Learning Bayesian Networks with Thousands of Variables

We present a method for learning Bayesian networks from data sets containing thousands of variables without the need for structure constraints. Our approach is made of two parts. The first is a novel algorithm that effectively explores the space of possible parent sets of a node. It guides the exploration towards the most promising parent sets on the basis of an approximated score function that is computed in constant time. The second part is an improvement of an existing ordering-based algorithm for structure optimization. The new algorithm provably achieves a higher score compared to its original formulation. Our novel approach consistently outperforms the state of the art on very large data sets.

Learning Bounded Tree-Width Bayesian Networks via Sampling

Learning Bayesian networks with bounded tree-width has attracted much attention recently, because low tree-width allows exact inference to be performed efficiently. Some existing methods [12, 14] tackle the problem by using k-trees to learn the optimal Bayesian network with tree-width up to k. In this paper, we propose a sampling method to efficiently find representative k-trees by introducing an Informative score function to characterize the quality of a k-tree. The proposed algorithm can efficiently learn a Bayesian network with tree-width at most k. Experiment results indicate that our approach is comparable with exact methods, but is much more computationally efficient.

MRZ-99030 – a novel modulator of Aβ aggregation: II – reversal of Aβ oligomer-induced deficits in long-term potentiation (LTP) and cognitive performance in rats and mice.

β-amyloid1-42 (Aβ1-42) is a major endogenous pathogen underlying the aetiology of Alzheimer's disease (AD). Recent evidence indicates that soluble Aβ oligomers, rather than plaques, are the major cause of synaptic dysfunction and neurodegeneration. Small molecules that suppress Aβ aggregation, reduce oligomer stability or promote off-pathway non-toxic oligomerization represent a promising alternative strategy for neuroprotection in AD. MRZ-99030 was recently identified as a dipeptide that modulates Aβ1-42 aggregation by triggering a non-amyloidogenic aggregation pathway, thereby reducing the amount of intermediate toxic soluble oligomeric Aβ species. The present study evaluated the relevance of these promising results with MRZ-99030 under pathophysiological conditions i.e. against the synaptotoxic effects of Aβ oligomers on hippocampal long term potentiation (LTP) and two different memory tasks. Aβ1-42 interferes with the glutamatergic system and with neuronal Ca2+ signalling and abolishes the induction of LTP. Here we demonstrate that MRZ-99030 (100–500 nM) at a 10:1 stoichiometric excess to Aβ clearly reversed the synaptotoxic effects of Aβ1-42 oligomers on CA1-LTP in murine hippocampal slices. Co-application of MRZ-99030 also prevented the two-fold increase in resting Ca2+ levels in pyramidal neuron dendrites and spines triggered by Aβ1-42 oligomers. In anaesthetized rats, pre-administration of MRZ-99030 (50 mg/kg s.c.) protected against deficits in hippocampal LTP following i.c.v. injection of oligomeric Aβ1-42. Furthermore, similar treatment significantly ameliorated cognitive deficits in an object recognition task and under an alternating lever cyclic ratio schedule after the i.c.v. application of Aβ1-42 and 7PA2 conditioned medium, respectively. Altogether, these results demonstrate the potential therapeutic benefit of MRZ-99030 in AD.

Nuclear cataract shows significant familial aggregation in an older population after adjustment for possible shared environmental factors.

PURPOSE: To quantify the association between siblings in age-related nuclear cataract, after adjusting for known environmental and personal risk factors. METHODS: All participants (probands) in the Salisbury Eye Evaluation (SEE) project and their locally resident siblings underwent digital slit lamp photography and were administered a questionnaire to assess risk factors for cataract including: age, gender, lifetime sun exposure, smoking and diabetes history, and use of alcohol and medications such as estrogens and steroids. In addition, blood pressure, body mass index, and serum antioxidants were measured in all participants. Lens photographs were graded by trained observers masked to the subjects' identity, using the Wilmer Cataract Grading System. The odds ratio for siblings for affectedness with nuclear cataract and the sibling correlation of nuclear cataract grade, after adjusting for covariates, were estimated with generalized estimating equations. RESULTS: Among 307 probands (mean age, 77.6 +/- 4.5 years) and 434 full siblings (mean age, 72.4 +/- 7.4 years), the average sibship size was 2.7 per family. After adjustment for covariates, the probability of development of nuclear cataract was significantly increased (odds ratio [OR] = 2.07, 95% confidence interval [CI], 1.30-3.30) among individuals with a sibling with nuclear cataract (nuclear grade > or = 3.0). The final fitted model indicated a magnitude of heritability for nuclear cataract of 35.6% (95% CI: 21.0%-50.3%) after adjustment for the covariates. CONCLUSIONS: Findings in this study are consistent with a genetic effect for age-related nuclear cataract, a common and clinically significant form of lens opacity.

Cortical, but not posterior subcapsular, cataract shows significant familial aggregation in an older population after adjustment for possible shared environmental factors.

PURPOSE:

To quantify the risk for age-related cortical cataract and posterior subcapsular cataract (PSC) associated with having an affected sibling after adjusting for known environmental and personal risk factors.

