Nowadays self-paced learning (SPL) is an important machine learning paradigm that mimics the cognitive process of humans and animals. The SPL regime involves a self-paced regularizer and a gradually increasing age parameter, which plays a key role in SPL but where to optimally terminate this process is still non-trivial to determine. A natural idea is to compute the solution path w.r.t. age parameter (i.e., age-path). However, current age-path algorithms are either limited to the simplest regularizer, or lack solid theoretical understanding as well as computational efficiency. To address this challenge, we propose a novel \underline{G}eneralized \underline{Ag}e-path \underline{A}lgorithm (GAGA) for SPL with various self-paced regularizers based on ordinary differential equations (ODEs) and sets control, which can learn the entire solution spectrum w.r.t. a range of age parameters. To the best of our knowledge, GAGA is the first exact path-following algorithm tackling the age-path for general self-paced regularizer. Finally the algorithmic steps of classic SVM and Lasso are described in detail. We demonstrate the performance of GAGA on real-world datasets, and find considerable speedup between our algorithm and competing baselines.

We discuss \emph{Cross-Lingual Text Quantification} (CLTQ), the task of performing text quantification (i.e., estimating the relative frequency $p_{c}(D)$ of all classes $c\in\mathcal{C}$ in a set $D$ of unlabelled documents) when training documents are available for a source language $\mathcal{S}$ but not for the target language $\mathcal{T}$ for which quantification needs to be performed. CLTQ has never been discussed before in the literature; we establish baseline results for the binary case by combining state-of-the-art quantification methods with methods capable of generating cross-lingual vectorial representations of the source and target documents involved. We present experimental results obtained on publicly available datasets for cross-lingual sentiment classification; the results show that the presented methods can perform CLTQ with a surprising level of accuracy.