Structural learning and estimation of joint causal effects among network-dependent variables

Bayesian networks in the form of Directed Acyclic Graphs (DAGs) represent an effective tool for modeling and inferring dependence relations among variables, a process known as structural learning. In addition, when equipped with the notion of intervention, a causal DAG model can be adopted to quantify the causal effect on a response due to a hypothetical intervention on some variable. Observational data cannot distinguish between DAGs encoding the same set of conditional independencies (Markov equivalent DAGs), which however can be different from a causal perspective. In addition, because causal effects depend on the underlying network structure, uncertainty around the DAG generating model crucially affects the causal estimation results. We propose a Bayesian methodology which combines structural learning of Gaussian DAG models and inference of causal effects as arising from simultaneous interventions on any given set of variables in the system. Our approach fully accounts for the uncertainty around both the network structure and causal relationships through a joint posterior distribution over DAGs, DAG parameters and then causal effects.

Teachers' Inner Group and Professional Identity: A Study Based on the DAG Model

This article focuses on the inner self as symbolized in examples of Ada Abraham's Draw a Group (DAG) model. Almost 300 primary school teachers in Seville were invited to take part in a DAG sample survey, and the observations and subsequent conclusions are recounted with particular reference to the teachers' professional self: Suggestions are put forward as to further applications of the model in group analysis.

PROCESSOR LOWER BOUND FORMULAS FOR ARRAY COMPUTATIONS AND PARAMETRIC DIOPHANTINE SYSTEMS

Using a directed acyclic graph (dag) model of algorithms, we solve a problem related to precedence-constrained multiprocessor schedules for array computations: Given a sequence of dags and linear schedules parametrized by n, compute a lower bound on the number of processors required by the schedule as a function of n. In our formulation, the number of tasks that are scheduled for execution during any fixed time step is the number of non-negative integer solutions dn to a set of parametric linear Diophantine equations. We present an algorithm based on generating functions for constructing a formula for these numbers dn. The algorithm has been implemented as a Mathematica program. Example runs and the symbolic formulas for processor lower bounds automatically produced by the algorithm for Matrix-Vector Product, Triangular Matrix Product, and Gaussian Elimination problems are presented. Our approach actually solves the following more general problem: Given an arbitrary r× s integral matrix A and r-dimensional integral vectors b and c, let dn(n=0,1,…) be the number of solutions in non-negative integers to the system Az=nb+c. Calculate the (rational) generating function ∑n≥ 0dntn and construct a formula for dn.

A PROCESSOR-TIME-MINIMAL DESIGN FOR 3D RECTILINEAR MESH ALGORITHMS

The paper, using a directed acyclic graph (dag) model of algorithms, investigates precedence constrained multiprocessor schedules for the nx×ny×nz directed rectilinear mesh. Its completion requires at least nx+ny+nz−2 multiprocessor steps. Time-minimal multiprocessor schedules that use as few processors as possible are called processor-time-minimal. Lower bounds are shown for the nx×ny×nz directed mesh, and these bounds are shown to be exact by constructing a processor-time-minimal multiprocessor schedule that can be realized on a systolic array whose topology is either a two dimensional mesh or skewed cylinder.