相关论文: Has the Deep Neural Network learned the Stochastic…
The estimation of entropy rates for stationary discrete-valued stochastic processes is a well studied problem in information theory. However, estimating the entropy rate for stationary continuous-valued stochastic processes has not received…
Animals are known to make efficient probabilistic inferences based on uncertain and noisy information from the outside world. Although it is known that generic neural networks can perform near-optimal point estimation by probabilistic…
As deep neural networks (DNNs) are increasingly used in safety-critical applications, there is a growing concern for their reliability. Even highly trained, high-performant networks are not 100% accurate. However, it is very difficult to…
In this chapter we take a look at the universal approximation question for stochastic feedforward neural networks. In contrast to deterministic networks, which represent mappings from a set of inputs to a set of outputs, stochastic networks…
This paper poses a theoretical characterization of the stochastic reachability problem in terms of probability measures, capturing the probability measure of the state of the system that satisfies the reachability specification for all…
Deep neural networks (DNNs) are powerful tools for compressing and distilling information. Their scale and complexity, often involving billions of inter-dependent parameters, render direct microscopic analysis difficult. Under such…
In recent years, the question of the reliability of Machine Learning (ML) methods has acquired significant importance, and the analysis of the associated uncertainties has motivated a growing amount of research. However, most of these…
Deep learning has been the engine powering many successes of data science. However, the deep neural network (DNN), as the basic model of deep learning, is often excessively over-parameterized, causing many difficulties in training,…
Deep Neural Networks (DNNs) have revolutionized computer vision. We now have DNNs that achieve top (performance) results in many problems, including object recognition, facial expression analysis, and semantic segmentation, to name but a…
Training deep neural networks (DNNs) takes signifcant time and resources. A practice for expedited deployment is to use pre-trained deep neural networks (PTNNs), often from model zoos -- collections of PTNNs; yet, the reliability of model…
This paper integrates deep neural networks (DNNs) into structural economic models to increase flexibility and capture rich heterogeneity while preserving interpretability. Economic structure and machine learning are complements in empirical…
The intrinsic capability to continuously learn a changing data stream is a desideratum of deep neural networks (DNNs). However, current DNNs suffer from catastrophic forgetting, which interferes with remembering past knowledge. To mitigate…
In this article, we investigate the existence of a deep neural network (DNN) capable of approximating solutions to partial integro-differential equations while circumventing the curse of dimensionality. Using the Feynman-Kac theorem, we…
While the success of deep neural networks (DNNs) is well-established across a variety of domains, our ability to explain and interpret these methods is limited. Unlike previously proposed local methods which try to explain particular…
The success of deep learning has inspired recent interests in applying neural networks in statistical inference. In this paper, we investigate the use of deep neural networks for nonparametric regression with measurement errors. We propose…
Physics-informed neural networks (PINNs) have recently emerged as an alternative way of solving partial differential equations (PDEs) without the need of building elaborate grids, instead, using a straightforward implementation. In…
Inference latency and trustworthiness of Deep Neural Networks (DNNs) are the bottlenecks in deploying them in critical applications like sensitive tasks. Early Exit (EE) DNNs overcome the latency issues by allowing samples to exit from…
Catastrophe theory was originally proposed to study dynamical systems that exhibit sudden shifts in behavior arising from small changes in input. These models can generate reasonable explanation behind abrupt jumps in nonlinear dynamic…
We propose a new algorithm for training deep neural networks (DNNs) with binary weights. In particular, we first cast the problem of training binary neural networks (BiNNs) as a bilevel optimization instance and subsequently construct…
Deep neural networks (DNNs) have made significant strides in Natural Language Processing (NLP), yet their interpretability remains elusive, particularly when evaluating their intricate decision-making processes. Traditional methods often…