Related papers: Algorithms and Complexity Results for Exact Bayesi…
We consider the problem of learning Bayesian network classifiers that maximize the marginover a set of classification variables. We find that this problem is harder for Bayesian networks than for undirected graphical models like maximum…
The graph structure of a Bayesian network (BN) can be learned from data using the well-known score-and-search approach. Previous work has shown that incorporating structured representations of the conditional probability distributions…
The score-based structure learning of Bayesian network (BN) is an effective way to learn BN models, which are regarded as some of the most compelling probabilistic graphical models in the field of representation and reasoning under…
In this paper, we provide new complexity results for algorithms that learn discrete-variable Bayesian networks from data. Our results apply whenever the learning algorithm uses a scoring criterion that favors the simplest model able to…
The adaptive processing of structured data is a long-standing research topic in machine learning that investigates how to automatically learn a mapping from a structured input to outputs of various nature. Recently, there has been an…
The problem of learning the structure of Bayesian networks from complete discrete data with a limit on parent set size is considered. Learning is cast explicitly as an optimisation problem where the goal is to find a BN structure which…
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…
One of the basic tasks for Bayesian networks (BNs) is that of learning a network structure from data. The BN-learning problem is NP-hard, so the standard solution is heuristic search. Many approaches have been proposed for this task, but…
Gaussian Bayesian networks (a.k.a. linear Gaussian structural equation models) are widely used to model causal interactions among continuous variables. In this work, we study the problem of learning a fixed-structure Gaussian Bayesian…
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…
Causal Bayesian networks are widely used tools for summarising the dependencies between variables and elucidating their putative causal relationships. By restricting the search to trees, for example, learning the optimum from data is…
This dissertation investigates integer linear programming (ILP) formulation of Bayesian Network structure learning problem. We review the definition and key properties of Bayesian network and explain score metrics used to measure how well…
The fastest known exact algorithms for scorebased structure discovery in Bayesian networks on n nodes run in time and space 2nnO(1). The usage of these algorithms is limited to networks on at most around 25 nodes mainly due to the space…
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…
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…
This paper presents new results for the (partial) maximum a posteriori (MAP) problem in Bayesian networks, which is the problem of querying the most probable state configuration of some of the network variables given evidence. First, it is…
In this paper, we study the problem of structure learning for Bayesian networks in which nodes take discrete values. The problem is NP-hard in general but we show that under certain conditions we can recover the true structure of a Bayesian…
This paper builds on recent developments in Bayesian network (BN) structure learning under the controversial assumption that the input variables are dependent. This assumption can be viewed as a learning constraint geared towards cases…
Previous work has shown that the problem of learning the optimal structure of a Bayesian network can be formulated as a shortest path finding problem in a graph and solved using A* search. In this paper, we improve the scalability of this…
The maximum common subtree isomorphism problem asks for the largest possible isomorphism between subtrees of two given input trees. This problem is a natural restriction of the maximum common subgraph problem, which is ${\sf NP}$-hard in…