Consistency guarantees for greedy permutation-based causal inference algorithms

The Consistency of Greedy Algorithms for Classification

Robust Guarantees of Stochastic Greedy Algorithms

In this paper we analyze the robustness of stochastic variants of the greedy algorithm for submodular maximization. Our main result shows that for maximizing a monotone submodular function under a cardinality constraint, iteratively selecting an element whose marginal contribution is approximately maximal in expectation is a sufficient condition to obtain the optimal approximation guarantee wit...

Uniform consistency in causal inference

There is a long tradition of representing causal relationships by directed acyclic graphs (Wright, 1934). Spirtes (1994), Spirtes et al. (1993) and Pearl & Verma (1991) describe procedures for inferring the presence or absence of causal arrows in the graph even if there might be unobserved confounding variables, and/or an unknown time order, and that under weak conditions, for certain combinati...

Greedy Algorithms for Cone Constrained Optimization with Convergence Guarantees

Greedy optimization methods such as Matching Pursuit (MP) and Frank-Wolfe (FW) algorithms regained popularity in recent years due to their simplicity, effectiveness and theoretical guarantees. MP and FW address optimization over the linear span and the convex hull of a set of atoms, respectively. In this paper, we consider the intermediate case of optimization over the convex cone, parametrized...

The Greedy Fast Causal Inference (GFCI) Algorithm for Continuous Variables

GFCIc [Ogarrio, 2016] is an algorithm that takes as input a dataset of continuous variables and outputs a graphical model called a PAG (see the appendix), which is a representation of a set of causal networks that may include hidden confounders. The PAG that GFCIc returns serves as a data-supported hypothesis about causal relationships that exist among the variables in the dataset. Such models ...