The generalized lasso is a natural generalization of the celebrated lasso approach to handle structural regularization problems. Many important methods and applications fall into this framework, including fused lasso, clustered lasso, and constrained lasso. To elevate its effectiveness in large-scale problems, extensive research has been conducted on the computational strategies of generalized lasso. However, to our knowledge, most studies are under the linear setup, with limited advances in non-Gaussian and non-linear models. We propose a majorization-minimization dual stagewise (MM-DUST) algorithm to efficiently trace out the full solution paths of the generalized lasso problem. The majorization technique is incorporated to handle different convex loss functions through their quadratic majorizers. Utilizing the connection between primal and dual problems and the idea of ``slow-brewing'' from stagewise learning, the minimization step is carried out in the dual space through a sequence of simple coordinate-wise updates on the dual coefficients with a small step size. Consequently, selecting an appropriate step size enables a trade-off between statistical accuracy and computational efficiency. We analyze the computational complexity of MM-DUST and establish the uniform convergence of the approximated solution paths. Extensive simulation studies and applications with regularized logistic regression and Cox model demonstrate the effectiveness of the proposed approach.

Decision-focused learning (DFL) offers an end-to-end approach to the predict-then-optimize (PO) framework by training predictive models directly on decision loss (DL), enhancing decision-making performance within PO contexts. However, the implementation of DFL poses distinct challenges. Primarily, DL can result in deviation from the physical significance of the predictions under limited data. Additionally, some predictive models are non-differentiable or black-box, which cannot be adjusted using gradient-based methods. To tackle the above challenges, we propose a novel framework, Decision-Focused Fine-tuning (DFF), which embeds the DFL module into the PO pipeline via a novel bias correction module. DFF is formulated as a constrained optimization problem that maintains the proximity of the DL-enhanced model to the original predictive model within a defined trust region. We theoretically prove that DFF strictly confines prediction bias within a predetermined upper bound, even with limited datasets, thereby substantially reducing prediction shifts caused by DL under limited data. Furthermore, the bias correction module can be integrated into diverse predictive models, enhancing adaptability to a broad range of PO tasks. Extensive evaluations on synthetic and real-world datasets, including network flow, portfolio optimization, and resource allocation problems with different predictive models, demonstrate that DFF not only improves decision performance but also adheres to fine-tuning constraints, showcasing robust adaptability across various scenarios.

This study explores how causal inference models, specifically the Linear Non-Gaussian Acyclic Model (LiNGAM), can extract causal relationships between demographic factors, treatments, conditions, and outcomes from observational patient data, enabling insights beyond correlation. Unlike traditional randomized controlled trials (RCTs), which establish causal relationships within narrowly defined populations, our method leverages broader observational data, improving generalizability. Using over 40 features in the Duke MRI Breast Cancer dataset, we found that Adjuvant Anti-Her2 Neu Therapy increased local recurrence-free survival by 169 days, while Skin/Nipple involvement reduced it by 351 days. These findings highlight the therapy's importance for Her2-positive patients and the need for targeted interventions for high-risk cases, informing personalized treatment strategies.

Training transformer-based encoder-decoder models for long document summarization poses a significant challenge due to the quadratic memory consumption during training. Several approaches have been proposed to extend the input length at test time, but training with these approaches is still difficult, requiring truncation of input documents and causing a mismatch between training and test conditions. In this work, we propose CachED (Gradient $\textbf{Cach}$ing for $\textbf{E}$ncoder-$\textbf{D}$ecoder models), an approach that enables end-to-end training of existing transformer-based encoder-decoder models, using the entire document without truncation. Specifically, we apply non-overlapping sliding windows to input documents, followed by fusion in decoder. During backpropagation, the gradients are cached at the decoder and are passed through the encoder in chunks by re-computing the hidden vectors, similar to gradient checkpointing. In the experiments on long document summarization, we extend BART to CachED BART, processing more than 500K tokens during training and achieving superior performance without using any additional parameters.

In this paper, we conduct a data-scientific investigation of Maass forms. We find that averaging the Fourier coefficients of Maass forms with the same Fricke sign reveals patterns analogous to the recently discovered "murmuration" phenomenon, and that these patterns become more pronounced when parity is incorporated as an additional feature. Approximately 43% of the forms in our dataset have an unknown Fricke sign. For the remaining forms, we employ Linear Discriminant Analysis (LDA) to machine learn their Fricke sign, achieving 96% (resp. 94%) accuracy for forms with even (resp. odd) parity. We apply the trained LDA model to forms with unknown Fricke signs to make predictions. The average values based on the predicted Fricke signs are computed and compared to those for forms with known signs to verify the reasonableness of the predictions. Additionally, a subset of these predictions is evaluated against heuristic guesses provided by Hejhal's algorithm, showing a match approximately 95% of the time. We also use neural networks to obtain results comparable to those from the LDA model.

