Design and accuracy trade-offs in Computational Statistics

2025-09-13

AI Summary

In statistical computing, extremely small probabilities frequently cause numerical underflow; while traditional logarithmic-space arithmetic mitigates this issue, it incurs substantial precision loss, increased resource consumption, and degraded performance. This paper presents the first systematic analysis of the precision cost inherent in logarithmic representations for statistical computation and proposes replacing them with the novel posit floating-point format to jointly optimize accuracy, efficiency, and hardware resource utilization. We implement and evaluate posit-based accelerators on an FPGA platform, benchmarking basic arithmetic operations and representative bioinformatics statistical workloads against binary64 and logarithmic representations. Experimental results demonstrate that the posit accelerator achieves up to two orders-of-magnitude higher accuracy than the logarithmic accelerator, reduces logic resource usage by 60%, improves execution speed by 1.3×, and doubles throughput per unit hardware resource.

Technology Category

• Machine Learning: Statistical Relational/Logic Learning
• Reasoning under Uncertainty: Probabilistic Programming
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

Statistical computations are becoming increasingly important. These computations often need to be performed in log-space because probabilities become extremely small due to repeated multiplications. While using logarithms effectively prevents numerical underflow, this paper shows that its cost is high in performance, resource utilization, and, notably, numerical accuracy. This paper then argues that using posit, a recently proposed floating-point format, is a better strategy for statistical computations operating on extremely small numbers because of its unique encoding mechanism. To that end, this paper performs a comprehensive analysis comparing posit, binary64, and logarithm representations, examining both individual arithmetic operations, statistical bioinformatics applications, and their accelerators. FPGA implementation results highlight that posit-based accelerators can achieve up to two orders of magnitude higher accuracy, up to 60% lower resource utilization, and up to $1.3 imes$ speedup, compared to log-space accelerators. Such improvement translates to $2 imes$ performance per unit resource on the FPGA.

Problem

• Evaluating performance and accuracy trade-offs in statistical computations
• Addressing numerical underflow and inefficiency in log-space computations
• Proposing posit format for improved accuracy and resource efficiency

Innovation

• Using posit format for statistical computations
• Comparing posit with binary64 and logarithm representations
• Achieving higher accuracy and lower resource utilization