Self-paced learning (SPL) is a recently raised methodology designed through simulating the learning principle of humans animals. A variety of SPL realization schemes have been designed for different computer vision and pattern recognition tasks, and empirically substantiated to be effective in these applications. However, the investigation on its theoretical insight is still a blank. To this issue, this study attempts to provide some new theoretical understanding under the SPL scheme. Specifically, we prove that the solving strategy on SPL accords with a majorization minimization algorithm implemented on a latent objective function. Furthermore, we find that the loss function contained in this latent objective has a similar configuration with non-convex regularized penalty (NSPR) known in statistics and machine learning. Such connection inspires us discovering more intrinsic relationship between SPL regimes and NSPR forms, like SCAD, LOG and EXP. The robustness insight under SPL can then be finely explained. We also analyze the capability of SPL on its easy loss prior embedding property, and provide an insightful interpretation to the effectiveness mechanism under previous SPL variations. Besides, we design a group-partial-order loss prior, which is especially useful to weakly labeled large-scale data processing tasks. Through applying SPL with this loss prior to the FCVID dataset, which is currently one of the biggest manually annotated video dataset, our method achieves state-of-the-art performance beyond previous methods, which further helps supports the proposed theoretical arguments.
@cite_6: Abstract The well-known EM algorithm is an optimization transfer algorithm that depends on the notion of incomplete or missing data. By invoking convexity arguments, one can construct a variety of other optimization transfer algorithms that do not involve missing data. These algorithms all rely on a majorizing or minorizing function that serves as a surrogate for the objective function. Optimizing the surrogate function drives the objective function in the correct direction. This article illustrates this general principle by a number of specific examples drawn from the statistical literature. Because optimization transfer algorithms often exhibit the slow convergence of EM algorithms, two methods of accelerating optimization transfer are discussed and evaluated in the context of specific problems.
MM algorithms have wide applications in machine learning and statistical inference @cite_6 . It aims to turn a complicated optimization problem into a tractable one by alternatively iterating the majorization and minimization steps. In particular, considering a minimization problem with objective @math , given an estimate @math at the @math iteration, a typical MM algorithm consists of the following two steps: