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Bayesian network is a complete model for the variables and their relationships, it can be used to answer probabilistic queries about them. A Bayesian network can thus be considered a mechanism for automatically applying Bayes' theorem to…
We present a new method to propagate lower bounds on conditional probability distributions in conventional Bayesian networks. Our method guarantees to provide outer approximations of the exact lower bounds. A key advantage is that we can…
A new method is developed to represent probabilistic relations on multiple random events. Where previously knowledge bases containing probabilistic rules were used for this purpose, here a probability distribution over the relations is…
Probability estimation is one of the fundamental tasks in statistics and machine learning. However, standard methods for probability estimation on discrete objects do not handle object structure in a satisfactory manner. In this paper, we…
In this paper we examine the problem of inference in Bayesian Networks with discrete random variables that have very large or even unbounded domains. For example, in a domain where we are trying to identify a person, we may have variables…
Recently several researchers have investigated techniques for using data to learn Bayesian networks containing compact representations for the conditional probability distributions (CPDs) stored at each node. The majority of this work has…
This work initiates a systematic investigation of testing high-dimensional structured distributions by focusing on testing Bayesian networks -- the prototypical family of directed graphical models. A Bayesian network is defined by a…
We consider the problem of selecting important nodes in a random network, where the nodes connect to each other randomly with certain transition probabilities. The node importance is characterized by the stationary probabilities of the…
Bayesian approaches to learn the graphical structure of Bayesian Belief Networks (BBNs) from databases share the assumption that the database is complete, that is, no entry is reported as unknown. Attempts to relax this assumption involve…
In this paper, we provide a method to learn the directed structure of a Bayesian network using data. The data is accessed by making conditional probability queries to a black-box model. We introduce a notion of simplicity of representation…
This paper presents analytical and experimental results on the ranked nodes method (RNM) that is used to construct conditional probability tables for Bayesian networks by expert elicitation. The majority of the results are focused on a…
Instead of requiring a domain expert to specify the probabilistic dependencies of the data, in this work we present an approach that uses the relational DB schema to automatically construct a Bayesian graphical model for a database. This…
This paper discusses a method for implementing a probabilistic inference system based on an extended relational data model. This model provides a unified approach for a variety of applications such as dynamic programming, solving sparse…
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…
The number of probability distributions required to populate a conditional probability table (CPT) in a Bayesian network, grows exponentially with the number of parent-nodes associated with that table. If the table is to be populated…
We develop simple methods for constructing likelihoods and parameter priors for learning about the parameters and structure of a Bayesian network. In particular, we introduce several assumptions that permit the construction of likelihoods…
A Bayesian network is a graphical model that encodes probabilistic relationships among variables of interest. When used in conjunction with statistical techniques, the graphical model has several advantages for data analysis. One, because…
This paper describes a Bayesian method for learning causal networks using samples that were selected in a non-random manner from a population of interest. Examples of data obtained by non-random sampling include convenience samples and…
In many supervised learning tasks, the entities to be labeled are related to each other in complex ways and their labels are not independent. For example, in hypertext classification, the labels of linked pages are highly correlated. A…
Conditional probabilities are a core concept in machine learning. For example, optimal prediction of a label $Y$ given an input $X$ corresponds to maximizing the conditional probability of $Y$ given $X$. A common approach to inference tasks…