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Dynamic treatment regimes or policies are a sequence of decision functions over multiple stages that are tailored to individual features. One important class of treatment policies in practice, namely multi-stage stationary treatment policies, prescribes treatment assignment probabilities using the same decision function across stages, where the decision is based on the same set of features consisting of time-evolving variables (e.g., routinely collected disease biomarkers). Although there has been extensive literature on constructing valid inference for the value function associated with dynamic treatment policies, little work has focused on the policies themselves, especially in the presence of high-dimensional feature variables. We aim to fill the gap in this work. Specifically, we first obtain the multi-stage stationary treatment policy by minimizing the negative augmented inverse probability weighted estimator of the value function to increase asymptotic efficiency. A penalty is applied on the policy parameters to select important feature variables. We then construct one-step improvements of the policy parameter estimators for valid inference. Theoretically, we show that the improved estimators are asymptotically normal, even if nuisance parameters are estimated at a slow convergence rate and the dimension of the feature variables increases with the sample size. Our numerical studies demonstrate that the proposed method estimates a sparse policy with a near-optimal value function and conducts valid inference for the policy parameters. 

Clustering is a fundamental tool for exploratory data analysis. One central problem in clustering is deciding if the clusters discovered by clustering methods are reliable as opposed to being artifacts of natural sampling variation. Statistical significance of clustering (SigClust) is a recently developed cluster evaluation tool for high-dimension, low-sample size data. Despite its successful application to many scientific problems, there are cases where the original SigClust may not work well. Furthermore, for specific applications, researchers may not have access to the original data and only have the dissimilarity matrix. In this case, clustering is still a valuable exploratory tool, but the original SigClust is not applicable. To address these issues, we propose a new SigClust method using multidimensional scaling (MDS). The underlying idea behind MDS-based SigClust is that one can achieve low-dimensional representations of the original data via MDS using only the dissimilarity matrix and then apply SigClust on the low-dimensional MDS space. The proposed MDS-based SigClust can circumvent the challenge of parameter estimation of the original method in high-dimensional spaces while keeping the essential clustering structure in the MDS space. Both simulations and real data applications demonstrate that the proposed method works remarkably well for assessing the statistical significance of clustering. Supplementary materials for this article are available online. 

Multi-modal data are prevalent in many scientific fields. In this study, we consider the parameter estimation and variable selection for a multi-response regression using block-missing multi-modal data. Our method allows the dimensions of both the responses and the predictors to be large, and the responses to be incomplete and correlated, a common practical problem in high-dimensional settings. Our proposed method uses two steps to make a prediction from a multi-response linear regression model with block-missing multi-modal predictors. In the first step, without imputing missing data, we use all available data to estimate the covariance matrix of the predictors and the cross-covariance matrix between the predictors and the responses. In the second step, we use these matrices and a penalized method to simultaneously estimate the precision matrix of the response vector, given the predictors, and the sparse regression parameter matrix. Lastly, we demonstrate the effectiveness of the proposed method using theoretical studies, simulated examples, and an analysis of a multi-modal imaging data set from the Alzheimer’s Disease Neuroimaging Initiative. 

Contextual dynamic pricing aims to set personalized prices based on sequential interactions with customers. At each time period, a customer who is interested in purchasing a product comes to the platform. The customer’s valuation for the product is a linear function of contexts, including product and customer features, plus some random market noise. The seller does not observe the customer’s true valuation, but instead needs to learn the valuation by leveraging contextual information and historic binary purchase feedback. Existing models typically assume full or partial knowledge of the random noise distribution. In this paper, we consider contextual dynamic pricing with unknown random noise in the linear valuation model. Our distribution-free pricing policy learns both the contextual function and the market noise simultaneously. A key ingredient of our method is a novel perturbed linear bandit framework, in which a modified linear upper confidence bound algorithm is proposed to balance the exploration of market noise and the exploitation of the current knowledge for better pricing. We establish the regret upper bound and a matching lower bound of our policy in the perturbed linear bandit framework and prove a sublinear regret bound in the considered pricing problem. Finally, we demonstrate the superior performance of our policy on simulations and a real-life auto loan data set. Funding: Y. Liu and W.W. Sun acknowledge support from the National Science Foundation Division of Social and Economic Sciences [Grant NSF-SES 2217440]. Supplemental Material: The supplementary material is available at https://doi.org/10.1287/moor.2023.1369 . 

ABSTRACT The next generation of wide-field deep astronomical surveys will deliver unprecedented amounts of images through the 2020s and beyond. As both the sensitivity and depth of observations increase, more blended sources will be detected. This reality can lead to measurement biases that contaminate key astronomical inferences. We implement new deep learning models available through Facebook AI Research’s detectron2 repository to perform the simultaneous tasks of object identification, deblending, and classification on large multiband co-adds from the Hyper Suprime-Cam (HSC). We use existing detection/deblending codes and classification methods to train a suite of deep neural networks, including state-of-the-art transformers. Once trained, we find that transformers outperform traditional convolutional neural networks and are more robust to different contrast scalings. Transformers are able to detect and deblend objects closely matching the ground truth, achieving a median bounding box Intersection over Union of 0.99. Using high-quality class labels from the Hubble Space Telescope, we find that when classifying objects as either stars or galaxies, the best-performing networks can classify galaxies with near 100 per cent completeness and purity across the whole test sample and classify stars above 60 per cent completeness and 80 per cent purity out to HSC i-band magnitudes of 25 mag. This framework can be extended to other upcoming deep surveys such as the Legacy Survey of Space and Time and those with the Roman Space Telescope to enable fast source detection and measurement. Our code, deepdisc, is publicly available at https://github.com/grantmerz/deepdisc. 

Large-scale high throughput metabolomic technologies are indispensable components of systems biology in terms of discovering and defining the metabolite parts of the system. However, the lack of a plant metabolite spectral library limits the metabolite identification of plant metabolomic studies. Here, we have created a plant metabolite spectral library using 544 authentic standards, which increased the efficiency of identification for untargeted metabolomic studies. The process of creating the spectral library was described, and the mzVault library was deposited in the public repository for free download. Furthermore, based on the spectral library, we describe a process of creating a pseudo-targeted method, which was applied to a proof-of-concept study of Arabidopsis leaf extracts. As authentic standards become available, more metabolite spectra can be easily incorporated into the spectral library to improve the mzVault package.