64,705 research outputs found
Learning Discrete Bayesian Networks from Continuous Data
Learning Bayesian networks from raw data can help provide insights into the relationships between variables. While real data often contains a mixture of discrete and continuous-valued variables, many Bayesian network structure learning algorithms assume all random variables are discrete. Thus, continuous variables are often discretized when learning a Bayesian network. However, the choice of discretization policy has significant impact on the accuracy, speed, and interpretability of the resulting models. This paper introduces a principled Bayesian discretization method for continuous variables in Bayesian networks with quadratic complexity instead of the cubic complexity of other standard techniques. Empirical demonstrations show that the proposed method is superior to the established minimum description length algorithm. In addition, this paper shows how to incorporate existing methods into the structure learning process to discretize all continuous variables and simultaneously learn Bayesian network structures
Learning Mixtures of Polynomials of Conditional Densities from Data
Mixtures of polynomials (MoPs) are a non-parametric density estimation technique for hybrid Bayesian networks with continuous and discrete variables. We propose two methods for learning MoP approximations of conditional densities from data. Both approaches are based on learning MoP approximations of the joint density and the marginal density of the conditioning variables, but they differ as to how the MoP approximation of the quotient of the two densities is found. We illustrate the methods using data sampled from a simple Gaussian Bayesian network. We study and compare the performance of these methods with the approach for learning mixtures of truncated basis functions from data
Hybrid Bayesian Networks Using Mixtures of Truncated Basis Functions
This paper introduces MoTBFs, an R package for manipulating mixtures of truncated basis functions. This class of functions allows the representation of joint probability distributions involving discrete and continuous variables simultaneously, and includes mixtures of truncated exponentials and mixtures of polynomials as special cases. The package implements functions for learning the parameters of univariate, multivariate, and conditional distributions, and provides support for parameter learning in Bayesian networks with both discrete and continuous variables. Probabilistic inference using forward sampling is also implemented. Part of the functionality of the
MoTBFs package relies on the bnlearn package, which includes functions for learning the structure of a Bayesian network from a data set. Leveraging this functionality, the MoTBFs package supports learning of MoTBF-based Bayesian networks over hybrid domains. We give a brief introduction to the methodological context and algorithms implemented in the package. An extensive illustrative example is used to describe the package, its functionality, and its usage
Parameter Learning for Hybrid Bayesian Networks With Gaussian Mixture and Dirac Mixture Conditional Densities
In this paper, the first algorithm for learning hybrid Bayesian Networks with Gaussian mixture and Dirac mixture conditional densities from data given their structure is presented. The mixture densities to be learned allow for nonlinear dependencies between the variables and exact closedform inference. For learning the network\u27s parameters, an incremental gradient ascent algorithm is derived. Analytic expressions for the partial derivatives and their combination with messages are presented. This hybrid approach subsumes the existing approach for purely discrete-valued networks and is applicable to partially observable networks, too. Its practicability is demonstrated by a reference example
Numeric Input Relations for Relational Learning with Applications to Community Structure Analysis
Most work in the area of statistical relational learning (SRL) is focussed on
discrete data, even though a few approaches for hybrid SRL models have been
proposed that combine numerical and discrete variables. In this paper we
distinguish numerical random variables for which a probability distribution is
defined by the model from numerical input variables that are only used for
conditioning the distribution of discrete response variables. We show how
numerical input relations can very easily be used in the Relational Bayesian
Network framework, and that existing inference and learning methods need only
minor adjustments to be applied in this generalized setting. The resulting
framework provides natural relational extensions of classical probabilistic
models for categorical data. We demonstrate the usefulness of RBN models with
numeric input relations by several examples.
In particular, we use the augmented RBN framework to define probabilistic
models for multi-relational (social) networks in which the probability of a
link between two nodes depends on numeric latent feature vectors associated
with the nodes. A generic learning procedure can be used to obtain a
maximum-likelihood fit of model parameters and latent feature values for a
variety of models that can be expressed in the high-level RBN representation.
Specifically, we propose a model that allows us to interpret learned latent
feature values as community centrality degrees by which we can identify nodes
that are central for one community, that are hubs between communities, or that
are isolated nodes. In a multi-relational setting, the model also provides a
characterization of how different relations are associated with each community
Penalized Estimation of Directed Acyclic Graphs From Discrete Data
Bayesian networks, with structure given by a directed acyclic graph (DAG),
are a popular class of graphical models. However, learning Bayesian networks
from discrete or categorical data is particularly challenging, due to the large
parameter space and the difficulty in searching for a sparse structure. In this
article, we develop a maximum penalized likelihood method to tackle this
problem. Instead of the commonly used multinomial distribution, we model the
conditional distribution of a node given its parents by multi-logit regression,
in which an edge is parameterized by a set of coefficient vectors with dummy
variables encoding the levels of a node. To obtain a sparse DAG, a group norm
penalty is employed, and a blockwise coordinate descent algorithm is developed
to maximize the penalized likelihood subject to the acyclicity constraint of a
DAG. When interventional data are available, our method constructs a causal
network, in which a directed edge represents a causal relation. We apply our
method to various simulated and real data sets. The results show that our
method is very competitive, compared to many existing methods, in DAG
estimation from both interventional and high-dimensional observational data.Comment: To appear in Statistics and Computin
Learning the structure of Bayesian Networks: A quantitative assessment of the effect of different algorithmic schemes
One of the most challenging tasks when adopting Bayesian Networks (BNs) is
the one of learning their structure from data. This task is complicated by the
huge search space of possible solutions, and by the fact that the problem is
NP-hard. Hence, full enumeration of all the possible solutions is not always
feasible and approximations are often required. However, to the best of our
knowledge, a quantitative analysis of the performance and characteristics of
the different heuristics to solve this problem has never been done before.
For this reason, in this work, we provide a detailed comparison of many
different state-of-the-arts methods for structural learning on simulated data
considering both BNs with discrete and continuous variables, and with different
rates of noise in the data. In particular, we investigate the performance of
different widespread scores and algorithmic approaches proposed for the
inference and the statistical pitfalls within them
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