This paper investigates sequential change-point detection in reconfigurable sensor networks. In this problem, data from multiple sensors are observed sequentially. Each sensor can have a unique change point, and the data distribution differs before and after the change. We aim to detect these changes as quickly as possible once they have occurred while controlling the false discovery rate at all times. Our setting is more realistic than traditional settings in that (1) the set of active sensors – i.e., those from which data can be collected – can change over time through the deactivation of existing sensors and the addition of new sensors, and (2) dependencies can occur both between sensors and across time points. We propose powerful e-value-based detection procedures that control the false discovery rate uniformly over time. Numerical experiments demonstrate that, with the same false discovery rate target, our procedures achieve superior performance compared to existing methods, exhibiting lower false non-discovery rates and reduced detection delays.

Motivated by modern applications such as computerized adaptive testing, sequential rank aggregation, and heterogeneous data source selection, we study the problem of active sequential estimation. The goal is to design an adaptive experiment selection rule and an estimator for more accurate parameter estimation. Greedy information-based experiment selection rules, which optimize information gain one step ahead, have been employed in practice thanks to their computational convenience, flexibility to context or task changes, and broad applicability. However, the optimality of greedy methods under a sequential decision theory framework is only established in the one-dimensional case, partly due to the problem’s combinatorial nature and the seemingly limited capacity of greedy algorithms. In this study, we close the gap for multidimensional problems. We cast the problem under a sequential decision theory framework with generalized risk measures for a large class of design-and-estimation methods. We propose adopting the maximum likelihood estimator with a class of greedy experiment selection rules. This class encompasses both existing methods and introduces new methods with improved numerical efficiency. We prove that these methods achieve asymptotic optimality when the risk measure aligns with the selection rule. Additionally, we establish that the proposed estimators are consistent and asymptotically normal, and further extend the results to allow early stopping rules. We also perform extensive numerical studies on both simulated and real data to illustrate the efficacy of the proposed methods.

This note studies matrix completion for a partially observed $n$ by $p$ data matrix involving mixed types of variables (e.g., continuous, binary, ordinal). A general family of non-linear factor models is considered, under which the matrix completion problem becomes the estimation of an $n$ by $p$ low-rank matrix ${\mathbf M}$. For existing methods in the literature, estimation consistency is established by showing $\Vert \hat {\mathbf M} - {\mathbf M}^*\Vert_F/\sqrt{np}$, the scaled Frobenius norm of the difference between the estimated and true ${\mathbf M}$ matrices, converges to zero in probability as $n$ and $p$ grow to infinity. However, this notion of consistency does not guarantee the convergence of each individual entry and, thus, may not be sufficient when specific data entries or the worst-case scenario is of interest. To address this issue, we consider the notion of entrywise consistency based on $\Vert \hat {\mathbf M} - {\mathbf M}^* \Vert_{\mbox{max}}$, the max norm of the estimation error matrix. We propose refinement procedures that turn estimators, which are consistent in the Frobenius norm sense, into entrywise estimators through a one-step refinement. Tight probabilistic error bounds are derived for the proposed estimators. The proposed methods are evaluated by simulation studies and real-data applications for collaborative filtering and large-scale educational assessment.