Given the damping factor $\alpha$ and precision tolerance $\epsilon$, \citet{andersen2006local} introduced Approximate Personalized PageRank (APPR), the \textit{de facto local method} for approximating the PPR vector, with runtime bounded by $\Theta(1/(\alpha\epsilon))$ independent of the graph size. Recently, \citet{fountoulakis2022open} asked whether faster local algorithms could be developed using $\tilde{O}(1/(\sqrt{\alpha}\epsilon))$ operations. By noticing that APPR is a local variant of Gauss-Seidel, this paper explores the question of \textit{whether standard iterative solvers can be effectively localized}. We propose to use the \textit{locally evolving set process}, a novel framework to characterize the algorithm locality, and demonstrate that many standard solvers can be effectively localized. Let $\overline{\operatorname{vol}}{ (S_t)}$ and $\overline{\gamma}_{t}$ be the running average of volume and the residual ratio of active nodes $\textstyle S_{t}$ during the process. We show $\overline{\operatorname{vol}}{ (S_t)}/\overline{\gamma}_{t} \leq 1/\epsilon$ and prove APPR admits a new runtime bound $\tilde{O}(\overline{\operatorname{vol}}(S_t)/(\alpha\overline{\gamma}_{t}))$ mirroring the actual performance. Furthermore, when the geometric mean of residual reduction is $\Theta(\sqrt{\alpha})$, then there exists $c \in (0,2)$ such that the local Chebyshev method has runtime $\tilde{O}(\overline{\operatorname{vol}}(S_{t})/(\sqrt{\alpha}(2-c)))$ without the monotonicity assumption. Numerical results confirm the efficiency of this novel framework and show up to a hundredfold speedup over corresponding standard solvers on real-world graphs.

Accurate forecasting of electrical demand is essential for maintaining a stable and reliable power grid, optimizing the allocation of energy resources, and promoting efficient energy consumption practices. This study investigates the effectiveness of five hyperparameter optimization (HPO) algorithms -- Random Search, Covariance Matrix Adaptation Evolution Strategy (CMA--ES), Bayesian Optimization, Partial Swarm Optimization (PSO), and Nevergrad Optimizer (NGOpt) across univariate and multivariate Short-Term Load Forecasting (STLF) tasks. Using the Panama Electricity dataset (n=48,049), we evaluate HPO algorithms' performances on a surrogate forecasting algorithm, XGBoost, in terms of accuracy (i.e., MAPE, $R^2$) and runtime. Performance plots visualize these metrics across varying sample sizes from 1,000 to 20,000, and Kruskal--Wallis tests assess the statistical significance of the performance differences. Results reveal significant runtime advantages for HPO algorithms over Random Search. In univariate models, Bayesian optimization exhibited the lowest accuracy among the tested methods. This study provides valuable insights for optimizing XGBoost in the STLF context and identifies areas for future research.

The k-means clustering algorithm is a popular algorithm that partitions data into k clusters. There are many improvements to accelerate the standard algorithm. Most current research employs upper and lower bounds on point-to-cluster distances and the triangle inequality to reduce the number of distance computations, with only arrays as underlying data structures. These approaches cannot exploit that nearby points are likely assigned to the same cluster. We propose a new k-means algorithm based on the cover tree index, that has relatively low overhead and performs well, for a wider parameter range, than previous approaches based on the k-d tree. By combining this with upper and lower bounds, as in state-of-the-art approaches, we obtain a hybrid algorithm that combines the benefits of tree aggregation and bounds-based filtering.

Aiming to accelerate the training of large deep neural models in an energy-efficient way, an analog in-memory computing (AIMC) accelerator emerges as a solution with immense potential. In AIMC accelerators, trainable weights are kept in memory without the need to move from memory to processors during the training, significantly reducing overhead. However, although the in-memory feature enables efficient computation, it also constrains the use of data parallelism since copying weights from one AIMC to another is expensive. To enable parallel training using AIMC, we propose synchronous and asynchronous pipeline parallelism for AIMC accelerators inspired by the pipeline in digital domains. This paper provides a theoretical convergence guarantee for both synchronous and asynchronous pipelines in terms of both sampling and clock cycle complexity, which is non-trivial since the physical characteristic of AIMC accelerators leads to analog updates that suffer from asymmetric bias. The simulations of training deep models on real datasets verify the efficiency of pipeline analog training.

Detecting the presence of anomalies in regression models is a crucial task in machine learning, as anomalies can significantly impact the accuracy and reliability of predictions. Random Sample Consensus (RANSAC) is one of the most popular robust regression methods for addressing this challenge. However, this method lacks the capability to guarantee the reliability of the anomaly detection (AD) results. In this paper, we propose a novel statistical method for testing the AD results obtained by RANSAC, named CTRL-RANSAC (controllable RANSAC). The key strength of the proposed method lies in its ability to control the probability of misidentifying anomalies below a pre-specified level $\alpha$ (e.g., $\alpha = 0.05$). By examining the selection strategy of RANSAC and leveraging the Selective Inference (SI) framework, we prove that achieving controllable RANSAC is indeed feasible. Furthermore, we introduce a more strategic and computationally efficient approach to enhance the true detection rate and overall performance of the CTRL-RANSAC. Experiments conducted on synthetic and real-world datasets robustly support our theoretical results, showcasing the superior performance of the proposed method.

