Amortized Causal Discovery: Learning to Infer Causal Graphs from Time-Series Data

Standard causal discovery methods must fit a new model whenever they encounter samples from a new underlying causal graph. However, these samples often share relevant information - for instance, the dynamics describing the effects of causal relations - which is lost when following this approach. We propose Amortized Causal Discovery, a novel framework that leverages such shared dynamics to learn to infer causal relations from time-series data. This enables us to train a single, amortized model that infers causal relations across samples with different underlying causal graphs, and thus makes use of the information that is shared. We demonstrate experimentally that this approach, implemented as a variational model, leads to significant improvements in causal discovery performance, and show how it can be extended to perform well under hidden confounding

Dietary fat and not calcium supplementation or dairy product consumption is associated with changes in anthropometrics during a randomized, placebo-controlled energy-restriction trial

Insufficient calcium intake has been proposed to cause unbalanced energy partitioning leading to obesity. However, weight loss interventions including dietary calcium or dairy product consumption have not reported changes in lipid metabolism measured by the plasma lipidome

Calcium-fortified beverage supplementation on body composition in postmenopausal women

BACKGROUND: We investigated the effects of a calcium-fortified beverage supplemented over 12 months on body composition in postmenopausal women (n = 37, age = 48–75 y). METHODS: Body composition (total-body percent fat, %Fat(TB); abdominal percent fat, %Fat(AB)) was measured with dual energy x-ray absorptiometry. After baseline assessments, subjects were randomly assigned to a free-living control group (CTL) or the supplement group (1,125 mg Ca(++)/d, CAL). Dietary intake was assessed with 3-day diet records taken at baseline and 12 months (POST). Physical activity was measured using the Yale Physical Activity Survey. RESULTS: At 12 months, the dietary calcium to protein ratio in the CAL group (32.3 ± 15.6 mg/g) was greater than the CTL group (15.2 ± 7.5 mg/g). There were no differences from baseline to POST between groups for changes in body weight (CAL = 0.1 ± 3.0 kg; CTL = 0.0 ± 2.9 kg), %Fat(TB )(CAL = 0.0 ± 2.4%; CTL = 0.5 ± 5.4%), %Fat(AB )(CAL = -0.4 ± 8.7%; CTL = 0.6 ± 8.7%), or fat mass (CAL = 1.3 ± 2.6 kg; CTL = 1.3 ± 2.7 kg). CONCLUSION: These results indicate that increasing the calcium to protein ratio over two-fold by consuming a calcium-fortified beverage for 12 months did not decrease body weight, body fat, or abdominal fat composition in postmenopausal women

Transformation Equivariant Boltzmann Machines

Abstract. We develop a novel modeling framework for Boltzmann machines, augmenting each hidden unit with a latent transformation assignment variable which describes the selection of the transformed view of the canonical connection weights associated with the unit. This enables the inferences of the model to transform in response to transformed input data in a stable and predictable way, and avoids learning multiple features differing only with respect to the set of transformations. Extending prior work on translation equivariant (convolutional) models, we develop translation and rotation equivariant restricted Boltzmann machines (RBMs) and deep belief nets (DBNs), and demonstrate their effectiveness in learning frequently occurring statistical structure from artificial and natural images

Fairness in Algorithmic Decision Making: An Excursion Through the Lens of Causality

As virtually all aspects of our lives are increasingly impacted by algorithmic decision making systems, it is incumbent upon us as a society to ensure such systems do not become instruments of unfair discrimination on the basis of gender, race, ethnicity, religion, etc. We consider the problem of determining whether the decisions made by such systems are discriminatory, through the lens of causal models. We introduce two definitions of group fairness grounded in causality: fair on average causal effect (FACE), and fair on average causal effect on the treated (FACT). We use the Rubin-Neyman potential outcomes framework for the analysis of cause-effect relationships to robustly estimate FACE and FACT. We demonstrate the effectiveness of our proposed approach on synthetic data. Our analyses of two real-world data sets, the Adult income data set from the UCI repository (with gender as the protected attribute), and the NYC Stop and Frisk data set (with race as the protected attribute), show that the evidence of discrimination obtained by FACE and FACT, or lack thereof, is often in agreement with the findings from other studies. We further show that FACT, being somewhat more nuanced compared to FACE, can yield findings of discrimination that differ from those obtained using FACE.Comment: 7 pages, 2 figures, 2 tables.To appear in Proceedings of the International Conference on World Wide Web (WWW), 201

The effect of high intakes of casein and casein phosphopeptide on calcium absorption in the rat

peer-reviewedThe effect of the level or source of dietary protein or protein-derived peptides on Ca absorption is not well understood. We determined, therefore, the influence of habitual dietary casein level, meal casein and meal casein phosphopeptide (CPP) on Ca absorption in the rat. True fractional Ca absorption was investigated in male 7-week-old rats, Wistar strain, in three separate studies using a faecal 47Sc : 47Ca ratio method. In studies A and C, rats (n 8 per group) were fed on a purified diet containing 200 g casein/kg for 2 weeks. Rats were then given a 47Ca-labelled meal (10 g) containing (per kg) either 0, 100, 200, or 300 g casein (study A) or 0, 100, 200, 350 or 500 g CPP (study C). In study B, rats (n 24 per group) were fed on a purified diet containing (per kg) either 200, 350 or 500 g casein for 2 weeks. Each group was then further randomized into three groups (n 8 per group) and given a 47Ca-labelled meal (10 g of the same diet) containing (per kg) either 200, 350 or 500 g casein. Ca absorption from a meal was unaffected by increasing meal casein concentration from 0 to 300 g/kg (study A), but was increased with a meal casein content of 500 g/kg (study B). Fractional Ca absorption decreased with increasing usual dietary casein intake in the range 200±500 g/kg (study B), suggesting intestinal adaptation. Ca absorption was unaffected by inclusion of 100 g CPP/kg in a single meal but was significantly (P,0×001) reduced by 200, 350 and 500 g CPP/kg meal, with no evident dose-relationship. Thus, while Ca absorption was enhanced by high-casein meals, the mechanism remains unclear

The Relationship Between Fractures and DXA Measures of BMD in the Distal Femur of Children and Adolescents With Cerebral Palsy or Muscular Dystrophy

Children with limited or no ability to ambulate frequently sustain fragility fractures. Joint contractures, scoliosis, hip dysplasia, and metallic implants often prevent reliable measures of bone mineral density (BMD) in the proximal femur and lumbar spine, where BMD is commonly measured. Further, the relevance of lumbar spine BMD to fracture risk in this population is questionable. In an effort to obtain bone density measures that are both technically feasible and clinically relevant, a technique was developed involving dual-energy X-ray absorptiometry (DXA) measures of the distal femur projected in the lateral plane. The purpose of this study is to test the hypothesis that these new measures of BMD correlate with fractures in children with limited or no ability to ambulate. The relationship between distal femur BMD Z-scores and fracture history was assessed in a cross-sectional study of 619 children aged 6 to 18 years with muscular dystrophy or moderate to severe cerebral palsy compiled from eight centers. There was a strong correlation between fracture history and BMD Z-scores in the distal femur; 35% to 42% of those with BMD Z-scores less than −5 had fractured compared with 13% to 15% of those with BMD Z-scores greater than −1. Risk ratios were 1.06 to 1.15 (95% confidence interval 1.04–1.22), meaning a 6% to 15% increased risk of fracture with each 1.0 decrease in BMD Z-score. In clinical practice, DXA measure of BMD in the distal femur is the technique of choice for the assessment of children with impaired mobility. © 2010 American Society for Bone and Mineral Researc