Existing Multi-fidelity Bayesian Optimization (MFBO) methods ignore the convergence behavior of the multi-fidelity surrogate as the fidelity increases, leading to inefficient exploration and suboptimal performance. We introduce CAMO (Convergence-Aware Multi-fidelity Optimization), a principled framework based on Linear Fidelity Differential Equations (LFiDEs) that explicitly encodes convergence of fidelity-indexed outputs and employs a closed-form nonstationary kernel. We rigorously prove the existence and pointwise/uniform convergence to the high fidelity surrogate under mild restrictions and provide new convergence results for general FiDEs using smooth, non-smooth and even non-convex Lyapunov functions, establishing a bridge between MFBO and the theory of subgradient flows in non-smooth optimisation theory. Combined with a fidelity-aware acquisition function, CAMO outperforms state-of-the-art MFBO methods on a majority of synthetic and real-world benchmarks, with up to a four-fold improvement in optimisation performance and a dramatic speed-up in convergence. CAMO offers a tractable and theoretically grounded approach to convergence-aware MFBO.

Human spine is a multifunctional structure of human body consisting of bones, joints, ligaments, and muscles which all undergo a process of change with the age. A sudden change in these features either naturally or through injury can lead to some serious medical conditions which puts huge burden on health services and economy. While aging is inevitable, the effect of aging on different areas of spine is of clinical significance. This paper reports the growth and degenerative pattern of human spine using principal component analysis. Some noticeable lumbar spine features such as vertebral heights, disc heights, disc signal intensities, paraspinal muscles, subcutaneous fats, psoas muscles, and cerebrospinal fluid were used to study the variations seen on lumbar spine with the natural aging. These features were extracted from lumbar spine magnetic resonance images of 61 subjects with age ranging from 2 to 93 years. Principal component analysis is used to transform complex and multivariate feature space to a smaller meaningful representation. PCA transformation provided 2-D visualization and knowledge of variations among spinal features. Further useful information about correlation among the spinal features is acquired through factor analysis. The knowledge of age related changes in spinal features are important in understanding different spine related problems.