Discovering a junction tree behind a Markov network by a greedy algorithm

In an earlier paper we introduced a special kind of k-width junction tree, called k-th order t-cherry junction tree in order to approximate a joint probability distribution. The approximation is the best if the Kullback-Leibler divergence between the true joint probability distribution and the approximating one is minimal. Finding the best approximating k-width junction tree is NP-complete if k>2. In our earlier paper we also proved that the best approximating k-width junction tree can be embedded into a k-th order t-cherry junction tree. We introduce a greedy algorithm resulting very good approximations in reasonable computing time. In this paper we prove that if the Markov network underlying fullfills some requirements then our greedy algorithm is able to find the true probability distribution or its best approximation in the family of the k-th order t-cherry tree probability distributions. Our algorithm uses just the k-th order marginal probability distributions as input. We compare the results of the greedy algorithm proposed in this paper with the greedy algorithm proposed by Malvestuto in 1991.Comment: The paper was presented at VOCAL 2010 in Veszprem, Hungar

Nemkonvex és diszkrét sztochasztikus programozási feladatok megoldása és alkalmazása = Solution and applications of nonconvex and discrete stochastic programming problems

A nemkonvex feladatok megoldására három területen is lényeges haladást értünk el: a valószínűségek kiszámítása, általános sztochasztikus feladatok optimalizálásában és a diszkrét sztochasztikus programozási feladatok megoldásában. A normális valószínűségek kiszámítására használt számítógépes szubrutinok olyan gyors működését értük el, hogy normális eloszlás esetén még 1000 dimenziós egyszerű konvex alakzatok valószínűségét is meg lehet határozni egy másodperc körüli időben. A poliéderek használatán alapuló módszer egy új elvi alapokat felhasználó eljárás valószínűségek kiszámítására. Ezen kívül a Dirichlet és a gamma eloszlás valószínűségeinek kiszámításában sikerült eredményeket elérni. Sztochasztikus feladatok megoldó algoritmusaira négy új eljárást dolgoztunk ki: a megengedett megoldások halmazának közelitésén (Bukszár), a szukcesszív regressziós approximációk véletlen egyenletrendszerekre való alkalmazása (Deák), metszősík algoritmusokat használó algoritmus (Fábián), a valószínűségi korláton belül tetszőleges helyen véletlent tartalmazó modell megoldása (Vizvári). A többdimenziós momentumproblémák megoldására kifejlesztett eljárásokat hasznossági függvény becslésére alkalmaztuk. | In our research for solving nonconvex problems we achieved progress in three areas: computing probabilities, optimizing general stochastic programming problems and discrete programming problems. The computer subroutines determining multinormal probabilities became so fast, that even for 1000 dimensional simple convex sets we were able to compute probabilities in about 1 sec. Employing polyhedra is a theoretically new path in computing probabilities. Also we developed some algorithms for computing probabilities for the Dirichlet and the gamma distribution. Four new procedures have been developed fo optimizing stochastic programming models: approximating the set of feasible solutions (Bukszár), applying the successive regression approximations for solving random linear systems of equations (Deák), cutting plane techniques (Fábián), solving problems where the random variables may be in any place inside the probabilistic constraint (Vizvari. In the multidimensional discrete moment problems we proved some theorems, and using these results new algorithm could be presented for approximating the expected utility function

Risk Related to Pre-Diabetes Mellitus and Diabetes Mellitus in Heart Failure With Reduced Ejection Fraction: Insights From Prospective Comparison of ARNI With ACEI to Determine Impact on Global Mortality and Morbidity in Heart Failure Trial

BACKGROUND: The prevalence of pre-diabetes mellitus and its consequences in patients with heart failure and reduced ejection fraction are not known. We investigated these in the Prospective Comparison of ARNI With ACEI to Determine Impact on Global Mortality and Morbidity in Heart Failure (PARADIGM-HF) trial. METHODS AND RESULTS: We examined clinical outcomes in 8399 patients with heart failure and reduced ejection fraction according to history of diabetes mellitus and glycemic status (baseline hemoglobin A1c [HbA1c]: /=6.5% [>/=48 mmol/mol; diabetes mellitus]), in Cox regression models adjusted for known predictors of poor outcome. Patients with a history of diabetes mellitus (n=2907 [35%]) had a higher risk of the primary composite outcome of heart failure hospitalization or cardiovascular mortality compared with those without a history of diabetes mellitus: adjusted hazard ratio, 1.38; 95% confidence interval, 1.25 to 1.52; P6.5%) and known diabetes mellitus compared with those with HbA1c<6.0% was 1.39 (1.17-1.64); P<0.001 and 1.64 (1.43-1.87); P<0.001, respectively. Patients with pre-diabetes mellitus were also at higher risk (hazard ratio, 1.27 [1.10-1.47]; P<0.001) compared with those with HbA1c<6.0%. The benefit of LCZ696 (sacubitril/valsartan) compared with enalapril was consistent across the range of HbA1c in the trial. CONCLUSIONS: In patients with heart failure and reduced ejection fraction, dysglycemia is common and pre-diabetes mellitus is associated with a higher risk of adverse cardiovascular outcomes (compared with patients with no diabetes mellitus and HbA1c <6.0%). LCZ696 was beneficial compared with enalapril, irrespective of glycemic status. CLINICAL TRIAL REGISTRATION: URL: http://www.clinicaltrials.gov. Unique identifier: NCT01035255

Angiotensin Receptor Neprilysin Inhibition Compared With Enalapril on the Risk of Clinical Progression in Surviving Patients With Heart Failure

BACKGROUND: -Clinical trials in heart failure have focused on the improvement in symptoms or decreases in the risk of death and other cardiovascular events. Little is known about the effect of drugs on the risk of clinical deterioration in surviving patients. METHODS AND RESULTS: -We compared the angiotensin-neprilysin inhibitor LCZ696 (400 mg daily) with the angiotensinconverting enzyme inhibitor enalapril (20 mg daily) in 8399 patients with heart failure and reduced ejection fraction in a double-blind trial. The analyses focused on prespecified measures of nonfatal clinical deterioration. In comparison with the enalapril group, fewer LCZ696-treated patients required intensification of medical treatment for heart failure (520 versus 604; hazard ratio, 0.84; 95% confidence interval, 0.74-0.94; P=0.003) or an emergency department visit for worsening heart failure (hazard ratio, 0.66; 95% confidence interval, 0.52-0.85; P=0.001). The patients in the LCZ696 group had 23% fewer hospitalizations for worsening heart failure (851 versus 1079; P<0.001) and were less likely to require intensive care (768 versus 879; 18% rate reduction, P=0.005), to receive intravenous positive inotropic agents (31% risk reduction, P<0.001), and to have implantation of a heart failure device or cardiac transplantation (22% risk reduction, P=0.07). The reduction in heart failure hospitalization with LCZ696 was evident within the first 30 days after randomization. Worsening of symptom scores in surviving patients was consistently more common in the enalapril group. LCZ696 led to an early and sustained reduction in biomarkers of myocardial wall stress and injury (N-terminal pro-Btype natriuretic peptide and troponin) versus enalapril. CONCLUSIONS: -Angiotensin-neprilysin inhibition prevents the clinical progression of surviving patients with heart failure more effectively than angiotensin-converting enzyme inhibition. Clinical Trial Registration-URL: http://www.clinicaltrials.gov. Unique identifier: NCT01035255