A time series is a sequence of data points, typically consisting of successive measurements made over a time interval.

The problem of sampling constrained continuous distributions has frequently appeared in many machine/statistical learning models. Many Monte Carlo Markov Chain (MCMC) sampling methods have been adapted to handle different types of constraints on the random variables. Among these methods, Hamilton Monte Carlo (HMC) and the related approaches have shown significant advantages in terms of computational efficiency compared to other counterparts. In this article, we first review HMC and some extended sampling methods, and then we concretely explain three constrained HMC-based sampling methods, reflection, reformulation, and spherical HMC. For illustration, we apply these methods to solve three well-known constrained sampling problems, truncated multivariate normal distributions, Bayesian regularized regression, and nonparametric density estimation. In this review, we also connect constrained sampling with another similar problem in the statistical design of experiments of constrained design space. Keywords: constrained sampling; Hamilton Monte Carlo; Riemannian Monte Carlo; regularized regression; truncated multivariate Gaussian.

The concept of small modular reactor has changed the outlook for tackling future energy crises. This new reactor technology is very promising considering its lower investment requirements, modularity, design simplicity, and enhanced safety features. The application of artificial intelligence-driven multi-scale modeling (neutronics, thermal hydraulics, fuel performance, etc.) incorporating Digital Twin and associated uncertainties in the research of small modular reactors is a recent concept. In this work, a comprehensive study is conducted on the multiscale modeling of accident-tolerant fuels. The application of these fuels in the light water-based small modular reactors is explored. This chapter also focuses on the application of machine learning and artificial intelligence in the design optimization, control, and monitoring of small modular reactors. Finally, a brief assessment of the research gap on the application of artificial intelligence to the development of high burnup composite accident-tolerant fuels is provided. Necessary actions to fulfill these gaps are also discussed.

As children grow older, they develop an intuitive understanding of the physical processes around them. They move along developmental trajectories, which have been mapped out extensively in previous empirical research. We investigate how children's developmental trajectories compare to the learning trajectories of artificial systems. Specifically, we examine the idea that cognitive development results from some form of stochastic optimization procedure. For this purpose, we train a modern generative neural network model using stochastic gradient descent. We then use methods from the developmental psychology literature to probe the physical understanding of this model at different degrees of optimization. We find that the model's learning trajectory captures the developmental trajectories of children, thereby providing support to the idea of development as stochastic optimization.

This article provides convergence analysis of online stochastic gradient descent algorithms for functional linear models. Adopting the characterizations of the slope function regularity, the kernel space capacity, and the capacity of the sampling process covariance operator, significant improvement on the convergence rates is achieved. Both prediction problems and estimation problems are studied, where we show that capacity assumption can alleviate the saturation of the convergence rate as the regularity of the target function increases. We show that with properly selected kernel, capacity assumptions can fully compensate for the regularity assumptions for prediction problems (but not for estimation problems). This demonstrates the significant difference between the prediction problems and the estimation problems in functional data analysis.

We study the problem of deleting user data from machine learning models trained using empirical risk minimization. Our focus is on learning algorithms which return the empirical risk minimizer and approximate unlearning algorithms that comply with deletion requests that come streaming minibatches. Leveraging the infintesimal jacknife, we develop an online unlearning algorithm that is both computationally and memory efficient. Unlike prior memory efficient unlearning algorithms, we target models that minimize objectives with non-smooth regularizers, such as the commonly used $\ell_1$, elastic net, or nuclear norm penalties. We also provide generalization, deletion capacity, and unlearning guarantees that are consistent with state of the art methods. Across a variety of benchmark datasets, our algorithm empirically improves upon the runtime of prior methods while maintaining the same memory requirements and test accuracy. Finally, we open a new direction of inquiry by proving that all approximate unlearning algorithms introduced so far fail to unlearn in problem settings where common hyperparameter tuning methods, such as cross-validation, have been used to select models.

