Association Analysis Techniques for Discovering Functional Modules from Microarray Data

An application of great interest in microarray data analysis is the identification of a group of genes that show very similar patterns of expression in a data set, and are expected to represent groups of genes that perform common/similar functions, also known as functional modules. Although clustering offers a natural solution to this problem, it suffers from the limitation that it uses all the conditions to compare two genes, whereas only a subset of them may be relevant. Association analysis offers an alternative route for finding such groups of genes that may be co-expressed only over a subset of the experimental conditions used to prepare the data set. The techniques in this field attempt to find groups of data objects that contain coherent values across a set of attributes, in an exhaustive and efficient manner. In this paper, we illustrate how a generalization of the techniques in association analysis for real-valued data can be utilized to extract coherent functional modules from large microarray data sets

Effects of passive porous walls on the first Mack mode instability of hypersonic boundary layers over a sharp cone

Passive porous coatings have been proposed in literature as a means of delaying transition to turbulence in hypersonic boundary layers. The nonlinear stability of hypersonic viscous flow over a sharp slender cone with passive porous walls is investigated in this study. Hypersonic flows are unstable to viscous and inviscid disturbances, and following Mack (1984) these have been called the first and second Mack modes. A weakly nonlinear analysis of the instability of the flow to axisymmetric and non-axisymmetric viscous (first Mack mode) disturbances is performed here. The attached shock and effect of curvature are taken into account. Asymptotic methods are used at large Reynolds number and large Mach number to examine the viscous modes of instability, which may be described by a triple-deck structure. Various porous wall models have been incorporated into the stability analysis. The eigenrelations governing the linear stability of the problem are derived. Neutral and spatial instability results show the presence of multiple unstable modes and the destabilising effect of the porous wall models on them. The weakly nonlinear stability analysis carried out allows an equation for the amplitude of disturbances to be derived. The stabilising or destabilising effect of nonlinearity is found to depend on the cone radius. It is shown that porous walls significantly influences the effect of nonlinearity. They allow nonlinear effects to destabilise linearly unstable lower frequency modes and stabilise linearly unstable higher frequency modes

Mining Novel Multivariate Relationships in Time Series Data Using Correlation Networks

In many domains, there is significant interest in capturing novel relationships between time series that represent activities recorded at different nodes of a highly complex system. In this paper, we introduce multipoles, a novel class of linear relationships between more than two time series. A multipole is a set of time series that have strong linear dependence among themselves, with the requirement that each time series makes a significant contribution to the linear dependence. We demonstrate that most interesting multipoles can be identified as cliques of negative correlations in a correlation network. Such cliques are typically rare in a real-world correlation network, which allows us to find almost all multipoles efficiently using a clique-enumeration approach. Using our proposed framework, we demonstrate the utility of multipoles in discovering new physical phenomena in two scientific domains: climate science and neuroscience. In particular, we discovered several multipole relationships that are reproducible in multiple other independent datasets and lead to novel domain insights.Comment: This is the accepted version of article submitted to IEEE Transactions on Knowledge and Data Engineering 201

Realization of Causal Representation Learning and Redefined DAG for Causal AI

DAG(Directed Acyclic Graph) from causal inference does not differentiate causal effects and correlated changes. And the general effect of a population is usually approximated by averaging correlations over all individuals. Since AI(Artificial Intelligence) enables large-scale structure modeling on big data, the complex hidden confoundings have made these approximation errors no longer ignorable but snowballed to considerable modeling bias - Such Causal Representation Bias (CRB) leads to many problems: ungeneralizable causal models, unrevealed individual-level features, hardly utilized causal knowledge in DL(Deep Learning), etc. In short, DAG must be redefined to enable a new framework for causal AI. The observational time series in statistics can only represent correlated changes, while the DL-based autoencoder can represent them as individualized feature changes in latent space to estimate the causal effects directly. In this paper, we introduce the redefined do-DAG to visualize CRB, propose a generic solution Causal Representation Learning (CRL) framework, along with a novel architecture for its realization, and experimentally verify the feasibility

Teaching deep learning causal effects improves predictive performance

Causal inference is a powerful statistical methodology for explanatory analysis and individualized treatment effect (ITE) estimation, a prominent causal inference task that has become a fundamental research problem. ITE estimation, when performed naively, tends to produce biased estimates. To obtain unbiased estimates, counterfactual information is needed, which is not directly observable from data. Based on mature domain knowledge, reliable traditional methods to estimate ITE exist. In recent years, neural networks have been widely used in clinical studies. Specifically, recurrent neural networks (RNN) have been applied to temporal Electronic Health Records (EHR) data analysis. However, RNNs are not guaranteed to automatically discover causal knowledge, correctly estimate counterfactual information, and thus correctly estimate the ITE. This lack of correct ITE estimates can hinder the performance of the model. In this work we study whether RNNs can be guided to correctly incorporate ITE-related knowledge and whether this improves predictive performance. Specifically, we first describe a Causal-Temporal Structure for temporal EHR data; then based on this structure, we estimate sequential ITE along the timeline, using sequential Propensity Score Matching (PSM); and finally, we propose a knowledge-guided neural network methodology to incorporate estimated ITE. We demonstrate on real-world and synthetic data (where the actual ITEs are known) that the proposed methodology can significantly improve the prediction performance of RNN.Comment: 9 pages, 8 figures, in the process of SDM 202