Future advancement of engineering applications is dependent on design of novel materials with desired properties. Enormous size of known chemical space necessitates use of automated high throughput screening to search the desired material. The high throughput screening uses quantum chemistry calculations to predict material properties, however, computational complexity of these calculations often imposes prohibitively high cost on the search for desired material. This critical bottleneck is resolved by using deep machine learning to emulate the quantum computations. However, the deep learning algorithms require a large training dataset to ensure an acceptable generalization, which is often unavailable a-priory. In this paper, we propose a deep Gaussian process based approach to develop an emulator for quantum calculations. We further propose a novel molecular descriptor that enables implementation of the proposed approach. As demonstrated in this paper, the proposed approach can be implemented using a small dataset. We demonstrate efficacy of our approach for prediction of formation energy of inorganic molecules.

Clustering is the process of finding and analyzing underlying group structures in data. In recent years, data as become increasingly higher dimensional and therefore an increased need for dimension reduction techniques for use in clustering. Although such techniques are firmly established in the literature for multivariate data, there is a relative paucity in the area of matrix variate or three way data. Furthermore, these few methods all assume matrix variate normality which is not always sensible if skewness is present. We propose a mixture of bilinear factor analyzers model using four skewed matrix variate distributions, namely the matrix variate skew-t, generalized hyperbolic, variance gamma and normal inverse Gaussian distributions.

Dimensionality is an ever present concern with data becoming increasingly higher dimensional over the last few years. To combat this issue, dimension reduction techniques have become very important tools, especially in the area of clustering (unsupervised classification) as well as semi-supervised and supervised classification. For multivariate data, the mixture of factor analyzers model has proved to be very useful in this regard as the model performs clustering and dimension reduction simultaneously, details in Section 2. However, there is 1 relative paucity in the area of dimension reduction for use in model-based clustering for matrix variate data. Matrix variate distributions have been shown to be useful for modelling three way data such as images and multivariate longitudinal data; however, the methods presented in the literature do suffer from dimensionality concerns. In this paper, we present a mixture of matrix variate bilinear factor analyzers (MMVBFA) model for use in clustering for higher dimensional matrix data. The matrix variate bilinear factor analyzers model can be viewed as a generalization of bilinear principal component analysis (BPCA; Zhao et al. 2012), and contains BPCA as a special case. An alternating expectation conditional maximization (AECM) algorithm (Meng & van Dyk 1997) is used for parameter estimation. The proposed method is illustrated using both simulated and real datasets.

Mahalanobis Metric Learning (MML) has been actively studied recently in machine learning community. Most of existing MML methods aim to learn a powerful Mahalanobis distance for computing similarity of two objects. More recently, multiple methods use matrix norm regularizers to constrain the learned distance matrixMto improve the performance. However, in real applications, the structure of the distance matrix M is complicated and cannot be characterized well by the simple matrix norm. In this paper, we propose a novel robust metric learning method with learning the structure of the distance matrix in a new and natural way. We partition M into blocks and consider each block as a random matrix variate, which is fitted by matrix variate Gaussian mixture distribution. Different from existing methods, our model has no any assumption on M and automatically learns the structure of M from the real data, where the distance matrix M often is neither sparse nor low-rank. We design an effective algorithm to optimize the proposed model and establish the corresponding theoretical guarantee. We conduct extensive evaluations on the real-world data. Experimental results show our method consistently outperforms the related state-of-the-art methods.

One crucial assumption made by both principal component analysis (PCA) and probabilistic PCA (PPCA) is that the instances are independent and identically distributed (i.i.d.). However, this common i.i.d. assumption is unreasonable for relational data. In this paper, by explicitly modeling covariance between instances as derived from the relational information, we propose a novel probabilistic dimensionality reduction method, called probabilistic relational PCA (PRPCA), for relational data analysis. Although the i.i.d. assumption is no longer adopted in PRPCA, the learning algorithms for PRPCA can still be devised easily like those for PPCA which makes explicit use of the i.i.d. assumption. Experiments on real-world data sets show that PRPCA can effectively utilize the relational information to dramatically outperform PCA and achieve state-of-the-art performance.