arXiv subjects

Qing Cui

Publications and source records attributed to Qing Cui.

44 records · Page 3Linked to original sources

arXiv2021

Multi-Interactive Attention Network for Fine-grained Feature Learning in CTR Prediction

In the Click-Through Rate (CTR) prediction scenario, user's sequential behaviors are well utilized to capture the user interest in the recent literature. However, despite being extensively studied, these sequential methods still suffer from three limitations. First, existing methods mostly utilize attention on the behavior of users, which is not always suitable for CTR prediction, because users often click on new products that are irrelevant to any historical behaviors. Second, in the real scenario, there exist numerous users that have operations a long time ago, but turn relatively inactive in recent times. Thus, it is hard to precisely capture user's current preferences through early behaviors. Third, multiple representations of user's historical behaviors in different feature subspaces are largely ignored. To remedy these issues, we propose a Multi-Interactive Attention Network (MIAN) to comprehensively extract the latent relationship among all kinds of fine-grained features (e.g., gender, age and occupation in user-profile). Specifically, MIAN contains a Multi-Interactive Layer (MIL) that integrates three local interaction modules to capture multiple representations of user preference through sequential behaviors and simultaneously utilize the fine-grained user-specific as well as context information. In addition, we design a Global Interaction Module (GIM) to learn the high-order interactions and balance the different impacts of multiple features. Finally, Offline experiment results from three datasets, together with an Online A/B test in a large-scale recommendation system, demonstrate the effectiveness of our proposed approach.

cs.IR↗

arXiv2020

Tight gaps in the cycle spectrum of 3-connected planar graphs

For any positive integer $k$, define $f(k)$ (respectively, $f_3(k)$) to be the minimal integer $\ge k$ such that every 3-connected planar graph $G$ (respectively, 3-connected cubic planar graph $G$) of circumference $\ge k$ has a cycle whose length is in the interval $[k, f(k)]$ (respectively, $[k, f_3(k)]$). Merker showed that $f_3(k) \le 2k + 9$ for any $k \ge 2$, and $f_3(k) \ge 2k + 2$ for any even $k \ge 4$. He conjectured that $f_3(k) \le 2k + 2$ for any $k \ge 2$. This conjecture was disproved by Zamfirescu, who gave an infinite family of counterexamples for every even $k \ge 6$ whose graphs have no cycle length in $[k, 2k + 2]$, i.e. $f_3(k) \ge 2k + 3$ for any even $k \ge 6$. However, the exact value of $f_3(k)$ was only known for $k \le 4$, and it was left open to determine $f_3(k)$ for $k \ge 5$. In this paper we improve Merker's upper bound, and give the exact value of $f_3(k)$ for every $k \ge 5$. We show that $f_3(5) = 10$, $f_3(7) = 15$, $f_3(9) = 20$, and $f_3(k) = 2k + 3$ for any $k = 6, 8$ or $\ge 10$. For general 3-connected planar graphs, Merker conjectured that there exists some positive integer $c$ such that $f(k) \le 2k + c$ for any positive integer $k$. We give a complete positive answer to this conjecture. We prove that $f(k) = 5$ for any $k \le 3$, $f(4) = 10$, and $f(k) = 2k + 3$ for any $k \ge 5$.

math.CO↗

arXiv2019

Value-aware Recommendation based on Reinforced Profit Maximization in E-commerce Systems

Existing recommendation algorithms mostly focus on optimizing traditional recommendation measures, such as the accuracy of rating prediction in terms of RMSE or the quality of top-$k$ recommendation lists in terms of precision, recall, MAP, etc. However, an important expectation for commercial recommendation systems is to improve the final revenue/profit of the system. Traditional recommendation targets such as rating prediction and top-$k$ recommendation are not directly related to this goal. In this work, we blend the fundamental concepts in online advertising and micro-economics into personalized recommendation for profit maximization. Specifically, we propose value-aware recommendation based on reinforcement learning, which directly optimizes the economic value of candidate items to generate the recommendation list. In particular, we generalize the basic concept of click conversion rate (CVR) in computational advertising into the conversation rate of an arbitrary user action (XVR) in E-commerce, where the user actions can be clicking, adding to cart, adding to wishlist, etc. In this way, each type of user action is mapped to its monetized economic value. Economic values of different user actions are further integrated as the reward of a ranking list, and reinforcement learning is used to optimize the recommendation list for the maximum total value. Experimental results in both offline benchmarks and online commercial systems verified the improved performance of our framework, in terms of both traditional top-$k$ ranking tasks and the economic profits of the system.

cs.IR↗

arXiv2018

Some sharp differential sphere theorems for nonnegative scalar curvature manifolds

