While analyzing the importance of features has become ubiquitous in interpretable machine learning, the joint signal from a group of related features is sometimes overlooked or inadvertently excluded. Neglecting the joint signal could bypass a critical insight: in many instances, the most significant predictors are not isolated features, but rather the combined effect of groups of features. This can be especially problematic for datasets that contain natural groupings of features, including multimodal datasets. This paper introduces a novel approach to determine the importance of a group of features for Generalized Additive Models (GAMs) that is efficient, requires no model retraining, allows defining groups posthoc, permits overlapping groups, and remains meaningful in high-dimensional settings. Moreover, this definition offers a parallel with explained variation in statistics. We showcase properties of our method on three synthetic experiments that illustrate the behavior of group importance across various data regimes. We then demonstrate the importance of groups of features in identifying depressive symptoms from a multimodal neuroscience dataset, and study the importance of social determinants of health after total hip arthroplasty. These two case studies reveal that analyzing group importance offers a more accurate, holistic view of the medical issues compared to a single-feature analysis.

Clustered Federated Learning (CFL) addresses the challenges posed by non-IID data by training multiple group- or cluster-specific expert models. However, existing methods often overlook the shared information across clusters, which represents the generalizable knowledge valuable to all participants in the Federated Learning (FL) system. To overcome this limitation, this paper introduces a novel FL framework that distills a universal expert model from the knowledge of multiple clusters. This universal expert captures globally shared information across all clients and is subsequently distributed to each client as the initialization for the next round of model training. The proposed FL framework operates in three iterative steps: (1) local model training at each client, (2) cluster-specific model aggregation, and (3) universal expert distillation. This three-step learning paradigm ensures the preservation of fine-grained non-IID characteristics while effectively incorporating shared knowledge across clusters. Compared to traditional gradient-based aggregation methods, the distillation-based model aggregation introduces greater flexibility in handling model heterogeneity and reduces conflicts among cluster-specific experts. Extensive experimental results demonstrate the superior performance of the proposed method across various scenarios, highlighting its potential to advance the state of CFL by balancing personalized and shared knowledge more effectively.

The attention mechanism in Transformers is an important primitive for accurate and scalable sequence modeling. Its quadratic-compute and linear-memory complexity however remain significant bottlenecks. Linear attention and state-space models enable linear-time, constant-memory sequence modeling and can moreover be trained efficiently through matmul-rich parallelization across sequence length. However, at their core these models are still RNNs, and thus their use of a fixed-size hidden state to model the context is a fundamental limitation. This paper develops log-linear attention, an attention mechanism that balances linear attention's efficiency and the expressiveness of softmax attention. Log-linear attention replaces the fixed-size hidden state with a logarithmically growing set of hidden states. We show that with a particular growth function, log-linear attention admits a similarly matmul-rich parallel form whose compute cost is log-linear in sequence length. Log-linear attention is a general framework and can be applied on top of existing linear attention variants. As case studies, we instantiate log-linear variants of two recent architectures -- Mamba-2 and Gated DeltaNet -- and find they perform well compared to their linear-time variants.

Insurance fraud detection represents a pivotal advancement in modern insurance service, providing intelligent and digitalized monitoring to enhance management and prevent fraud. It is crucial for ensuring the security and efficiency of insurance systems. Although AI and machine learning algorithms have demonstrated strong performance in detecting fraudulent claims, the absence of standardized defense mechanisms renders current systems vulnerable to emerging adversarial threats. In this paper, we propose a GAN-based approach to conduct adversarial attacks on fraud detection systems. Our results indicate that an attacker, without knowledge of the training data or internal model details, can generate fraudulent cases that are classified as legitimate with a 99\% attack success rate (ASR). By subtly modifying real insurance records and claims, adversaries can significantly increase the fraud risk, potentially bypassing compromised detection systems. These findings underscore the urgent need to enhance the robustness of insurance fraud detection models against adversarial manipulation, thereby ensuring the stability and reliability of different insurance systems.

Trajectory analysis is not only about obtaining movement data, but it is also of paramount importance in understanding the pattern in which an object moves through space and time, as well as in predicting its next move. Due to the significant interest in the area, data collection has improved substantially, resulting in a large number of features becoming available for training and predicting models. However, this introduces a high-dimensionality-induced feature explosion problem, which reduces the efficiency and interpretability of the data, thereby reducing the accuracy of machine learning models. To overcome this issue, feature selection has become one of the most prevalent tools. Thus, the objective of this paper was to introduce a taxonomy-based feature selection method that categorizes features based on their internal structure. This approach classifies the data into geometric and kinematic features, further categorizing them into curvature, indentation, speed, and acceleration. The comparative analysis indicated that a taxonomy-based approach consistently achieved comparable or superior predictive performance. Furthermore, due to the taxonomic grouping, which reduces combinatorial space, the time taken to select features was drastically reduced. The taxonomy was also used to gain insights into what feature sets each dataset was more sensitive to. Overall, this study provides robust evidence that a taxonomy-based feature selection method can add a layer of interpretability, reduce dimensionality and computational complexity, and contribute to high-level decision-making. It serves as a step toward providing a methodological framework for researchers and practitioners dealing with trajectory datasets and contributing to the broader field of explainable artificial intelligence.

