arXiv:2602.02190v2 Announce Type: replace-cross Abstract: A common approach to perform PCA on probability measures is to embed them into a Hilbert space where standard functional PCA techniques apply. While convergence rates for estimating the embedding of a single measure from $m$ samples are well understood, the literature has not addressed the setting involving multiple measures. In this paper, we study PCA in a double asymptotic regime where $n$ probability measures are observed, each through $m$ samples. We derive convergence rates of the form $n^{-1/2} + m^{-\alpha}$ for the empirical co
This paper refines statistical methods for Principal Component Analysis in machine learning, addressing a gap in understanding multi-measure sampling regimes.
Improved PCA techniques, particularly for probabilistic measures, can lead to more robust and efficient AI models, impacting various downstream applications that rely on complex data analysis.
The understanding of convergence rates for PCA when dealing with multiple probability measures, each observed through samples, becomes more precise, potentially enhancing the reliability of ML models.
- · AI researchers
- · Machine learning engineers
- · Data scientists
More accurate and scalable dimensionality reduction techniques become available for complex datasets.
This could enable better performance and efficiency in AI applications dealing with uncertainty or distributions, such as reinforcement learning or generative models.
The enhanced foundational mathematics of AI might subtly accelerate general AI development by improving core analytical tools.
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