A Provable Smoothing Approach for High Dimensional Generalized Regression with Applications in Genomics

In many applications, linear models fit the data poorly. This article studies an appealing alternative, the generalized regression model. This model only assumes that there exists an unknown monotonically increasing link function connecting the response $Y$ to a single index $X^T\beta^*$ of explanatory variables $X\in\mathbb{R}^d$. The generalized regression model is flexible and covers many widely used statistical models. It fits the data generating mechanisms well in many real problems, which makes it useful in a variety of applications where regression models are regularly employed. In low dimensions, rank-based M-estimators are recommended to deal with the generalized regression model, giving root-$n$ consistent estimators of $\beta^*$. Applications of these estimators to high dimensional data, however, are questionable. This article studies, both theoretically and practically, a simple yet powerful smoothing approach to handle the high dimensional generalized regression model. Theoretically, a family of smoothing functions is provided, and the amount of smoothing necessary for efficient inference is carefully calculated. Practically, our study is motivated by an important and challenging scientific problem: decoding gene regulation by predicting transcription factors that bind to cis-regulatory elements. Applying our proposed method to this problem shows substantial improvement over the state-of-the-art alternative in real data.Comment: 53 page

Mining Frequent Neighborhood Patterns in Large Labeled Graphs

Over the years, frequent subgraphs have been an important sort of targeted patterns in the pattern mining literatures, where most works deal with databases holding a number of graph transactions, e.g., chemical structures of compounds. These methods rely heavily on the downward-closure property (DCP) of the support measure to ensure an efficient pruning of the candidate patterns. When switching to the emerging scenario of single-graph databases such as Google Knowledge Graph and Facebook social graph, the traditional support measure turns out to be trivial (either 0 or 1). However, to the best of our knowledge, all attempts to redefine a single-graph support resulted in measures that either lose DCP, or are no longer semantically intuitive. This paper targets mining patterns in the single-graph setting. We resolve the "DCP-intuitiveness" dilemma by shifting the mining target from frequent subgraphs to frequent neighborhoods. A neighborhood is a specific topological pattern where a vertex is embedded, and the pattern is frequent if it is shared by a large portion (above a given threshold) of vertices. We show that the new patterns not only maintain DCP, but also have equally significant semantics as subgraph patterns. Experiments on real-life datasets display the feasibility of our algorithms on relatively large graphs, as well as the capability of mining interesting knowledge that is not discovered in prior works.Comment: 9 page

A novel dimensionality reduction technique based on independent component analysis for modeling microarray gene expression data

DNA microarray experiments generating thousands of gene expression measurements, are being used to gather information from tissue and cell samples regarding gene expression differences that will be useful in diagnosing disease. But one challenge of microarray studies is the fact that the number n of samples collected is relatively small compared to the number p of genes per sample which are usually in thousands. In statistical terms this very large number of predictors compared to a small number of samples or observations makes the classification problem difficult. This is known as the ”curse of dimensionality problem”. An efficient way to solve this problem is by using dimensionality reduction techniques. Principle Component Analysis(PCA) is a leading method for dimensionality reduction of gene expression data which is optimal in the sense of least square error. In this paper we propose a new dimensionality reduction technique for specific bioinformatics applications based on Independent component Analysis(ICA). Being able to exploit higher order statistics to identify a linear model result, this ICA based dimensionality reduction technique outperforms PCA from both statistical and biological significance aspects. We present experiments on NCI 60 dataset to show this result