Related papers: Bayesian Networks, Total Variation and Robustness

Approximate Bayesian computation (ABC) is one of the most popular "likelihood-free" methods. These methods have been applied in a wide range of fields by providing solutions to intractable likelihood problems in which exact Bayesian…

Bayesian network (BN) structure learning from complete data has been extensively studied in the literature. However, fewer theoretical results are available for incomplete data, and most are related to the Expectation-Maximisation (EM)…

The deepening penetration of renewable resources into power systems entails great difficulties that have not been surmounted satisfactorily. An issue that merits special attention is the short-term planning of power systems under net load…

Bayesian neural networks (BNNs) have been long considered an ideal, yet unscalable solution for improving the robustness and the predictive uncertainty of deep neural networks. While they could capture more accurately the posterior…

We introduce a methodology for robust Bayesian estimation with robust divergence (e.g., density power divergence or {\gamma}-divergence), indexed by a single tuning parameter. It is well known that the posterior density induced by robust…

Distance covariance is a popular measure of dependence between random variables. It has some robustness properties, but not all. We prove that the influence function of the usual distance covariance is bounded, but that its breakdown value…

Bayesian network (BN) modelling is extensively used in systems epidemiology. Usually it consists in selecting and reporting the best-fitting structure conditional to the data. A major practical concern is avoiding overfitting, on account of…

Bayesian Belief Networks (BBNs) are a powerful formalism for reasoning under uncertainty but bear some severe limitations: they require a large amount of information before any reasoning process can start, they have limited contradiction…

Artificial neural networks (NNs) have become the de facto standard in machine learning. They allow learning highly nonlinear transformations in a plethora of applications. However, NNs usually only provide point estimates without…

This paper develops a quantitative framework to assess the robustness of Bayes-optimal decisions in finite decision problems under model uncertainty. We introduce two complementary stability notions for acts: the robustness radius,…

The recent advances in machine learning in various fields of applications can be largely attributed to the rise of deep learning (DL) methods and architectures. Despite being a key technology behind autonomous cars, image processing, speech…

Bayesian neural networks (BNNs) with latent variables are probabilistic models which can automatically identify complex stochastic patterns in the data. We describe and study in these models a decomposition of predictive uncertainty into…

Adversarial examples pose a security threat to many critical systems built on neural networks. Given that deterministic robustness often comes with significantly reduced accuracy, probabilistic robustness (i.e., the probability of having…

Regression methods are fundamental for scientific and technological applications. However, fitted models can be highly unreliable outside of their training domain, and hence the quantification of their uncertainty is crucial in many of…

Deep neural networks (NNs) are powerful black box predictors that have recently achieved impressive performance on a wide spectrum of tasks. Quantifying predictive uncertainty in NNs is a challenging and yet unsolved problem. Bayesian NNs,…

Sensitivity forecasts inform the design of experiments and the direction of theoretical efforts. To arrive at representative results, Bayesian forecasts should marginalize their conclusions over uncertain parameters and noise realizations…

Neural network quantization methods often involve simulating the quantization process during training, making the trained model highly dependent on the target bit-width and precise way quantization is performed. Robust quantization offers…

Suppose that multiple experts (or learning algorithms) provide us with alternative Bayesian network (BN) structures over a domain, and that we are interested in combining them into a single consensus BN structure. Specifically, we are…

In this paper, we present a guide to the foundations of learning Dynamic Bayesian Networks (DBNs) from data in the form of multiple samples of trajectories for some length of time. We present the formalism for a generic as well as a set of…

Adversarial examples pose a security threat to many critical systems built on neural networks. While certified training improves robustness, it also decreases accuracy noticeably. Despite various proposals for addressing this issue, the…