Related papers: Analysis of Bayesian Networks via Prob-Solvable Lo…
In this paper, we introduce BNN-DP, an efficient algorithmic framework for analysis of adversarial robustness of Bayesian Neural Networks (BNNs). Given a compact set of input points $T\subset \mathbb{R}^n$, BNN-DP computes lower and upper…
Probabilistic Boolean Networks (PBNs) have been previously proposed so as to gain insights into complex dy- namical systems. However, identification of large networks and of the underlying discrete Markov Chain which describes their…
The process of dynamic state estimation (filtering) based on point process observations is in general intractable. Numerical sampling techniques are often practically useful, but lead to limited conceptual insight about optimal…
Quasi-Bayesian theory uses convex sets of probability distributions and expected loss to represent preferences about plans. The theory focuses on decision robustness, i.e., the extent to which plans are affected by deviations in subjective…
Neural network based generative models with discriminative components are a powerful approach for semi-supervised learning. However, these techniques a) cannot account for model uncertainty in the estimation of the model's discriminative…
We study the problem of certifying the robustness of Bayesian neural networks (BNNs) to adversarial input perturbations. Given a compact set of input points $T \subseteq \mathbb{R}^m$ and a set of output points $S \subseteq \mathbb{R}^n$,…
Neural Networks (NNs) have provided state-of-the-art results for many challenging machine learning tasks such as detection, regression and classification across the domains of computer vision, speech recognition and natural language…
After experimenting with a number of non-probabilistic methods for dealing with uncertainty many researchers reaffirm a preference for probability methods [1] [2], although this remains controversial. The importance of being able to form…
We present an exact Bayesian inference method for discrete statistical models, which can find exact solutions to a large class of discrete inference problems, even with infinite support and continuous priors. To express such models, we…
Compared to point estimates calculated by standard neural networks, Bayesian neural networks (BNN) provide probability distributions over the output predictions and model parameters, i.e., the weights. Training the weight distribution of a…
Probabilistic models such as Gaussian processes (GPs) are powerful tools to learn unknown dynamical systems from data for subsequent use in control design. While learning-based control has the potential to yield superior performance in…
Bayesian networks are a versatile and powerful tool to model complex phenomena and the interplay of their components in a probabilistically principled way. Moving beyond the comparatively simple case of completely observed, static data,…
The idea of computer vision as the Bayesian inverse problem to computer graphics has a long history and an appealing elegance, but it has proved difficult to directly implement. Instead, most vision tasks are approached via complex…
Artificial Neural Networks are connectionist systems that perform a given task by learning on examples without having prior knowledge about the task. This is done by finding an optimal point estimate for the weights in every node.…
Exponential random graph models (ERGMs) are a widely used framework for network data, enabling hypothesis testing on the structural mechanisms underlying observed networks. Bayesian ERGMs provide principled uncertainty quantification and…
The emergent field of probabilistic numerics has thus far lacked clear statistical principals. This paper establishes Bayesian probabilistic numerical methods as those which can be cast as solutions to certain inverse problems within the…
We investigate the problem of learning Bayesian networks in a robust model where an $\epsilon$-fraction of the samples are adversarially corrupted. In this work, we study the fully observable discrete case where the structure of the network…
Bayesian Belief Networks have been largely overlooked by Expert Systems practitioners on the grounds that they do not correspond to the human inference mechanism. In this paper, we introduce an explanation mechanism designed to generate…
Bayesian neural networks (BNNs) augment deep networks with uncertainty quantification by Bayesian treatment of the network weights. However, such models face the challenge of Bayesian inference in a high-dimensional and usually…
Deep Neural Networks (DNNs) are powerful tools for various computer vision tasks, yet they often struggle with reliable uncertainty quantification - a critical requirement for real-world applications. Bayesian Neural Networks (BNN) are…