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Deep neural networks are complex and opaque. As they enter application in a variety of important and safety critical domains, users seek methods to explain their output predictions. We develop an approach to explaining deep neural networks…
Uncertainty estimation is a key factor that makes deep learning reliable in practical applications. Recently proposed evidential neural networks explicitly account for different uncertainties by treating the network's outputs as evidence to…
The layered structure of deep neural networks hinders the use of numerous analysis tools and thus the development of its interpretability. Inspired by the success of functional brain networks, we propose a novel framework for…
We introduce provenance networks, a novel class of neural models designed to provide end-to-end, training-data-driven explainability. Unlike conventional post-hoc methods, provenance networks learn to link each prediction directly to its…
Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…
The belief function approach to uncertainty quantification as proposed in the Demspter-Shafer theory of evidence is established upon the general mathematical models for set-valued observations, called random sets. Set-valued predictions are…
This paper investigates the learnability of the nonlinearity property of Boolean functions using neural networks. We train encoder style deep neural networks to learn to predict the nonlinearity of Boolean functions from examples of…
A widely believed explanation for the remarkable generalization capacities of overparameterized neural networks is that the optimization algorithms used for training induce an implicit bias towards benign solutions. To grasp this…
Polynomial regression is a recurrent problem with a large number of applications. In computer vision it often appears in motion analysis. Whatever the application, standard methods for regression of polynomial models tend to deliver biased…
Auxiliary information can be exploited in machine learning models using the paradigm of evidence based conditional inference. Multi-modal techniques in Deep Neural Networks (DNNs) can be seen as perturbing the latent feature representation…
Deep learning requires regularization mechanisms to reduce overfitting and improve generalization. We address this problem by a new regularization method based on distributional robust optimization. The key idea is to modify the…
We present a novel approach for training deep neural networks in a Bayesian way. Classical, i.e. non-Bayesian, deep learning has two major drawbacks both originating from the fact that network parameters are considered to be deterministic.…
A deep neural network model is a powerful framework for learning representations. Usually, it is used to learn the relation $x \to y$ by exploiting the regularities in the input $x$. In structured output prediction problems, $y$ is…
Statistical hypothesis testing, as formalized by 20th Century statisticians and taught in college statistics courses, has been a cornerstone of 100 years of scientific progress. Nevertheless, the methodology is increasingly questioned in…
Despite impressive capabilities and outstanding performance, deep neural networks (DNNs) have captured increasing public concern about their security problems, due to their frequently occurred erroneous behaviors. Therefore, it is necessary…
Deep neural networks provide flexible frameworks for learning data representations and functions relating data to other properties and are often claimed to achieve 'super-human' performance in inferring relationships between input data and…
The topic of deep learning has seen a surge of interest in recent years both within and outside of the field of Statistics. Deep models leverage both nonlinearity and interaction effects to provide superior predictions in many cases when…
Deep learning techniques have demonstrated significant capacity in modeling some of the most challenging real world problems of high complexity. Despite the popularity of deep models, we still strive to better understand the underlying…
A trained neural network can be interpreted as a structural causal model (SCM) that provides the effect of changing input variables on the model's output. However, if training data contains both causal and correlational relationships, a…
Learning monotonic models with respect to a subset of the inputs is a desirable feature to effectively address the fairness, interpretability, and generalization issues in practice. Existing methods for learning monotonic neural networks…