Related papers: Learning the Dimensionality of Hidden Variables
Learning the structure of dependencies among multiple random variables is a problem of considerable theoretical and practical interest. Within the context of Bayesian Networks, a practical and surprisingly successful solution to this…
In this paper we investigate the geometry of the likelihood of the unknown parameters in a simple class of Bayesian directed graphs with hidden variables. This enables us, before any numerical algorithms are employed, to obtain certain…
In this paper we address the problem of discretization in the context of learning Bayesian networks (BNs) from data containing both continuous and discrete variables. We describe a new technique for <EM>multivariate</EM> discretization,…
We consider the problem of model-based clustering in the presence of many correlated, mixed continuous and discrete variables, some of which may have missing values. Discrete variables are treated with a latent continuous variable approach…
Hidden Markov models (HMM) have been widely used by scientists to model stochastic systems: the underlying process is a discrete Markov chain and the observations are noisy realizations of the underlying process. Determining the number of…
Identifiability of parameters is an essential property for a statistical model to be useful in most settings. However, establishing parameter identifiability for Bayesian networks with hidden variables remains challenging. In the context of…
In recent years, there is a growing interest in learning Bayesian networks with continuous variables. Learning the structure of such networks is a computationally expensive procedure, which limits most applications to parameter learning.…
Testing the validity of probabilistic models containing unmeasured (hidden) variables is shown to be a hard task. We show that the task of testing whether models are structurally incompatible with the data at hand, requires an exponential…
All physical laws are described as relationships between state variables that give a complete and non-redundant description of the relevant system dynamics. However, despite the prevalence of computing power and AI, the process of…
In many networks, vertices have hidden attributes, or types, that are correlated with the networks topology. If the topology is known but these attributes are not, and if learning the attributes is costly, we need a method for choosing…
Statistical learning in high-dimensional spaces is challenging without a strong underlying data structure. Recent advances with foundational models suggest that text and image data contain such hidden structures, which help mitigate the…
Data clustering, including problems such as finding network communities, can be put into a systematic framework by means of a Bayesian approach. The application of Bayesian approaches to real problems can be, however, quite challenging. In…
Machine learning provides algorithms that can learn from data and make inferences or predictions on data. Bayesian networks are a class of graphical models that allow to represent a collection of random variables and their condititional…
Connectivity estimation is challenging in the context of high-dimensional data. A useful preprocessing step is to group variables into clusters, however, it is not always clear how to do so from the perspective of connectivity estimation.…
Dynamical models underpin our ability to understand and predict the behavior of natural systems. Whether dynamical models are developed from first-principles derivations or from observational data, they are predicated on our choice of state…
Variable selection, also known as feature selection in machine learning, plays an important role in modeling high dimensional data and is key to data-driven scientific discoveries. We consider here the problem of detecting influential…
This thesis responds to the challenges of using a large number, such as thousands, of features in regression and classification problems. There are two situations where such high dimensional features arise. One is when high dimensional…
As technology advanced, collecting data via automatic collection devices become popular, thus we commonly face data sets with lengthy variables, especially when these data sets are collected without specific research goals beforehand. It…
Latent variable models are used to estimate variables of interest quantities which are observable only up to some measurement error. In many studies, such variables are known but not precisely quantifiable (such as "job satisfaction" in…
Biclustering is used for simultaneous clustering of the observations and variables when there is no group structure known \textit{a priori}. It is being increasingly used in bioinformatics, text analytics, etc. Previously, biclustering has…