The expressive power of a Gaussian process (GP) model comes at a cost of poor scalability in the data size. To improve its scalability, this paper presents a low-rankcum-Markov approximation (LMA) of the GP model that is novel in leveraging the dual computational advantages stemming from complementing a low-rank approximate representation of the full-rank GP based on a support set of inputs wit...

In this study we present an advanced Bayesian framework for the analysis of functional Magnetic Resonance Imaging (fMRI) data that simultaneously employs both spatial and sparse properties. The basic building block of our method is the general linear model (GML) that constitute a well-known probabilistic approach for regression. By treating regression coefficients as random variables, we can ap...

Sparse coding of visual information has been of interest to the neuroscientific community for many decades and it is widely recognised that sparse codes should exhibit a high degree of statistical independence, typically measured by the kurtosis of the response distributions. In this paper we extend work on the hierarchical temporal memory model by studying the suitability of the augmented spat...

Few replies get published. Many that do get published could be more effective. A reply can be effective only if it is published, readable, and credible. This article suggests guidelines for writing good replies. The guidelines begin with things to keep in mind—for example, that you might be wrong—and things to do before you begin to write. The latter include considering not responding, consider...

Virial theorem is important for understanding stellar structures. It produces an interesting connection between magnetic and gravitational energies. Using the general form of the virial theorem including the magnetic field (toroidal magnetic field), we may explain the solar dynamo model in relation to variations of the magnetic and gravitational energies. We emphasize the role of the gravitatio...

The sparse Cholesky factorization of some large matrices can require a two dimensional partitioning of the matrix. The sparse hypermatrix storage scheme produces a recursive 2D partitioning of a sparse matrix. The subblocks are stored as dense matrices so BLAS3 routines can be used. However, since we are dealing with sparse matrices some zeros may be stored in those dense blocks. The overhead i...

We consider recovery of low-rank matrices from noisy data by hard thresholding of singular values, in which empirical singular values below a prescribed threshold λ are set to 0. We study the asymptotic MSE (AMSE) in a framework where the matrix size is large compared to the rank of the matrix to be recovered, and the signal-to-noise ratio of the low-rank piece stays constant. The AMSE-optimal ...

parcel delivery is a complex logistic service, as it serves many small or medium-sized customers who may send or receive parcels. modeling such delivery system needs to integrate two different research areas of hub location and vehicle routing. as it totally depends on the network and the linkage of the nodes, in this paper, some door-to-door service providers are taken into account to provide ...

Motivation This work addresses two common issues in building classification models for biological or medical studies: learning a sparse model, where only a subset of a large number of possible predictors is used, and training in the presence of missing data. This work focuses on supervised generative binary classification models, specifically linear discriminant analysis (LDA). The parameters a...