Healthcare datasets obtained from Electronic Health Records have proven to be extremely useful to assess associations between patients' predictors and outcomes of interest. However, these datasets often suffer from missing values in a high proportion of cases and the simple removal of these cases may introduce severe bias. For these reasons, several multiple imputation algorithms have been proposed to attempt to recover the missing information. Each algorithm presents strengths and weaknesses, and there is currently no consensus on which multiple imputation algorithms works best in a given scenario. Furthermore, the selection of each algorithm parameters and data-related modelling choices are also both crucial and challenging. In this paper, we propose a novel framework to numerically evaluate strategies for handling missing data in the context of statistical analysis, with a particular focus on multiple imputation techniques. We demonstrate the feasibility of our approach on a large cohort of type-2 diabetes patients provided by the National COVID Cohort Collaborative (N3C) Enclave, where we explored the influence of various patient characteristics on outcomes related to COVID-19. Our analysis included classic multiple imputation techniques as well as simple complete-case Inverse Probability Weighted models. The experiments presented here show that our approach could effectively highlight the most valid and performant missing-data handling strategy for our case study. Moreover, our methodology allowed us to gain an understanding of the behavior of the different models and of how it changed as we modified their parameters. Our method is general and can be applied to different research fields and on datasets containing heterogeneous types.

Traditional federated optimization methods perform poorly with heterogeneous data (ie, accuracy reduction), especially for highly skewed data. In this paper, we investigate the label distribution skew in FL, where the distribution of labels varies across clients. First, we investigate the label distribution skew from a statistical view. We demonstrate both theoretically and empirically that previous methods based on softmax cross-entropy are not suitable, which can result in local models heavily overfitting to minority classes and missing classes. Additionally, we theoretically introduce a deviation bound to measure the deviation of the gradient after local update. At last, we propose FedLC (\textbf {Fed} erated learning via\textbf {L} ogits\textbf {C} alibration), which calibrates the logits before softmax cross-entropy according to the probability of occurrence of each class. FedLC applies a fine-grained calibrated cross-entropy loss to local update by adding a pairwise label margin. Extensive experiments on federated datasets and real-world datasets demonstrate that FedLC leads to a more accurate global model and much improved performance. Furthermore, integrating other FL methods into our approach can further enhance the performance of the global model.

Recent studies on Click-Through Rate (CTR) prediction has reached new levels by modeling longer user behavior sequences. Among others, the two-stage methods stand out as the state-of-the-art (SOTA) solution for industrial applications. The two-stage methods first train a retrieval model to truncate the long behavior sequence beforehand and then use the truncated sequences to train a CTR model. However, the retrieval model and the CTR model are trained separately. So the retrieved subsequences in the CTR model is inaccurate, which degrades the final performance. In this paper, we propose an end-to-end paradigm to model long behavior sequences, which is able to achieve superior performance along with remarkable cost-efficiency compared to existing models. Our contribution is three-fold: First, we propose a hashing-based efficient target attention (TA) network named ETA-Net to enable end-to-end user behavior retrieval based on low-cost bit-wise operations. The proposed ETA-Net can reduce the complexity of standard TA by orders of magnitude for sequential data modeling. Second, we propose a general system architecture as one viable solution to deploy ETA-Net on industrial systems. Particularly, ETA-Net has been deployed on the recommender system of Taobao, and brought 1.8% lift on CTR and 3.1% lift on Gross Merchandise Value (GMV) compared to the SOTA two-stage methods. Third, we conduct extensive experiments on both offline datasets and online A/B test. The results verify that the proposed model outperforms existing CTR models considerably, in terms of both CTR prediction performance and online cost-efficiency. ETA-Net now serves the main traffic of Taobao, delivering services to hundreds of millions of users towards billions of items every day.

In medicine, curated image datasets often employ discrete labels to describe what is known to be a continuous spectrum of healthy to pathological conditions, such as e.g. the Alzheimer's Disease Continuum or other areas where the image plays a pivotal point in diagnosis. We propose an architecture for image stratification based on a conditional variational autoencoder. Our framework, VAESim, leverages a continuous latent space to represent the continuum of disorders and finds clusters during training, which can then be used for image/patient stratification. The core of the method learns a set of prototypical vectors, each associated with a cluster. First, we perform a soft assignment of each data sample to the clusters. Then, we reconstruct the sample based on a similarity measure between the sample embedding and the prototypical vectors of the clusters. To update the prototypical embeddings, we use an exponential moving average of the most similar representations between actual prototypes and samples in the batch size. We test our approach on the MNIST-handwritten digit dataset and on a medical benchmark dataset called PneumoniaMNIST. We demonstrate that our method outperforms baselines in terms of kNN accuracy measured on a classification task against a standard VAE (up to 15% improvement in performance) in both datasets, and also performs at par with classification models trained in a fully supervised way. We also demonstrate how our model outperforms current, end-to-end models for unsupervised stratification.