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13
Using Bayesian Networks for Bankruptcy Prediction: Some Methodological Issues
, 2006
"... This study provides operational guidance for using naïve Bayes Bayesian network (BN) models in bankruptcy prediction. First, we suggest a heuristic method that guides the selection of bankruptcy predictors from a pool of potential variables. The method is based upon the assumption that the joint dis ..."
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This study provides operational guidance for using naïve Bayes Bayesian network (BN) models in bankruptcy prediction. First, we suggest a heuristic method that guides the selection of bankruptcy predictors from a pool of potential variables. The method is based upon the assumption that the joint distribution of the variables is multivariate normal. Variables are selected based upon correlations and partial correlations information. A naïve Bayes model is developed using the proposed heuristic method and is found to perform well based upon a tenfold analysis, for both samples with complete information and samples with incomplete information. Second, we analyze whether the number of states into which continuous variables are discretized has an impact on a naïve Bayes model performance in bankruptcy prediction. We compare the model’s performance when continuous variables are discretized into two, three, …, ten, fifteen, and twenty states. Based upon a relatively large training sample, our results show that the naïve Bayes model’s performance increases when the number of states for discretization increases from two to three, and from three to four. Surprisingly, when the number of states increases to more than four, the model’s overall performance neither increases nor decreases. It
Learning Ground CPlogic Theories by means of Bayesian Network Techniques
"... Abstract. Causal relationships are present in many application domains. CPlogic is a probabilistic modeling language that is especially designed to express such relationships. This paper investigates the learning of CPtheories from examples, and focusses on structure learning. The proposed approac ..."
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Abstract. Causal relationships are present in many application domains. CPlogic is a probabilistic modeling language that is especially designed to express such relationships. This paper investigates the learning of CPtheories from examples, and focusses on structure learning. The proposed approach is based on a transformation between CPlogic theories and Bayesian networks, that is, the method applies Bayesian network learning techniques to learn a CPtheory in the form of an equivalent Bayesian network. We propose a constrained refinement operator for such networks that guarantees equivalence to a valid CPtheory. We experimentally compare our method to a standard method for learning Bayesian networks. This shows that CPtheories can be learned more efficiently than Bayesian networks given that causal relationships are present in the domain. 1
Knowledge Intensive Learning: Combining Qualitative Constraints with Causal Independence for Parameter Learning in Probabilistic Models
"... Abstract. In Bayesian networks, prior knowledge has been used in the form of causal independencies between random variables or as qualitative constraints such as monotonicities. In this work, we extend and combine the two different ways of providing domain knowledge. We derive an algorithm based on ..."
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Abstract. In Bayesian networks, prior knowledge has been used in the form of causal independencies between random variables or as qualitative constraints such as monotonicities. In this work, we extend and combine the two different ways of providing domain knowledge. We derive an algorithm based on gradient descent for estimating the parameters of a Bayesian network in the presence of causal independencies in the form of NoisyOr and qualitative constraints such as monotonicities and synergies. NoisyOr structure can decrease the data requirements by separating the influence of each parent thereby reducing greatly the number of parameters. Qualitative constraints on the other hand, allow for imposing constraints on the parameter space making it possible to learn more accurate parameters from a very small number of data points. Our exhaustive empirical validation conclusively proves that the synergy constrained NoisyOR leads to more accurate models in the presence of smaller amount of data. 1
EM Algorithm for Symmetric Causal Independence Models
"... Abstract. Causal independence modelling is a wellknown method both for reducing the size of probability tables and for explaining the underlying mechanisms in Bayesian networks. In this paper, we present the EM algorithm to learn the parameters in causal independence models based on the symmetric B ..."
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Abstract. Causal independence modelling is a wellknown method both for reducing the size of probability tables and for explaining the underlying mechanisms in Bayesian networks. In this paper, we present the EM algorithm to learn the parameters in causal independence models based on the symmetric Boolean function. The developed algorithm enables us to assess the practical usefulness of the symmetric causal independence models, which has not been done previously. We evaluate the classification performance of the symmetric causal independence models learned with the presented EM algorithm. The results show the competitive performance of these models in comparison to noisy OR and noisy AND models as well as other stateoftheart classifiers. 1
Symmetric causal independence models for classification
 In The third European Workshop on Probabilistic Graphical Models
, 2006
"... Causal independence modelling is a wellknown method both for reducing the size of probability tables and for explaining the underlying mechanisms in Bayesian networks. In this paper, we propose an application of an extended class of causal independence models, causal independence models based on th ..."
