arXiv subjects

Han Xiao

Publications and source records attributed to Han Xiao.

156 records · Page 9Linked to original sources

arXiv2017

SSP: Semantic Space Projection for Knowledge Graph Embedding with Text Descriptions

Knowledge representation is an important, long-history topic in AI, and there have been a large amount of work for knowledge graph embedding which projects symbolic entities and relations into low-dimensional, real-valued vector space. However, most embedding methods merely concentrate on data fitting and ignore the explicit semantic expression, leading to uninterpretable representations. Thus, traditional embedding methods have limited potentials for many applications such as question answering, and entity classification. To this end, this paper proposes a semantic representation method for knowledge graph \textbf{(KSR)}, which imposes a two-level hierarchical generative process that globally extracts many aspects and then locally assigns a specific category in each aspect for every triple. Since both aspects and categories are semantics-relevant, the collection of categories in each aspect is treated as the semantic representation of this triple. Extensive experiments justify our model outperforms other state-of-the-art baselines substantially.

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arXiv2016

Discovering topically- and temporally-coherent events in interaction networks

With the increasing use of online communication platforms, such as email, twitter, and messaging applications, we are faced with a growing amount of data that combine content (what is said), time (when), and user (by whom) information. An important computational challenge is to analyze these data, discover meaningful patterns, and understand what is happening. We consider the problem of mining online communication data and finding top-k temporal events. We define a temporal event to be a coherent topic that is discussed frequently, in a relatively short time span, while the information ow of the event respects the underlying network structure. We construct our model for detecting temporal events in two steps. We first introduce the notion of interaction meta-graph, which connects associated interactions. Using this notion, we define a temporal event to be a subset of interactions that (i) are topically and temporally close and (ii) correspond to a tree that captures the information ow. Finding the best temporal event leads to budget version of the prize-collecting Steiner-tree (PCST) problem, which we solve using three different methods: a greedy approach, a dynamic-programming algorithm, and an adaptation to an existing approximation algorithm. The problem of finding the top- k events among a set of candidate events maps to maximum set-cover problem, and thus, solved by greedy. We compare and analyze our algorithms in both synthetic and real datasets, such as twitter and email communication. The results show that our methods are able to detect meaningful temporal events.

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arXiv2016

Wald tests of singular hypotheses

Motivated by the problem of testing tetrad constraints in factor analysis, we study the large-sample distribution of Wald statistics at parameter points at which the gradient of the tested constraint vanishes. When based on an asymptotically normal estimator, the Wald statistic converges to a rational function of a normal random vector. The rational function is determined by a homogeneous polynomial and a covariance matrix. For quadratic forms and bivariate monomials of arbitrary degree, we show unexpected relationships to chi-square distributions that explain conservative behavior of certain Wald tests. For general monomials, we offer a conjecture according to which the reciprocal of a certain quadratic form in the reciprocals of dependent normal random variables is chi-square distributed.

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arXiv2015

On Kernel Mengerian Orientations of Line Multigraphs

We present a polyhedral description of kernels in orientations of line multigraphs. Given a digraph $D$, let $FK(D)$ denote the fractional kernel polytope defined on $D$, and let $σ(D)$ denote the linear system defining $FK(D)$. A digraph $D$ is called kernel perfect if every induced subdigraph $D^\prime$ has a kernel, called kernel ideal if $FK(D^\prime)$ is integral for each induced subdigraph $D^\prime$, and called kernel Mengerian if $σ (D^\prime)$ is TDI for each induced subdigraph $D^\prime$. We show that an orientation of a line multigraph is kernel perfect iff it is kernel ideal iff it is kernel Mengerian. Our result strengthens the theorem of Borodin et al. [3] on kernel perfect digraphs and generalizes the theorem of Kiraly and Pap [7] on stable matching problem.

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arXiv2015

TransA: An Adaptive Approach for Knowledge Graph Embedding

Knowledge representation is a major topic in AI, and many studies attempt to represent entities and relations of knowledge base in a continuous vector space. Among these attempts, translation-based methods build entity and relation vectors by minimizing the translation loss from a head entity to a tail one. In spite of the success of these methods, translation-based methods also suffer from the oversimplified loss metric, and are not competitive enough to model various and complex entities/relations in knowledge bases. To address this issue, we propose \textbf{TransA}, an adaptive metric approach for embedding, utilizing the metric learning ideas to provide a more flexible embedding method. Experiments are conducted on the benchmark datasets and our proposed method makes significant and consistent improvements over the state-of-the-art baselines.

