Distinguishing cause from effect using observational data: methods and benchmarks

The discovery of causal relationships from purely observational data is a fundamental problem in science. The most elementary form of such a causal discovery problem is to decide whether X causes Y or, alternatively, Y causes X, given joint observations of two variables X, Y. An example is to decide whether altitude causes temperature, or vice versa, given only joint measurements of both variables. Even under the simplifying assumptions of no confounding, no feedback loops, and no selection bias, such bivariate causal discovery problems are challenging. Nevertheless, several approaches for addressing those problems have been proposed in recent years. We review two families of such methods: Additive Noise Methods (ANM) and Information Geometric Causal Inference (IGCI). We present the benchmark CauseEffectPairs that consists of data for 100 different cause-effect pairs selected from 37 datasets from various domains (e.g., meteorology, biology, medicine, engineering, economy, etc.) and motivate our decisions regarding the "ground truth" causal directions of all pairs. We evaluate the performance of several bivariate causal discovery methods on these real-world benchmark data and in addition on artificially simulated data. Our empirical results on real-world data indicate that certain methods are indeed able to distinguish cause from effect using only purely observational data, although more benchmark data would be needed to obtain statistically significant conclusions. One of the best performing methods overall is the additive-noise method originally proposed by Hoyer et al. (2009), which obtains an accuracy of 63+-10 % and an AUC of 0.74+-0.05 on the real-world benchmark. As the main theoretical contribution of this work we prove the consistency of that method.Comment: 101 pages, second revision submitted to Journal of Machine Learning Researc

Multimodal population brain imaging in the UK Biobank prospective epidemiological study

Medical imaging has enormous potential for early disease prediction, but is impeded by the difficulty and expense of acquiring data sets before symptom onset. UK Biobank aims to address this problem directly by acquiring high-quality, consistently acquired imaging data from 100,000 predominantly healthy participants, with health outcomes being tracked over the coming decades. The brain imaging includes structural, diffusion and functional modalities. Along with body and cardiac imaging, genetics, lifestyle measures, biological phenotyping and health records, this imaging is expected to enable discovery of imaging markers of a broad range of diseases at their earliest stages, as well as provide unique insight into disease mechanisms. We describe UK Biobank brain imaging and present results derived from the first 5,000 participants' data release. Although this covers just 5% of the ultimate cohort, it has already yielded a rich range of associations between brain imaging and other measures collected by UK Biobank

A Survey on Causal Discovery Methods for Temporal and Non-Temporal Data

Causal Discovery (CD) is the process of identifying the cause-effect relationships among the variables from data. Over the years, several methods have been developed primarily based on the statistical properties of data to uncover the underlying causal mechanism. In this study we introduce the common terminologies in causal discovery, and provide a comprehensive discussion of the approaches designed to identify the causal edges in different settings. We further discuss some of the benchmark datasets available for evaluating the performance of the causal discovery algorithms, available tools to perform causal discovery readily, and the common metrics used to evaluate these methods. Finally, we conclude by presenting the common challenges involved in CD and also, discuss the applications of CD in multiple areas of interest

Deep Causal Learning: Representation, Discovery and Inference

Causal learning has attracted much attention in recent years because causality reveals the essential relationship between things and indicates how the world progresses. However, there are many problems and bottlenecks in traditional causal learning methods, such as high-dimensional unstructured variables, combinatorial optimization problems, unknown intervention, unobserved confounders, selection bias and estimation bias. Deep causal learning, that is, causal learning based on deep neural networks, brings new insights for addressing these problems. While many deep learning-based causal discovery and causal inference methods have been proposed, there is a lack of reviews exploring the internal mechanism of deep learning to improve causal learning. In this article, we comprehensively review how deep learning can contribute to causal learning by addressing conventional challenges from three aspects: representation, discovery, and inference. We point out that deep causal learning is important for the theoretical extension and application expansion of causal science and is also an indispensable part of general artificial intelligence. We conclude the article with a summary of open issues and potential directions for future work

Bone and Phosphate in Relation to Health, Survival and Genetic Factors

In this thesis, we found that a) low bone mineral density was related to increased mortality from chronic obstructive pulmonary disease and b) increased serum phosphate, even at normal levels, was related to fracture risk, low BMD at the lumbar spine and coronary artery calcification. For the latter association, we found evidence of causality, due to the implementation of Mendelian Randomization technique. All our results were more consistent or even unique in men. The genetic analyses on phosphate levels identified 264 loci in the human genome and highlighted the importance of the Major Histocompatibility Complex (6p21.3) also on phosphate levels, as the top hit mapped to the flanking region of the MHC. Interestingly, the same finding has been described in White British and East Asian Japanese populations. Our next step will be the replication in BioBank Japan followed by trans-ethnic meta-analysis and Bayesian fine-mapping

