input and are trained using zig-zag trajectories within a desired sparsity, requiring no additional sensors after training. Compared to fixed offset compensation, the Deep Neural Network calibration model can further reduce 76 percent of error and achieve accuracy of 0.104 deg, 0.120 deg, and 0.118 mm in joints 1, 2, and 3, respectively. In contrast to end-to-end models, experiments suggest that the DNN model achieves better accuracy and faster convergence when outputting the error to correct original inaccurate joint positions. Furthermore, a linear regression model is shown to have 160 times faster inference speed than DNN models for application within the 1000 Hz servo control loop, with slightly compromised accuracy.

Counterfactual explanations (CEs) aim to enhance the interpretability of machine learning models by illustrating how alterations in input features would affect the resulting predictions. Common CE approaches require an additional model and are typically constrained to binary counterfactuals. In contrast, we propose a novel method that operates directly on the latent space of a generative model, specifically a Diffusion Autoencoder (DAE). This approach offers inherent interpretability by enabling the generation of CEs and the continuous visualization of the model's internal representation across decision boundaries. Our method leverages the DAE's ability to encode images into a semantically rich latent space in an unsupervised manner, eliminating the need for labeled data or separate feature extraction models. We show that these latent representations are helpful for medical condition classification and the ordinal regression of severity pathologies, such as vertebral compression fractures (VCF) and diabetic retinopathy (DR). Beyond binary CEs, our method supports the visualization of ordinal CEs using a linear model, providing deeper insights into the model's decision-making process and enhancing interpretability. Experiments across various medical imaging datasets demonstrate the method's advantages in interpretability and versatility. The linear manifold of the DAE's latent space allows for meaningful interpolation and manipulation, making it a powerful tool for exploring medical image properties. Our code is available at https://github.com/matanat/dae_counterfactual.

Advancements in modern science have led to the increasing availability of non-Euclidean data in metric spaces. This paper addresses the challenge of modeling relationships between non-Euclidean responses and multivariate Euclidean predictors. We propose a flexible regression model capable of handling high-dimensional predictors without imposing parametric assumptions. Two primary challenges are addressed: the curse of dimensionality in nonparametric regression and the absence of linear structure in general metric spaces. The former is tackled using deep neural networks, while for the latter we demonstrate the feasibility of mapping the metric space where responses reside to a low-dimensional Euclidean space using manifold learning. We introduce a reverse mapping approach, employing local Fr\'echet regression, to map the low-dimensional manifold representations back to objects in the original metric space. We develop a theoretical framework, investigating the convergence rate of deep neural networks under dependent sub-Gaussian noise with bias. The convergence rate of the proposed regression model is then obtained by expanding the scope of local Fr\'echet regression to accommodate multivariate predictors in the presence of errors in predictors. Simulations and case studies show that the proposed model outperforms existing methods for non-Euclidean responses, focusing on the special cases of probability measures and networks.

Reliable performance metrics are necessary prerequisites to building large-scale end-to-end integrated workflows for collaborative scientific research, particularly within context of use-inspired decision making platforms with many concurrent users and when computing real-time and urgent results using large data. This work is a building block for the National Data Platform, which leverages multiple use-cases including the WIFIRE Data and Model Commons for wildfire behavior modeling and the EarthScope Consortium for collaborative geophysical research. This paper presents an artificial intelligence and machine learning (AI/ML) approach to performance assessment and optimization of scientific workflows. An associated early AI/ML framework spanning performance data collection, prediction and optimization is applied to wildfire science applications within the WIFIRE BurnPro3D (BP3D) platform for proactive fire management and mitigation.

Explainable Artificial Intelligence (XAI) is central to the debate on integrating Artificial Intelligence (AI) and Machine Learning (ML) algorithms into clinical practice. High-performing AI/ML models, such as ensemble learners and deep neural networks, often lack interpretability, hampering clinicians' trust in their predictions. To address this, XAI techniques are being developed to describe AI/ML predictions in human-understandable terms. One promising direction is the adaptation of sensitivity analysis (SA) and global sensitivity analysis (GSA), which inherently rank model inputs by their impact on predictions. Here, we introduce a novel delta-XAI method that provides local explanations of ML model predictions by extending the delta index, a GSA metric. The delta-XAI index assesses the impact of each feature's value on the predicted output for individual instances in both regression and classification problems. We formalize the delta-XAI index and provide code for its implementation. The delta-XAI method was evaluated on simulated scenarios using linear regression models, with Shapley values serving as a benchmark. Results showed that the delta-XAI index is generally consistent with Shapley values, with notable discrepancies in models with highly impactful or extreme feature values. The delta-XAI index demonstrated higher sensitivity in detecting dominant features and handling extreme feature values. Qualitatively, the delta-XAI provides intuitive explanations by leveraging probability density functions, making feature rankings clearer and more explainable for practitioners. Overall, the delta-XAI method appears promising for robustly obtaining local explanations of ML model predictions. Further investigations in real-world clinical settings will be conducted to evaluate its impact on AI-assisted clinical workflows.

This research combines Knowledge Distillation (KD) and Mixture of Experts (MoE) to develop modular, efficient multilingual language models. Key objectives include evaluating adaptive versus fixed alpha methods in KD and comparing modular MoE architectures for handling multi-domain inputs and preventing catastrophic forgetting. KD compresses large language models (LLMs) into smaller, efficient models, while MoE enhances modularity with specialized tasks. Experiments showed similar performance for both KD methods, with marginal improvements from adaptive alpha. A combined loss approach provided more stable learning. The router, trained to classify input sequences into English, French, German, or Python, achieved 99.95% precision, recall, and F1 score, with Logistic Regression being the most effective classifier. Evaluations of modular MoE architectures revealed that Pre-trained Language Experts (PLE) and Joint Expert Embedding Training (JEET) performed similarly, while the MoE with Common Expert (MoE-CE) setup showed slightly lower performance. Including a common expert in MoE-CE improved its performance. Studies on catastrophic forgetting indicated that sequential training led to significant forgetting, while single-session training with balanced batches and the MoE approach mitigated this issue. The MoE architecture preserved knowledge across multiple languages effectively. The research contributes open-sourced resources including the dataset (https://zenodo.org/doi/10.5281/zenodo.12677631), a balanced dataset creation tool (https://github.com/padas-lab-de/multi-language-dataset-creator), and the research codebase (https://github.com/ModMaamari/mixture-modular-experts).

Simple function classes have emerged as toy problems to better understand in-context-learning in transformer-based architectures used for large language models. But previously proposed simple function classes like linear regression or multi-layer-perceptrons lack the structure required to explore things like prompting and alignment within models capable of in-context-learning. We propose univariate polynomial regression as a function class that is just rich enough to study prompting and alignment, while allowing us to visualize and understand what is going on clearly.