BiBit google
Binary datasets represent a compact and simple way to store data about the relationships between a group of objects and their possible properties. In the last few years, different biclustering algorithms have been specially developed to be applied to binary datasets. Several approaches based on matrix factorization, suffix trees or divide-and-conquer techniques have been proposed to extract useful biclusters from binary data, and these approaches provide information about the distribution of patterns and intrinsic correlations. A novel approach to extracting biclusters from binary datasets, BiBit, is introduced here. The results obtained from different experiments with synthetic data reveal the excellent performance and the robustness of BiBit to density and size of input data. Also, BiBit is applied to a central nervous system embryonic tumor gene expression dataset to test the quality of the results. A novel gene expression preprocessing methodology, based on expression level layers, and the selective search performed by BiBit, based on a very fast bit-pattern processing technique, provide very satisfactory results in quality and computational cost. The power of biclustering in finding genes involved simultaneously in different cancer processes is also shown. Finally, a comparison with Bimax, one of the most cited binary biclustering algorithms, shows that BiBit is faster while providing essentially the same results.

Hybrid Monte Carlo google
In mathematics and physics, the hybrid Monte Carlo algorithm, also known as Hamiltonian Monte Carlo, is a Markov chain Monte Carlo method for obtaining a sequence of random samples from a probability distribution for which direct sampling is difficult. This sequence can be used to approximate the distribution (i.e., to generate a histogram), or to compute an integral (such as an expected value). It differs from the Metropolis-Hastings algorithm by reducing the correlation between successive sampled states by using a Hamiltonian evolution between states and additionally by targeting states with a higher acceptance criteria than the observed probability distribution. This causes it to converge more quickly to the absolute probability distribution. It was devised by Simon Duane, A.D. Kennedy, Brian Pendleton and Duncan Roweth in 1987.
“Hamiltonian Monte Carlo”

Variational Bayesian Sparse Gaussian Process Regression (VBSGPR) google
This paper presents a novel variational inference framework for deriving a family of Bayesian sparse Gaussian process regression (SGPR) models whose approximations are variationally optimal with respect to the full-rank GPR model enriched with various corresponding correlation structures of the observation noises. Our variational Bayesian SGPR (VBSGPR) models jointly treat both the distributions of the inducing variables and hyperparameters as variational parameters, which enables the decomposability of the variational lower bound that in turn can be exploited for stochastic optimization. Such a stochastic optimization involves iteratively following the stochastic gradient of the variational lower bound to improve its estimates of the optimal variational distributions of the inducing variables and hyperparameters (and hence the predictive distribution) of our VBSGPR models and is guaranteed to achieve asymptotic convergence to them. We show that the stochastic gradient is an unbiased estimator of the exact gradient and can be computed in constant time per iteration, hence achieving scalability to big data. We empirically evaluate the performance of our proposed framework on two real-world, massive datasets. …