Fairness in machine learning has become a critical concern, particularly in high-stakes applications. Existing approaches often focus on achieving full fairness across all score ranges generated by predictive models, ensuring fairness in both high and low-scoring populations. However, this stringent requirement can compromise predictive performance and may not align with the practical fairness concerns of stakeholders. In this work, we propose a novel framework for building partially fair machine learning models, which enforce fairness within a specific score range of interest, such as the middle range where decisions are most contested, while maintaining flexibility in other regions. We introduce two statistical metrics to rigorously evaluate partial fairness within a given score range, such as the top 20%-40% of scores. To achieve partial fairness, we propose an in-processing method by formulating the model training problem as constrained optimization with difference-of-convex constraints, which can be solved by an inexact difference-of-convex algorithm (IDCA). We provide the complexity analysis of IDCA for finding a nearly KKT point. Through numerical experiments on real-world datasets, we demonstrate that our framework achieves high predictive performance while enforcing partial fairness where it matters most.

Anomaly detection is a fundamental problem in domains such as healthcare, manufacturing, and cybersecurity. This thesis proposes new unsupervised methods for anomaly detection in both structured and streaming data settings. In the first part, we focus on structure-based anomaly detection, where normal data follows low-dimensional manifolds while anomalies deviate from them. We introduce Preference Isolation Forest (PIF), which embeds data into a high-dimensional preference space via manifold fitting, and isolates outliers using two variants: Voronoi-iForest, based on geometric distances, and RuzHash-iForest, leveraging Locality Sensitive Hashing for scalability. We also propose Sliding-PIF, which captures local manifold information for streaming scenarios. Our methods outperform existing techniques on synthetic and real datasets. We extend this to structure-based clustering with MultiLink, a novel method for recovering multiple geometric model families in noisy data. MultiLink merges clusters via a model-aware linkage strategy, enabling robust multi-class structure recovery. It offers key advantages over existing approaches, such as speed, reduced sensitivity to thresholds, and improved robustness to poor initial sampling. The second part of the thesis addresses online anomaly detection in evolving data streams. We propose Online Isolation Forest (Online-iForest), which uses adaptive, multi-resolution histograms and dynamically updates tree structures to track changes over time. It avoids retraining while achieving accuracy comparable to offline models, with superior efficiency for real-time applications. Finally, we tackle anomaly detection in cybersecurity via open-set recognition for malware classification. We enhance a Gradient Boosting classifier with MaxLogit to detect unseen malware families, a method now integrated into Cleafy's production system.

This paper introduces a novel nonparametric method for estimating high-dimensional dynamic covariance matrices with multiple conditioning covariates, leveraging random forests and supported by robust theoretical guarantees. Unlike traditional static methods, our dynamic nonparametric covariance models effectively capture distributional heterogeneity. Furthermore, unlike kernel-smoothing methods, which are restricted to a single conditioning covariate, our approach accommodates multiple covariates in a fully nonparametric framework. To the best of our knowledge, this is the first method to use random forests for estimating high-dimensional dynamic covariance matrices. In high-dimensional settings, we establish uniform consistency theory, providing nonasymptotic error rates and model selection properties, even when the response dimension grows sub-exponentially with the sample size. These results hold uniformly across a range of conditioning variables. The method's effectiveness is demonstrated through simulations and a stock dataset analysis, highlighting its ability to model complex dynamics in high-dimensional scenarios.