In survival analysis, subjects often face competing risks; for example, individuals with cancer may also suffer from heart disease or other illnesses, which can jointly influence the prognosis of risks and censoring. Traditional survival analysis methods often treat competing risks as independent and fail to accommodate the dependencies between different conditions. In this paper, we introduce HACSurv, a survival analysis method that learns Hierarchical Archimedean Copulas structures and cause-specific survival functions from data with competing risks. HACSurv employs a flexible dependency structure using hierarchical Archimedean copulas to represent the relationships between competing risks and censoring. By capturing the dependencies between risks and censoring, HACSurv achieves better survival predictions and offers insights into risk interactions. Experiments on synthetic datasets demonstrate that our method can accurately identify the complex dependency structure and precisely predict survival distributions, whereas the compared methods exhibit significant deviations between their predictions and the true distributions. Experiments on multiple real-world datasets also demonstrate that our method achieves better survival prediction compared to previous state-of-the-art methods.

The shape of the brain's white matter connections is relatively unexplored in diffusion MRI tractography analysis. While it is known that tract shape varies in populations and across the human lifespan, it is unknown if the variability in dMRI tractography-derived shape may relate to the brain's functional variability across individuals. This work explores the potential of leveraging tractography fiber cluster shape measures to predict subject-specific cognitive performance. We implement machine learning models to predict individual cognitive performance scores. We study a large-scale database from the HCP-YA study. We apply an atlas-based fiber cluster parcellation to the dMRI tractography of each individual. We compute 15 shape, microstructure, and connectivity features for each fiber cluster. Using these features as input, we train a total of 210 models to predict 7 different NIH Toolbox cognitive performance assessments. We apply an explainable AI technique, SHAP, to assess the importance of each fiber cluster for prediction. Our results demonstrate that shape measures are predictive of individual cognitive performance. The studied shape measures, such as irregularity, diameter, total surface area, volume, and branch volume, are as effective for prediction as microstructure and connectivity measures. The overall best-performing feature is a shape feature, irregularity, which describes how different a cluster's shape is from an idealized cylinder. Further interpretation using SHAP values suggest that fiber clusters with features highly predictive of cognitive ability are widespread throughout the brain, including fiber clusters from the superficial association, deep association, cerebellar, striatal, and projection pathways. This study demonstrates the strong potential of shape descriptors to enhance the study of the brain's white matter and its relationship to cognitive function.

The substantial effect of air pollution on cardiovascular disease and mortality burdens is well-established. Emissions-reducing interventions on coal-fired power plants -- a major source of hazardous air pollution -- have proven to be an effective, but costly, strategy for reducing pollution-related health burdens. Targeting the power plants that achieve maximum health benefits while satisfying realistic cost constraints is challenging. The primary difficulty lies in quantifying the health benefits of intervening at particular plants. This is further complicated because interventions are applied on power plants, while health impacts occur in potentially distant communities, a setting known as bipartite network interference (BNI). In this paper, we introduce novel policy learning methods based on Q- and A-Learning to determine the optimal policy under arbitrary BNI. We derive asymptotic properties and demonstrate finite sample efficacy in simulations. We apply our novel methods to a comprehensive dataset of Medicare claims, power plant data, and pollution transport networks. Our goal is to determine the optimal strategy for installing power plant scrubbers to minimize ischemic heart disease (IHD) hospitalizations under various cost constraints. We find that annual IHD hospitalization rates could be reduced in a range from 20.66-44.51 per 10,000 person-years through optimal policies under different cost constraints.

This contrasts with traditional models that process text in a single direction, and it has been widely demonstrated that BERT effectively captures contextual and semantic relationships in text, thereby providing a more comprehensive understanding of context. The embedding components of BERT include word embeddings, segment embeddings, and position embeddings. In essence, word embeddings map each word individually into a vector within a high-dimensional space. The segment embeddings allow BERT to differentiate and process single texts or pairs of texts, thereby enabling the understanding of semantic information at the sentence level. The position embeddings provide sequential information to the structure, allowing the model to mark the position of words in a sentence, which aids in further processing at a higher level. Finally, the CLS token at the beginning of the input sequence represents the final hidden state in the embedding vector, which is commonly used as the representation of the entire input sequence.

Traditional statistical inference for parameters is based on asymptotic/non-asymptotic coverage guarantees at fixed sample sizes. Such guarantees tend to become problematic in sequential experimental design due to the issue of "peeking", i.e., experimenters deciding whether to collect more data for further experiments after looking at current results in order to make the outcome more significant (Feller, 1940; Anscombe, 1954; Robbins, 1952). Recently, there has been an emerging literature on safe anytime-valid inference (Johari et al., 2022; Howard et al., 2021; Grünwald et al., 2020; Shafer, 2021; Pace and Salvan, 2020; Ramdas et al., 2023) that partially solve such problems. At a high level, they utilize a su-permartingale method coupled with Ville's inequality (Ville, 1939) to obtain time-uniform coverage guarantees for the quantities of interest, which is also equivalent to coverage guarantees for arbitrary stopping times (Ramdas et al., 2020): P ( t 1: θ