Probabilistic graphical models have emerged as a powerful modeling tool for several real-world scenarios where one needs to reason under uncertainty. A graphical model's partition function is a central quantity of interest, and its computation is key to several probabilistic reasoning tasks. Given the #P-hardness of computing the partition function, several techniques have been proposed over the years with varying guarantees on the quality of estimates and their runtime behavior. This paper seeks to present a survey of 18 techniques and a rigorous empirical study of their behavior across an extensive set of benchmarks. Our empirical study draws up a surprising observation: exact techniques are as efficient as the approximate ones, and therefore, we conclude with an optimistic view of opportunities for the design of approximate techniques with enhanced scalability. Motivated by the observation of an order of magnitude difference between the Virtual Best Solver and the best performing tool, we envision an exciting line of research focused on the development of portfolio solvers.

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Introduction:Waldenstorm's macroglobulinemia (WM) is a type of indolent B cell lymphoma characterized by immunoglobulin M monoclonal gammopathy and bone marrow infiltration by lymphoplasmacytic cells. Being an uncommon hematologic malignancy, studies on epidemiology of this disease are limited. Median survival is 5-11 years and depends on disease progression, treatment complication and transformation to high-grade lymphoma. In the nationally representative database, we aimed to find out the trends and outcomes of hospitalizations primarily due to WM. Methods:We used National Inpatient Sample (NIS) for the years 2007-2017 by Healthcare Cost and Utilization Project. We extracted a study cohort of adult hospitalizations due to WM using International Classification of Diseases (9th/10th editions) Clinical Modification diagnosis codes. Our primary and secondary objectives were to estimate the trends of hospitalization and outcomes as well as identify predictors of poor outcomes. Poor outcomes were defined as in-hospital mortality and discharge to facility. We utilized Cochran Armitage trend test and multivariable survey regression modeling to analyze trends and predictors of poor outcomes using SAS software, version 9.4 (SAS Institute, North Carolina, USA). Results:We studied a total of 7,379 patients who were hospitalized with WM during 2007-2017. Overall from 2007 to 2017 the burden of hospitalizations has decreased from 804 to 645 . The cohort consisted of elderly patients with a median age of 69-years (IQR:61-78), 60.2% were males, 78% Caucasians, and 10.5% African American. Mean length of stay was 7-days which remained stable over the period. A decline in the proportion of WM patients being discharged to facility (20.1% in 2007 to 13.9% in 2017; pTrend<0.001) and in-hospital mortality (4.7% in 2007 to 2.3% in 2017; pTrend<0.001) was observed. Furthermore, in multivariable logistic regression analysis, rural hospitals (OR 4.3; 95%CI 1.5-12.4; p<0.001), lower median household income (OR 4.1; 95%CI 1.4-12.2; p<0.05) and concurrent conditions like septicemia (OR 10.7; 95%CI 4.2-26.7; p<0.001), and pulmonary circulatory disease (OR 3.6; 95%CI 1.4-9.1; p< 0.001) were associated with higher odds of in-hospital mortality. Conclusion:In this nationally representative study, we observed that the hospitalizations due to WM had mildly declined and outcomes were improved during the study period which might be an indication of improvements in treatment modalities. WM in benign state is rarely a grave prognosis and does not require frequent hospitalization but mortality is usually due to other comorbidities and hyperviscosity. We were able to identify several risk predictors that were associated with poor outcomes which require further studies to better risk stratification and develop preventive measures. Disclosures No relevant conflicts of interest to declare.

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Probabilistic graphical models have emerged as a powerful modeling tool for several real-world scenarios where one needs to reason under uncertainty. A graphical model's partition function is a central quantity of interest, and its computation is key to several probabilistic reasoning tasks. Given the #Phardness of computing the partition function, several techniques have been proposed over the years with varying guarantees on the quality of estimates and their runtime behavior. This paper seeks to present a survey of 18 techniques and a rigorous empirical study of their behavior across an extensive set of benchmarks. Our empirical study draws up a surprising observation: exact techniques are as efficient as the approximate ones, and therefore, we conclude with an optimistic view of opportunities for the design of approximate techniques with enhanced scalability. Motivated by the observation of an order of magnitude difference between the Virtual Best Solver and the best performing tool, we envision an exciting line of research focused on the development of portfolio solvers.