  A rich supply of data and innovative algorithms have made data-driven
modeling a popular technique in modern industry. Among various data-driven
methods, latent variable models (LVMs) and their counterparts account for a
major share and play a vital role in many industrial modeling areas. LVM can be
generally divided into statistical learning-based classic LVM and neural
networks-based deep LVM (DLVM). We first discuss the definitions, theories and
applications of classic LVMs in detail, which serves as both a comprehensive
tutorial and a brief application survey on classic LVMs. Then we present a
thorough introduction to current mainstream DLVMs with emphasis on their
theories and model architectures, soon afterwards provide a detailed survey on
industrial applications of DLVMs. The aforementioned two types of LVM have
obvious advantages and disadvantages. Specifically, classic LVMs have concise
principles and good interpretability, but their model capacity cannot address
complicated tasks. Neural networks-based DLVMs have sufficient model capacity
to achieve satisfactory performance in complex scenarios, but it comes at
sacrifices in model interpretability and efficiency. Aiming at combining the
virtues and mitigating the drawbacks of these two types of LVMs, as well as
exploring non-neural-network manners to build deep models, we propose a novel
concept called lightweight deep LVM (LDLVM). After proposing this new idea, the
article first elaborates the motivation and connotation of LDLVM, then provides
two novel LDLVMs, along with thorough descriptions on their principles,
architectures and merits. Finally, outlooks and opportunities are discussed,
including important open questions and possible research directions.
