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Comprehensible explanations of probabilistic reasoning are a prerequisite for wider acceptance of Bayesian methods in expert systems and decision support systems. A study of human reasoning under uncertainty suggests two different…
Comparing Bayesian neural networks (BNNs) with different widths is challenging because, as the width increases, multiple model properties change simultaneously, and, inference in the finite-width case is intractable. In this work, we…
We analyse a quantum-like Bayesian Network that puts together cause/effect relationships and semantic similarities between events. These semantic similarities constitute acausal connections according to the Synchronicity principle and…
Despite the huge success of deep neural networks (NNs), finding good mechanisms for quantifying their prediction uncertainty is still an open problem. Bayesian neural networks are one of the most popular approaches to uncertainty…
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…
Bayesian estimation is a powerful theoretical paradigm for the operation of quantum sensors. However, the Bayesian method for statistical inference generally suffers from demanding calibration requirements that have so far restricted its…
We show that ensembles of deep neural networks, called deep ensembles, can be used to perform quantum parameter estimation while also providing a means for quantifying uncertainty in parameter estimates, which is a key advantage of using…
Bayesian learning is built on an assumption that the model space contains a true reflection of the data generating mechanism. This assumption is problematic, particularly in complex data environments. Here we present a Bayesian…
Treating neural network inputs and outputs as random variables, we characterize the structure of neural networks that can be used to model data that are invariant or equivariant under the action of a compact group. Much recent research has…
We consider the goal of predicting how complex networks respond to chronic (press) perturbations when characterizations of their network topology and interaction strengths are associated with uncertainty. Our primary result is the…
Negative probabilities emerged at intermediate steps in various attempts to predict the distributions of quantum interference. There is no consensus on their meaning yet. It has been suggested (Khrennikov, 1998) that negative probabilities…
In many real-world problems, there is a limited set of training data, but an abundance of unlabeled data. We propose a new method, Generative Posterior Networks (GPNs), that uses unlabeled data to estimate epistemic uncertainty in…
Quantum neural networks (QNNs) represent a pioneering intersection of quantum computing and deep learning. In this study, we unveil a fundamental convolution property inherent to QNNs, stemming from the natural parallelism of quantum gate…
Although equivariant machine learning has proven effective at many tasks, success depends heavily on the assumption that the ground truth function is symmetric over the entire domain matching the symmetry in an equivariant neural network. A…
'Capsule' models try to explicitly represent the poses of objects, enforcing a linear relationship between an object's pose and that of its constituent parts. This modelling assumption should lead to robustness to viewpoint changes since…
Modern neural networks have found to be miscalibrated in terms of confidence calibration, i.e., their predicted confidence scores do not reflect the observed accuracy or precision. Recent work has introduced methods for post-hoc confidence…
Multi-class classification methods that produce sets of probabilistic classifiers, such as ensemble learning methods, are able to model aleatoric and epistemic uncertainty. Aleatoric uncertainty is then typically quantified via the Bayes…
The application of Bayesian networks (BNs) to cognitive assessment and intelligent tutoring systems poses new challenges for model construction. When cognitive task analyses suggest constructing a BN with several latent variables, empirical…
Nonlinear properties of quantum states are essential to quantum information and many-body physics, but assessing them experimentally is challenging, as it typically requires multi-copy operations or a large number of measurement settings.…
Quantum filtering is a signal processing technique that estimates the posterior state of a quantum system under continuous measurements and has become a standard tool in quantum information processing, with applications in quantum state…