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Deep Neural Networks (DNNs) have achieved great success in a variety of machine learning (ML) applications, delivering high-quality inferencing solutions in computer vision, natural language processing, and virtual reality, etc. However,…
The deep Kolmogorov method is a simple and popular deep learning based method for approximating solutions of partial differential equations (PDEs) of the Kolmogorov type. In this work we provide an error analysis for the deep Kolmogorov…
The theoretical analysis of deep neural networks (DNN) is arguably among the most challenging research directions in machine learning (ML) right now, as it requires from scientists to lay novel statistical learning foundations to explain…
We develop a minimax rate analysis to describe the reason that deep neural networks (DNNs) perform better than other standard methods. For nonparametric regression problems, it is well known that many standard methods attain the minimax…
Advances in deep neural network (DNN) based molecular property prediction have recently led to the development of models of remarkable accuracy and generalization ability, with graph convolution neural networks (GCNNs) reporting…
Theoretical understanding of deep learning is one of the most important tasks facing the statistics and machine learning communities. While deep neural networks (DNNs) originated as engineering methods and models of biological networks in…
Deep neural network (DNN) regression models are widely used in applications requiring state-of-the-art predictive accuracy. However, until recently there has been little work on accurate uncertainty quantification for predictions from such…
Mixture models are regularly used in density estimation applications, but the problem of estimating the mixing distribution remains a challenge. Nonparametric maximum likelihood produce estimates of the mixing distribution that are…
We show the existence of a deep neural network capable of approximating a wide class of high-dimensional approximations. The construction of the proposed neural network is based on a quasi-optimal polynomial approximation. We show that this…
Even though Deep Neural Networks (DNNs) are widely celebrated for their practical performance, they possess many intriguing properties related to depth that are difficult to explain both theoretically and intuitively. Understanding how…
Deep neural networks (DNNs) exhibit high performance in image recognition; however, the reasons for their strong generalization abilities remain unclear. A plausible hypothesis is that DNNs achieve robust and accurate predictions by…
Deep metric learning (DML) aims to minimize empirical expected loss of the pairwise intra-/inter- class proximity violations in the embedding space. We relate DML to feasibility problem of finite chance constraints. We show that minimizer…
Deep Metric Learning (DML) is a group of techniques that aim to measure the similarity between objects through the neural network. Although the number of DML methods has rapidly increased in recent years, most previous studies cannot…
Efficient probability density estimation is a core challenge in statistical machine learning. Tensor-based probabilistic graph methods address interpretability and stability concerns encountered in neural network approaches. However, a…
In deep learning, dense layer connectivity has become a key design principle in deep neural networks (DNNs), enabling efficient information flow and strong performance across a range of applications. In this work, we model densely connected…
Weighted model counting (WMC) has emerged as a prevalent approach for probabilistic inference. In its most general form, WMC is #P-hard. Weighted DNF counting (weighted #DNF) is a special case, where approximations with probabilistic…
Uncertainty estimation is an important research area to make deep neural networks (DNNs) more trustworthy. While extensive research on uncertainty estimation has been conducted with unimodal data, uncertainty estimation for multimodal data…
The concepts of conditional mutual information (CMI) and normalized conditional mutual information (NCMI) are introduced to measure the concentration and separation performance of a classification deep neural network (DNN) in the output…
Linear mixed models (LMMs) are used as an important tool in the data analysis of repeated measures and longitudinal studies. The most common form of LMMs utilize a normal distribution to model the random effects. Such assumptions can often…
Score estimation is the backbone of score-based generative models (SGMs), especially denoising diffusion probabilistic models (DDPMs). A key result in this area shows that with accurate score estimates, SGMs can efficiently generate samples…