BONE LOSS IN RELATION TO HYPOTHALAMIC ATROPHY IN ALZHEIMER'S DISEASE

Epidemiologic projections indicate that the incidence of Alzheimer's disease (AD) will increase dramatically in the coming decades due largely to the demographics of the disease and our aging population. Associated cognitive and physical decline greatly contributes to disability in older adults and places considerable burden on the health system, patients, and caregivers. Bone loss and increased risk of fractures are associated with AD, however little is known about mechanisms of this association. The body of presented work extends the literature on a relationship between bone loss and AD. Overall, the presented work provides initial evidence that accelerated bone loss observed in individuals in the early stages of AD may be partially due to distortion of central regulatory mechanisms by neurodegeneration. This is the first work to demonstrate that hypothalamic atrophy is related to bone loss and this relationship may be mediated by leptin-dependent mechanisms in humans in the early stages of AD. The work in Chapter 2 assessed bone health in the earliest clinical stages of AD in comparison to non-demented aging and examined the relationship of bone mineral density (BMD) with cognitive performance and brain atrophy, both of which are used as surrogate markers of neurodegeneration. We tested the hypothesis that bone density would be lower in early AD and associated with brain atrophy and cognitive decline. The results of this cross-sectional study supported our hypothesis and found that BMD is reduced in men and women in the earliest clinical stages of AD and associated with brain atrophy and memory decline, suggesting that central mechanisms may contribute to bone loss in early Alzheimer's disease. AD is associated with pathological changes in the hypothalamus, a key regulatory structure of bone remodeling. The aim of Chapter 3 was to extend previous findings of the association between BMD and neuroimaging markers of neurodegeneration by looking at global and regional, hypothalamus specifically, measures of brain volume in early AD and non-demented aging. The results demonstrated that in early AD, low BMD was associated with low volume of gray matter in brain structures predominantly affected by AD early in the disease, including the hypothalamus, cingulate, and parahippocampal gyri and in the left superior temporal gyrus and left inferior parietal cortex. No relationship between BMD and regional gray matter volume was found in non-demented controls. These results suggest that central mechanisms of bone remodeling may be disrupted by neurodegeneration. There is very limited guidance in the literature regarding useful and reliable techniques for studying hypothalamic anatomy using neuroimaging. In Chapter 4, we compared an automated neuroimaging technique - voxel-based morphometry (VBM) - to a "gold standard" manual method assessing volumetry of the hypothalamus. The atlas-based VBM volumetry showed promise as a useful tool for regional volumetry of the hypothalamus and has advantages over manual tracing as it is currently used. The results of this study provided guidance for method selection in future work. In Chapter 5, we further examined the hypothesis that AD may influence bone density in cortical skeletal sites directly through atrophy of the hypothalamus, the major central regulatory structure of bone remodeling. We previously reported in cross-section that BMD was lower in those with early AD and suggested that brain atrophy, specifically of the hypothalamus, was associated with lower BMD in AD. We now examined if similar results were apparent in a two year longitudinal study to extend our previous finding of an association between hypothalamic atrophy and bone density. We also explore predictors of bone loss in AD and healthy aging. Our results demonstrate that bone loss may be accelerated in AD compared with non-demented controls. For AD participants, bone loss was associated with hypothalamic atrophy over two years. Additionally, bone loss was associated with baseline levels of the vitamin D. For non-demented participants, bone loss was associated with age, female gender and decline in physical activity. Different predictors of bone loss may suggest that mechanisms of bone loss may differ in aging and AD and that neurodegeneration may contribute to bone loss in early AD. These results extend and strengthen the cross-sectional observations in Chapters 2&3. The purpose of the work presented in Chapter 6 was to further extend previous observations by assessing the roles of leptin, growth hormone (GH) and insulin-like growth factor-1 (IGF-1) , two important regulators of hypothalamic control of bone remodeling, in mediating relationship between hypothalamic structural changes and bone loss in AD. We used a hypothetical model with statistical structural equation or path modeling to examine if leptin, GH, and IGF-I may mediate the relationship between hypothalamic structural changes. The model demonstrated that hypothalamic atrophy had a direct relationship with bone loss. There was no apparent association between baseline IGF-1 and leptin with bone loss but we observed changes in both leptin and IGF-1 over two years that were associated with hypothalamic atrophy. Leptin increased over two years in AD and increase in leptin was associated with hypothalamic atrophy. On the other hand, IGF-1 declined over two year and this decrease was associated with increase in leptin. These results suggest that it is conceivable that central regulatory mechanisms of bone mass may be disturbed by neurodegeneration leading to bone loss in participants in the early stages of AD. In summary, this body of work demonstrates that bone density is reduced in women and men with early stages of AD and continues to decline over time, exceeding bone loss in non-demented older adults. While the causes of bone loss in AD remain unclear, the observed association of hypothalamic atrophy with bone loss suggests neurodegeneration may play a role in bone loss observed in AD and highlights a need for further studies. This work also corroborates other studies on the importance of vitamin D and physical activity for bone health. The findings of this body of work are important because evidence that bone loss in AD is associated with the atrophy in regions involved in the central regulation of bone mass may be relevant to therapeutic strategies to prevent or treat bone loss in AD and neurodegenerative diseases