Detecting direct associations or inferring networks based on the observed data is an important issue in many fields, including biology, physics, engineering and social studies. In this work, we focus on the informatio...Detecting direct associations or inferring networks based on the observed data is an important issue in many fields, including biology, physics, engineering and social studies. In this work, we focus on the information theoretic approaches in the network reconstruction or the direct association detection, in particular,for biological networks. We not only review the traditional approaches or measurements on the associations among the observed variables, such as correlation coefficient, mutual information and conditional mutual information(CMI), but also summarize recently developed theories and methods. The new theoretic works include:information geometry to give a unified framework in detecting causality/association, the partial independence to alleviate the singularity of CMI, and multiscale analysis of CMI to avoid the underestimation issue of CMI.The new methods include part mutual information(PMI) and partial associations(PA), which improve the old measurements in avoiding both overestimation and underestimation. All those theories and methods make important contributions as major advances in the development of network inference.展开更多
Causal relationships among variables can be depicted by a causal network of these variables. We propose a local structure learning approach for discovering the direct causes and the direct effects of a given target va...Causal relationships among variables can be depicted by a causal network of these variables. We propose a local structure learning approach for discovering the direct causes and the direct effects of a given target variable. In the approach, we first find the variable set of parents, children, and maybe some descendants （PCD） of the target variable, but generally we cannot distinguish the parents from the children in the PCD of the target variable. Next, to distinguish the causes from the effects of the target variable, we find the PCD of each variable in the PCD of the target variable, and we repeat the process of finding PCDs along the paths starting from the target variable. Without constructing a whole network over all variables, we find only a local structure around the target variable. Theoretically, we show the correctness of the proposed approach under the assumptions of faithfulness, causal sufficiency, and that conditional independencies are correctly checked.展开更多
We discuss the discovery of causal mechanisms and identifiability of intermediate variables on a causal path. Different from variable selection, we try to distinguish intermediate variables on the causal path from oth...We discuss the discovery of causal mechanisms and identifiability of intermediate variables on a causal path. Different from variable selection, we try to distinguish intermediate variables on the causal path from other variables. It is also different from ordinary model selection approaches which do not concern the causal relationships and do not contain unobserved variables. We propose an approach for selecting a causal mechanism depicted by a directed acyclic graph （DAG） with an unobserved variable. We consider several causal networks, and discuss their identifiability by observed data. We show that causal mechanisms of linear structural equation models are not identifiable. Furthermore, we present that causal mechanisms of nonlinear models are identifiable, and we demonstrate the identifiability of causal mechanisms of quadratic equation models. Sensitivity analysis is conducted for the identifiability.展开更多
基金supported by the National Key R&D Program of China (Grant No. 2017YFA0505500)the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB13040700)National Natural Science Foundation of China (Grant Nos. 31771476, 91529303, 91439103, 11421101 and 91530322)
文摘Detecting direct associations or inferring networks based on the observed data is an important issue in many fields, including biology, physics, engineering and social studies. In this work, we focus on the information theoretic approaches in the network reconstruction or the direct association detection, in particular,for biological networks. We not only review the traditional approaches or measurements on the associations among the observed variables, such as correlation coefficient, mutual information and conditional mutual information(CMI), but also summarize recently developed theories and methods. The new theoretic works include:information geometry to give a unified framework in detecting causality/association, the partial independence to alleviate the singularity of CMI, and multiscale analysis of CMI to avoid the underestimation issue of CMI.The new methods include part mutual information(PMI) and partial associations(PA), which improve the old measurements in avoiding both overestimation and underestimation. All those theories and methods make important contributions as major advances in the development of network inference.
文摘Causal relationships among variables can be depicted by a causal network of these variables. We propose a local structure learning approach for discovering the direct causes and the direct effects of a given target variable. In the approach, we first find the variable set of parents, children, and maybe some descendants （PCD） of the target variable, but generally we cannot distinguish the parents from the children in the PCD of the target variable. Next, to distinguish the causes from the effects of the target variable, we find the PCD of each variable in the PCD of the target variable, and we repeat the process of finding PCDs along the paths starting from the target variable. Without constructing a whole network over all variables, we find only a local structure around the target variable. Theoretically, we show the correctness of the proposed approach under the assumptions of faithfulness, causal sufficiency, and that conditional independencies are correctly checked.
文摘We discuss the discovery of causal mechanisms and identifiability of intermediate variables on a causal path. Different from variable selection, we try to distinguish intermediate variables on the causal path from other variables. It is also different from ordinary model selection approaches which do not concern the causal relationships and do not contain unobserved variables. We propose an approach for selecting a causal mechanism depicted by a directed acyclic graph （DAG） with an unobserved variable. We consider several causal networks, and discuss their identifiability by observed data. We show that causal mechanisms of linear structural equation models are not identifiable. Furthermore, we present that causal mechanisms of nonlinear models are identifiable, and we demonstrate the identifiability of causal mechanisms of quadratic equation models. Sensitivity analysis is conducted for the identifiability.
