Stable Training of Probabilistic Models Using the Leave-One-Out Maximum Log-Likelihood Objective
This addresses data quality assessment and generation in power systems when historical data is limited, but it is an incremental improvement over existing KDE methods.
The paper tackled the problem of kernel density estimation models failing to adapt to varying data densities by proposing an adaptive KDE model with individual kernel bandwidths and a leave-one-out maximum log-likelihood objective to prevent singular solutions, showing promising performance on power systems datasets compared to Gaussian mixture models.
Probabilistic modelling of power systems operation and planning processes depends on data-driven methods, which require sufficiently large datasets. When historical data lacks this, it is desired to model the underlying data generation mechanism as a probability distribution to assess the data quality and generate more data, if needed. Kernel density estimation (KDE) based models are popular choices for this task, but they fail to adapt to data regions with varying densities. In this paper, an adaptive KDE model is employed to circumvent this, where each kernel in the model has an individual bandwidth. The leave-one-out maximum log-likelihood (LOO-MLL) criterion is proposed to prevent the singular solutions that the regular MLL criterion gives rise to, and it is proven that LOO-MLL prevents these. Relying on this guaranteed robustness, the model is extended by adjustable weights for the kernels. In addition, a modified expectation-maximization algorithm is employed to accelerate the optimization speed reliably. The performance of the proposed method and models are exhibited on two power systems datasets using different statistical tests and by comparison with Gaussian mixture models. Results show that the proposed models have promising performance, in addition to their singularity prevention guarantees.