Algorithm 1.

Low-rank MNE block coordinate descent algorithm (globally optimal domain)

1:	inputs: maximum rank r, paired data samples (st, yt) for all t, initial guess for weights a, h, U, and V, set πk for all k = 1, … , r, maximum number of iterations Mmax, regularization parameter precision δϵ, convergence precision δx
2:	initialization: J ← UVT
3:
4:	for m ← 1, … , Mmax do
5:	for k ← 1, … , r do
6:	a′ ← a, h′ ← h, U′ ← U, V′ ← V
7:	$\text{J}\leftarrow \text{J}-{\text{U}}_{•,k}^{\prime }{\text{V}}_{•,k}^{\prime \text{T}}$                                                                         ⊳ remove block k from J
8:	λL ← max(|λmax(∇JL)|, |λmin(∇JL)|) evaluated with primed variables and J
9:	do
10:	ϵk ← λL
11:	a′, h′, ${\text{U}}_{•,k}^{\prime }$, ${\text{V}}_{•,k}^{\prime }\leftarrow$ Solve the block k subproblem (Equation 13) using an
12:	interior-point method algorithm with inputs a′, h′, ${\text{U}}_{•,k}^{\prime }$, ${\text{V}}_{•,k}^{\prime }$, J,
13:	ϵk, πk, (st, yt):∀t
14:	λL ← max(|λmax(∇JL)|, |λmin(∇JL)|)                                ⊳ update eigenvalue threshold
15:	while ϵk ∉ [λL, λL + δϵ]
16:	$\text{J}\leftarrow \text{J}+{\text{U}}_{•,k}^{\prime }{\text{V}}_{•,k}^{\prime \text{T}}$                                                                   ⊳ include kth block solution in J
17:	a ← a′, h ← h′, U ← U′, V ← V′
18:	if ${\Vert \text{x}-{\text{x}}^{\prime \Vert }}_2\le {\delta }_x$ and {ϵk:ϵk ∉ [λL, λL + δϵ], ∀k} = ∅ then
19:	(where $\text{x}=\left[a,{\text{h}}^{\text{T}},{\text{Q}}_{•,1}^{\text{T}},\dots ,{\text{Q}}_{•,r}^{\text{T}}\right]$ and x′ is the analogous vector for primed weights)
20:	break                                                                                              ⊳ optimization has finished
21:
22:	outputs: a, h, J