We present a Bayesian dynamic borrowing (BDB) approach to enhance the quantitative identification of adverse events (AEs) in spontaneous reporting systems (SRSs). The method embeds a robust meta-analytic predictive (MAP) prior with a Bayesian hierarchical model and incorporates semantic similarity measures (SSMs) to enable weighted information sharing from clinically similar MedDRA Preferred Terms (PTs) to the target PT. This continuous similarity-based borrowing overcomes limitations of rigid hierarchical grouping in current disproportionality analysis (DPA). Using data from the FDA Adverse Event Reporting System (FAERS) between 2015 and 2019, we evaluate our approach -- termed IC SSM -- against traditional Information Component (IC) analysis and IC with borrowing at the MedDRA high-level group term level (IC HLGT). A reference set (PVLens), derived from FDA product label update, enabled prospective evaluation of method performance in identifying AEs prior to official labeling. The IC SSM approach demonstrated higher sensitivity (1332/2337=0.570, Youden's J=0.246) than traditional IC (Se=0.501, J=0.250) and IC HLGT (Se=0.556, J=0.225), consistently identifying more true positives and doing so on average 5 months sooner than traditional IC. Despite a marginally lower aggregate F1-score and Youden's index, IC SSM showed higher performance in early post-marketing periods or when the detection threshold was raised, providing more stable and relevant alerts than IC HLGT and traditional IC. These findings support the use of SSM-informed Bayesian borrowing as a scalable and context-aware enhancement to traditional DPA methods, with potential for validation across other datasets and exploration of additional similarity metrics and Bayesian strategies using case-level data.

Recent Large Reasoning Models significantly improve the reasoning ability of Large Language Models by learning to reason, exhibiting the promising performance in solving complex tasks. LRMs solve tasks that require complex reasoning by explicitly generating reasoning trajectories together with answers. Nevertheless, judging the quality of such an output answer is not easy because only considering the correctness of the answer is not enough and the soundness of the reasoning trajectory part matters as well. Logically, if the soundness of the reasoning part is poor, even if the answer is correct, the confidence of the derived answer should be low. Existing methods did consider jointly assessing the overall output answer by taking into account the reasoning part, however, their capability is still not satisfactory as the causal relationship of the reasoning to the concluded answer cannot properly reflected. In this paper, inspired by classical mechanics, we present a novel approach towards establishing a CoT-Kinetics energy equation. Specifically, our CoT-Kinetics energy equation formulates the token state transformation process, which is regulated by LRM internal transformer layers, as like a particle kinetics dynamics governed in a mechanical field. Our CoT-Kinetics energy assigns a scalar score to evaluate specifically the soundness of the reasoning phase, telling how confident the derived answer could be given the evaluated reasoning. As such, the LRM's overall output quality can be accurately measured, rather than a coarse judgment (e.g., correct or incorrect) anymore.

Large Language Models (LLMs) have demonstrated strong capabilities in memorizing vast amounts of knowledge across diverse domains. However, the ability to selectively forget specific knowledge is critical for ensuring the safety and compliance of deployed models. Existing unlearning efforts typically fine-tune the model with resources such as forget data, retain data, and a calibration model. These additional gradient steps blur the decision boundary between forget and retain knowledge, making unlearning often at the expense of overall performance. To avoid the negative impact of fine-tuning, it would be better to unlearn solely at inference time by safely guarding the model against generating responses related to the forget target, without destroying the fluency of text generation. In this work, we propose Generation-time Unlearning via Adaptive Restriction and Detection (GUARD), a framework that enables dynamic unlearning during LLM generation. Specifically, we first employ a prompt classifier to detect unlearning targets and extract the corresponding forbidden token. We then dynamically penalize and filter candidate tokens during generation using a combination of token matching and semantic matching, effectively preventing the model from leaking the forgotten content. Experimental results on copyright content unlearning tasks over the Harry Potter dataset and the MUSE benchmark, as well as entity unlearning tasks on the TOFU dataset, demonstrate that GUARD achieves strong forget quality across various tasks while causing almost no degradation to the LLM's general capabilities, striking an excellent trade-off between forgetting and utility.

