The intrinsic ill-posedness of this problem can be addressed within the framework of regularization theory (Kaipio & Somersalo 2006), i.e., as the problem of minimizing a non-linear functional made of the sum of two terms: a fitting term in which the empirical risk is assessed by means of a loss function, and a penalty term that allows generalization while controlling the complexity of the solution. Finally, a real positive regularization parameter that balances the trade-off between the two terms has to be chosen by means of some regularization algorithm (Engl et al. 1996). When described in a Hilbert space setting, a representer theorem (Sch olkopf et al. 2001; De Vito et al. 2004) provides an analytical solution of the minimum problem that is given by the action of a feature-dependent kernel operator onto a vector whose components can be analytically determined by means of classical Tikhonov regularization (Tikhonov 1963). From an operational perspective, a feature-based supervised machine learning process works as follows. Given an archive of annotated descriptors of the physical phenomenon, named features, 1. A standardization procedure generates a corresponding archive of annotated standardized features that are re-scaled and made dimensionless.

Fairness-aware learning aims to mitigate discrimination against specific protected social groups (e.g., those categorized by gender, ethnicity, age) while minimizing predictive performance loss. Despite efforts to improve fairness in machine learning, prior studies have shown that many models remain unfair when measured against various fairness metrics. In this paper, we examine whether the way training and testing data are sampled affects the reliability of reported fairness metrics. Since training and test sets are often randomly sampled from the same population, bias present in the training data may still exist in the test data, potentially skewing fairness assessments. To address this, we propose FairMatch, a post-processing method that applies propensity score matching to evaluate and mitigate bias. FairMatch identifies control and treatment pairs with similar propensity scores in the test set and adjusts decision thresholds for different subgroups accordingly. For samples that cannot be matched, we perform probabilistic calibration using fairness-aware loss functions. Experimental results demonstrate that our approach can (a) precisely locate subsets of the test data where the model is unbiased, and (b) significantly reduce bias on the remaining data. Overall, propensity score matching offers a principled way to improve both fairness evaluation and mitigation, without sacrificing predictive performance.

Since data annotation is costly, benchmark datasets often incorporate labels from established image datasets. In this work, we assess the impact of label errors in MSCOCO on the frequently used object hallucination benchmark POPE. We re-annotate the benchmark images and identify an imbalance in annotation errors across different subsets. Evaluating multiple models on the revised labels, which we denote as RePOPE, we observe notable shifts in model rankings, highlighting the impact of label quality. Code and data are available at https://github.com/YanNeu/RePOPE .

Exosomes are small vesicles crucial for cell signaling and disease biomarkers. Due to their complexity, an "omics" approach is preferable to individual biomarkers. While Raman spectroscopy is effective for exosome analysis, it requires high sample concentrations and has limited sensitivity to lipids and proteins. Surface-enhanced Raman spectroscopy helps overcome these challenges. In this study, we leverage Neo4j graph databases to organize 3,045 Raman spectra of exosomes, enhancing data generalization. To further refine spectral analysis, we introduce a novel spectral filtering process that integrates the PageRank Filter with optimal Dimensionality Reduction. This method improves feature selection, resulting in superior classification performance. Specifically, the Extra Trees model, using our spectral processing approach, achieves 0.76 and 0.857 accuracy in classifying hyperglycemic, hypoglycemic, and normal exosome samples based on Raman spectra and surface, respectively, with group 10-fold cross-validation. Our results show that graph-based spectral filtering combined with optimal dimensionality reduction significantly improves classification accuracy by reducing noise while preserving key biomarker signals. This novel framework enhances Raman-based exosome analysis, expanding its potential for biomedical applications, disease diagnostics, and biomarker discovery.

Area under the receiving operator characteristic curve (AUC) is commonly reported alongside binary prediction models. However, there are concerns that AUC might be a misleading measure of prediction performance in the rare event setting. This setting is common since many events of clinical importance are rare events. We conducted a simulation study to determine when or whether AUC is unstable in the rare event setting. Specifically, we aimed to determine whether the bias and variance of AUC are driven by the number of events or the event rate. We also investigated the behavior of other commonly used measures of prediction performance, including positive predictive value, accuracy, sensitivity, and specificity. Our results indicate that poor AUC behavior -- as measured by empirical bias, variability of cross-validated AUC estimates, and empirical coverage of confidence intervals -- is driven by the minimum class size, not event rate. Performance of sensitivity is driven by the number of events, while that of specificity is driven by the number of non-events. Other measures, including positive predictive value and accuracy, depend on the event rate even in large samples. AUC is reliable in the rare event setting provided that the total number of events is moderately large.

