Related papers: On Conditional Independence Graph Learning From Mu…
Gaussian Graphical Models (GGMs) have wide-ranging applications in machine learning and the natural and social sciences. In most of the settings in which they are applied, the number of observed samples is much smaller than the dimension…
This thesis studies two problems in modern statistics. First, we study selective inference, or inference for hypothesis that are chosen after looking at the data. The motiving application is inference for regression coefficients selected by…
The graphoid axioms for conditional independence, originally described by Dawid [1979], are fundamental to probabilistic reasoning [Pearl, 19881. Such axioms provide a mechanism for manipulating conditional independence assertions without…
The dependencies of the lagged (Pearson) correlation function on the coefficients of multivariate autoregressive models are interpreted in the framework of time series graphs. Time series graphs are related to the concept of Granger…
Learning the dependence structure among variables in complex systems is a central problem across medical, natural, and social sciences. These structures can be naturally represented by graphs, and the task of inferring such graphs from data…
Standard likelihood penalties to learn Gaussian graphical models are based on regularising the off-diagonal entries of the precision matrix. Such methods, and their Bayesian counterparts, are not invariant to scalar multiplication of the…
A scenario-based testing approach can reduce the time required to obtain statistically significant evidence of the safety of Automated Driving Systems (ADS). Identifying these scenarios in an automated manner is a challenging task. Most…
The edge structure of the graph defining an undirected graphical model describes precisely the structure of dependence between the variables in the graph. In many applications, the dependence structure is unknown and it is desirable to…
Covariate-dependent graph learning has gained increasing interest in the graphical modeling literature for the analysis of heterogeneous data. This task, however, poses challenges to modeling, computational efficiency, and interpretability.…
Graphical models express conditional independence relationships among variables. Although methods for vector-valued data are well established, functional data graphical models remain underdeveloped. We introduce a notion of conditional…
Learning the directed acyclic graph (DAG) structure of a Bayesian network from observational data is a notoriously difficult problem for which many hardness results are known. In this paper we propose a provably polynomial-time algorithm…
Gaussian Graphical Models provide a convenient framework for representing dependencies between variables. Recently, this tool has received a high interest for the discovery of biological networks. The literature focuses on the case where a…
Decoding complex relationships among large numbers of variables with relatively few observations is one of the crucial issues in science. One approach to this problem is Gaussian graphical modeling, which describes conditional independence…
Multistep traffic forecasting on road networks is a crucial task in successful intelligent transportation system applications. To capture the complex non-stationary temporal dynamics and spatial dependency in multistep traffic-condition…
Computer-aided diagnosis (CADx) has become vital in medical imaging, but automated systems often struggle to replicate the nuanced process of clinical interpretation. Expert diagnosis requires a comprehensive analysis of how abnormalities…
Graphical models are widely used in scienti fic and engineering research to represent conditional independence structures between random variables. In many controlled experiments, environmental changes or external stimuli can often alter…
Modeling multivariate time series has long been a subject that has attracted researchers from a diverse range of fields including economics, finance, and traffic. A basic assumption behind multivariate time series forecasting is that its…
Directed acyclic graphs (DAGs) are commonly used to represent causal relationships among random variables in graphical models. Applications of these models arise in the study of physical, as well as biological systems, where directed edges…
Suppose that we observe a short time series where each time-t-specific data-structure consists of many slightly dependent data indexed by a and that we want to estimate a feature of the law of the experiment that depends neither on t nor on…
We study Granger causality in the context of wide-sense stationary time series, where our focus is on the topological aspects of the underlying causality graph. We establish sufficient conditions (in particular, we develop the notion of a…