We consider the problem of estimating change in the dependency structure of two p-dimensional Ising models, based on respectively n_1 and n_2 samples drawn from the models. The change is assumed to be structured, e.g., sparse, block sparse, node-perturbed sparse, etc., such that it can be characterized by a suitable (atomic) norm. We present and analyze a norm-regularized estimator for directly estimating the change in structure, without having to estimate the structures of the individual Ising models. The estimator can work with any norm, and can be generalized to other graphical models under mild assumptions. We show that only one set of samples, say n_2, needs to satisfy the sample complexity requirement for the estimator to work, and the estimation error decreases as \fracc\sqrt\min(n_1,n_2), where c depends on the Gaussian width of the unit norm ball. For example, for \ell_1 norm applied to s-sparse change, the change can be accurately estimated with \min(n_1,n_2)=O(s \log p) which is sharper than an existing result n_1= O(s^2 \log p) and n_2 = O(n_1^2). Experimental results illustrating the effectiveness of the proposed estimator are presented.

We consider the problem of estimating sparse precision matrix of Gaussian copula distributions using samples with missing values in high dimensions. Existing approaches, primarily designed for Gaussian distributions, suggest using plugin estimators by disregarding the missing values. In this paper, we propose double plugin Gaussian (DoPinG) copula estimators to estimate the sparse precision matrix corresponding to \emphnon-paranormal distributions. DoPinG uses two plugin procedures and consists of three steps: (1) estimate nonparametric correlations based on observed values, including Kendall’s tau and Spearman’s rho; (2) estimate the non-paranormal correlation matrix; (3) plug into existing sparse precision estimators. We prove that DoPinG copula estimators consistently estimate the non-paranormal correlation matrix at a rate of O(\frac1(1-δ)\sqrt\frac\log pn), where δis the probability of missing values. We provide experimental results to illustrate the effect of sample size and percentage of missing data on the model performance. Experimental results show that DoPinG is significantly better than estimators like mGlasso, which are primarily designed for Gaussian data.

Low-rank matrix completion methods have been successful in a variety of settings such as recommendation systems. However, most of the existing matrix completion methods only provide a point estimate of missing entries, and do not characterize uncertainties of the predictions. In this paper, we propose a Bayesian hierarchical probabilistic matrix factorization (BHPMF) model to 1) incorporate hierarchical side information, and 2) provide uncertainty quantified predictions. The former yields significant performance improvements in the problem of plant trait prediction, a key problem in ecology, by leveraging the taxonomic hierarchy in the plant kingdom. The latter is helpful in identifying predictions of low confidence which can in turn be used to guide field work for data collection efforts. A Gibbs sampler is designed for inference in the model. Further, we propose a multiple inheritance BHPMF (MI-BHPMF) which can work with a general directed acyclic graph (DAG) structured hierarchy, rather than a tree. We present comprehensive experimental results on the problem of plant trait prediction using the largest database of plant traits, where BHPMF shows strong empirical performance in uncertainty quantified trait prediction, outperforming the state-of-the-art based on point estimates. Further, we show that BHPMF is more accurate when it is confident, whereas the error is high when the uncertainty is high.

MOTIVATION: High-throughput sequencing technologies produce very large amounts of data and sequencing errors constitute one of the major problems in analyzing such data. Current algorithms for correcting these errors are not very accurate and do not automatically adapt to the given data. RESULTS: We present HiTEC, an algorithm that provides a highly accurate, robust and fully automated method to correct reads produced by high-throughput sequencing methods. Our approach provides significantly higher accuracy than previous methods. It is time and space efficient and works very well for all read lengths, genome sizes and coverage levels. AVAILABILITY: The source code of HiTEC is freely available at www.csd.uwo.ca/~ilie/HiTEC/.