By drawing analogy, I believe that Bayesian linear regression has a time complexity same to standard linear regression $(^2+^3)$ which is dominated by the number of features $p$ (What is the Time Complexity of Linear Regression?). To be more specific, the $O(p^3)$ term arises because we need to invert $X^TX$. On the other hand, in Gaussian process regression we need to invert a $n$ x $n$ covariance matrix (with noise), which results in $O(n^3)$. But Bayesian linear regression can be interpreted as Gaussian process at the same time. So why is there such an inconsistency or am I missing something?
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