Expand description
Bayesian linear regression (PRML ch 3.3) — a conjugate Gaussian model that returns a predictive distribution (mean + variance), not just a point estimate. This is the mission-aligned payoff: a model that can say “ŷ, and here is how sure” — calibrated uncertainty, with the predictive variance widening away from the data.
Prior w ~ N(0, α⁻¹I), noise precision β = 1/σ². Posterior (PRML 3.53–3.54):
S_N⁻¹ = αI + β ΦᵀΦ, m_N = β S_N Φᵀy. Predictive (3.58–3.59):
mean = m_Nᵀφ, var = 1/β + φᵀ S_N φ. The k×k solves reuse
linear_algebra::cholesky (no new solver). Kernel-class DenseLinear.
Structs§
- Bayesian
Linear - A fitted Bayesian linear model: the posterior over weights (
mean=m_N,cov=S_N) and the noise precisionbeta.