Marek Druzdzel is a professor in the School of Information Sciences and in the Intelligent Systems Program and the director of the Decision Systems Laboratory at the University of Pittsburgh. He holds a joint appointment as a visiting professor in the Computer Science Department, Bialystok University of Technology, Poland. He received his M.S. degrees in Computer Science (1985) and Electrical Engineering (1987) from the Delft University of Technology in The Netherlands (both with distinction) and his Ph.D. in Engineering and Public Policy (1992) from Carnegie Mellon University, Pittsburgh, PA, USA. Prof. Druzdzel is a recipient of the Faculty Early Career Development Grant (known as CAREER grant) from the National Science Foundation (1996-2000), Outstanding Mentor Award (1997), and University of Pittsburgh’s Chancellor’s Distinguished Teaching Award (2007). He is also a fellow of the Collegium of Eminent Scientists, Kosciuszko Foundation and recipient of the 2009-2010 and 2015-2016 Fulbright Awards for teaching and research at the Bialystok University of Technology. His research interests concentrate on probabilistic and decision theoretic methods in decision support systems and human aspect of decision support. His laboratory is widely known for the graphical modeling software GeNIe and SMILE, recently commercialized and available for academic teaching and research use at http://www.bayesfusion.com/. More details about Prof. Druzdzel’s research interests and publications are available on line at http://www.pitt.edu/~druzdzel. Address: Pittsburgh, Pennsylvania, United States
Maximum a Posteriori assignment (MAP) is the problem of finding the most probable instantiation o... more Maximum a Posteriori assignment (MAP) is the problem of finding the most probable instantiation of a set of variables given the partial evidence on the other variables in a Bayesian network. MAP has been shown to be a NP-hard problem [22], even for constrained networks, such as polytrees [18]. Hence, previous approaches often fail to yield any results for MAP problems in large complex Bayesian networks. To address this problem, we propose AnnealedMAP algorithm, a simulated annealing-based MAP algorithm. The AnnealedMAP algorithm simulates a non-homogeneous Markov chain whose invariant function is a probability density that concentrates itself on the modes of the target density. We tested this algorithm on several real Bayesian networks. The results show that, while maintaining good quality of the MAP solutions, the AnnealedMAP algorithm is also able to solve many problems that are beyond the reach of previous approaches.
BackgroundIn the era of extensive data collection, there is a growing need for a large scale data... more BackgroundIn the era of extensive data collection, there is a growing need for a large scale data analysis with tools that can handle many variables in one modeling framework. In this article, we present our recent applications of Bayesian network modeling to pathology informatics.MethodsBayesian networks (BNs) are probabilistic graphical models that represent domain knowledge and allow investigators to process this knowledge following sound rules of probability theory. BNs can be built based on expert opinion as well as learned from accumulating data sets. BN modeling is now recognized as a suitable approach for knowledge representation and reasoning under uncertainty. Over the last two decades BN have been successfully applied to many studies on medical prognosis and diagnosis.ResultsBased on data and expert knowledge, we have constructed several BN models to assess patient risk for subsequent specific histopathologic diagnoses and their related prognosis in gynecological cytopath...
A researcher testing a model will frequently question the reliability of the test results, unders... more A researcher testing a model will frequently question the reliability of the test results, understanding well the intuition that verification performed on a handful of cases is less reliable than verification based on very large numbers of cases. Because a limited number of verification cases happens pretty often in very specific domains, a question of practical importance is, thus, how reliable is a reported reliability measure. We propose a methodology based on deriving confidence intervals over various measures of accuracy of Bayesian network models by means of bootstrap confidence intervals. We evaluate our approach on ROC and calibration curves derived for a model derived from an UC Irvine Machine Learning Repository data set and a sizeable (over 300 variables) practical model constructed using expert knowledge and evaluated on merely 66 accumulated real patient cases. We show how increasing the number of test cases impacts the width of confidence intervals and how this can aid...
Given a good importance function, importance sampling is able to achieve satisfactory precisions ... more Given a good importance function, importance sampling is able to achieve satisfactory precisions within a reasonable time. In addition to the well known requirement that the importance function should have a similar shape to the target density (Rubinstein, 1981), it is also highly recommended that the importance function possess heavy tails (Geweke, 1989; MacKay, 1998; Yuan and Druzdzel, 2004). To achieve this, the -cutoff heuristic (Cheng and Druzdzel, 2000; Yuan and Druzdzel, 2003) was used to cut off extremely small probabilities in the importance function (Yuan and Druzdzel, 2003). However, cutoff demonstrates inconsistent performance on different networks. In this paper, we analyze the underlying reasons and propose another heuristic, if-tempering, based on simulated tempering. We test the new heuristic on three large real Bayesian networks and observe that if-tempering consistently helps the EPIS-BN algorithm (Yuan and Druzdzel, 2003) achieve better precisions than -cutoff.