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arXiv2015

Max-Entropy Feed-Forward Clustering Neural Network

The outputs of non-linear feed-forward neural network are positive, which could be treated as probability when they are normalized to one. If we take Entropy-Based Principle into consideration, the outputs for each sample could be represented as the distribution of this sample for different clusters. Entropy-Based Principle is the principle with which we could estimate the unknown distribution under some limited conditions. As this paper defines two processes in Feed-Forward Neural Network, our limited condition is the abstracted features of samples which are worked out in the abstraction process. And the final outputs are the probability distribution for different clusters in the clustering process. As Entropy-Based Principle is considered into the feed-forward neural network, a clustering method is born. We have conducted some experiments on six open UCI datasets, comparing with a few baselines and applied purity as the measurement . The results illustrate that our method outperforms all the other baselines that are most popular clustering methods.

cs.LG↗

arXiv2015

Margin-Based Feed-Forward Neural Network Classifiers

Margin-Based Principle has been proposed for a long time, it has been proved that this principle could reduce the structural risk and improve the performance in both theoretical and practical aspects. Meanwhile, feed-forward neural network is a traditional classifier, which is very hot at present with a deeper architecture. However, the training algorithm of feed-forward neural network is developed and generated from Widrow-Hoff Principle that means to minimize the squared error. In this paper, we propose a new training algorithm for feed-forward neural networks based on Margin-Based Principle, which could effectively promote the accuracy and generalization ability of neural network classifiers with less labelled samples and flexible network. We have conducted experiments on four UCI open datasets and achieved good results as expected. In conclusion, our model could handle more sparse labelled and more high-dimension dataset in a high accuracy while modification from old ANN method to our method is easy and almost free of work.

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arXiv2012

Covariance matrix estimation for stationary time series

We obtain a sharp convergence rate for banded covariance matrix estimates of stationary processes. A precise order of magnitude is derived for spectral radius of sample covariance matrices. We also consider a thresholded covariance matrix estimator that can better characterize sparsity if the true covariance matrix is sparse. As our main tool, we implement Toeplitz [Math. Ann. 70 (1911) 351-376] idea and relate eigenvalues of covariance matrices to the spectral densities or Fourier transforms of the covariances. We develop a large deviation result for quadratic forms of stationary processes using m-dependence approximation, under the framework of causal representation and physical dependence measures.

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arXiv2011

Simultaneous Inference of Covariances

We consider asymptotic distributions of maximum deviations of sample covariance matrices, a fundamental problem in high-dimensional inference of covariances. Under mild dependence conditions on the entries of the data matrices, we establish the Gumbel convergence of the maximum deviations. Our result substantially generalizes earlier ones where the entries are assumed to be independent and identically distributed, and it provides a theoretical foundation for high-dimensional simultaneous inference of covariances.

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arXiv2011

Asymptotic Inference of Autocovariances of Stationary Processes

The paper presents a systematic theory for asymptotic inference of autocovariances of stationary processes. We consider nonparametric tests for serial correlations based on the maximum (or ${\cal L}^\infty$) and the quadratic (or ${\cal L}^2$) deviations. For these two cases, with proper centering and rescaling, the asymptotic distributions of the deviations are Gumbel and Gaussian, respectively. To establish such an asymptotic theory, as byproducts, we develop a normal comparison principle and propose a sufficient condition for summability of joint cumulants of stationary processes. We adopt a simulation-based block of blocks bootstrapping procedure that improves the finite-sample performance.

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arXiv2009

Smoothness of Gaussian conditional independence models

Conditional independence in a multivariate normal (or Gaussian) distribution is characterized by the vanishing of subdeterminants of the distribution's covariance matrix. Gaussian conditional independence models thus correspond to algebraic subsets of the cone of positive definite matrices. For statistical inference in such models it is important to know whether or not the model contains singularities. We study this issue in models involving up to four random variables. In particular, we give examples of conditional independence relations which, despite being probabilistically representable, yield models that non-trivially decompose into a finite union of several smooth submodels.

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arXiv2009

Finiteness of small factor analysis models

We consider small factor analysis models with one or two factors. Fixing the number of factors, we prove a finiteness result about the covariance matrix parameter space when the size of the covariance matrix increases. According to this result, there exists a distinguished matrix size starting at which one can determine whether a given covariance matrix belongs to the parameter space by determining whether all principal submatrices of the distinguished size belong to the corresponding parameter space. We show that the distinguished matrix size is equal to four in the one-factor model and six with two factors.

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