Causal discovery beyond Markov equivalence

The focus of the dissertation is on learning causal diagrams beyond Markov equivalence. The baseline assumptions in causal structure learning are the acyclicity of the underlying structure and causal sufficiency, which requires that there are no unobserved confounder variables in the system. Under these assumptions, conditional independence relationships contain all the information in the distribution that can be used for structure learning. Therefore, the causal diagram can be identified only up to Markov equivalence, which is the set of structures reflecting the same conditional independence relationships. Hence, for many ground truth structures, the direction of a large portion of the edges will remain unidentified. Hence, in order to learn the structure beyond Markov equivalence, generating or having access to extra joint distributions from the perturbed causal system is required. There are two main scenarios for acquiring the extra joint distributions. The first and main scenario is when an experimenter is directly performing a sequence of interventions on subsets of the variables of the system to generate interventional distributions. We refer to the task of causal discovery from such interventional data as interventional causal structure learning. In this setting, the key question is determining which variables should be intervened on to gain the most information. This is the first focus of this dissertation. The second scenario for acquiring the extra joint distributions is when a subset of causal mechanisms, and consequently the joint distribution of the system, have varied or evolved due to reasons beyond the control of the experimenter. In this case, it is not even a priori known to the experimenter which causal mechanisms have varied. We refer to the task of causal discovery from such multi-domain data as multi-domain causal structure learning. In this setup the main question is how one can take the most advantage of the changes across domains for the task of causal discovery. This is the second focus of this dissertation. Next, we consider cases under which conditional independency may not reflect all the information in the distribution that can be used to identify the underlying structure. One such case is when cycles are allowed in the underlying structure. Unfortunately, a suitable characterization for equivalence for the case of cyclic directed graphs has been unknown so far. The third focus of this dissertation is on bridging the gap between cyclic and acyclic directed graphs by introducing a general approach for equivalence characterization and structure learning. Another case in which conditional independency may not reflect all the information in the distribution is when there are extra assumptions on the generating causal modules. A seminal result in this direction is that a linear model with non-Gaussian exogenous variables is uniquely identifiable. As the forth focus of this dissertation, we consider this setup, yet go one step further and allow for violation of causal sufficiency, and investigate how this generalization affects the identifiability

Counting and Sampling from Markov Equivalent DAGs Using Clique Trees

A directed acyclic graph (DAG) is the most common graphical model for representing causal relationships among a set of variables. When restricted to using only observational data, the structure of the ground truth DAG is identifiable only up to Markov equivalence, based on conditional independence relations among the variables. Therefore, the number of DAGs equivalent to the ground truth DAG is an indicator of the causal complexity of the underlying structure--roughly speaking, it shows how many interventions or how much additional information is further needed to recover the underlying DAG. In this paper, we propose a new technique for counting the number of DAGs in a Markov equivalence class. Our approach is based on the clique tree representation of chordal graphs. We show that in the case of bounded degree graphs, the proposed algorithm is polynomial time. We further demonstrate that this technique can be utilized for uniform sampling from a Markov equivalence class, which provides a stochastic way to enumerate DAGs in the equivalence class and may be needed for finding the best DAG or for causal inference given the equivalence class as input. We also extend our counting and sampling method to the case where prior knowledge about the underlying DAG is available, and present applications of this extension in causal experiment design and estimating the causal effect of joint interventions

Drug Delivery Based on Micro Electro-Mechanical Systems: A Review

The aim of controlled drug delivery is to manage the time and site of drug release according to the patients’ need.In this paper, Micro Electro-Mechanical Systems (MEMS) technology is described.This technology employs microelectronics and microprocessor circuits in order to reach individualized, targeted and controlled drug release and would construct the future drug delivery systems. Introduction: Controlled drug delivery systems are the state of the art in drug delivery technology with the goal of controlling the drug release at right time and site to satisfy the patient’s pathophysiological requirements. In spite of great improvements in this field, it still remains an open research area.MEMS employs sophisticated systems in a small scale. In last few decades, this technology has increasingly attracted the researchers’ attention due to its successful miniaturization of complicated drug delivery systems to address unmet dosing requirements more precisely.MEMS drug delivery systems are fabricated using the microelectronics and microprocessor circuits of highly-advanced technology. This provides the opportunity to implement several drug reservoirs and billions of electronic devices in few millimeters. Methods and Results:In this study, MEMS technology is introduced along with describing the fabrication process. Two main categories of MEMS devices including internal and transdermal devices and their applications in drug delivery systems are presented. Various actuators applied in these devices are described, including electrical, electrochemical, electromechanical, and electrothermal types. Finally, emerging technologies and prospects are briefly reviewed. Conclusions: MEMS techniques can be easily combined with microprocessors and sensors to implement an intelligent system which can determine the proper drug dosage and release time according to the signals received by biosensors. When placed inside the body, biocompatibility and biofouling issues should be well-considered, since the device will remain in the patient’s body for a long time. Therefore, MEMS technology seems to be the future aspect of targeted drug delivery systems