Despite significant advancements in the area, adversarial robustness remains a critical challenge in systems employing machine learning models. The removal of adversarial perturbations at inference time, known as adversarial purification, has emerged as a promising defense strategy. To achieve this, state-of-the-art methods leverage diffusion models that inject Gaussian noise during a forward process to dilute adversarial perturbations, followed by a denoising step to restore clean samples before classification. In this work, we propose FlowPure, a novel purification method based on Continuous Normalizing Flows (CNFs) trained with Conditional Flow Matching (CFM) to learn mappings from adversarial examples to their clean counterparts. Unlike prior diffusion-based approaches that rely on fixed noise processes, FlowPure can leverage specific attack knowledge to improve robustness under known threats, while also supporting a more general stochastic variant trained on Gaussian perturbations for settings where such knowledge is unavailable. Experiments on CIFAR-10 and CIFAR-100 demonstrate that our method outperforms state-of-the-art purification-based defenses in preprocessor-blind and white-box scenarios, and can do so while fully preserving benign accuracy in the former. Moreover, our results show that not only is FlowPure a highly effective purifier but it also holds a strong potential for adversarial detection, identifying preprocessor-blind PGD samples with near-perfect accuracy.

Large Language Models (LLMs) have become foundational in modern artificial intelligence, powering a wide range of applications from code generation and virtual assistants to scientific research and enterprise automation. However, concerns about data contamination--where test data overlaps with training data--have raised serious questions about the reliability of these applications. Despite awareness of this issue, existing methods fall short in effectively identifying or mitigating contamination. In this paper, we propose Residual-Noise Fingerprinting (RN-F), a novel framework for detecting contaminated data in LLMs. RN-F is a single-pass, gradient-free detection method that leverages residual signal patterns without introducing additional floating-point operations. Our approach is lightweight, model-agnostic, and efficient. We evaluate RN-F on multiple LLMs across various contaminated datasets and show that it consistently outperforms existing state-of-the-art methods, achieving performance improvements of up to 10.5% in contamination detection metrics.

As machine learning is increasingly applied in an online fashion to deal with evolving data streams, the fairness of these algorithms is a matter of growing ethical and legal concern. In many use cases, class imbalance in the data also needs to be dealt with to ensure predictive performance. Current fairness-aware stream learners typically attempt to solve these issues through in- or post-processing by focusing on optimizing one specific discrimination metric, addressing class imbalance in a separate processing step. While C-SMOTE is a highly effective model-agnostic pre-processing approach to mitigate class imbalance, as a side effect of this method, algorithmic bias is often introduced. Therefore, we propose CFSMOTE - a fairness-aware, continuous SMOTE variant - as a pre-processing approach to simultaneously address the class imbalance and fairness concerns by employing situation testing and balancing fairness-relevant groups during oversampling. Unlike other fairness-aware stream learners, CFSMOTE is not optimizing for only one specific fairness metric, therefore avoiding potentially problematic trade-offs. Our experiments show significant improvement on several common group fairness metrics in comparison to vanilla C-SMOTE while maintaining competitive performance, also in comparison to other fairness-aware algorithms.

We introduce MMAR, a new benchmark designed to evaluate the deep reasoning capabilities of Audio-Language Models (ALMs) across massive multi-disciplinary tasks. MMAR comprises 1,000 meticulously curated audio-question-answer triplets, collected from real-world internet videos and refined through iterative error corrections and quality checks to ensure high quality. Unlike existing benchmarks that are limited to specific domains of sound, music, or speech, MMAR extends them to a broad spectrum of real-world audio scenarios, including mixed-modality combinations of sound, music, and speech. Each question in MMAR is hierarchically categorized across four reasoning layers: Signal, Perception, Semantic, and Cultural, with additional sub-categories within each layer to reflect task diversity and complexity. To further foster research in this area, we annotate every question with a Chain-of-Thought (CoT) rationale to promote future advancements in audio reasoning. Each item in the benchmark demands multi-step deep reasoning beyond surface-level understanding. Moreover, a part of the questions requires graduate-level perceptual and domain-specific knowledge, elevating the benchmark's difficulty and depth. We evaluate MMAR using a broad set of models, including Large Audio-Language Models (LALMs), Large Audio Reasoning Models (LARMs), Omni Language Models (OLMs), Large Language Models (LLMs), and Large Reasoning Models (LRMs), with audio caption inputs. The performance of these models on MMAR highlights the benchmark's challenging nature, and our analysis further reveals critical limitations of understanding and reasoning capabilities among current models. We hope MMAR will serve as a catalyst for future advances in this important but little-explored area.