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Bayesian networks (BNs) are a probabilistic graphical model widely used for representing expert knowledge and reasoning under uncertainty. Traditionally, they are based on directed acyclic graphs that capture dependencies between random…
In recent times, neural networks have become a powerful tool for the analysis of complex and abstract data models. However, their introduction intrinsically increases our uncertainty about which features of the analysis are model-related…
We develop a novel deep learning method for uncertainty quantification in stochastic partial differential equations based on Bayesian neural network (BNN) and Hamiltonian Monte Carlo (HMC). A BNN efficiently learns the posterior…
We investigate uncertainty estimation and multimodality via the non-deterministic predictions of Bayesian neural networks (BNNs) in fluid simulations. To this end, we deploy BNNs in three challenging experimental test-cases of increasing…
Probabilistic vehicle trajectory prediction is essential for robust safety of autonomous driving. Current methods for long-term trajectory prediction cannot guarantee the physical feasibility of predicted distribution. Moreover, their…
Convolutional neural networks (CNNs) work well on large datasets. But labelled data is hard to collect, and in some applications larger amounts of data are not available. The problem then is how to use CNNs with small data -- as CNNs…
Tree tensor networks (TTNs) offer powerful models for image classification. While these TTN image classifiers already show excellent performance on classical hardware, embedding them into quantum neural networks (QNNs) may further improve…
In this paper, we establish some theoretical connections between Sum-Product Networks (SPNs) and Bayesian Networks (BNs). We prove that every SPN can be converted into a BN in linear time and space in terms of the network size. The key…
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…
A tensor network is a type of decomposition used to express and approximate large arrays of data. A given data-set, quantum state or higher dimensional multi-linear map is factored and approximated by a composition of smaller multi-linear…
Uncertainty awareness is crucial to develop reliable machine learning models. In this work, we propose the Natural Posterior Network (NatPN) for fast and high-quality uncertainty estimation for any task where the target distribution belongs…
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,…
Obtaining heteroscedastic predictive uncertainties from a Bayesian Neural Network (BNN) is vital to many applications. Often, heteroscedastic aleatoric uncertainties are learned as outputs of the BNN in addition to the predictive means,…
This research introduces a novel methodology for optimizing Bayesian Neural Networks (BNNs) by synergistically integrating them with traditional machine learning algorithms such as Random Forests (RF), Gradient Boosting (GB), and Support…
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…
We show an alternative way of representing a Bayesian belief network by sensitivities and probability distributions. This representation is equivalent to the traditional representation by conditional probabilities, but makes dependencies…
Although deep neural network (DNN) has achieved many state-of-the-art results, estimating the uncertainty presented in the DNN model and the data is a challenging task. Problems related to uncertainty such as classifying unknown classes…
Structure and parameters in a Bayesian network uniquely specify the probability distribution of the modeled domain. The locality of both structure and probabilistic information are the great benefits of Bayesian networks and require the…
We present a variation of a quantum algorithm for the machine learning task of classification with graph-structured data. The algorithm implements a feature extraction strategy that is based on Gaussian boson sampling (GBS) a near term…
A general Bayesian framework for model selection on random network models regarding their features is considered. The goal is to develop a principle Bayesian model selection approach to compare different fittable, not necessarily nested,…