Tracking Dynamic Gaussian Density with a Theoretically Optimal Sliding
  Window Approach
Yinsong Wang Yu Ding Shahin Shahrampour
Dynamic density estimation is ubiquitous in many applications, including
computer vision and signal processing. One popular method to tackle this
problem is the "sliding window" kernel density estimator. There exist various
implementations of this method that use heuristically defined weight sequences
for the observed data. The weight sequence, however, is a key aspect of the
estimator affecting the tracking performance significantly. In this work, we
study the exact mean integrated squared error (MISE) of "sliding window"
Gaussian Kernel Density Estimators for evolving Gaussian densities. We provide
a principled guide for choosing the optimal weight sequence by theoretically
characterizing the exact MISE, which can be formulated as constrained quadratic
programming. We present empirical evidence with synthetic datasets to show that
our weighting scheme indeed improves the tracking performance compared to
heuristic approaches.