The identification of light sources is very important for the development of photonic technologies such as light detection and ranging (LiDAR), and microscopy. Typically, a large number of measurements are needed to classify light sources such as sunlight, laser radiation, and molecule fluorescence. The identification has required collection of photon statistics or quantum state tomography. In recently published work, researchers have used a neural network to dramatically reduce the number of measurements required to discriminate thermal light from coherent light at the single-photon level. In their paper, authors from Louisiana State University, Universidad Nacional Autónoma de México and Max-Born-Institut describe their experimental and theoretical techniques.

LWF chain graphs combine directed acyclic graphs and undirected graphs. We present a PC-like algorithm that finds the structure of chain graphs under the faithfulness assumption to resolve the problem of scalability of the proposed algorithm by Studeny (1997). We prove that our PC-like algorithm is order dependent, in the sense that the output can depend on the order in which the variables are given. This order dependence can be very pronounced in high-dimensional settings. We propose two modifications of the PC-like algorithm that remove part or all of this order dependence. Simulation results under a variety of settings demonstrate the competitive performance of the PC-like algorithms in comparison with the decomposition-based method, called LCD algorithm, proposed by Ma et al. (2008) in low-dimensional settings and improved performance in high-dimensional settings.

With both the introduction of new ways of storing, sharing and streaming data and the drastic development of the capacity of computers to handle large computations, the conception of models have changed. Mathematical models were first designed following prior ideas or conjectures from physical or biological models, then tested by designing experiments to test the validity of the ideas of their inventors. The model holds until new observations enable to reject its assumptions. The so-called Big Data's area introduced a new paradigm. The observed data convey enough information to understand the complexity of real life and the more the data, the better the description of the reality. Hence building models optimised to fit the data has become an efficient way to obtain generalizable models able to describe and forecast the real world. In this framework, the principle of supervised machine learning is to build a decision rule from a set of labeled examples called the learning sample, that fits the data.

This paper demonstrates the application of Bayesian Artificial Neural Networks to Ordinary Differential Equation (ODE) inverse problems. We consider the case of estimating an unknown chaotic dynamical system transition model from state observation data. Inverse problems for chaotic systems are numerically challenging as small perturbations in model parameters can cause very large changes in estimated forward trajectories. Bayesian Artificial Neural Networks can be used to simultaneously fit a model and estimate model parameter uncertainty. Knowledge of model parameter uncertainty can then be incorporated into the probabilistic estimates of the inferred system's forward time evolution. The method is demonstrated numerically by analysing the chaotic Sprott B system. Observations of the system are used to estimate a posterior predictive distribution over the weights of a parametric polynomial kernel Artificial Neural Network. It is shown that the proposed method is able to perform accurate time predictions. Further, the proposed method is able to correctly account for model uncertainties and provide useful prediction uncertainty bounds.

Machine learning has seen in the last 5-10 years an explosion in its growth from a research centered area of computer science and mathematics to a driving force for innovation in every aspect of our lives [1, 2, 3]. This was driven mainly by the success of deep learning and the significant investment of big technology firms in open source machine learning research [4, 5, 6]. Real life machine learning based solutions often require a number of models to work together to achieve the business goal of the product(s) [7]. Such models can be trained independently or as part of an optimised training pipeline [8, 9]. Breaking down the product into multiple models has several advantages: I) It allows for parallel model development with model designers focused on solving relatively small and well-defined problems.

Bayesian Networks (BN) are probabilistic graphical models that are widely used for uncertainty modeling, stochastic prediction and probabilistic inference. A Quantum Bayesian Network (QBN) is a quantum version of the Bayesian network that utilizes the principles of quantum mechanical systems to improve the computational performance of various analyses. In this paper, we experimentally evaluate the performance of QBN on various IBM QX hardware against Qiskit simulator and classical analysis. We consider a 4-node BN for stock prediction for our experimental evaluation. We construct a quantum circuit to represent the 4-node BN using Qiskit, and run the circuit on nine IBM quantum devices: Yorktown, Vigo, Ourense, Essex, Burlington, London, Rome, Athens and Melbourne. We will also compare the performance of each device across the four levels of optimization performed by the IBM Transpiler when mapping a given quantum circuit to a given device. We use the root mean square percentage error as the metric for performance comparison of various hardware.

This paper presents a new approach to generate samples from conditional belief functions for a restricted but non trivial subset of conditional belief functions. It assumes the factorization (decomposition) of a belief function along a bayesian network structure. It applies general conditional belief functions. The most profoundly studied measure of uncertainty is the probability. There exist methods of so-called graphoidal representation of joint probability distribution - called Bayesian networks [7] - allowing for expression of qualitative independence, causality, efficient reasoning, explanation, learning from data and sample generation.

This technical report tries to fill a gap in current literature on Timescale Graphical Event Models. I propose and evaluate different heuristics to determine hyper-parameters during the structure learning algorithm and refine an existing distance measure. A comprehensive benchmark on synthetic data will be conducted allowing conclusions about the applicability of the different heuristics.

Estimation of the number of components (or order) of a finite mixture model is a long standing and challenging problem in statistics. We propose the Group-Sort-Fuse (GSF) procedure---a new penalized likelihood approach for simultaneous estimation of the order and mixing measure in multidimensional finite mixture models. Unlike methods which fit and compare mixtures with varying orders using criteria involving model complexity, our approach directly penalizes a continuous function of the model parameters. More specifically, given a conservative upper bound on the order, the GSF groups and sorts mixture component parameters to fuse those which are redundant. For a wide range of finite mixture models, we show that the GSF is consistent in estimating the true mixture order and achieves the $n^{-1/2}$ convergence rate for parameter estimation up to polylogarithmic factors. The GSF is implemented for several univariate and multivariate mixture models in the R package GroupSortFuse. Its finite sample performance is supported by a thorough simulation study, and its application is illustrated on two real data examples.

In order to keep trace of information, the brain has to resolve the problem where information is and how to index new ones. We propose that the neural mechanism used by the prefrontal cortex (PFC) to detect structure in temporal sequences, based on the temporal order of incoming information, has served as second purpose to the spatial ordering and indexing of brain networks. We call this process, apparent to the manipulation of neural 'addresses' to organize the brain's own network, the 'digitalization' of information. Such tool is important for information processing and preservation, but also for memory formation and retrieval.