Quantum-enhanced Markov chain Monte Carlo

Sampling from complicated probability distributions is a hard computational problem arising in many fields, including statistical physics, optimization, and machine learning. Quantum computers have recently been used to sample from complicated distributions that are hard to sample from classically, but which seldom arise in applications. Here we introduce a quantum algorithm to sample from distributions that pose a bottleneck in several applications, which we implement on a superconducting quantum processor. The algorithm performs Markov chain Monte Carlo (MCMC), a popular iterative sampling technique, to sample from the Boltzmann distribution of classical Ising models. In each step, the quantum processor explores the model in superposition to propose a random move, which is then accepted or rejected by a classical computer and returned to the quantum processor, ensuring convergence to the desired Boltzmann distribution. We find that this quantum algorithm converges in fewer iterations than common classical MCMC alternatives on relevant problem instances, both in simulations and experiments. It therefore opens a new path for quantum computers to solve useful--not merely difficult--problems in the near term.

Accuracy analysis of Educational Data Mining using Feature Selection Algorithm

Abstract - Gathering relevant information to predict student academic progress is a tedious task. Due to the large amount of irrelevant data present in databases which provides inaccurate results. Currently, it is not possible to accurately measure and analyze student data because there are too many irrelevant attributes and features in the data. With the help of Educational Data Mining (EDM), the quality of information can be improved. This research demonstrates how EDM helps to measure the accuracy of data using relevant attributes and machine learning algorithms performed. With EDM, irrelevant features are removed without changing the original data. The data set used in this study was taken from Kaggle.com. The results compared on the basis of recall, precision and f-measure to check the accuracy of the student data. The importance of this research is to help improve the quality of educational research by providing more accurate results for researchers.

Required sample size for learning sparse Bayesian networks with many variables

Learning joint probability distributions on n random variables requires exponential sample size in the generic case. Here we consider the case that a temporal (or causal) order of the variables is known and that the (unknown) graph of causal dependencies has bounded in-degree Delta. Then the joint measure is uniquely determined by the probabilities of all (2 Delta+1)-tuples. Upper bounds on the sample size required for estimating their probabilities can be given in terms of the VC-dimension of the set of corresponding cylinder sets. The sample size grows less than linearly with n.