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AbstractFor statistical analysis of network data, the β -model has emerged as a useful tool, thanks to its flexibility in incorporating nodewise heterogeneity and theoretical tractability. To generalize the β -model, this paper proposes the Sparse β -Regression Model (S β RM) that unites two research themes developed recently in modelling homophily and sparsity. In particular, we employ differential heterogeneity that assigns weights only to important nodes and propose penalized likelihood with an ℓ1 penalty for parameter estimation. While our estimation method is closely related to the LASSO method for logistic regression, we develop a new theory emphasizing the use of our model for dealing with a parameter regime that can handle sparse networks usually seen in practice. More interestingly, the resulting inference on the homophily parameter demands no debiasing normally employed in LASSO type estimation. We provide extensive simulation and data analysis to illustrate the use of the model. As a special case of our model, we extend the Erdős-Rényi model by including covariates and develop the associated statistical inference for sparse networks, which may be of independent interest. [ABSTRACT FROM AUTHOR]

AbstractHigher-order multiway data is ubiquitous in machine learning and statistics and often exhibits community-like structures, where each component (node) along each different mode has a community membership associated with it. In this paper we propose the (subgaussian) tensor mixed-membership blockmodel, a generalization of the tensor blockmodel positing that memberships need not be discrete, but instead are convex combinations of latent communities. We establish the identifiability of our model and propose a computationally efficient estimation procedure based on the higher-order orthogonal iteration algorithm (HOOI) for tensor SVD composed with a simplex corner-finding algorithm. We then demonstrate the consistency of our estimation procedure by providing a per-node error bound under subgaussian noise, which showcases the effect of higher-order structures on estimation accuracy. To prove our consistency result, we develop the ℓ2,∞ tensor perturbation bound for HOOI under independent, heteroskedastic, subgaussian noise that may be of independent interest. Our analysis uses a novel leave-one-out construction for the iterates, and our bounds depend only on spectral properties of the underlying low-rank tensor under nearly optimal signal-to-noise ratio conditions such that tensor SVD is computationally feasible. Finally, we apply our methodology to real and simulated data, demonstrating some effects not identifiable from the model with discrete community memberships. [ABSTRACT FROM AUTHOR]

AbstractLow-rank approximation is a popular strategy to tackle the “big n problem” associated with large-scale Gaussian process regressions. Basis functions for developing low-rank structures are crucial and should be carefully specified. Predictive processes simplify the problem by inducing basis functions with a covariance function and a set of knots. The existing literature suggests certain practical implementations of knot selection and covariance estimation; however, theoretical foundations explaining the influence of these two factors on predictive processes are lacking. In this paper, the asymptotic prediction performance of the predictive process and Gaussian process predictions are derived and the impacts of the selected knots and estimated covariance are studied. The use of support points as knots, which best represent data locations, is advocated. Extensive simulation studies demonstrate the superiority of support points and verify our theoretical results. Real data of precipitation and ozone are used as examples, and the efficiency of our method over other widely used low-rank approximation methods is verified. [ABSTRACT FROM AUTHOR]

AbstractIn this paper, we study the transfer learning problem in functional classification, aiming to improve the classification accuracy of the target data by leveraging information from related source datasets. To facilitate transfer learning, we propose a novel transferability function tailored for classification problems, enabling a more accurate evaluation of the similarity between source and target dataset distributions. Interestingly, we find that a source dataset can offer more substantial benefits under certain conditions than another dataset with an identical distribution to the target dataset. This observation renders the commonly-used debiasing step in the parameter-based transfer learning algorithm unnecessary under some circumstances to the classification problem. In particular, we propose two adaptive transfer learning algorithms based on the functional Distance Weighted Discrimination (DWD) classifier for scenarios with and without prior knowledge regarding informative sources. Furthermore, we establish the upper bound on the excess risk of the proposed classifiers, providing the statistical gain via transfer learning mathematically provable. Simulation studies are conducted to thoroughly examine the finite-sample performance of the proposed algorithms. Finally, we implement the proposed method to Beijing air-quality data, and significantly improve the prediction of the PM 2.5 level of a target station by effectively incorporating information from source datasets. [ABSTRACT FROM AUTHOR]

AbstractWith the rapid development of quantum computers, researchers have shown quantum advantages in physics-oriented problems. Quantum algorithms tackling computational biology problems are still lacking. In this paper, we demonstrate the quantum advantage in analyzing CITE-seq data. CITE-seq, a single-cell technology, enables researchers to simultaneously measure expressions of RNA and surface protein detected by antibody-derived tags (ADTs) in the same cells. CITE-seq data hold tremendous potential for identifying the ADTs associated with targeted genes and identifying cell types effectively. However, both tasks are challenging since the best subset of ADTs needs to be identified from enormous candidate subsets. To surmount the challenge, we develop a quantum algorithm named bisection Grover’s search (BGS) for the best subset selection of ADT markers in CITE-seq data. BGS takes advantage of quantum parallelism by integrating binary search and Grover’s algorithm to enable fast computation. Theoretical results are provided to show the privilege of BGS in the estimation error and computational complexity. The empirical performance of the BGS algorithm is demonstrated on both the IBM quantum computer and simulator. [ABSTRACT FROM AUTHOR]