Cox’s proportional hazard (CPH) model is a statistical technique that captures the interaction be... more Cox’s proportional hazard (CPH) model is a statistical technique that captures the interaction between a set of risk factors and an effect variable. While the CPH model is popular in survival analysis, Bayesian networks offer an attractive alternative that is intuitive, general, theoretically sound, and avoids CPH model’s restrictive assumptions. Existing CPH models are a great source of existing knowledge that can be reused in Bayesian networks. The main problem with applying Bayesian networks to survival analysis is their exponential growth in complexity as the number of risk factors increases. It is not uncommon to see complex CPH models with as many as 20 risk factors. Our paper focuses on making large survival analysis models derived from the CPH model tractable in Bayesian networks. We evaluate the effect of two complexity reduction techniques: (1) parent divorcing, and (2) removing less important risk factors based on the accuracy of the resulting models.
We describe a performance budget planning model developed for a research university, comprised of... more We describe a performance budget planning model developed for a research university, comprised of a set of 88 key variables and 38 non-linear structural equations that describe interactions among them. These equations, based on the knowledge of research university’s financial working and theoretical considerations, relate expenditures and revenues to teaching and research operations. We demonstrate the value of this model for developing insight into the financial structure of the university. In particular, we show how the model aids in (1) comparing the effect of various policy alternatives on the performance of the university, (2) performing comparative statics analysis of any subset of variables of interest, (3) choice of policy variables and policy alternatives, and (4) gaining insight into the structure of the interactions for a given policy alternative in terms of the causal chain between policy variables and outcome variables. We also describe a computer implementation of the model and discuss a class of mathematical tools for policy planning analysis that facilitate the use and manipulation of models based on sets of nonlinear constraints.
In this practical application, we describe the steps to build a decision-support tool using GeNIe... more In this practical application, we describe the steps to build a decision-support tool using GeNIe 2.1 software. The method incorporates principles of decision analyses and allows for a systematic strategy to balance treatment efficacy data with patient preferences. We illustrate the utility for helping clinicians and patients choose between two or more efficacious treatment options (CBT, medication, or their combination). Preliminary pilot data from families (n = 5) seeking services at a specialty clinic for childhood anxiety disorders support the usability of the tool and high patient satisfaction. We use case examples and sample graphical output to illustrate how the decision-support system can be used to integrate data on, 1) baseline symptom severity 2) the relative effectiveness of two or more treatment options, and 3) patient preferences and values, to arrive at a personalized treatment recommendation. The decision-support tool enabled child and parent preferences to be explicitly stated and facilitated discussions about how best to incorporate their preferences into an evidenced-based treatment strategy.
Maximum a Posteriori assignment (MAP) is the problem of finding the most probable instantiation o... more Maximum a Posteriori assignment (MAP) is the problem of finding the most probable instantiation of a set of variables given the partial evidence on the other variables in a Bayesian network. MAP has been shown to be a NP-hard problem [22], even for constrained networks, such as polytrees [18]. Hence, previous approaches often fail to yield any results for MAP problems in large complex Bayesian networks. To address this problem, we propose AnnealedMAP algorithm, a simulated annealing-based MAP algorithm. The AnnealedMAP algorithm simulates a non-homogeneous Markov chain whose invariant function is a probability density that concentrates itself on the modes of the target density. We tested this algorithm on several real Bayesian networks. The results show that, while maintaining good quality of the MAP solutions, the AnnealedMAP algorithm is also able to solve many problems that are beyond the reach of previous approaches.
BackgroundIn the era of extensive data collection, there is a growing need for a large scale data... more BackgroundIn the era of extensive data collection, there is a growing need for a large scale data analysis with tools that can handle many variables in one modeling framework. In this article, we present our recent applications of Bayesian network modeling to pathology informatics.MethodsBayesian networks (BNs) are probabilistic graphical models that represent domain knowledge and allow investigators to process this knowledge following sound rules of probability theory. BNs can be built based on expert opinion as well as learned from accumulating data sets. BN modeling is now recognized as a suitable approach for knowledge representation and reasoning under uncertainty. Over the last two decades BN have been successfully applied to many studies on medical prognosis and diagnosis.ResultsBased on data and expert knowledge, we have constructed several BN models to assess patient risk for subsequent specific histopathologic diagnoses and their related prognosis in gynecological cytopath...