Health outcomes depend on complex environmental and sociodemographic factors whose effects change over location and time. Only recently has fine-grained spatial and temporal data become available to study these effects, namely the MEDSAT dataset of English health, environmental, and sociodemographic information. Leveraging this new resource, we use a variety of variable importance techniques to robustly identify the most informative predictors across multiple health outcomes. We then develop an interpretable machine learning framework based on Generalized Additive Models (GAMs) and Multiscale Geographically Weighted Regression (MGWR) to analyze both local and global spatial dependencies of each variable on various health outcomes. Our findings identify NO2 as a global predictor for asthma, hypertension, and anxiety, alongside other outcome-specific predictors related to occupation, marriage, and vegetation. Regional analyses reveal local variations with air pollution and solar radiation, with notable shifts during COVID. This comprehensive approach provides actionable insights for addressing health disparities, and advocates for the integration of interpretable machine learning in public health.

We introduce the spiked mixture model (SMM) to address the problem of estimating a set of signals from many randomly scaled and noisy observations. Subsequently, we design a novel expectation-maximization (EM) algorithm to recover all parameters of the SMM. Numerical experiments show that in low signal-to-noise ratio regimes, and for data types where the SMM is relevant, SMM surpasses the more traditional Gaussian mixture model (GMM) in terms of signal recovery performance. The broad relevance of the SMM and its corresponding EM recovery algorithm is demonstrated by applying the technique to different data types. The first case study is a biomedical research application, utilizing an imaging mass spectrometry dataset to explore the molecular content of a rat brain tissue section at micrometer scale. The second case study demonstrates SMM performance in a computer vision application, segmenting a hyperspectral imaging dataset into underlying patterns. While the measurement modalities differ substantially, in both case studies SMM is shown to recover signals that were missed by traditional methods such as k-means clustering and GMM.

Algorithmic fairness of machine learning (ML) models has raised significant concern in the recent years. Many testing, verification, and bias mitigation techniques have been proposed to identify and reduce fairness issues in ML models. The existing methods are model-centric and designed to detect fairness issues under static settings. However, many ML-enabled systems operate in a dynamic environment where the predictive decisions made by the system impact the environment, which in turn affects future decision-making. Such a self-reinforcing feedback loop can cause fairness violations in the long term, even if the immediate outcomes are fair. In this paper, we propose a simulation-based framework called FairSense to detect and analyze long-term unfairness in ML-enabled systems. Given a fairness requirement, FairSense performs Monte-Carlo simulation to enumerate evolution traces for each system configuration. Then, FairSense performs sensitivity analysis on the space of possible configurations to understand the impact of design options and environmental factors on the long-term fairness of the system. We demonstrate FairSense's potential utility through three real-world case studies: Loan lending, opioids risk scoring, and predictive policing.

Humanoid robots have great potential to perform various human-level skills. These skills involve locomotion, manipulation, and cognitive capabilities. Driven by advances in machine learning and the strength of existing model-based approaches, these capabilities have progressed rapidly, but often separately. Therefore, a timely overview of current progress and future trends in this fast-evolving field is essential. This survey first summarizes the model-based planning and control that have been the backbone of humanoid robotics for the past three decades. We then explore emerging learning-based methods, with a focus on reinforcement learning and imitation learning that enhance the versatility of loco-manipulation skills. We examine the potential of integrating foundation models with humanoid embodiments, assessing the prospects for developing generalist humanoid agents. In addition, this survey covers emerging research for whole-body tactile sensing that unlocks new humanoid skills that involve physical interactions. The survey concludes with a discussion of the challenges and future trends.

A high-fidelity digital simulation environment is crucial for accurately replicating physical operational processes. However, inconsistencies between simulation and physical environments result in low confidence in simulation outcomes, limiting their effectiveness in guiding real-world production. Unlike the traditional step-by-step point cloud "segmentation-registration" generation method, this paper introduces, for the first time, a novel Multi-Robot Manufacturing Digital Scene Generation (MRG) method that leverages multi-instance point cloud registration, specifically within manufacturing scenes. Tailored to the characteristics of industrial robots and manufacturing settings, an instance-focused transformer module is developed to delineate instance boundaries and capture correlations between local regions. Additionally, a hypothesis generation module is proposed to extract target instances while preserving key features. Finally, an efficient screening and optimization algorithm is designed to refine the final registration results. Experimental evaluations on the Scan2CAD and Welding-Station datasets demonstrate that: (1) the proposed method outperforms existing multi-instance point cloud registration techniques; (2) compared to state-of-the-art methods, the Scan2CAD dataset achieves improvements in MR and MP by 12.15% and 17.79%, respectively; and (3) on the Welding-Station dataset, MR and MP are enhanced by 16.95% and 24.15%, respectively. This work marks the first application of multi-instance point cloud registration in manufacturing scenes, significantly advancing the precision and reliability of digital simulation environments for industrial applications.