Related papers: Learning Bayesian Networks with Low Rank Condition…
A Bayesian net (BN) is more than a succinct way to encode a probabilistic distribution; it also corresponds to a function used to answer queries. A BN can therefore be evaluated by the accuracy of the answers it returns. Many algorithms for…
When the historical data are limited, the conditional probabilities associated with the nodes of Bayesian networks are uncertain and can be empirically estimated. Second order estimation methods provide a framework for both estimating the…
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…
In recent years there has been a flurry of works on learning Bayesian networks from data. One of the hard problems in this area is how to effectively learn the structure of a belief network from incomplete data- that is, in the presence of…
This paper identifies a structural property of data distributions that enables deep neural networks to learn hierarchically. We define the "staircase" property for functions over the Boolean hypercube, which posits that high-order Fourier…
We develop the theory and practice of an approach to modelling and probabilistic inference in causal networks that is suitable when application-specific or analysis-specific constraints should inform such inference or when little or no data…
Methods for learning Bayesian network structure can discover dependency structure between observed variables, and have been shown to be useful in many applications. However, in domains that involve a large number of variables, the space of…
We study constraint-based structure learning of Markov networks and Bayesian networks in the presence of an unreliable conditional independence oracle that makes at most a bounded number of errors. For Markov networks, we observe that a low…
To learn (statistical) dependencies among random variables requires exponentially large sample size in the number of observed random variables if any arbitrary joint probability distribution can occur. We consider the case that sparse data…
Bayesian networks are probabilistic graphical models widely employed to understand dependencies in high dimensional data, and even to facilitate causal discovery. Learning the underlying network structure, which is encoded as a directed…
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…
Joint distributions over many variables are frequently modeled by decomposing them into products of simpler, lower-dimensional conditional distributions, such as in sparsely connected Bayesian networks. However, automatically learning such…
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 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…
We study the problem of learning the Markov order in categorical sequences that represent paths in a network, i.e. sequences of variable lengths where transitions between states are constrained to a known graph. Such data pose challenges…
Many learning tasks require observing a sequence of images and making a decision. In a transportation problem of designing and planning for shipping boxes between nodes, we show how to treat the network of nodes and the flows between them…
Contagion processes are strongly linked to the network structures on which they propagate, and learning these structures is essential for understanding and intervention on complex network processes such as epidemics and (mis)information…
In a Bayesian network, we wish to evaluate the marginal probability of a query variable, which may be conditioned on the observed values of some evidence variables. Here we first present our "border algorithm," which converts a BN into a…
We study the Bayesian model averaging approach to learning Bayesian network structures (DAGs) from data. We develop new algorithms including the first algorithm that is able to efficiently sample DAGs according to the exact structure…
Despite several advances in recent years, learning causal structures represented by directed acyclic graphs (DAGs) remains a challenging task in high dimensional settings when the graphs to be learned are not sparse. In this paper, we…