This study introduces an innovative design for a Variable Stiffness 3 Degrees of Freedom actuated wrist capable of actively and continuously adjusting its overall stiffness by modulating the active length of non-linear elastic elements. This modulation is akin to human muscular cocontraction and is achieved using only four motors. The mechanical configuration employed results in a compact and lightweight device with anthropomorphic characteristics, making it potentially suitable for applications such as prosthetics and humanoid robotics. This design aims to enhance performance in dynamic tasks, improve task adaptability, and ensure safety during interactions with both people and objects. The paper details the first hardware implementation of the proposed design, providing insights into the theoretical model, mechanical and electronic components, as well as the control architecture. System performance is assessed using a motion capture system. The results demonstrate that the prototype offers a broad range of motion ($[55, -45]${\deg} for flexion/extension, $\pm48${\deg} for radial/ulnar deviation, and $\pm180${\deg} for pronation/supination) while having the capability to triple its stiffness. Furthermore, following proper calibration, the wrist posture can be reconstructed through multivariate linear regression using rotational encoders and the forward kinematic model. This reconstruction achieves an average Root Mean Square Error of 6.6{\deg}, with an $R^2$ value of 0.93.

Human cognition operates on a "Global-first" cognitive mechanism, prioritizing information processing based on coarse-grained details. This mechanism inherently possesses an adaptive multi-granularity description capacity, resulting in computational traits such as efficiency, robustness, and interpretability. The analysis pattern reliance on the finest granularity and single-granularity makes most existing computational methods less efficient, robust, and interpretable, which is an important reason for the current lack of interpretability in neural networks. Multi-granularity granular-ball computing employs granular-balls of varying sizes to daptively represent and envelop the sample space, facilitating learning based on these granular-balls. Given that the number of coarse-grained "granular-balls" is fewer than sample points, granular-ball computing proves more efficient. Moreover, the inherent coarse-grained nature of granular-balls reduces susceptibility to fine-grained sample disturbances, enhancing robustness. The multi-granularity construct of granular-balls generates topological structures and coarse-grained descriptions, naturally augmenting interpretability. Granular-ball computing has successfully ventured into diverse AI domains, fostering the development of innovative theoretical methods, including granular-ball classifiers, clustering techniques, neural networks, rough sets, and evolutionary computing. This has notably ameliorated the efficiency, noise robustness, and interpretability of traditional methods. Overall, granular-ball computing is a rare and innovative theoretical approach in AI that can adaptively and simultaneously enhance efficiency, robustness, and interpretability. This article delves into the main application landscapes for granular-ball computing, aiming to equip future researchers with references and insights to refine and expand this promising theory.

Projecting climate change is a generalization problem: we extrapolate the recent past using physical models across past, present, and future climates. Current climate models require representations of processes that occur at scales smaller than model grid size, which have been the main source of model projection uncertainty. Recent machine learning (ML) algorithms hold promise to improve such process representations, but tend to extrapolate poorly to climate regimes they were not trained on. To get the best of the physical and statistical worlds, we propose a new framework - termed "climate-invariant" ML - incorporating knowledge of climate processes into ML algorithms, and show that it can maintain high offline accuracy across a wide range of climate conditions and configurations in three distinct atmospheric models. Our results suggest that explicitly incorporating physical knowledge into data-driven models of Earth system processes can improve their consistency, data efficiency, and generalizability across climate regimes.

The adoption of deep neural networks (DNNs) in safety-critical contexts is often prevented by the lack of effective means to explain their results, especially when they are erroneous. In our previous work, we proposed a white-box approach (HUDD) and a black-box approach (SAFE) to automatically characterize DNN failures. They both identify clusters of similar images from a potentially large set of images leading to DNN failures. However, the analysis pipelines for HUDD and SAFE were instantiated in specific ways according to common practices, deferring the analysis of other pipelines to future work. In this paper, we report on an empirical evaluation of 99 different pipelines for root cause analysis of DNN failures. They combine transfer learning, autoencoders, heatmaps of neuron relevance, dimensionality reduction techniques, and different clustering algorithms. Our results show that the best pipeline combines transfer learning, DBSCAN, and UMAP. It leads to clusters almost exclusively capturing images of the same failure scenario, thus facilitating root cause analysis. Further, it generates distinct clusters for each root cause of failure, thus enabling engineers to detect all the unsafe scenarios. Interestingly, these results hold even for failure scenarios that are only observed in a small percentage of the failing images.

Learning from Label Proportions (LLP) is a learning problem where only aggregate level labels are available for groups of instances, called bags, during training, and the aim is to get the best performance at the instance-level on the test data. This setting arises in domains like advertising and medicine due to privacy considerations. We propose a novel algorithmic framework for this problem that iteratively performs two main steps. For the first step (Pseudo Labeling) in every iteration, we define a Gibbs distribution over binary instance labels that incorporates a) covariate information through the constraint that instances with similar covariates should have similar labels and b) the bag level aggregated label. We then use Belief Propagation (BP) to marginalize the Gibbs distribution to obtain pseudo labels. In the second step (Embedding Refinement), we use the pseudo labels to provide supervision for a learner that yields a better embedding. In the final iteration, a classifier is trained using the pseudo labels. Our algorithm displays strong gains against several SOTA baselines (up to 15%) for the LLP Binary Classification problem on various dataset types - tabular and Image. We achieve these improvements with minimal computational overhead above standard supervised learning due to Belief Propagation, for large bag sizes, even for a million samples. Learning from Label Proportions (henceforth LLP) has seen renewed interest in recent times due to the rising concerns of privacy and leakage of sensitive information (Ardehaly & Culotta, 2017; Busa-Fekete et al., 2023; Zhang et al., 2022; Kobayashi et al., 2022; Yu et al., 2014). In the LLP binary classification setting, all the training instances are aggregated into bags and only the aggregated label count for a bag is available, i.e. proportion of 1's in a bag. Features of all instances are available. This can be seen as a form of weak supervision compared to providing instance-level labels.

