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.
Instead of using the heuristic strategies, @cite_15 formulated the key principle of CL as a concise SPL model. Formally, given a training dataset @math , in which @math and @math denote the @math observed sample and its label, respectively, @math denotes the loss function which calculates the cost between the ground truth label @math and the estimated one @math , and @math represents the model parameter in decision function @math . The SPL model includes a weighted loss term on all samples and a general self-paced regularizer imposed on sample weights, expressed as:
@cite_15
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We observe a training set Q composed of l labeled samples (X sub 1 , spl theta sub 1 ),...,(X sub l , spl theta sub l ) and u unlabeled samples X sub 1 ',...,X sub u ' . The labels spl theta sub i are independent random variables satisfying Pr spl theta sub i =1 = spl eta , Pr spl theta sub i =2 =1- spl eta . The labeled observations X sub i are independently distributed with conditional density f sub spl theta i ( spl middot ) given spl theta sub i . Let (X sub 0 , spl theta sub 0 ) be a new sample, independently distributed as the samples in the training set. We observe X sub 0 and we wish to infer the classification spl theta sub 0 . In this paper we first assume that the distributions f sub 1 ( spl middot ) and f sub 2 ( spl middot ) are given and that the mixing parameter is unknown. We show that the relative value of labeled and unlabeled samples in reducing the risk of optimal classifiers is the ratio of the Fisher informations they carry about the parameter spl eta . We then assume that two densities g sub 1 ( spl middot ) and g sub 2 ( spl middot ) are given, but we do not know whether g sub 1 ( spl middot )=f sub 1 ( spl middot ) and g sub 2 ( spl middot )=f sub 2 ( spl middot ) or if the opposite holds, nor do we know spl eta . Thus the learning problem consists of both estimating the optimum partition of the observation space and assigning the classifications to the decision regions. Here, we show that labeled samples are necessary to construct a classification rule and that they are exponentially more valuable than unlabeled samples.