相关论文: Copula Representations and Error Surface Projectio…

We propose a new semi-parametric distributional regression smoother that is based on a copula decomposition of the joint distribution of the vector of response values. The copula is high-dimensional and constructed by inversion of a pseudo…

Nonlinear regression has been extensively employed in many computer vision problems (e.g., crowd counting, age estimation, affective computing). Under the umbrella of deep learning, two common solutions exist i) transforming nonlinear…

Recent papers on the theory of representation learning has shown the importance of a quantity called diversity when generalizing from a set of source tasks to a target task. Most of these papers assume that the function mapping shared…

This paper aims to interpret the mechanism of feedforward ReLU networks by exploring their solutions for piecewise linear functions, through the deduction from basic rules. The constructed solution should be universal enough to explain some…

The open-world assumption in model development suggests that a model might lack sufficient information to adequately handle data that is entirely distinct or out of distribution (OOD). While deep learning methods have shown promising…

In this paper, we analyze the relative errors in various reliability measures due to the tacit assumption that the components associated with a $n$-component series system or a parallel system are independently working where the components…

Deep neural network with rectified linear units (ReLU) is getting more and more popular recently. However, the derivatives of the function represented by a ReLU network are not continuous, which limit the usage of ReLU network to situations…

Recurrent neural networks are powerful tools for handling incomplete data problems in computer vision, thanks to their significant generative capabilities. However, the computational demand for these algorithms is too high to work in real…

Neural networks have recently become popular for a wide variety of uses, but have seen limited application in safety-critical domains such as robotics near and around humans. This is because it remains an open challenge to train a neural…

Iterative approximation methods using backpropagation enable the optimization of neural networks, but they remain computationally expensive, especially when used at scale. This paper presents an efficient alternative for optimizing neural…

The paper briefy reviews several recent results on hierarchical architectures for learning from examples, that may formally explain the conditions under which Deep Convolutional Neural Networks perform much better in function approximation…

A possible path to the interpretability of neural networks is to (approximately) represent them in the regional format of piecewise linear functions, where regions of inputs are associated to linear functions computing the network outputs.…

In computer vision, machine unlearning aims to remove the influence of specific visual concepts or training images without retraining from scratch. Studies show that existing approaches often modify the classifier while leaving internal…

We are interested in assessing the use of neural networks as surrogate models to approximate and minimize objective functions in optimization problems. While neural networks are widely used for machine learning tasks such as classification…

Dependence strucuture estimation is one of the important problems in machine learning domain and has many applications in different scientific areas. In this paper, a theoretical framework for such estimation based on copula and copula…

This paper studies the problem of range analysis for feedforward neural networks, which is a basic primitive for applications such as robustness of neural networks, compliance to specifications and reachability analysis of neural-network…

Implicit copulas are the most common copula choice for modeling dependence in high dimensions. This broad class of copulas is introduced and surveyed, including elliptical copulas, skew $t$ copulas, factor copulas, time series copulas and…

Copulas provide an attractive approach for constructing multivariate distributions with flexible marginal distributions and different forms of dependences. Of particular importance in many areas is the possibility of explicitly forecasting…

Many recent theoretical works on \emph{meta-learning} aim to achieve guarantees in leveraging similar representational structures from related tasks towards simplifying a target task. The main aim of theoretical guarantees on the subject is…

Can we effectively learn a nonlinear representation in time comparable to linear learning? We describe a new algorithm that explicitly and adaptively expands higher-order interaction features over base linear representations. The algorithm…