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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]

Many scientific studies collect data where the response and predictor variables are both functions of time, location, or some other covariate. Understanding the relationship between these functional variables is a common goal in these studies. Motivated from two real-life examples, we present in this article a function-on-function regression model that can be used to analyze such kind of functional data. Our estimator of the 2D coefficient function is the optimizer of a form of penalized least squares where the penalty enforces a certain level of smoothness on the estimator. Our first result is the representer theorem which states that the exact optimizer of the penalized least squares actually resides in a data-adaptive finite-dimensional subspace although the optimization problem is defined on a function space of infinite dimensions. This theorem then allows us an easy incorporation of the Gaussian quadrature into the optimization of the penalized least squares, which can be carried out through standard numerical procedures. We also show that our estimator achieves the minimax convergence rate in mean prediction under the framework of function-on-function regression. Extensive simulation studies demonstrate the numerical advantages of our method over the existing ones, where a sparse functional data extension is also introduced. The proposed method is then applied to our motivating examples of the benchmark Canadian weather data and a histone regulation study. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

For massive data, the family of subsampling algorithms is popular to downsize the data volume and reduce computational burden. Existing studies focus on approximating the ordinary least-square estimate in linear regression, where statistical leverage scores are often used to define subsampling probabilities. In this article, we propose fast subsampling algorithms to efficiently approximate the maximum likelihood estimate in logistic regression. We first establish consistency and asymptotic normality of the estimator from a general subsampling algorithm, and then derive optimal subsampling probabilities that minimize the asymptotic mean squared error of the resultant estimator. An alternative minimization criterion is also proposed to further reduce the computational cost. The optimal subsampling probabilities depend on the full data estimate, so we develop a two-step algorithm to approximate the optimal subsampling procedure. This algorithm is computationally efficient and has a significant reduction in computing time compared to the full data approach. Consistency and asymptotic normality of the estimator from a two-step algorithm are also established. Synthetic and real datasets are used to evaluate the practical performance of the proposed method. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]