Verification and search algorithms for causal DAGs

• URL: http://arxiv.org/abs/2206.15374v1
• Date: Thu, 30 Jun 2022 15:52:30 GMT
• Title: Verification and search algorithms for causal DAGs
• Authors: Davin Choo, Kirankumar Shiragur, Arnab Bhattacharyya
• Abstract summary: We give a characterization of a minimal sized set of atomic interventions to check the correctness of a claimed causal graph. We generalize our results to the settings of bounded size interventions and node-dependent interventional costs. Our result is the first known algorithm that gives a non-trivial approximation guarantee to the verifying size on general unweighted graphs.
• Score: 11.038866111306728
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study two problems related to recovering causal graphs from interventional data: (i) $\textit{verification}$, where the task is to check if a purported causal graph is correct, and (ii) $\textit{search}$, where the task is to recover the correct causal graph. For both, we wish to minimize the number of interventions performed. For the first problem, we give a characterization of a minimal sized set of atomic interventions that is necessary and sufficient to check the correctness of a claimed causal graph. Our characterization uses the notion of $\textit{covered edges}$, which enables us to obtain simple proofs and also easily reason about earlier results. We also generalize our results to the settings of bounded size interventions and node-dependent interventional costs. For all the above settings, we provide the first known provable algorithms for efficiently computing (near)-optimal verifying sets on general graphs. For the second problem, we give a simple adaptive algorithm based on graph separators that produces an atomic intervention set which fully orients any essential graph while using $\mathcal{O}(\log n)$ times the optimal number of interventions needed to $\textit{verify}$ (verifying size) the underlying DAG on $n$ vertices. This approximation is tight as $\textit{any}$ search algorithm on an essential line graph has worst case approximation ratio of $\Omega(\log n)$ with respect to the verifying size. With bounded size interventions, each of size $\leq k$, our algorithm gives an $\mathcal{O}(\log n \cdot \log \log k)$ factor approximation. Our result is the first known algorithm that gives a non-trivial approximation guarantee to the verifying size on general unweighted graphs and with bounded size interventions.

Related papers

• Linear Causal Bandits: Unknown Graph and Soft Interventions [18.412177974475526]
  designing causal bandit algorithms depends on two central categories of assumptions. The problem in its general form, i.e., unknown graph and unknown intervention models, remains open. This paper addresses this problem and establishes that in a graph with $N$ nodes, maximum in-degree $d$ and maximum causal path length $L$, after $T$ interaction rounds the regret upper bound scales.
  arXiv  Detail & Related papers  (2024-11-04T18:50:39Z)
• On the instance optimality of detecting collisions and subgraphs [7.055459105099637]
  We investigate the unlabeled instance optimality of substructure detection problems in graphs and functions. A problem is $g(n)$-instance optimal if it admits an algorithm $A$ satisfying that for any possible input. Our results point to a trichotomy of unlabeled instance optimality among substructure detection problems in graphs and functions.
  arXiv  Detail & Related papers  (2023-12-15T20:50:03Z)
• Fast Maximum $k$-Plex Algorithms Parameterized by Small Degeneracy Gaps [30.06993761032835]
  The maximum $k$-plex problem is important but computationally challenging in applications such as graph mining and community detection. We present an exact algorithm parameterized by $g_k(G)$, which has the worst-case running time in the size of the input graph and exponential in $g_k(G)$. We further extend our discussion to an even smaller parameter $cg_k(G)$, the gap between the community-degeneracy bound and the size of the maximum $k$-plex.
  arXiv  Detail & Related papers  (2023-06-23T01:28:24Z)
• Causal Bandits for Linear Structural Equation Models [58.2875460517691]
  This paper studies the problem of designing an optimal sequence of interventions in a causal graphical model. It is assumed that the graph's structure is known and has $N$ nodes. Two algorithms are proposed for the frequentist (UCB-based) and Bayesian settings.
  arXiv  Detail & Related papers  (2022-08-26T16:21:31Z)
• Robust Estimation for Random Graphs [47.07886511972046]
  We study the problem of robustly estimating the parameter $p$ of an ErdHos-R'enyi random graph on $n$ nodes. We give an inefficient algorithm with similar accuracy for all $gamma 1/2$, the information-theoretic limit.
  arXiv  Detail & Related papers  (2021-11-09T18:43:25Z)
• Random Graph Matching with Improved Noise Robustness [2.294014185517203]
  We propose a new algorithm for graph matching under probabilistic models. Our algorithm recovers the underlying matching with high probability when $alpha le 1 / (log log n)C$. This improves the condition $alpha le 1 / (log n)C$ achieved in previous work.
  arXiv  Detail & Related papers  (2021-01-28T02:39:27Z)
• Adversarial Linear Contextual Bandits with Graph-Structured Side Observations [80.95090605985042]
  A learning agent repeatedly chooses from a set of $K$ actions after being presented with a $d$-dimensional context vector. The agent incurs and observes the loss of the chosen action, but also observes the losses of its neighboring actions in the observation structures. Two efficient algorithms are developed based on textttEXP3.
  arXiv  Detail & Related papers  (2020-12-10T15:40:07Z)
• Hybrid Stochastic-Deterministic Minibatch Proximal Gradient: Less-Than-Single-Pass Optimization with Nearly Optimal Generalization [83.80460802169999]
  We show that HSDMPG can attain an $mathcalObig (1/sttnbig)$ which is at the order of excess error on a learning model. For loss factors, we prove that HSDMPG can attain an $mathcalObig (1/sttnbig)$ which is at the order of excess error on a learning model.
  arXiv  Detail & Related papers  (2020-09-18T02:18:44Z)
• Streaming Complexity of SVMs [110.63976030971106]
  We study the space complexity of solving the bias-regularized SVM problem in the streaming model. We show that for both problems, for dimensions of $frac1lambdaepsilon$, one can obtain streaming algorithms with spacely smaller than $frac1lambdaepsilon$.
  arXiv  Detail & Related papers  (2020-07-07T17:10:00Z)
• Online Dense Subgraph Discovery via Blurred-Graph Feedback [87.9850024070244]
  We introduce a novel learning problem for dense subgraph discovery. We first propose a edge-time algorithm that obtains a nearly-optimal solution with high probability. We then design a more scalable algorithm with a theoretical guarantee.
  arXiv  Detail & Related papers  (2020-06-24T11:37:33Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.