The objective of transfer learning is to enhance estimation and inference in a target data by leveraging knowledge gained from additional sources. Recent studies have explored transfer learning for independent observations in complex, high-dimensional models assuming sparsity, yet research on time series models remains limited. Our focus is on transfer learning for sequences of observations with temporal dependencies and a more intricate model parameter structure. Specifically, we investigate the vector autoregressive model (VAR), a widely recognized model for time series data, where the transition matrix can be deconstructed into a combination of a sparse matrix and a low-rank one. We propose a new transfer learning algorithm tailored for estimating high-dimensional VAR models characterized by low-rank and sparse structures. Additionally, we present a novel approach for selecting informative observations from auxiliary datasets. Theoretical guarantees are established, encompassing model parameter consistency, informative set selection, and the asymptotic distribution of estimators under mild conditions. The latter facilitates the construction of entry-wise confidence intervals for model parameters. Finally, we demonstrate the empirical efficacy of our methodologies through both simulated and real-world datasets.

We give new results for problems in computational and statistical machine learning using tools from high-dimensional geometry and probability. We break up our treatment into two parts. In Part I, we focus on computational considerations in optimization. Specifically, we give new algorithms for approximating convex polytopes in a stream, sparsification and robust least squares regression, and dueling optimization. In Part II, we give new statistical guarantees for data science problems. In particular, we formulate a new model in which we analyze statistical properties of backdoor data poisoning attacks, and we study the robustness of graph clustering algorithms to ``helpful'' misspecification.

Detecting collaborative and problem-solving behaviours from digital traces to interpret students' collaborative problem solving (CPS) competency is a long-term goal in the Artificial Intelligence in Education (AIEd) field. Although multimodal data and advanced models are argued to have the potential to detect complex CPS behaviours, empirical evidence on their value remains limited with some contrasting evidence. In this study, we investigated the potential of multimodal data to improve model performance in diagnosing 78 secondary school students' CPS subskills and indicators in authentic educational settings. In particular, text embeddings from verbal data and acoustic embed-dings from audio data were used in a multimodal classification model for CPS diagnosis. Both unimodal and multimodal transformer-based models outperformed traditional models in detecting CPS classes. Although the inclusion of multimodality did not improve the performance of traditional unimodal models, its integration into transformer-based models demonstrated improved performance for diagnosing social-cognitive CPS classes compared to unimodal transformer-based models. Based on the results, the paper argues that multimodality and the selection of a particular modelling technique should not be taken for granted to achieve the best performance in the automated detection of every CPS subskill and indicator. Rather, their value is limited to certain types of CPS indicators, affected by the complexity of the labels, and dependent on the composition of indicators in the dataset. We conclude the paper by discussing the required nuance when considering the value of LLMs and multimodality in automated CPS diagnosis, highlighting the need for human-AI complementarity, and proposing the exploration of relevant model architectures and techniques to improve CPS diagnosis in authentic educational contexts.

While hallucinations of large language models could been alleviated through retrieval-augmented generation and citation generation, how the model utilizes internal knowledge is still opaque, and the trustworthiness of its generated answers remains questionable. In this work, we introduce Context-Prior Augmented Citation Generation task, requiring models to generate citations considering both external and internal knowledge while providing trustworthy references, with 5 evaluation metrics focusing on 3 aspects: answer helpfulness, citation faithfulness, and trustworthiness. We introduce RAEL, the paradigm for our task, and also design INTRALIGN, an integrated method containing customary data generation and an alignment algorithm. Our experimental results show that our method achieves a better cross-scenario performance with regard to other baselines. Our extended experiments further reveal that retrieval quality, question types, and model knowledge have considerable influence on the trustworthiness in citation generation.

Vision-language models (VLMs) excel in various multimodal tasks but frequently suffer from poor calibration, resulting in misalignment between their verbalized confidence and response correctness. This miscalibration undermines user trust, especially when models confidently provide incorrect or fabricated information. In this work, we propose a novel Confidence Calibration through Semantic Perturbation (CSP) framework to improve the calibration of verbalized confidence for VLMs in response to object-centric queries. We first introduce a perturbed dataset where Gaussian noise is applied to the key object regions to simulate visual uncertainty at different confidence levels, establishing an explicit mapping between visual ambiguity and confidence levels. We further enhance calibration through a two-stage training process combining supervised fine-tuning on the perturbed dataset with subsequent preference optimization. Extensive experiments on popular benchmarks demonstrate that our method significantly improves the alignment between verbalized confidence and response correctness while maintaining or enhancing overall task performance. These results highlight the potential of semantic perturbation as a practical tool for improving the reliability and interpretability of VLMs.