Model selection and local geometry

We consider problems in model selection caused by the geometry of models close to their points of intersection. In some cases---including common classes of causal or graphical models, as well as time series models---distinct models may nevertheless have identical tangent spaces. This has two immediate consequences: first, in order to obtain constant power to reject one model in favour of another we need local alternative hypotheses that decrease to the null at a slower rate than the usual parametric $n^{-1/2}$ (typically we will require $n^{-1/4}$ or slower); in other words, to distinguish between the models we need large effect sizes or very large sample sizes. Second, we show that under even weaker conditions on their tangent cones, models in these classes cannot be made simultaneously convex by a reparameterization. This shows that Bayesian network models, amongst others, cannot be learned directly with a convex method similar to the graphical lasso. However, we are able to use our results to suggest methods for model selection that learn the tangent space directly, rather than the model itself. In particular, we give a generic algorithm for learning Bayesian network models

Graphical methods for inequality constraints in marginalized DAGs

We present a graphical approach to deriving inequality constraints for directed acyclic graph (DAG) models, where some variables are unobserved. In particular we show that the observed distribution of a discrete model is always restricted if any two observed variables are neither adjacent in the graph, nor share a latent parent; this generalizes the well known instrumental inequality. The method also provides inequalities on interventional distributions, which can be used to bound causal effects. All these constraints are characterized in terms of a new graphical separation criterion, providing an easy and intuitive method for their derivation.Comment: A final version will appear in the proceedings of the 22nd Workshop on Machine Learning and Signal Processing, 201

Graphs for margins of Bayesian networks

Directed acyclic graph (DAG) models, also called Bayesian networks, impose conditional independence constraints on a multivariate probability distribution, and are widely used in probabilistic reasoning, machine learning and causal inference. If latent variables are included in such a model, then the set of possible marginal distributions over the remaining (observed) variables is generally complex, and not represented by any DAG. Larger classes of mixed graphical models, which use multiple edge types, have been introduced to overcome this; however, these classes do not represent all the models which can arise as margins of DAGs. In this paper we show that this is because ordinary mixed graphs are fundamentally insufficiently rich to capture the variety of marginal models. We introduce a new class of hyper-graphs, called mDAGs, and a latent projection operation to obtain an mDAG from the margin of a DAG. We show that each distinct marginal of a DAG model is represented by at least one mDAG, and provide graphical results towards characterizing when two such marginal models are the same. Finally we show that mDAGs correctly capture the marginal structure of causally-interpreted DAGs under interventions on the observed variables

Margins of discrete Bayesian networks

Bayesian network models with latent variables are widely used in statistics and machine learning. In this paper we provide a complete algebraic characterization of Bayesian network models with latent variables when the observed variables are discrete and no assumption is made about the state-space of the latent variables. We show that it is algebraically equivalent to the so-called nested Markov model, meaning that the two are the same up to inequality constraints on the joint probabilities. In particular these two models have the same dimension. The nested Markov model is therefore the best possible description of the latent variable model that avoids consideration of inequalities, which are extremely complicated in general. A consequence of this is that the constraint finding algorithm of Tian and Pearl (UAI 2002, pp519-527) is complete for finding equality constraints. Latent variable models suffer from difficulties of unidentifiable parameters and non-regular asymptotics; in contrast the nested Markov model is fully identifiable, represents a curved exponential family of known dimension, and can easily be fitted using an explicit parameterization.Comment: 41 page

Causal Inference through a Witness Protection Program

One of the most fundamental problems in causal inference is the estimation of a causal effect when variables are confounded. This is difficult in an observational study, because one has no direct evidence that all confounders have been adjusted for. We introduce a novel approach for estimating causal effects that exploits observational conditional independencies to suggest "weak" paths in a unknown causal graph. The widely used faithfulness condition of Spirtes et al. is relaxed to allow for varying degrees of "path cancellations" that imply conditional independencies but do not rule out the existence of confounding causal paths. The outcome is a posterior distribution over bounds on the average causal effect via a linear programming approach and Bayesian inference. We claim this approach should be used in regular practice along with other default tools in observational studies.Comment: 41 pages, 7 figure

One-Component Regular Variation and Graphical Modeling of Extremes

The problem of inferring the distribution of a random vector given that its norm is large requires modeling a homogeneous limiting density. We suggest an approach based on graphical models which is suitable for high-dimensional vectors. We introduce the notion of one-component regular variation to describe a function that is regularly varying in its first component. We extend the representation and Karamata's theorem to one-component regularly varying functions, probability distributions and densities, and explain why these results are fundamental in multivariate extreme-value theory. We then generalize Hammersley-Clifford theorem to relate asymptotic conditional independence to a factorization of the limiting density, and use it to model multivariate tails

Asthma management: an ecosocial framework for disparity research

Background: Asthma management disparities (AMD) between African and White Americans are significant and alarming. Various determinants have been suggested by research frameworks that affect the unfair distribution of resources for asthma management to groups who are more or less advantaged socially. Ecosocial models organize determinants into individual/family, healthcare, community, and sociocultural levels. Multilevel interventions can affect AMD through simultaneous actions on different levels and pathways between determinants. Objective: Provide a comprehensive summary of the known determinants of AMD. Method: Peer reviewed research frameworks of AMD from 1998-2009 were retrieved from PubMed/ Web of Science databases using (“Socioeconomic Factors”[Mesh] OR (“Healthcare Disparities”[Mesh] OR “Health Status Disparities”[Mesh])) AND “Asthma”[Mesh] AND “African Americans”[Mesh] OR “Ethnic Groups”[Mesh]). Abstracts assessed for a focus on AMD, and determinants. Articles were analyzed for ecosocial levels and determinants. Results: 13 research frameworks described 34 determinants. Compared to other levels, Individual/family levels had the most emphasis, and frameworks using healthcare and community levels were the most narrow in focus. Stress, poverty, violence/crime, quality of care, healthcare access, and indoor air quality were well described determinants. Conclusions: Multilevel investigations should include those well described determinants of AMD and increase knowledge of pathway interactions between healthcare and community levels

Predicting and controlling the dynamics of infectious diseases

This paper introduces a new optimal control model to describe and control the dynamics of infectious diseases. In the present model, the average time of isolation (i.e. hospitalization) of infectious population is the main time-dependent parameter that defines the spread of infection. All the preventive measures aim to decrease the average time of isolation under given constraints

Dynamics of Ebola epidemics in West Africa 2014

This paper investigates the dynamics of Ebola virus transmission in West Africa during 2014. The reproduction numbers for the total period of epidemic and for different consequent time intervals are estimated based on a newly suggested linear model. It contains one major variable - the average time of infectiousness (time from onset to hospitalization) that is considered as a parameter for controlling the future dynamics of epidemics. Numerical implementations are carried out on data collected from three countries Guinea, Sierra Leone and Liberia as well as the total data collected worldwide. Predictions are provided by considering different scenarios involving the average times of infectiousness for the next few months and the end of the current epidemic is estimated according to each scenario