Correlation-based Data Representation

The Dagstuhl Seminar \u27Similarity-based Clustering and its Application to Medicine and Biology\u27 (07131) held in March 25--30, 2007, provided an excellent atmosphere for in-depth discussions about the research frontier of computational methods for relevant applications of biomedical clustering and beyond. We address some highlighted issues about correlation-based data analysis in this seminar postribution. First, some prominent correlation measures are briefly revisited. Then, a focus is put on Pearson correlation, because of its widespread use in biomedical sciences and because of its analytic accessibility. A connection to Euclidean distance of z-score transformed data outlined. Cost function optimization of correlation-based data representation is discussed for which, finally, applications to visualization and clustering of gene expression data are given

Common Representation Learning Using Step-based Correlation Multi-Modal CNN

Deep learning techniques have been successfully used in learning a common representation for multi-view data, wherein the different modalities are projected onto a common subspace. In a broader perspective, the techniques used to investigate common representation learning falls under the categories of canonical correlation-based approaches and autoencoder based approaches. In this paper, we investigate the performance of deep autoencoder based methods on multi-view data. We propose a novel step-based correlation multi-modal CNN (CorrMCNN) which reconstructs one view of the data given the other while increasing the interaction between the representations at each hidden layer or every intermediate step. Finally, we evaluate the performance of the proposed model on two benchmark datasets - MNIST and XRMB. Through extensive experiments, we find that the proposed model achieves better performance than the current state-of-the-art techniques on joint common representation learning and transfer learning tasks.Comment: Accepted in Asian Conference of Pattern Recognition (ACPR-2017

Multiplicity dependence of identical particle correlations in the quantum optical approach

Identical particle correlations at fixed multiplicity are consideres in the presence of chaotic and coherent fields. The multiplicity distribution, one-particle momentum density, and two-particle correlation function are obtained based on the diagrammatic representation for cmulants in semi-inclusive events. Our formulation is applied to the analysis of the experimental data on the multiplicity dependence of correlation functions reported by the UA1 and the OPAL Collaborations.Comment: 14 pages, 7 figure

H-matrix accelerated second moment analysis for potentials with rough correlation

We consider the efficient solution of partial differential equationsfor strongly elliptic operators with constant coefficients and stochastic Dirichlet data by the boundary integral equation method. The computation of the solution's two-point correlation is well understood if the two-point correlation of the Dirichlet data is known and sufficiently smooth.Unfortunately, the problem becomes much more involved in case of rough data. We will show that the concept of the H-matrix arithmetic provides a powerful tool to cope with this problem. By employing a parametric surface representation, we end up with an H-matrix arithmetic based on balanced cluster trees. This considerably simplifies the implementation and improves the performance of the H-matrix arithmetic. Numerical experiments are provided to validate and quantify the presented methods and algorithms

CausaLM: Causal Model Explanation Through Counterfactual Language Models

Understanding predictions made by deep neural networks is notoriously difficult, but also crucial to their dissemination. As all ML-based methods, they are as good as their training data, and can also capture unwanted biases. While there are tools that can help understand whether such biases exist, they do not distinguish between correlation and causation, and might be ill-suited for text-based models and for reasoning about high level language concepts. A key problem of estimating the causal effect of a concept of interest on a given model is that this estimation requires the generation of counterfactual examples, which is challenging with existing generation technology. To bridge that gap, we propose CausaLM, a framework for producing causal model explanations using counterfactual language representation models. Our approach is based on fine-tuning of deep contextualized embedding models with auxiliary adversarial tasks derived from the causal graph of the problem. Concretely, we show that by carefully choosing auxiliary adversarial pre-training tasks, language representation models such as BERT can effectively learn a counterfactual representation for a given concept of interest, and be used to estimate its true causal effect on model performance. A byproduct of our method is a language representation model that is unaffected by the tested concept, which can be useful in mitigating unwanted bias ingrained in the data.Comment: Our code and data are available at: https://amirfeder.github.io/CausaLM/ Under review for the Computational Linguistics journa