James M. Robins

JMLR Journal 2021 Journal Article

Adaptive estimation of nonparametric functionals

• Lin Liu
• Rajarshi Mukherjee
• James M. Robins
• Eric Tchetgen Tchetgen

We provide general adaptive upper bounds for estimating nonparametric functionals based on second-order U-statistics arising from finite-dimensional approximation of the infinite-dimensional models. We then provide examples of functionals for which the theory produces rate optimally matching adaptive upper and lower bounds. Our results are automatically adaptive in both parametric and nonparametric regimes of estimation and are automatically adaptive and semiparametric efficient in the regime of parametric convergence rate. [abs] [ pdf ][ bib ] &copy JMLR 2021. ( edit, beta )

UAI Conference 2019 Conference Paper

Identification In Missing Data Models Represented By Directed Acyclic Graphs

• Rohit Bhattacharya
• Razieh Nabi
• Ilya Shpitser
• James M. Robins

Missing data is a pervasive problem in data analyses, resulting in datasets that contain censored realizations of a target distribution. Many approaches to inference on the target distribution using censored observed data, rely on missing data models represented as a factorization with respect to a directed acyclic graph. In this paper we consider the identifiability of the target distribution within this class of models, and show that the most general identification strategies proposed so far retain a significant gap in that they fail to identify a wide class of identifiable distributions. To address this gap, we propose a new algorithm that significantly generalizes the types of manipulations used in the ID algorithm [14, 16], developed in the context of causal inference, in order to obtain identification.

UAI Conference 2013 Conference Paper

Sparse Nested Markov models with Log-linear Parameters

• Ilya Shpitser
• Robin J. Evans 0002
• Thomas S. Richardson 0001
• James M. Robins

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.

UAI Conference 2012 Conference Paper

Nested Markov Properties for Acyclic Directed Mixed Graphs

• Thomas S. Richardson 0001
• James M. Robins
• Ilya Shpitser

Directed acyclic graph (DAG) models may be characterized in four different ways: via a factorization, the dseparation criterion, the moralization criterion, and the local Markov property. As pointed out by Robins [2, 1], Verma and Pearl [6], and Tian and Pearl [5], 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 [3], and an efficient variable elimination scheme [4]. Using acyclic directed mixed graphs (ADMGs) we provide a graphical characterization of the constraints given in [5] via a nested Markov property that uses a ‘fixing’ transformation on graphs. We give four characterizations of our nested model that are analogous to those given for DAGs. We show that marginal distributions of DAG models obey this property.

UAI Conference 2011 Conference Paper

An Efficient Algorithm for Computing Interventional Distributions in Latent Variable Causal Models

• Ilya Shpitser
• Thomas S. Richardson 0001
• James M. Robins

UAI Conference 2010 Conference Paper

On the Validity of Covariate Adjustment for Estimating Causal Effects

• Ilya Shpitser
• Tyler J. VanderWeele
• James M. Robins

Identifying effects of actions (treatments) on outcome variables from observational data and causal assumptions is a fundamental problem in causal inference. This identification is made difficult by the presence of confounders which can be related to both treatment and outcome variables. Confounders are often handled, both in theory and in practice, by adjusting for covariates, in other words considering outcomes conditioned on treatment and covariate values, weighed by probability of observing those covariate values. In this paper, we give a complete graphical criterion for covariate adjustment, which we term the adjustment criterion, and derive some interesting corollaries of the completeness of this criterion.

IJCAI Conference 2009 Conference Paper

• Ilya Shpitser
• Thomas S. Richardson
• James M. Robins

We consider the problem of testing whether two variables should be adjacent (either due to a direct effect between them, or due to a hidden common cause) given an observational distribution, and a set of causal assumptions encoded as a causal diagram. In other words, given a set of edges in the diagram known to be true, we are interested in testing whether another edge ought to be in the diagram. In fully observable faithful models this problem can be easily solved with conditional independence tests. Latent variables make the problem significantly harder since they can imply certain non-adjacent variable pairs, namely those connected by so called inducing paths, are not independent conditioned on any set of variables. We characterize which variable pairs can be determined to be non-adjacent by a class of constraints due to dormant independence, that is conditional independence in identifiable interventional distributions. Furthermore, we show that particular operations on joint distributions, which we call truncations are sufficient for exhibiting these non-adjacencies. This suggests a causal discovery procedure taking advantage of these constraints in the latent variable case can restrict itself to truncations.

JMLR Journal 2009 Journal Article

Properties of Monotonic Effects on Directed Acyclic Graphs

• Tyler J. VanderWeele
• James M. Robins

Various relationships are shown hold between monotonic effects and weak monotonic effects and the monotonicity of certain conditional expectations. Counterexamples are provided to show that the results do not hold under less restrictive conditions. Monotonic effects are furthermore used to relate signed edges on a causal directed acyclic graph to qualitative effect modification. The theory is applied to an example concerning the direct effect of smoking on cardiovascular disease controlling for hypercholesterolemia. Monotonicity assumptions are used to construct a test for whether there is a variable that confounds the relationship between the mediator, hypercholesterolemia, and the outcome, cardiovascular disease. [abs] [ pdf ][ bib ] &copy JMLR 2009. ( edit, beta )

UAI Conference 1997 Conference Paper

Estimation of Effects of Sequential Treatments by Reparameterizing Directed Acyclic Graphs

• James M. Robins
• Larry A. Wasserman

UAI Conference 1995 Conference Paper

Probabilistic evaluation of sequential plans from causal models with hidden variables

• Judea Pearl
• James M. Robins

The paper concerns the probabilistic evaluation of plans in the presence of unmeasured variables, each plan consisting of several concurrent or sequential actions. We establish a graphical criterion for recognizing when the effects of a given plan can be predicted from passive observations on measured variables only. When the criterion is satisfied, a closed-form expression is provided for the probability that the plan will achieve a specified goal.