In this paper, we obtain several new intrinsic and extrinsic differential sphere theorems via Ricci flow. For intrinsic case, we show that a closed simply connected $n(\ge 4)$-dimensional Riemannian manifold $M$ is diffeomorphic to $S^n$ if one of the following conditions holds pointwisely: $$ (i)\ R_0>\left(1-\frac{24(\sqrt{10}-3)}{n(n-1)}\right)K_{max};\quad \ (ii)\ \frac{Ric^{[4]}}{4(n-1)}>\left(1-\frac{6(\sqrt{10}-3)}{n-1}\right)K_{max}.$$ Here $K_{max}$, $Ric^{[k]}$ and $R_0$ stand for the maximal sectional curvature, the $k$-th weak Ricci curvature and the normalized scalar curvature. For extrinsic case, i.e., when $M$ is a closed simply connected $n(\ge 4)$-dimensional submanifold immersed in $\bar{M}$. We prove that $M$ is diffeomorphic to $S^n$ if it satisfies some pinching curvature conditions. The only involved extrinsic quantities in our pinching conditions are the maximal sectional curvature $\bar K_{max}$ and the squared norm of mean curvature vector $\vert H\vert^2$. More precisely, we show that $M$ is diffeomorphic to $S^n$ if one of the following conditions holds: \begin{itemize} \item[(1)] $R_0\ge \left(1-\frac{2}{n(n-1)}\right)\bar{K}_{max} +\frac{n(n-2)}{(n-1)^2}\vert H\vert^2$, and strict inequality is achieved at some point; \item[(2)] $\dfrac{Ric^{[2]}}{2}\ge (n-2)\bar K_{max}+\frac{n^2}{8}\vert H\vert^2,$ and strict inequality is achieved at some point; \item[(3)] $\dfrac{Ric^{[2]}}{2} \ge\frac{n(n-3)}{n-2}\left(\bar K_{max}+\vert H\vert^2\right),$ and strict inequality is achieved at some point. \end{itemize} It is worth pointing out that, in the proof of extrinsic case, we apply suitable complex orthonormal frame and simplify the calculations considerably. We also emphasize that both of the pinching constants in (2) and (3) are optimal for $n=4$.

math.DG↗

arXiv2017

Optimal lower eigenvalue estimates for Hodge-Laplacian and applications

In this paper, we consider the eigenvalue problem for Hodge-Laplacian on a Riemannian manifold $M$ isometrically immersed into another Riemannian manifold $\bar M$ for arbitrary codimension. We first assume the pull back Weitzenböck operator (defined in Section 2) of $\bar M$ bounded from below, and obtain an extrinsic lower bound for the first eigenvalue of Hodge-Laplacian. As applications, we obtain some rigidity results and a homology sphere theorem. Second, when the pull back Weitzenböck operator of $\bar M$ bounded from both sides, we give a lower bound of the first eigenvalue by the Ricci curvature of $M$ and some extrinsic geometry. As a consequence, we prove a weak Ejiri type theorem, that is, if the Ricci curvature bounded from below pointwisely by a function of the norm square of the mean curvature vector, then $M$ is a homology sphere. In the end, we give an example to show that all the eigenvalue estimates and homology sphere theorems are optimal when $\bar M$ has constant curvature.

math.DG↗

arXiv2017

On the volume of locally conformally flat 4 dimensional hypersphere

Let $M$ be a 5 dimensional Riemannian manifold with $Sec_M\in[0,1]$, $Σ$ be a locally conformally flat hypersphere in $M$ with mean curvature $H$. We prove that, there exists $\varepsilon_0>0$, such that $\int_Σ(1+H^2)^2 \ge 8π^2/3$, provided $H \le \varepsilon_0$. In particular, if $Σ$ is a locally conformally flat minimal hypersphere in $M$, then $Vol(Σ) \ge 8π^2/3$, which partially answer a question proposed by Mazet and Rosenberg \cite{Ma&Rosen}. For an $(n+1)-$ dimensional rotationally symmetric Riemannian manifold $M$, we show that an immersed hypersurface $Σ$ is locally conformally flat if and only if ($n-1$) of the principal curvatures of $Σ$ are the same, which is a generalization of Cartan's result \cite{Cartan}. As an application, we prove that if $M$ is (some special but large class) rotationally symmetric 5-manifold with $Sec_M\in [0,1]$, and $Σ$ is a locally conformally flat hypersphere with mean curvature $H$, the inequality $\int_Σ(1+H^2)^2 \ge 8π^2/3$ holds for all $H$.

math.DG↗

arXiv2016

Second Order Necessary Conditions for Optimal Control Problems on Riemannian Manifolds

This work is concerned with an optimal control problem on a Riemannian manifold, for which two typical cases are considered. The first case is when the endpoint is free. For this case, the control set is assumed to be a separable metric space. By introducing suitable dual equations, which depend on the curvature tensor of the manifold, we establish the second order necessary and sufficient optimality conditions of integral form. In particular, when the control set is a Polish space, the second order necessary condition is reduced to a pointwise form. As a key preliminary result and also an interesting byproduct, we derive a geometric lemma, which may have some independent interest. The second case is when the endpoint is fixed. For this more difficult case, the control set is assumed to be open in an Euclidian space. We obtain the second order necessary and sufficient optimality conditions, in which the curvature tensor also appears explicitly. Our optimality conditions can be used to recover the following famous geometry result: Any geodesic connecting two fixed points on a Riemannian manifold satisfies the second variation of energy; while the existing optimality conditions in control literatures fail to give the same result.

math.OC↗

arXiv2014

KNET: A General Framework for Learning Word Embedding using Morphological Knowledge

Neural network techniques are widely applied to obtain high-quality distributed representations of words, i.e., word embeddings, to address text mining, information retrieval, and natural language processing tasks. Recently, efficient methods have been proposed to learn word embeddings from context that captures both semantic and syntactic relationships between words. However, it is challenging to handle unseen words or rare words with insufficient context. In this paper, inspired by the study on word recognition process in cognitive psychology, we propose to take advantage of seemingly less obvious but essentially important morphological knowledge to address these challenges. In particular, we introduce a novel neural network architecture called KNET that leverages both contextual information and morphological word similarity built based on morphological knowledge to learn word embeddings. Meanwhile, the learning architecture is also able to refine the pre-defined morphological knowledge and obtain more accurate word similarity. Experiments on an analogical reasoning task and a word similarity task both demonstrate that the proposed KNET framework can greatly enhance the effectiveness of word embeddings.

cs.CL↗