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We study the generalization performance of gradient methods in the fundamental stochastic convex optimization setting, focusing on its dimension dependence. First, for full-batch gradient descent (GD) we give a construction of a learning…
The curvature regularities are well-known for providing strong priors in the continuity of edges, which have been applied to a wide range of applications in image processing and computer vision. However, these models are usually non-convex,…
We develop a framework to study posterior contraction rates in sparse high dimensional generalized linear models (GLM). We introduce a new family of GLMs, denoted by clipped GLM, which subsumes many standard GLMs and makes minor…
In many clinical trials, individuals in different subgroups have experience differential treatment effects. This leads to individualized differences in treatment benefit. In this article, we introduce the general concept of predictive…
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…
Precise control over dimension of nanocrystals is critical to tune the properties for various applications. However, the traditional control through experimental optimization is slow, tedious and time consuming. Herein a robust deep neural…
Stochastic gradient descent (SGD) provides a simple and efficient way to solve a broad range of machine learning problems. Here, we focus on distribution regression (DR), involving two stages of sampling: Firstly, we regress from…
An important theme in modern inverse problems is the reconstruction of time-dependent data from only finitely many measurements. To obtain satisfactory reconstruction results in this setting it is essential to strongly exploit temporal…
Graph representation learning (GRL) is a fundamental task in machine learning, aiming to encode high-dimensional graph-structured data into low-dimensional vectors. Self-supervised learning (SSL) methods are widely used in GRL because they…
Graph contrastive learning (GCL) learns node and graph representations by contrasting multiple views of the same graph. Existing methods typically rely on fixed, handcrafted views-usually a local and a global perspective, which limits their…
We develop a scalable algorithmic framework for sparse convex quantile regression (SCQR), addressing key computational challenges in the literature. Enhancing the classical CQR model, we introduce L2-norm regularization and an…
In this paper, we present a novel approach for contour detection with Convolutional Neural Networks. A multi-scale CNN learning framework is designed to automatically learn the most relevant features for contour patch detection. Our method…
The Convolutional Neural Network (CNN) has achieved great success in image classification. The classification model can also be utilized at image or patch level for many other applications, such as object detection and segmentation. In this…
The generalized orthogonal Procrustes problem (GOPP) plays a fundamental role in several scientific disciplines including statistics, imaging science and computer vision. Despite its tremendous practical importance, it is generally an…
Many deblurring and blur kernel estimation methods use a maximum a posteriori (MAP) approach or deep learning-based classification techniques to sharpen an image and/or predict the blur kernel. We propose a regression approach using…
We consider the problem of sufficient dimension reduction (SDR) for multi-index models. The estimators of the central mean subspace in prior works either have slow (non-parametric) convergence rates, or rely on stringent distributional…
Model reduction is essential for real-time simulation of deformable objects. Linear techniques such as PCA provide structured and predictable behavior, but their limited expressiveness restricts accuracy under large or nonlinear…
Supervised-contrastive loss (SCL) is an alternative to cross-entropy (CE) for classification tasks that makes use of similarities in the embedding space to allow for richer representations. In this work, we propose methods to engineer the…
The use of Convolutional Neural Networks (CNN) to estimate the galaxy photometric redshift probability distribution by analysing the images in different wavelength bands has been developed in the recent years thanks to the rapid development…
Variable selection and dimension reduction are two commonly adopted approaches for high-dimensional data analysis, but have traditionally been treated separately. Here we propose an integrated approach, called sparse gradient learning…