In this paper, we propose a computationally efficient approach —space(Sparse PArtial Correlation Estimation)— for selecting non-zero partial correlations under the high-dimension-low-sample-size setting. This method assumes the overall sparsity of the partial correlation matrix and employs sparse regression techniques for model fitting. We illustrate the performance of space by extensive simulation studies. It is shown that space performs well in both non-zero partial correlation selection and the identification of hub variables, and also outperforms two existing methods. We then apply space to a microarray breast cancer data set and identify a set of hub genes which may provide important insights on genetic regulatory networks. Finally, we prove that, under a set of suitable assumptions, the proposed procedure is asymptotically consistent in terms of model selection and parameter estimation.

In many engineering and scientific applications, prediction variables are grouped, for example, in biological applications where assayed genes or proteins can be grouped by biological roles or biological pathways. Common statistical analysis methods such as ANOVA, factor analysis, and functional modeling with basis sets also exhibit natural variable groupings. Existing successful group variable selection methods such as Antoniadis and Fan (2001), Yuan and Lin (2006) and Zhao, Rocha and Yu ( 2009) have the limitation of selecting variables in an "all-in-all-out" fashion, i.e., when one variable in a group is selected, all other variables in the same group are also selected. In many real problems, however, we may want to keep the flexibility of selecting variables within a group, such as in gene-set selection. In this paper, we develop a new group variable selection method that not only removes unimportant groups effectively, but also keeps the flexibility of selecting variables within a group. We also show that the new method offers the potential for achieving the theoretical "oracle" property as in Fan and Li (2001) and Fan and Peng (2004).

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In many organisms the expression levels of each gene are controlled by the activation levels of known “Transcription Factors” (TF). A problem of considerable interest is that of estimating the “Transcription Regulation Networks” (TRN) relating the TFs and genes. While the expression levels of genes can be observed, the activation levels of the corresponding TFs are usually unknown, greatly increasing the difficulty of the problem. Based on previous experimental work, it is often the case that partial information about the TRN is available. For example, certain TFs may be known to regulate a given gene or in other cases a connection may be predicted with a certain probability. In general, the biology of the problem indicates there will be very few connections between TFs and genes. Several methods have been proposed for estimating TRNs. However, they all suffer from problems such as unrealistic assumptions about prior knowledge of the network structure or computational limitations. We propose a new approach that can directly utilize prior information about the network structure in conjunction with observed gene expression data to estimate the TRN. Our approach uses L1 penalties on the network to ensure a sparse structure. This has the advantage of being computationally efficient as well as making many fewer assumptions about the network structure. We use our methodology to construct the TRN for E. coli and show that the estimate is biologically sensible and compares favorably with previous estimates.

Summary The advent of artificial intelligence (AI) and machine learning algorithms has led to opportunities as well as challenges in their use. In this overview paper, we begin with a discussion of bias and fairness issues that arise with the use of AI techniques, with a focus on supervised machine learning algorithms. We then describe the types and sources of data bias and discuss the nature of algorithmic unfairness. In addition, we provide a review of fairness metrics in the literature, discuss their limitations, and describe de‐biasing (or mitigation) techniques in the model life cycle.