We consider a statistical problem to estimate variables (effects) that are associated with the edges of a complete bipartite graph $K_{v_1, v_2}=(V_1, V_2 \, ; E)$. Each data is obtained as a sum of selected effects, a subset of $E$. In order to estimate efficiently, we propose a design called Spanning Bipartite Block Design (SBBD). For SBBDs such that the effects are estimable, we proved that the estimators have the same variance (variance balanced). If each block (a subgraph of $K_{v_1, v_2}$) of SBBD is a semi-regular or a regular bipartite graph, we show that the design is A-optimum. We also show a construction of SBBD using an ($r,\lambda$)-design and an ordered design. A BIBD with prime power blocks gives an A-optimum semi-regular or regular SBBD. At last, we mention that this SBBD is able to use for deep learning.

翻译：考虑一个统计问题，旨在估计与完全二部图 $K_{v_1, v_2}=(V_1, V_2 \, ; E)$ 的边相关联的变量（效应）。每个数据点通过选取的效应子集之和获得，该子集是 $E$ 的一个子集。为实现高效估计，我们提出一种名为生成二部块设计（Spanning Bipartite Block Design, SBBD）的设计方案。对于效应可估计的SBBD，我们证明了估计量具有相同的方差（方差平衡性）。若SBBD的每个块（$K_{v_1, v_2}$ 的子图）为半正则或正则二部图，则证明该设计是A最优的。我们还展示了利用$(r,\lambda)$-设计和有序设计构造SBBD的方法。具有素幂阶块的平衡不完全区组设计（BIBD）可生成A最优的半正则或正则SBBD。最后，我们指出该SBBD可应用于深度学习领域。