In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
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Question: Self-paced learning (SPL) has been attracting increasing attention in machine learning and computer vision. Albeit empirically substantiated to be effective, the investigation on its theoretical insight is still a blank. It is even unknown that what objective a general SPL regime converges to. To this issue, this study attempts to initially provide some new insights under this “heuristic” learning scheme. Specifically, we prove that the solving strategy on SPL exactly accords with a majorization minimization algorithm, a well known technique in optimization and machine learning, implemented on a latent objective. A more interesting finding is that, the loss function contained in this latent objective has a similar configuration with non-convex regularized penalty, an attractive topic in statistics and machine learning. In particular, we show that the previous hard and linear self-paced regularizers are equivalent to the capped norm and minimax concave plus penalties, respectively, both being widely investigated in statistics. Such connections between SPL and previous known researches enhance new insightful comprehension on SPL, like convergence and parameter setting rationality. The correctness of the proposed theory is substantiated by experimental results on synthetic and UCI data sets.

Answer: What Objective Does Self-paced Learning Indeed Optimize?


Question: Standard belief change assumes an underlying logic containing full classical propositional logic. However, there are good reasons for considering belief change in less expressive logics as well. In this paper we build on recent investigations by Delgrande on contraction for Horn logic. We show that the standard basic form of contraction, partial meet, is too strong in the Horn case. This result stands in contrast to Delgrande’s conjecture that orderly maxichoice is the appropriate form of contraction for Horn logic. We then define a more appropriate notion of basic contraction for the Horn case, influenced by the convexity property holding for full propositional logic and which we refer to as infra contraction. The main contribution of this work is a result which shows that the construction method for Horn contraction for belief sets based on our infra remainder sets corresponds exactly to Hansson’s classical kernel contraction for belief sets, when restricted to Horn logic. This result is obtained via a detour through contraction for belief bases. We prove that kernel contraction for belief bases produces precisely the same results as the belief base version of infra contraction. The use of belief bases to obtain this result provides evidence for the conjecture that Horn belief change is best viewed as a ‘hybrid’ version of belief set change and belief base change. One of the consequences of the link with base contraction is the provision of a representation result for Horn contraction for belief sets in which a version of the Core-retainment postulate features.

Answer: On the Link between Partial Meet, Kernel, and Infra Contraction and its Application to Horn Logic


Question: Pattern classification systems are commonly used in adversarial applications, like biometric authentication, network intrusion detection, and spam filtering, in which data can be purposely manipulated by humans to undermine their operation. As this adversarial scenario is not taken into account by classical design methods, pattern classification systems may exhibit vulnerabilities, whose exploitation may severely affect their performance, and consequently limit their practical utility. Extending pattern classification theory and design methods to adversarial settings is thus a novel and very relevant research direction, which has not yet been pursued in a systematic way. In this paper, we address one of the main open issues: evaluating at design phase the security of pattern classifiers, namely, the performance degradation under potential attacks they may incur during operation. We propose a framework for empirical evaluation of classifier security that formalizes and generalizes the main ideas proposed in the literature, and give examples of its use in three real applications. Reported results show that security evaluation can provide a more complete understanding of the classifier’s behavior in adversarial environments, and lead to better design choices.

Answer:
Security Evaluation of Pattern Classifiers under Attack