AcceleratedLiNGAM: Learning Causal DAGs at the speed of GPUs
(2403.03772)Abstract
Existing causal discovery methods based on combinatorial optimization or search are slow, prohibiting their application on large-scale datasets. In response, more recent methods attempt to address this limitation by formulating causal discovery as structure learning with continuous optimization but such approaches thus far provide no statistical guarantees. In this paper, we show that by efficiently parallelizing existing causal discovery methods, we can in fact scale them to thousands of dimensions, making them practical for substantially larger-scale problems. In particular, we parallelize the LiNGAM method, which is quadratic in the number of variables, obtaining up to a 32-fold speed-up on benchmark datasets when compared with existing sequential implementations. Specifically, we focus on the causal ordering subprocedure in DirectLiNGAM and implement GPU kernels to accelerate it. This allows us to apply DirectLiNGAM to causal inference on large-scale gene expression data with genetic interventions yielding competitive results compared with specialized continuous optimization methods, and Var-LiNGAM for causal discovery on U.S. stock data.
Overview
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Introduces AcceleratedLiNGAM, an optimization of LiNGAM for GPU for enhanced computational efficiency enabling application to large-scale datasets.
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Utilizes GPU parallelization to significantly reduce execution time for causal discovery, achieving up to a 32-fold speed increase over CPU executions.
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Validated on NVIDIA RTX 6000 Ada GPU, balancing memory and computational efficiency, and showing accuracy and reliability through simulated datasets.
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Potential applications range from genomics to finance, showcasing versatility and the prospect for significant contributions across various fields.
Accelerating Causal Discovery with GPUs: An Analysis of LiNGAM Methods on Large-Scale Data
Introduction to AcceleratedLiNGAM
Causal discovery techniques play a pivotal role in various scientific fields by enabling the identification of causal relationships from observational data. Among the renowned causal discovery methods, the LiNGAM (Linear Non-Gaussian Acyclic Model) family stands out due to its unique utilization of non-Gaussian data properties to discern causal relationships within a directed acyclic graph (DAG) framework. However, the computational complexity of existing LiNGAM implementations, primarily due to their reliance on quadratic or cubic operations relative to the number of variables, severely limits their applicability to large datasets. This paper introduces AcceleratedLiNGAM, an optimized implementation leveraging GPU processing capabilities to significantly enhance computational efficiency, thus enabling the application of LiNGAM methodologies to large-scale problems.
GPU Parallelization: A Path to Efficiency
The cornerstone of accelerating LiNGAM on GPUs is the parallelization of costly computational patterns, particularly the causal ordering discovery procedure, which is the most time-consuming aspect of DirectLiNGAM and VarLiNGAM analyses. Through careful allocation of computational tasks across GPU threads, and optimizing memory usage and operations such as parallel reductions within GPU memory hierarchies, the AcceleratedLiNGAM approach realizes a substantial reduction in execution time. Notably, this optimization achieves up to a 32-fold speed-up compared to conventional CPU-based executions without compromising the statistical properties and guarantees inherent to the LiNGAM methodology.
Implementation and Validation
The actualization of AcceleratedLiNGAM is validated on a NVIDIA RTX 6000 Ada GPU, with implementation details meticulously crafted to balance memory usage and computational efficiency. This balanced approach ensures that while the vast parallel processing power of GPUs is harnessed, sensitivities such as non-associative floating-point operation errors and synchronization overheads are adequately addressed. Empirical validation on simulated datasets confirms that AcceleratedLiNGAM faithfully reproduces results consistent with traditional LiNGAM implementations, thereby validating its accuracy and reliability.
Applications and Impact
AcceleratedLiNGAM's application to large-scale gene expression data with genetic interventions showcases its potential to facilitate advanced causal inference in genomics, a domain where understanding genetic interactions can lead to breakthroughs in medicine and biology. Similarly, applying AcceleratedLiNGAM to financial data, such as stock indices, provides insights into causal relationships within complex economic systems, highlighting AcceleratedLiNGAM's versatility and its potential to contribute meaningfully across varied domains where causal discovery is crucial.
Future Directions and Community Engagement
While AcceleratedLiNGAM marks a significant advancement in the scalable application of causal discovery methodologies, it also opens avenues for further optimizations and applications. Future work could explore deeper GPU-specific optimizations, incorporation of emerging GPU technologies, and expansions to accommodate a broader array of causal discovery models. Recognizing the broader community's role in this evolutionary process, the decision to open-source AcceleratedLiNGAM seeks to foster collaborative enhancements and applications, inviting contributions and explorations from varied fields.
Concluding Remarks
In summary, AcceleratedLiNGAM represents a significant leap forward in enabling the application of LiNGAM causal discovery techniques to large-scale datasets. By leveraging GPU technologies, it overcomes computational barriers and opens new horizons for causal analysis across scientific domains. This work not only contributes a practical tool for researchers but also sets the stage for future innovations in the field of causal discovery.
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