# cuPC: CUDA-based Parallel PC Algorithm for Causal Structure Learning on GPU

## TL;DR

This paper introduces cuPC, a GPU-accelerated parallel algorithm for causal structure learning using the PC algorithm, achieving significant speedups over CPU implementations.

## Contribution

The paper presents a novel CUDA-based parallel PC algorithm with two variants, enabling scalable causal discovery on GPUs for large datasets.

## Key findings

- Achieves up to 1300x speedup over CPU implementations.
- Reduces runtime from over 11 hours to about 4 seconds on challenging datasets.
- Demonstrates scalability with respect to variables, samples, and graph density.

## Abstract

The main goal in many fields in the empirical sciences is to discover causal relationships among a set of variables from observational data. PC algorithm is one of the promising solutions to learn underlying causal structure by performing a number of conditional independence tests. In this paper, we propose a novel GPU-based parallel algorithm, called cuPC, to execute an order-independent version of PC. The proposed solution has two variants, cuPC-E and cuPC-S, which parallelize PC in two different ways for multivariate normal distribution. Experimental results show the scalability of the proposed algorithms with respect to the number of variables, the number of samples, and different graph densities. For instance, in one of the most challenging datasets, the runtime is reduced from more than 11 hours to about 4 seconds. On average, cuPC-E and cuPC-S achieve 500 X and 1300 X speedup, respectively, compared to serial implementation on CPU. The source code of cuPC is available online [1].