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Causal independence modelling is a wellknown method both for reducing the size of probability tables and for explaining the underlying mechanisms in Bayesian networks. In this paper, we propose an application of an extended class of causal independence models, causal independence models based on the symmetric Boolean function, for classification. We present an EM algorithm to learn the parameters of these models, and study convergence of the algorithm. Experimental results on the Reuters data collection show the competitive classification performance of causal independence models based on the symmetric Boolean function in comparison to noisy OR model and, consequently, with other stateoftheart classifiers. 1
Pattern Recognition
"... This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or sel ..."
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This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit:
Sisterhood of Classifiers: A Comparative Study of Naive Bayes and Noisyor Networks
"... Classification is a task central to many machine learning problems. In this paper we examine two Bayesian network classifiers, the naive Bayes and the noisyor models. They are of particular interest because of their simple structures. We compare them on two dimensions: expressive power and ability ..."
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Classification is a task central to many machine learning problems. In this paper we examine two Bayesian network classifiers, the naive Bayes and the noisyor models. They are of particular interest because of their simple structures. We compare them on two dimensions: expressive power and ability to learn. As it turns out, naive Bayes, noisyor, and logistic regression classifiers all have equivalent expressiveness. We show mathematical derivations of how to transform a classifer in one model into the other two. These classifiers differ on their ability to learn though. We conducted an experiment confirming the intuition that naive Bayes performs better than noisyor when the data fits its independence assumptions, and vice versa. However, we still do not have a clear set of criteria for determining under exactly what conditions would each classifier excel. Further study of the strenghts and weaknesses of each classifier should provide deeper insight on how to improve the current models. One possible extension would be to combine the naive Bayes and noisyor model so that the network will more closely depict the actual relationship between the attributes. 1
Variational Learning for NoisyOR Component Analysis
"... Latent factor models offer a very useful framework for modeling dependencies in highdimensional multivariate data. In this work we investigate a class of latent factor models with hidden noisyor units that let us decouple high dimensional vectors of observable binary random variables using a ’smal ..."
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Latent factor models offer a very useful framework for modeling dependencies in highdimensional multivariate data. In this work we investigate a class of latent factor models with hidden noisyor units that let us decouple high dimensional vectors of observable binary random variables using a ’small ’ number of hidden binary factors. Since the problem of learning of such models from data is intractable, we develop its variational approximation. We analyze special properties of the optimization problem, in particular its “builtin ” regularization effect and discuss its importance for model recovery. We test the noisyor model on an image deconvolution problem and illustrate the ability of the variational method to succesfully learn the underlying image components. Finally, we apply the latent noisyor model to analyze citations in a large collection of Statistical Machine Learning papers and show the benefit of the model and algorithms by discovering useful and semantically sound components characterizing the dataset.
LEARNING DIRECTED PROBABILISTIC LOGICAL MODELS FROM RELATIONAL DATA
"... Proefschrift voorgedragen tot het behalen van het doctoraat in de ingenieurswetenschappen door ..."
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Proefschrift voorgedragen tot het behalen van het doctoraat in de ingenieurswetenschappen door
IOS Press Learning Ground CPLogic Theories by Leveraging Bayesian Network Learning Techniques
"... Abstract. Causal relations are present in many application domains. Causal Probabilistic Logic (CPlogic) is a probabilistic modeling language that is especially designed to express such relations. This paper investigates the learning of CPlogic theories (CPtheories) from training data. Its first ..."
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Abstract. Causal relations are present in many application domains. Causal Probabilistic Logic (CPlogic) is a probabilistic modeling language that is especially designed to express such relations. This paper investigates the learning of CPlogic theories (CPtheories) from training data. Its first contribution is SEMCPlogic, an algorithm that learns CPtheories by leveraging Bayesian network (BN) learning techniques. SEMCPlogic is based on a transformation between CPtheories and BNs. That is, the method applies BN learning techniques to learn a CPtheory in the form of an equivalent BN. To this end, certain modifications are required to the BN parameter learning and structure search, the most important one being that the refinement operator used by the search must guarantee that the constructed BNs represent valid CPtheories. The paper’s second contribution is a theoretical and experimental comparison between CPtheory and BN learning. We show that the most simple CPtheories can be represented with BNs consisting of noisyOR nodes, while more complex theories require close to fully connected networks (unless additional unobserved nodes are introduced in the network). Experiments in a controlled artificial domain show that in the latter cases CPtheory learning with SEMCPlogic requires fewer training data than BN learning. We also apply SEMCPlogic in a medical application in the context of HIV research, and show that it can compete with stateoftheart methods in this domain. Keywords: Statistical Relational Learning, CPlogic