We study methods for identifying heterogeneous parameter components in distributed M-estimation with minimal data transmission. One is based on a re-normalized Wald test, which is shown to be consistent as long as the number of distributed data blocks $K$ is of a smaller order of the minimum block sample size and the level of heterogeneity is dense. The second one is an extreme contrast test (ECT) based on the difference between the largest and smallest component-wise estimated parameters among data blocks. By introducing a sample splitting procedure, the ECT can avoid the bias accumulation arising from the M-estimation procedures, and exhibits consistency for $K$ being much larger than the sample size while the heterogeneity is sparse. The ECT procedure is easy to operate and communication-efficient. A combination of the Wald and the extreme contrast tests is formulated to attain more robust power under varying levels of sparsity of the heterogeneity. We also conduct intensive numerical experiments to compare the family-wise error rate (FWER) and the power of the proposed methods. Additionally, we conduct a case study to present the implementation and validity of the proposed methods.

Token embeddings play a crucial role in language modeling but, despite this practical relevance, their theoretical understanding remains limited. Our paper addresses the gap by characterizing the structure of embeddings obtained via gradient descent. Specifically, we consider a one-layer softmax attention model with a linear head for binary classification, i.e., $\texttt{Softmax}( p^\top E_X^\top ) E_X v = \frac{ \sum_{i=1}^T \exp(p^\top E_{x_i}) E_{x_i}^\top v}{\sum_{j=1}^T \exp(p^\top E_{x_{j}}) }$, where $E_X = [ E_{x_1} , \dots, E_{x_T} ]^\top$ contains the embeddings of the input sequence, $p$ is the embedding of the $\mathrm{\langle cls \rangle}$ token and $v$ the output vector. First, we show that, already after a single step of gradient training with the logistic loss, the embeddings $E_X$ capture the importance of tokens in the dataset by aligning with the output vector $v$ proportionally to the frequency with which the corresponding tokens appear in the dataset. Then, after training $p$ via gradient flow until convergence, the softmax selects the important tokens in the sentence (i.e., those that are predictive of the label), and the resulting $\mathrm{\langle cls \rangle}$ embedding maximizes the margin for such a selection. Experiments on real-world datasets (IMDB, Yelp) exhibit a phenomenology close to that unveiled by our theory.

Conformal prediction offers a distribution-free framework for constructing prediction sets with coverage guarantees. In practice, multiple valid conformal prediction sets may be available, arising from different models or methodologies. However, selecting the most desirable set, such as the smallest, can invalidate the coverage guarantees. To address this challenge, we propose a stability-based approach that ensures coverage for the selected prediction set. We extend our results to the online conformal setting, propose several refinements in settings where additional structure is available, and demonstrate its effectiveness through experiments.

Linear mixed models (LMMs), which incorporate fixed and random effects, are key tools for analyzing heterogeneous data, such as in personalized medicine or adaptive marketing. Nowadays, this type of data is increasingly wide, sometimes containing thousands of candidate predictors, necessitating sparsity for prediction and interpretation. However, existing sparse learning methods for LMMs do not scale well beyond tens or hundreds of predictors, leaving a large gap compared with sparse methods for linear models, which ignore random effects. This paper closes the gap with a new $\ell_0$ regularized method for LMM subset selection that can run on datasets containing thousands of predictors in seconds to minutes. On the computational front, we develop a coordinate descent algorithm as our main workhorse and provide a guarantee of its convergence. We also develop a local search algorithm to help traverse the nonconvex optimization surface. Both algorithms readily extend to subset selection in generalized LMMs via a penalized quasi-likelihood approximation. On the statistical front, we provide a finite-sample bound on the Kullback-Leibler divergence of the new method. We then demonstrate its excellent performance in synthetic experiments and illustrate its utility on two datasets from biology and journalism.

The interface between stochastic analysis and machine learning is a rapidly evolving field, with path signatures - iterated integrals that provide faithful, hierarchical representations of paths - offering a principled and universal feature map for sequential and structured data. Rooted in rough path theory, path signatures are invariant to reparameterization and well-suited for modelling evolving dynamics, long-range dependencies, and irregular sampling - common challenges in real-world time series and graph data. This thesis investigates how to harness the expressive power of path signatures within scalable machine learning pipelines. It introduces a suite of models that combine theoretical robustness with computational efficiency, bridging rough path theory with probabilistic modelling, deep learning, and kernel methods. Key contributions include: Gaussian processes with signature kernel-based covariance functions for uncertainty-aware time series modelling; the Seq2Tens framework, which employs low-rank tensor structure in the weight space for scalable deep modelling of long-range dependencies; and graph-based models where expected signatures over graphs induce hypo-elliptic diffusion processes, offering expressive yet tractable alternatives to standard graph neural networks. Further developments include Random Fourier Signature Features, a scalable kernel approximation with theoretical guarantees, and Recurrent Sparse Spectrum Signature Gaussian Processes, which combine Gaussian processes, signature kernels, and random features with a principled forgetting mechanism for multi-horizon time series forecasting with adaptive context length. We hope this thesis serves as both a methodological toolkit and a conceptual bridge, and provides a useful reference for the current state of the art in scalable, signature-based learning for sequential and structured data.