Related papers: Determining the Dimension and Structure of the Sub…

Modular structure is pervasive in many complex networks of interactions observed in natural, social and technological sciences. Its study sheds light on the relation between the structure and function of complex systems. Generally speaking,…

We consider the problem of causal discovery (structure learning) from heterogeneous observational data. Most existing methods assume a homogeneous sampling scheme, which leads to misleading conclusions when violated in many applications. To…

Correlation matrices are an essential tool for investigating the dependency structures of random vectors or comparing them. We introduce an approach for testing a variety of null hypotheses that can be formulated based upon the correlation…

Quantifying the similarity between two mathematical structures or datasets constitutes a particularly interesting and useful operation in several theoretical and applied problems. Aimed at this specific objective, the Jaccard index has been…

Correlated topic modeling has been limited to small model and problem sizes due to their high computational cost and poor scaling. In this paper, we propose a new model which learns compact topic embeddings and captures topic correlations…

This paper studies the problem of testing whether a system of linear equality and inequality constraints admits a solution when the coefficients of that system may have to be estimated. We show that a wide range of inferential questions in…

Model-Based Diagnosis deals with the identification of the real cause of a system's malfunction based on a formal system model and observations of the system behavior. When a malfunction is detected, there is usually not enough information…

Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. The data sets themselves are explicitly linked as a form of representation to an observational or otherwise empirical…

Most data is multi-dimensional. Discovering whether any subset of dimensions, or subspaces, of such data is significantly correlated is a core task in data mining. To do so, we require a measure that quantifies how correlated a subspace is.…

Confounding matters in almost all observational studies that focus on causality. In order to eliminate bias caused by connfounders, oftentimes a substantial number of features need to be collected in the analysis. In this case, large p…

Scanning probe experiments such as scanning tunneling microscopy (STM) and atomic force microscopy (AFM) on strongly correlated electronic systems often reveal complex pattern formation on multiple length scales. By studying the universal…

We review the theory and practice of determining what parts of a data set are ultrametric. It is assumed that the data set, to begin with, is endowed with a metric, and we include discussion of how this can be brought about if a…

The role of the normalized modularity matrix in finding homogeneous cuts will be presented. We also discuss the testability of the structural eigenvalues and that of the subspace spanned by the corresponding eigenvectors of this matrix. In…

Many complex systems in nature and society can be described in terms of networks capturing the intricate web of connections among the units they are made of. A key question is how to interpret the global organization of such networks as the…

We intend to identify relationships between cancer cases and pollutant emissions and attempt to understand whether cancer in children is typically located together with some specific chemical combinations or is independent. Co-location…

Many learning problems require predicting sets of objects when the number of objects is not known beforehand. Examples include object detection, molecular modeling, and scientific inference tasks such as astrophysical source detection.…

Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. "Structure" can be understood as symmetry and a range of symmetries are expressed by hierarchy. Such symmetries directly…

In observational studies, the causal effect of a treatment may be confounded with variables that are related to both the treatment and the outcome of interest. In order to identify a causal effect, such studies often rely on the…

The dynamics of systems of interacting agents is determined by the structure of their coupling network. The knowledge of the latter is, therefore, highly desirable, for instance, to develop efficient control schemes, to accurately predict…

In this paper we establish links between, and new results for, three problems that are not usually considered together. The first is a matrix decomposition problem that arises in areas such as statistical modeling and signal processing:…