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In recent years there has been an increasing interest in learning Bayesian networks from data. One of the most effective methods for learning such networks is based on the minimum description length (MDL) principle. Previous work has shown…

Network lasso is a method for solving a multi-task learning problem through the regularized maximum likelihood method. A characteristic of network lasso is setting a different model for each sample. The relationships among the models are…

Bayesian Decision Trees are known for their probabilistic interpretability. However, their construction can sometimes be costly. In this article we present a general Bayesian Decision Tree algorithm applicable to both regression and…

Bayesian networks are now being used in enormous fields, for example, diagnosis of a system, data mining, clustering and so on. In spite of their wide range of applications, the statistical properties have not yet been clarified, because…

Causal discovery from empirical data is a fundamental problem in many scientific domains. Observational data allows for identifiability only up to Markov equivalence class. In this paper we first propose a polynomial time algorithm for…

Finding the most probable explanation for observed variables in a Bayesian network is a notoriously intractable problem, particularly if there are hidden variables in the network. In this paper we examine the complexity of a related…

We give a new consistent scoring function for structure learning of Bayesian networks. In contrast to traditional approaches to scorebased structure learning, such as BDeu or MDL, the complexity penalty that we propose is data-dependent and…

Bayesian learning is built on an assumption that the model space contains a true reflection of the data generating mechanism. This assumption is problematic, particularly in complex data environments. Here we present a Bayesian…

We consider a Bayesian method for learning the Bayesian network structure from complete data. Recently, Koivisto and Sood (2004) presented an algorithm that for any single edge computes its marginal posterior probability in O(n 2^n) time,…

Naive Bayes is a simple Bayesian classifier with strong independence assumptions among the attributes. This classifier, desipte its strong independence assumptions, often performs well in practice. It is believed that relaxing the…

Learning-based methods for inverse problems, adapting to the data's inherent structure, have become ubiquitous in the last decade. Besides empirical investigations of their often remarkable performance, an increasing number of works…

Gaussian graphical models provide a powerful framework to reveal the conditional dependency structure between multivariate variables. The process of uncovering the conditional dependency network is known as structure learning. Bayesian…

In this paper, we study learning and testing decision tree of size and depth that are significantly smaller than the number of attributes $n$. Our main result addresses the problem of poly$(n,1/\epsilon)$ time algorithms with…

A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…

Structural learning of directed acyclic graphs (DAGs) or Bayesian networks has been studied extensively under the assumption that data are independent. We propose a new Gaussian DAG model for dependent data which assumes the observations…

Neural networks (NN) have achieved state-of-the-art performance in various applications. Unfortunately in applications where training data is insufficient, they are often prone to overfitting. One effective way to alleviate this problem is…

Many algorithms for score-based Bayesian network structure learning (BNSL), in particular exact ones, take as input a collection of potentially optimal parent sets for each variable in the data. Constructing such collections naively is…

We study the optimal sample complexity of learning a Gaussian directed acyclic graph (DAG) from observational data. Our main results establish the minimax optimal sample complexity for learning the structure of a linear Gaussian DAG model…

We consider the problem of learning the structure of undirected graphical models with bounded treewidth, within the maximum likelihood framework. This is an NP-hard problem and most approaches consider local search techniques. In this…

In this article, the optimal sample complexity of learning the underlying interactions or dependencies of a Linear Dynamical System (LDS) over a Directed Acyclic Graph (DAG) is studied. We call such a DAG underlying an LDS as dynamical DAG…