The inflation technique solves completely the classical inference problem

by   Miguel Navascues, et al.

The causal inference problem consists in determining whether a probability distribution over a set of observed variables is compatible with a given causal structure. In [arXiv:1609.00672], one of us introduced a hierarchy of necessary linear programming constraints which all the observed distributions compatible with the considered causal structure must satisfy. In this work, we prove that the inflation hierarchy is complete, i.e., any distribution of the observed variables which does not admit a realization within the considered causal structure will fail one of the inflation tests. More quantitatively, we show that any distribution of measurable events satisfying the n^th inflation test is O(1/√(n))-close in Euclidean norm to a distribution realizable within the given causal structure. In addition, we show that the corresponding n^th-order relaxation of the dual problem consisting in maximizing a k^th degree polynomial on the observed variables is O(k^2/n)-close to the optimal solution.



page 4


The Inflation Technique for Causal Inference with Latent Variables

The problem of causal inference is to determine if a given probability d...

Semidefinite tests for latent causal structures

Testing whether a probability distribution is compatible with a given Ba...

Symbolic Computation of Tight Causal Bounds

Causal inference involves making a set of assumptions about the nature o...

Causal inference via algebraic geometry: feasibility tests for functional causal structures with two binary observed variables

We provide a scheme for inferring causal relations from uncontrolled sta...

Combining the Causal Judgments of Experts with Possibly Different Focus Areas

In many real-world settings, a decision-maker must combine information p...

Factoring Perfect Reconstruction Filter Banks into Causal Lifting Matrices: A Diophantine Approach

The theory of linear Diophantine equations in two unknowns over polynomi...

Efficient inference of interventional distributions

We consider the problem of efficiently inferring interventional distribu...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.