Stochastic Trust Region Methods with Trust Region Radius Depending on Probabilistic Models

We present a stochastic trust-region model-based framework in which its radius is related to the probabilistic models. Especially, we propose a specific algorithm, termed STRME, in which the trust-region radius depends linearly on the latest model gradient. The complexity of STRME method in non-convex, convex and strongly convex settings has all been analyzed, which matches the existing algorithms based on probabilistic properties. In addition, several numerical experiments are carried out to reveal the benefits of the proposed methods compared to the existing stochastic trust-region methods and other relevant stochastic gradient methods

Task-specific Word Identification from Short Texts Using a Convolutional Neural Network

Task-specific word identification aims to choose the task-related words that best describe a short text. Existing approaches require well-defined seed words or lexical dictionaries (e.g., WordNet), which are often unavailable for many applications such as social discrimination detection and fake review detection. However, we often have a set of labeled short texts where each short text has a task-related class label, e.g., discriminatory or non-discriminatory, specified by users or learned by classification algorithms. In this paper, we focus on identifying task-specific words and phrases from short texts by exploiting their class labels rather than using seed words or lexical dictionaries. We consider the task-specific word and phrase identification as feature learning. We train a convolutional neural network over a set of labeled texts and use score vectors to localize the task-specific words and phrases. Experimental results on sentiment word identification show that our approach significantly outperforms existing methods. We further conduct two case studies to show the effectiveness of our approach. One case study on a crawled tweets dataset demonstrates that our approach can successfully capture the discrimination-related words/phrases. The other case study on fake review detection shows that our approach can identify the fake-review words/phrases.Comment: accepted by Intelligent Data Analysis, an International Journa

Competing electronic orders on Kagome lattices at van Hove filling

The electronic orders in Hubbard models on a Kagome lattice at van Hove filling are of intense current interest and debate. We study this issue using the singular-mode functional renormalization group theory. We discover a rich variety of electronic instabilities under short range interactions. With increasing on-site repulsion $U$, the system develops successively ferromagnetism, intra unit-cell antiferromagnetism, and charge bond order. With nearest-neighbor Coulomb interaction $V$ alone (U=0), the system develops intra-unit-cell charge density wave order for small $V$, s-wave superconductivity for moderate $V$, and the charge density wave order appears again for even larger $V$. With both $U$ and $V$, we also find spin bond order and chiral $d_{x^2 - y^2} + i d_{xy}$ superconductivity in some particular regimes of the phase diagram. We find that the s-wave superconductivity is a result of charge density wave fluctuations and the squared logarithmic divergence in the pairing susceptibility. On the other hand, the d-wave superconductivity follows from bond order fluctuations that avoid the matrix element effect. The phase diagram is vastly different from that in honeycomb lattices because of the geometrical frustration in the Kagome lattice.Comment: 8 pages with 9 color figure