Smooth, identifiable supermodels of discrete DAG models with latent variables

We provide a parameterization of the discrete nested Markov model, which is a supermodel that approximates DAG models (Bayesian network models) with latent variables. Such models are widely used in causal inference and machine learning. We explicitly evaluate their dimension, show that they are curved exponential families of distributions, and fit them to data. The parameterization avoids the irregularities and unidentifiability of latent variable models. The parameters used are all fully identifiable and causally-interpretable quantities.Comment: 30 page

Do Borders Matter? Soviet economic Reform after the Coup

macroeconomics, Soviet, borders, economic reform

Nested Markov Properties for Acyclic Directed Mixed Graphs

Directed acyclic graph (DAG) models may be characterized in at least four different ways: via a factorization, the d-separation criterion, the moralization criterion, and the local Markov property. As pointed out by Robins (1986, 1999), Verma and Pearl (1990), and Tian and Pearl (2002b), marginals of DAG models also imply equality constraints that are not conditional independences. The well-known `Verma constraint' is an example. Constraints of this type were used for testing edges (Shpitser et al., 2009), and an efficient marginalization scheme via variable elimination (Shpitser et al., 2011). We show that equality constraints like the `Verma constraint' can be viewed as conditional independences in kernel objects obtained from joint distributions via a fixing operation that generalizes conditioning and marginalization. We use these constraints to define, via Markov properties and a factorization, a graphical model associated with acyclic directed mixed graphs (ADMGs). We show that marginal distributions of DAG models lie in this model, prove that a characterization of these constraints given in (Tian and Pearl, 2002b) gives an alternative definition of the model, and finally show that the fixing operation we used to define the model can be used to give a particularly simple characterization of identifiable causal effects in hidden variable graphical causal models.Comment: 67 pages (not including appendix and references), 8 figure

Sparse Nested Markov models with Log-linear Parameters

Hidden variables are ubiquitous in practical data analysis, and therefore modeling marginal densities and doing inference with the resulting models is an important problem in statistics, machine learning, and causal inference. Recently, a new type of graphical model, called the nested Markov model, was developed which captures equality constraints found in marginals of directed acyclic graph (DAG) models. Some of these constraints, such as the so called `Verma constraint', strictly generalize conditional independence. To make modeling and inference with nested Markov models practical, it is necessary to limit the number of parameters in the model, while still correctly capturing the constraints in the marginal of a DAG model. Placing such limits is similar in spirit to sparsity methods for undirected graphical models, and regression models. In this paper, we give a log-linear parameterization which allows sparse modeling with nested Markov models. We illustrate the advantages of this parameterization with a simulation study.Comment: Appears in Proceedings of the Twenty-Ninth Conference on Uncertainty in Artificial Intelligence (UAI2013

Monopolists and Viscous Demand

We characterize the optimal dynamic price policy of a monopolist who faces "viscous" demand for its services. Demand is viscous if it adjusts relatively slowly to price changes. We show that with the optimal policy the monopolist stops short of achieving 100% market penetration, even when all of the consumers have the same long-run willingness to pay for the service. Furthermore, for certain parameter values in the model, the price policy requires rapid oscillations of the price path.Information Systems Working Papers Serie

Mechanisms of Bacterial Extracellular Electron Exchange.

The biochemical mechanisms by which microbes interact with extracellular soluble metal ions and insoluble redox-active minerals have been the focus of intense research over the last three decades. The process presents two challenges to the microorganism; firstly electrons have to be transported at the cell surface, which in Gram negative bacteria presents an additional problem of electron transfer across the ~ 6 nm of the outer membrane. Secondly the electrons must be transferred to or from the terminal electron acceptors or donors. This review covers the known mechanisms that bacteria use to transport electrons across the cell envelope to external electron donors/acceptors. In Gram negative bacteria electron transfer across the outer membrane involves the use of an outer membrane β-barrel and cytochrome. These can be in the form of a porin-cytochrome protein, such as Cyc2 of Acidothiobacillus ferrioxydans, or a multiprotein porin-cytochrome complex like MtrCAB of Shewanella oneidensis MR-1. For mineral respiring organisms there is the additional challenge of transferring the electrons from the cell to mineral surface. For the strict anaerobe Geobacter sulfurreducens this requires electron transfer through conductive pili to associated cytochrome OmcS that directly reduces Fe(III)oxides, while the facultative anaerobe S. oneidensis MR-1 accomplishes mineral reduction through direct membrane contact, contact through filamentous extentions and soluble flavin shuttles, all of which require the outer membrane cytochromes MtrC and OmcA in addition to secreted flavin