AbstractDetermining the number of factors in high-dimensional factor modeling is essential but challenging, especially when the data are heavy-tailed. In this paper, we introduce a new estimator based on the spectral properties of Spearman sample correlation matrix under the high-dimensional setting, where both dimension and sample size tend to infinity proportionally. Our estimator is robust against heavy tails in either the common factors or idiosyncratic errors. The consistency of our estimator is established under mild conditions. Numerical experiments demonstrate the superiority of our estimator compared to existing methods. [ABSTRACT FROM AUTHOR]

AbstractThis work aims to study off-policy evaluation (OPE) under scenarios where two key reinforcement learning (RL) assumptions – temporal stationarity and individual homogeneity are both violated. To handle the “double inhomogeneities”, we propose a class of latent factor models for the reward and transition functions, under which we develop a general OPE framework that consists of both model-based and model-free approaches. To our knowledge, this is the first paper that develops statistically sound OPE methods in offline RL with double inhomogeneities. It contributes to a deeper understanding of OPE in environments, where standard RL assumptions are not met, and provides several practical approaches in these settings. We establish the theoretical properties of the proposed value estimators and empirically show that our approach outperforms state-of-the-art methods. Finally, we illustrate our method on a data set from the Medical Information Mart for Intensive Care. An R implementation of the proposed procedure is available at https://github.com/ZeyuBian/2FEOPE. [ABSTRACT FROM AUTHOR]

AbstractGaussian graphical models provide a powerful framework to reveal the conditional dependency structure between multivariate variables. The process of uncovering the conditional dependency network is known as structure learning. Bayesian methods can measure the uncertainty of conditional relationships and include prior information. However, frequentist methods are often preferred due to the computational burden of the Bayesian approach. Over the last decade, Bayesian methods have seen substantial improvements, with some now capable of generating accurate estimates of graphs up to a thousand variables in mere minutes. Despite these advancements, a comprehensive review or empirical comparison of all recent methods has not been conducted. This paper delves into a wide spectrum of Bayesian approaches used for structure learning and evaluates their efficacy through a comprehensive simulation study. We also demonstrate how to apply Bayesian structure learning to a real-world data set and provide directions for future research. This study gives an exhaustive overview of this dynamic field for newcomers, practitioners, and experts. [ABSTRACT FROM AUTHOR]

AbstractThis paper proposes a novel dynamic forecasting method using a new supervised Principal Component Analysis (PCA) when a large number of predictors are available. The new supervised PCA provides an effective way to bridge the gap between predictors and the target variable of interest by scaling and combining the predictors and their lagged values, resulting in an effective dynamic forecasting. Unlike the traditional diffusion-index approach, which does not learn the relationships between the predictors and the target variable before conducting PCA, we first rescale each predictor according to their significance in forecasting the targeted variable in a dynamic fashion, and a PCA is then applied to a rescaled and additive panel, which establishes a connection between the predictability of the PCA factors and the target variable. We also propose to use penalized methods such as the LASSO to select the significant factors that have superior predictive power over the others. Theoretically, we show that our estimators are consistent and outperform the traditional methods in prediction under some mild conditions. We conduct extensive simulations to verify that the proposed method produces satisfactory forecasting results and outperforms most of the existing methods using the traditional PCA. An example of predicting U.S. macroeconomic variables using a large number of predictors showcases that our method fares better than most of the existing ones in applications. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work. [ABSTRACT FROM AUTHOR]

AbstractOur goal is to develop a general strategy to decompose a random variable X into multiple independent random variables, without sacrificing any information about unknown parameters. A recent paper showed that for some well-known natural exponential families, X can be thinned into independent random variables X(1),…,X(K) , such that X=∑k=1KX(k) . These independent random variables can then be used for various model validation and inference tasks, including in contexts where traditional sample splitting fails. In this article, we generalize their procedure by relaxing this summation requirement and simply asking that some known function of the independent random variables exactly reconstruct X. This generalization of the procedure serves two purposes. First, it greatly expands the families of distributions for which thinning can be performed. Second, it unifies sample splitting and data thinning, which on the surface seem to be very different, as applications of the same principle. This shared principle is sufficiency. We use this insight to perform generalized thinning operations for a diverse set of families. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work. [ABSTRACT FROM AUTHOR]

Recommender systems are the engine of online advertising. Not only do they suggest movies, music, or romantic partners, but they also are used to select which advertisements to show to users. This paper reviews the basics of recommender system methodology and then looks at the emerging arena of active recommender systems. [ABSTRACT FROM AUTHOR]

The probabilistic topic model imposes a low-rank structure on the expectation of the corpus matrix. Therefore, singular value decomposition (SVD) is a natural tool of dimension reduction. We propose an SVD-based method for estimating a topic model. Our method constructs an estimate of the topic matrix from only a few leading singular vectors of the data matrix, and has a great advantage in memory use and computational cost for large-scale corpora. The core ideas behind our method include a pre-SVD normalization to tackle severe word frequency heterogeneity, a post-SVD normalization to create a low-dimensional word embedding that manifests a simplex geometry, and a post-SVD procedure to construct an estimate of the topic matrix directly from the embedded word cloud. We provide the explicit rate of convergence of our method. We show that our method attains the optimal rate in the case of long and moderately long documents, and it improves the rates of existing methods in the case of short documents. The key of our analysis is a sharp row-wise large-deviation bound for empirical singular vectors, which is technically demanding to derive and potentially useful for other problems. We apply our method to a corpus of Associated Press news articles and a corpus of abstracts of statistical papers. for this article are available online. [ABSTRACT FROM AUTHOR]