Forecasting project expenses is a crucial step for businesses to avoid budget overruns and project failures. Traditionally, this has been done by financial analysts or data science techniques such as time-series analysis. However, these approaches can be uncertain and produce results that differ from the planned budget, especially at the start of a project with limited data points. This paper proposes a constrained non-negative matrix completion model that predicts expenses by learning the likelihood of the project correlating with certain expense patterns in the latent space. The model is constrained on three probability simplexes, two of which are on the factor matrices and the third on the missing entries. Additionally, the predicted expense values are guaranteed to meet the budget constraint without the need of post-processing. An inexact alternating optimization algorithm is developed to solve the associated optimization problem and is proven to converge to a stationary point. Results from two real datasets demonstrate the effectiveness of the proposed method in comparison to state-of-the-art algorithms.

翻译：预测项目费用是企业避免预算超支和项目失败的关键步骤。传统上，这一任务由财务分析师或通过时间序列分析等数据科学技术完成。然而，这些方法存在不确定性，尤其是在项目初期数据点有限的情况下，其结果可能与计划预算存在偏差。本文提出一种带约束的非负矩阵补全模型，通过学习项目在潜在空间中与特定费用模式相关联的概率来预测费用。该模型在三个概率单纯形上施加约束：其中两个约束作用于因子矩阵，第三个约束作用于缺失项。此外，预测的费用值能够在不需后处理的情况下确保满足预算约束。我们开发了一种非精确交替优化算法来求解相关优化问题，并证明其能收敛至驻点。在两个真实数据集上的实验结果表明，相较于现有先进算法，所提方法具有有效性。