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It has been widely assumed that a neural network cannot be recovered from its outputs, as the network depends on its parameters in a highly nonlinear way. Here, we prove that in fact it is often possible to identify the architecture,…

In the era of big data, it is necessary to split extremely large data sets across multiple computing nodes and construct estimators using the distributed data. When designing distributed estimators, it is desirable to minimize the amount of…

Real world data often exhibit low-dimensional geometric structures, and can be viewed as samples near a low-dimensional manifold. This paper studies nonparametric regression of H\"{o}lder functions on low-dimensional manifolds using deep…

ReLU networks, while prevalent for visual data, have sharp transitions, sometimes relying on individual pixels for predictions, making vanilla gradient-based explanations noisy and difficult to interpret. Existing methods, such as GradCAM,…

In this work, we propose a novel deep bootstrap framework for nonparametric regression based on conditional diffusion models. Specifically, we construct a conditional diffusion model to learn the distribution of the response variable given…

Generative models using neural network have opened a door to large-scale studies for various application domains, especially for studies that suffer from lack of real samples to obtain statistically robust inference. Typically, these…

This article describes a robust algorithm to estimate a conditional probability density f(t|x) as a non-parametric smooth regression function. It is based on a neural network and the Bayesian interpretation of the network output as a…

While it is common practice in applied network analysis to report various standard network summary statistics, these numbers are rarely accompanied by uncertainty quantification. Yet any error inherent in the measurements underlying the…

We consider the problem of constructing differentially private nonparametric confidence intervals (CIs) for an arbitrary quantity using resampling. A growing body of work has adapted resampling ideas to the private setting, including…

Expected shortfall (ES), also known as conditional value-at-risk, is a widely recognized risk measure that complements value-at-risk by capturing tail-related risks more effectively. Compared with quantile regression, which has been…

Having a regression model, we are interested in finding two-sided intervals that are guaranteed to contain at least a desired proportion of the conditional distribution of the response variable given a specific combination of predictors. We…

In this work we consider the task of constructing prediction intervals in an inductive batch setting. We present a discriminative learning framework which optimizes the expected error rate under a budget constraint on the interval sizes.…

Residual variance and the signal-to-noise ratio are important quantities in many statistical models and model fitting procedures. They play an important role in regression diagnostics, in determining the performance limits in estimation and…

In this work, we study the learning theory of reward modeling with pairwise comparison data using deep neural networks. We establish a novel non-asymptotic regret bound for deep reward estimators in a non-parametric setting, which depends…

To have a superior generalization, a deep learning neural network often involves a large size of training sample. With increase of hidden layers in order to increase learning ability, neural network has potential degradation in accuracy.…

The Rectified Linear Unit (ReLU) is a foundational activation function in artficial neural networks. Recent literature frequently misattributes its origin to the 2018 (initial) version of this paper, which exclusively investigated ReLU at…

Deploying deep learning models, comprising of non-linear combination of millions, even billions, of parameters is challenging given the memory, power and compute constraints of the real world. This situation has led to research into model…

Stochastic recurrent neural networks with latent random variables of complex dependency structures have shown to be more successful in modeling sequential data than deterministic deep models. However, the majority of existing methods have…

Overparametrized neural networks trained by gradient descent (GD) can provably overfit any training data. However, the generalization guarantee may not hold for noisy data. From a nonparametric perspective, this paper studies how well…

We introduce a variational framework to learn the activation functions of deep neural networks. Our aim is to increase the capacity of the network while controlling an upper-bound of the actual Lipschitz constant of the input-output…