Algorithm 1.

Alternating Imputation and Correction Method (AICM)

Hyperparameter: Dropping rate r, maximum iteration iter, regularization term λr, and hard constraint term λh.

Input: Two data matrices, of both n drugs and p cell-lines with summarized sensitivity data, denote as $A,B\in {ℝ}^{n\times p}$. We denote jth column of two matrices as aj; bj, j ∈ {1, 2,…,p} respectively. We denote the entry at ith row and jth column as Aij and Bij respectively, {i, j} ∈ {1, 2,…,n} × {1, 2,…, p}.

Initialization: For each j ∈ {1, 2,…,p} for all i ∈ {1, 2,…,n} such that Bij is missing while Aij is not, we denote such set as $B_{ij}^{\text{NA}}$, we fit a linear model such that αj, βj maximizes ${\Vert b^j-{\alpha }_j{a}^j+{\beta }_j\Vert }_2$ and then impute the missing values as $B_{ij}^{\text{NA}}={\alpha }_j{A}_{ij}+{\beta }_j$. Then swap the role of A and B and repeat the above process. Now we have two matrices with same missing indices.

for k in {1, 2,… Iter} do

Swap: A → B, B → A.

Drop: Randomly drop r × n × p data uniformly from A, we denote the indices of the dropped data as $\mathcal{D}\subseteq \{1,2,\dots ,n\}\times \{1,2,\dots ,p\}$, and hence dropped data as a set $A^{\text{DR}}:=\left\{{\cup }_{\{i,j\}\in \mathcal{D}}{A}_{ij}\right\}$. In a similar fashion, we denote dropped data of column k as $a_{\text{DR}}^k:=\left\{{\cup }_{\{i,j\}\in \mathcal{D},\forall i\text{ s.t.}j=k}{A}_{ij}\right\}$, we denote the corresponding data in kth column of B as $b_{\text{ADR}}^k$. We fit a set of parameters ${\alpha }_j\in ℝ$, ${\beta }_j\in ℝ$ for each j with the following objective function:

$\underset{{\alpha }_j,{\beta }_j}{\text{min}}\frac{1}{n}{\Vert b^j-\left({\alpha }_j{a}^j+{\beta }_j\right)\Vert }_2+{\text{λ}}_r{\Vert a_{\text{DR}}^j-\left({\alpha }_j{b}_{\text{ADR}}^j+{\beta }_j\right)\Vert }_{\infty }\text{(4)}$

Correction: Set $a_{\text{DR}}^j={\alpha }_j{b}_{\text{ADR}}^j+{\beta }_j$ or each j. We denote the set of corrected value as $\left\{A^{\text{IMP}}\right\}={\cup }_{j=1}^p\left\{a_{\text{DR}}^j\right\}$.

Threshold: For $\{i,j\}\in \mathcal{D}$, we set{AIMP}ij to

${\left\{A^{\text{IMP}}\right\}}_{ij}=\text{max}\left(\text{min}\left(A_{ij},\left(1-{\text{λ}}_h\right)A_{ij}\right),\left(1+{\text{λ}}_h\right)A_{ij}\right)\text{(5)}$

end for