  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.