We study the problem of distribution shift generally arising in machine-learning augmented hybrid simulation, where parts of simulation algorithms are replaced by data-driven surrogates. We first establish a mathematical framework to understand the structure of machine-learning augmented hybrid simulation problems, and the cause and effect of the associated distribution shift. We show correlations between distribution shift and simulation error both numerically and theoretically. Then, we propose a simple methodology based on tangent-space regularized estimator to control the distribution shift, thereby improving the long-term accuracy of the simulation results. In the linear dynamics case, we provide a thorough theoretical analysis to quantify the effectiveness of the proposed method. Moreover, we conduct several numerical experiments, including simulating a partially known reaction-diffusion equation and solving Navier-Stokes equations using the projection method with a data-driven pressure solver. In all cases, we observe marked improvements in simulation accuracy under the proposed method, especially for systems with high degrees of distribution shift, such as those with relatively strong non-linear reaction mechanisms, or flows at large Reynolds numbers.

Dealing with missing data is an important problem in statistical analysis that is often addressed with imputation procedures. The performance and validity of such methods are of great importance for their application in empirical studies. While the prevailing method of Multiple Imputation by Chained Equations (MICE) with Predictive Mean Matching (PMM) is considered standard in the social science literature, the increase in complex datasets may require more advanced approaches based on machine learning. In particular, tree-based imputation methods have emerged as very competitive approaches. However, the performance and validity are not completely understood, particularly compared to the standard MICE PMM. This is especially true for inference in linear models. In this study, we investigate the impact of various imputation methods on coefficient estimation, Type I error, and power, to gain insights that can help empirical researchers deal with missingness more effectively. We explore MICE PMM alongside different tree-based methods, such as MICE with Random Forest (RF), Chained Random Forests with and without PMM (missRanger), and Extreme Gradient Boosting (MIXGBoost), conducting a realistic simulation study using the German National Educational Panel Study (NEPS) as the original data source. Our results reveal that Random Forest-based imputations, especially MICE RF and missRanger with PMM, consistently perform better in most scenarios. Standard MICE PMM shows partially increased bias and overly conservative test decisions, particularly with non-true zero coefficients. Our results thus underscore the potential advantages of tree-based imputation methods, albeit with a caveat that all methods perform worse with an increased missingness, particularly missRanger.

This paper studies the effect of adding geometrically smoothed momentum to the randomized Kaczmarz algorithm, which is an instance of stochastic gradient descent on a linear least squares loss function. We prove a result about the expected error in the direction of singular vectors of the matrix defining the least squares loss. We present several numerical examples illustrating the utility of our result and pose several questions.

Data stream forecasts are essential inputs for decision making at digital platforms. Machine learning algorithms are appealing candidates to produce such forecasts. Yet, digital platforms require a large-scale forecast framework that can flexibly respond to sudden performance drops. Re-training ML algorithms at the same speed as new data batches enter is usually computationally too costly. On the other hand, infrequent re-training requires specifying the re-training frequency and typically comes with a severe cost of forecast deterioration. To ensure accurate and stable forecasts, we propose a simple data-driven monitoring procedure to answer the question when the ML algorithm should be re-trained. Instead of investigating instability of the data streams, we test if the incoming streaming forecast loss batch differs from a well-defined reference batch. Using a novel dataset constituting 15-min frequency data streams from an on-demand logistics platform operating in London, we apply the monitoring procedure to popular ML algorithms including random forest, XGBoost and lasso. We show that monitor-based re-training produces accurate forecasts compared to viable benchmarks while preserving computational feasibility. Moreover, the choice of monitoring procedure is more important than the choice of ML algorithm, thereby permitting practitioners to combine the proposed monitoring procedure with one's favorite forecasting algorithm.

Empirical process theory for i.i.d. observations has emerged as a ubiquitous tool for understanding the generalization properties of various statistical problems. However, in many applications where the data exhibit temporal dependencies (e.g., in finance, medical imaging, weather forecasting etc.), the corresponding empirical processes are much less understood. Motivated by this observation, we present a general bound on the expected supremum of empirical processes under standard $\beta/\rho$-mixing assumptions. Unlike most prior work, our results cover both the long and the short-range regimes of dependence. Our main result shows that a non-trivial trade-off between the complexity of the underlying function class and the dependence among the observations characterizes the learning rate in a large class of nonparametric problems. This trade-off reveals a new phenomenon, namely that even under long-range dependence, it is possible to attain the same rates as in the i.i.d. setting, provided the underlying function class is complex enough. We demonstrate the practical implications of our findings by analyzing various statistical estimators in both fixed and growing dimensions. Our main examples include a comprehensive case study of generalization error bounds in nonparametric regression over smoothness classes in fixed as well as growing dimension using neural nets, shape-restricted multivariate convex regression, estimating the optimal transport (Wasserstein) distance between two probability distributions, and classification under the Mammen-Tsybakov margin condition -- all under appropriate mixing assumptions. In the process, we also develop bounds on $L_r$ ($1\le r\le 2$)-localized empirical processes with dependent observations, which we then leverage to get faster rates for (a) tuning-free adaptation, and (b) set-structured learning problems.