A researcher testing a model will frequently question the reliability of the test results, unders... more A researcher testing a model will frequently question the reliability of the test results, understanding well the intuition that verification performed on a handful of cases is less reliable than verification based on very large numbers of cases. Because a limited number of verification cases happens pretty often in very specific domains, a question of practical importance is, thus, how reliable is a reported reliability measure. We propose a methodology based on deriving confidence intervals over various measures of accuracy of Bayesian network models by means of bootstrap confidence intervals. We evaluate our approach on ROC and calibration curves derived for a model derived from an UC Irvine Machine Learning Repository data set and a sizeable (over 300 variables) practical model constructed using expert knowledge and evaluated on merely 66 accumulated real patient cases. We show how increasing the number of test cases impacts the width of confidence intervals and how this can aid...
Given a good importance function, importance sampling is able to achieve satisfactory precisions ... more Given a good importance function, importance sampling is able to achieve satisfactory precisions within a reasonable time. In addition to the well known requirement that the importance function should have a similar shape to the target density (Rubinstein, 1981), it is also highly recommended that the importance function possess heavy tails (Geweke, 1989; MacKay, 1998; Yuan and Druzdzel, 2004). To achieve this, the -cutoff heuristic (Cheng and Druzdzel, 2000; Yuan and Druzdzel, 2003) was used to cut off extremely small probabilities in the importance function (Yuan and Druzdzel, 2003). However, cutoff demonstrates inconsistent performance on different networks. In this paper, we analyze the underlying reasons and propose another heuristic, if-tempering, based on simulated tempering. We test the new heuristic on three large real Bayesian networks and observe that if-tempering consistently helps the EPIS-BN algorithm (Yuan and Druzdzel, 2003) achieve better precisions than -cutoff.
Cox’s proportional hazard (CPH) model is a statistical technique that captures the interaction be... more Cox’s proportional hazard (CPH) model is a statistical technique that captures the interaction between a set of risk factors and an effect variable. While the CPH model is popular in survival analysis, Bayesian networks offer an attractive alternative that is intuitive, general, theoretically sound, and avoids CPH model’s restrictive assumptions. Existing CPH models are a great source of existing knowledge that can be reused in Bayesian networks. The main problem with applying Bayesian networks to survival analysis is their exponential growth in complexity as the number of risk factors increases. It is not uncommon to see complex CPH models with as many as 20 risk factors. Our paper focuses on making large survival analysis models derived from the CPH model tractable in Bayesian networks. We evaluate the effect of two complexity reduction techniques: (1) parent divorcing, and (2) removing less important risk factors based on the accuracy of the resulting models.
We describe a performance budget planning model developed for a research university, comprised of... more We describe a performance budget planning model developed for a research university, comprised of a set of 88 key variables and 38 non-linear structural equations that describe interactions among them. These equations, based on the knowledge of research university’s financial working and theoretical considerations, relate expenditures and revenues to teaching and research operations. We demonstrate the value of this model for developing insight into the financial structure of the university. In particular, we show how the model aids in (1) comparing the effect of various policy alternatives on the performance of the university, (2) performing comparative statics analysis of any subset of variables of interest, (3) choice of policy variables and policy alternatives, and (4) gaining insight into the structure of the interactions for a given policy alternative in terms of the causal chain between policy variables and outcome variables. We also describe a computer implementation of the model and discuss a class of mathematical tools for policy planning analysis that facilitate the use and manipulation of models based on sets of nonlinear constraints.
In this practical application, we describe the steps to build a decision-support tool using GeNIe... more In this practical application, we describe the steps to build a decision-support tool using GeNIe 2.1 software. The method incorporates principles of decision analyses and allows for a systematic strategy to balance treatment efficacy data with patient preferences. We illustrate the utility for helping clinicians and patients choose between two or more efficacious treatment options (CBT, medication, or their combination). Preliminary pilot data from families (n = 5) seeking services at a specialty clinic for childhood anxiety disorders support the usability of the tool and high patient satisfaction. We use case examples and sample graphical output to illustrate how the decision-support system can be used to integrate data on, 1) baseline symptom severity 2) the relative effectiveness of two or more treatment options, and 3) patient preferences and values, to arrive at a personalized treatment recommendation. The decision-support tool enabled child and parent preferences to be explicitly stated and facilitated discussions about how best to incorporate their preferences into an evidenced-based treatment strategy.
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