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Sufficient dimension reduction aims for reduction of dimensionality of a regression without loss of information by replacing the original predictor with its lower-dimensional subspace. Partial (sufficient) dimension reduction arises when…

Efficiently characterizing quantum dot (QD) devices is a critical bottleneck when scaling quantum processors based on confined spins. Measuring high-resolution charge stability diagrams (or CSDs, data maps which crucially define the…

We propose a function-valued evaluation metric for generative models based on the relative density ratio (RDR) designed to characterize distributional differences between real and generated samples. As an evaluation metric, the RDR function…

This paper addresses the problem of mapping high-dimensional data to a low-dimensional space, in the presence of other known features. This problem is ubiquitous in science and engineering as there are often controllable/measurable features…

Modeling and control of high-dimensional, nonlinear robotic systems remains a challenging task. While various model- and learning-based approaches have been proposed to address these challenges, they broadly lack generalizability to…

Stochastic gradient descent (SGD) is a popular algorithm for optimization problems arising in high-dimensional inference tasks. Here one produces an estimator of an unknown parameter from independent samples of data by iteratively…

Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…

Solving inverse problems in scientific and engineering fields has long been intriguing and holds great potential for many applications, yet most techniques still struggle to address issues such as high dimensionality, nonlinearity and model…

This paper investigates methods for improving generative data augmentation for deep learning. Generative data augmentation leverages the synthetic samples produced by generative models as an additional dataset for classification with small…

We address the problem of sufficient dimension reduction for feature matrices, which arises often in sensor network localization, brain neuroimaging, and electroencephalography analysis. In general, feature matrices have both row- and…

We present a framework for supervised subspace tracking, when there are two time series $x_t$ and $y_t$, one being the high-dimensional predictors and the other being the response variables and the subspace tracking needs to take into…

We introduce a novel 3D generative method, Generative 3D Reconstruction (G3DR) in ImageNet, capable of generating diverse and high-quality 3D objects from single images, addressing the limitations of existing methods. At the heart of our…

In recent years, accelerated MRI reconstruction based on deep learning has led to significant improvements in image quality with impressive results for high acceleration factors. However, from a clinical perspective image quality is only…

Discovering low-dimensional structure in real-world networks requires a suitable null model that defines the absence of meaningful structure. Here we introduce a spectral approach for detecting a network's low-dimensional structure, and the…

With the rapid development of data collection techniques, complex data objects that are not in the Euclidean space are frequently encountered in new statistical applications. Fr\'echet regression model (Peterson & M\"uller 2019) provides a…

We introduce Latent Space Distribution Matching (LSDM), a novel framework for semi-supervised generative modeling of conditional distributions. LSDM operates in two stages: (i) learning a low-dimensional latent space from both paired and…

We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…

Generative adversarial networks (GANs) have attracted intense interest in the field of generative models. However, few investigations focusing either on the theoretical analysis or on algorithm design for the approximation ability of the…

This paper proposes a supervised dimension reduction methodology for tensor data which has two advantages over most image-based prognostic models. First, the model does not require tensor data to be complete which expands its application to…

Generative Recommendation (GR) has emerged as a transformative paradigm that reformulates the traditional cascade ranking system into a sequence-to-item generation task, facilitated by the use of discrete Semantic IDs (SIDs). However,…