DESIGN:

Sibling cohort study.

PARTICIPANTS:

Participants in the ongoing Salisbury Eye Evaluation (SEE) study (n = 321; mean age, 78.1+/-4.2 years) and their locally resident siblings (n = 453; mean age, 72.6+/-7.4 years) were recruited at the time of Rounds 3 and 4 of the SEE study. INTERVENTION/TESTING METHODS: Retroillumination photographs of the lens were graded for the presence of cortical cataract and PSC with the Wilmer grading system. The residual correlation between siblings' cataract grades was estimated after adjustment for a number of factors (age; gender; race; lifetime exposure to ultraviolet-B light; cigarette, alcohol, estrogen, and steroid use; serum antioxidants; history of diabetes; blood pressure; and body mass index) suspected to be associated with the presence of cataract.

RESULTS:

The average sibship size was 2.7 per family. Multivariate analysis revealed the magnitude of heritability (h(2)) for cortical cataract to be 24% (95% CI, 6%-42%), whereas that for PSC was not statistically significant (h(2) 4%; 95% CI, 0%-11%) after adjustment for the covariates. The model revealed that increasing age, female gender, a history of diabetes, and black race increased the odds of cortical cataract, whereas higher levels of provitamin A were protective. A history of diabetes and steroid use increased the odds for PSC.

CONCLUSIONS:

This study is consistent with a significant genetic effect for age-related cortical cataract but not PSC.

Familial aggregation of hyperopia in an elderly population of siblings in Salisbury, Maryland.

PURPOSE: To determine whether hyperopia aggregates in families in an older mixed-race population. DESIGN: Cross-sectional familial aggregation study using sibships. METHODS: We recruited 759 subjects (mean age, 73.4 years) in 241 families through the population-based Salisbury Eye Evaluation study. Subjects underwent noncycloplegic refraction if best-corrected visual acuity (BCVA) was <or=20/40, had lensometry to measure their currently worn spectacles if BCVA was >20/40 with spectacles, or were considered to be plano (refraction of zero) if the BCVA was >20/40 without spectacles. Preoperative refraction from medical records was used for bilaterally pseudophakic subjects. RESULTS: Utilizing hyperopia cutoffs from 1.00 to 2.50 diopters, age-, race-, and gender-adjusted odds ratios for hyperopia with an affected sibling ranged from 2.72 (95% confidence interval [CI], 1.84-4.01) to 4.87 (95% CI, 2.54-9.30). The odds of hyperopia increased with age until 75 years, after which they remained relatively constant. Black men were significantly less likely to be hyperopic than white men, white women, or black women. CONCLUSIONS: Hyperopia appears to be under strong genetic control in this older population.

Heritability of refractive error and familial aggregation of myopia in an elderly American population.

PURPOSE: To determine the heritability of refractive error and the familial aggregation of myopia in an older population. METHODS: Seven hundred fifty-nine siblings (mean age, 73.4 years) in 241 families were recruited from the Salisbury Eye Evaluation (SEE) Study in eastern Maryland. Refractive error was determined by noncycloplegic subjective refraction (if presenting distance visual acuity was < or =20/40) or lensometry (if best corrected visual acuity was >20/40 with spectacles). Participants were considered plano (refractive error of zero) if uncorrected visual acuity was >20/40. Preoperative refraction from medical records was used for pseudophakic subjects. Heritability of refractive error was calculated with multivariate linear regression and was estimated as twice the residual between-sibling correlation after adjusting for age, gender, and race. Logistic regression models were used to estimate the odds ratio (OR) of myopia, given a myopic sibling relative to having a nonmyopic sibling. RESULTS: The estimated heritability of refractive error was 61% (95% confidence interval [CI]: 34%-88%) in this population. The age-, race-, and sex-adjusted ORs of myopia were 2.65 (95% CI: 1.67-4.19), 2.25 (95% CI: 1.31-3.87), 3.00 (95% CI: 1.56-5.79), and 2.98 (95% CI: 1.51-5.87) for myopia thresholds of -0.50, -1.00, -1.50, and -2.00 D, respectively. Neither race nor gender was significantly associated with an increased risk of myopia. CONCLUSIONS: Refractive error and myopia are highly heritable in this elderly population.

Learning Bayesian Networks with Bounded Tree-Width via Guided Search

Bounding the tree-width of a Bayesian network can reduce the chance of overfitting, and allows exact inference to be performed efficiently. Several existing algorithms tackle the problem of learning bounded tree-width Bayesian networks by learning from k-trees as super-structures, but they do not scale to large domains and/or large tree-width. We propose a guided search algorithm to find k-trees with maximum Informative scores, which is a measure of quality for the k-tree in yielding good Bayesian networks. The algorithm achieves close to optimal performance compared to exact solutions in small domains, and can discover better networks than existing approximate methods can in large domains. It also provides an optimal elimination order of variables that guarantees small complexity for later runs of exact inference. Comparisons with well-known approaches in terms of learning and inference accuracy illustrate its capabilities.