Algorithm 1.

MP-Boost

MP-Boost (X, y, n, m, μ)

Initialization (t = 0):

p(1) = U[N] // observation probabilities

q(1) = U[M] // feature probabilities

F(1) (xi) = 0, ∀i ∈ [N] // ensemble output

G(1) (xi) =0, ∀i ∈ [N] // out-of-patch output

while Stopping – Criterion(oop(t)) not met do t ← t +1

1) Sample a minipatch:

a) ${\mathcal{R}}^{(t)}=\mathrm{Sample}\left(N,n,p^{(t)}\right)$ // select n instances

b) ${\mathcal{C}}^{(t)}=\mathrm{Sample}\left(M,m,q^{(t)}\right)$ // select m features

c) $\left({\mathbf{X}}^{(t)},{\mathbf{y}}^{(t)}\right)=\left({\mathbf{X}}_{\mathcal{R}(t),\mathcal{C}(t)},{\mathbf{y}}_{\mathcal{R}(t)}\right)$ // minipatch

2) Train a weak learner on the minipatch:

a) $h^{(t)}\in \mathcal{H}$: weak learner trained on X(t), y(t)

3) Update outputs:

a) $F^{(t)}\left({\mathbf{x}}_i\right)=F^{(t-1)}\left({\mathbf{x}}_i\right)+h^{(t)}\left({\left({\mathbf{x}}_i\right)}_{\mathcal{C}(t)}\right),\forall i\in [N]$

4) Update probability distributions:

a) $p_i^{(t+1)}=\frac{\mathcal{L}\left(y_i,F^{(t)}\left({\mathbf{x}}_i\right)\right)}{{\sum }_{k=1}^N\mathcal{L}\left(y_k,F^{(t)}\left({\mathbf{x}}_k\right)\right)},\forall i\in [N]$

b) $q_j^{(t+1)}=(1-\mu )q_j^{(t)}+\mu r{\mathcal{I}}_j^{h^{(t)}},j\in {\mathcal{C}}^{(t)}$

where, $r=\sum _{j\in \mathcal{C}(t)}{q}_j^{(t)}$

5) Out-of-Patch Accuracy:

a) $G^{(t)}\left({\mathbf{x}}_i\right)=G^{(t-1)}\left({\mathbf{x}}_i\right)+h^{(t)}\left({\left({\mathbf{x}}_i\right)}_{\mathcal{C}(t)}\right),\forall i\notin {\mathcal{R}}^{(t)}$

b) ${\mathrm{oop}}^{(t)}=\frac{1}{N}{\sum }_{i=1}^N{\mathbb{1}}_{\left\{\mathrm{sgn}\left(G^{(t)}\left({\mathbf{x}}_i\right)\right)=y_i\right\}}$

end while

Return sgn(F(T)), p(T), q(T)