In this paper, we propose a framework to study a general class of strategic behavior in voting, which we call vote operations. We prove the following theorem: if we fix the number of alternatives, generate $n$ votes i.i.d. according to a distribution $\pi$, and let $n$ go to infinity, then for any $\epsilon >0$, with probability at least $1-\epsilon$, the minimum number of operations that are needed for the strategic individual to achieve her goal falls into one of the following four categories: (1) 0, (2) $\Theta(\sqrt n)$, (3) $\Theta(n)$, and (4) $\infty$. This theorem holds for any set of vote operations, any individual vote distribution $\pi$, and any integer generalized scoring rule, which includes (but is not limited to) almost all commonly studied voting rules, e.g., approval voting, all positional scoring rules (including Borda, plurality, and veto), plurality with runoff, Bucklin, Copeland, maximin, STV, and ranked pairs. We also show that many well-studied types of strategic behavior fall under our framework, including (but not limited to) constructive/destructive manipulation, bribery, and control by adding/deleting votes, margin of victory, and minimum manipulation coalition size. Therefore, our main theorem naturally applies to these problems.

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Composite Marginal Likelihood Methods for Random Utility Models

Jun 04, 2018

Zhibing Zhao, Lirong Xia

We propose a novel and flexible rank-breaking-then-composite-marginal-likelihood (RBCML) framework for learning random utility models (RUMs), which include the Plackett-Luce model. We characterize conditions for the objective function of RBCML to be strictly log-concave by proving that strict log-concavity is preserved under convolution and marginalization. We characterize necessary and sufficient conditions for RBCML to satisfy consistency and asymptotic normality. Experiments on synthetic data show that RBCML for Gaussian RUMs achieves better statistical efficiency and computational efficiency than the state-of-the-art algorithm and our RBCML for the Plackett-Luce model provides flexible tradeoffs between running time and statistical efficiency.
Jun 04, 2018

Zhibing Zhao, Lirong Xia

* 22 pages, 3 figures, accepted by ICML 2018

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We propose a simple approach which, given distributed computing resources, can nearly achieve the accuracy of $k$-NN prediction, while matching (or improving) the faster prediction time of $1$-NN. The approach consists of aggregating denoised $1$-NN predictors over a small number of distributed subsamples. We show, both theoretically and experimentally, that small subsample sizes suffice to attain similar performance as $k$-NN, without sacrificing the computational efficiency of $1$-NN.

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We formulate a general class of allocation problems called categorized domain allocation problems (CDAPs), where indivisible items from multiple categories are allocated to agents without monetary transfer and each agent gets at least one item per category. We focus on basic CDAPs, where the number of items in each category is equal to the number of agents. We characterize serial dictatorships for basic CDAPs by a minimal set of three axiomatic properties: strategy-proofness, non-bossiness, and category-wise neutrality. Then, we propose a natural extension of serial dictatorships called categorial sequential allocation mechanisms (CSAMs), which allocate the items in multiple rounds: in each round, the active agent chooses an item from a designated category. We fully characterize the worst-case rank efficiency of CSAMs for optimistic and pessimistic agents, and provide a bound for strategic agents. We also conduct experiments to compare expected rank efficiency of various CSAMs w.r.t. random generated data.

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Price Updating in Combinatorial Prediction Markets with Bayesian Networks

Feb 14, 2012

David M. Pennock, Lirong Xia

To overcome the #P-hardness of computing/updating prices in logarithm market scoring rule-based (LMSR-based) combinatorial prediction markets, Chen et al. [5] recently used a simple Bayesian network to represent the prices of securities in combinatorial predictionmarkets for tournaments, and showed that two types of popular securities are structure preserving. In this paper, we significantly extend this idea by employing Bayesian networks in general combinatorial prediction markets. We reveal a very natural connection between LMSR-based combinatorial prediction markets and probabilistic belief aggregation,which leads to a complete characterization of all structure preserving securities for decomposable network structures. Notably, the main results by Chen et al. [5] are corollaries of our characterization. We then prove that in order for a very basic set of securities to be structure preserving, the graph of the Bayesian network must be decomposable. We also discuss some approximation techniques for securities that are not structure preserving.
Feb 14, 2012

David M. Pennock, Lirong Xia

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Selective Sampling and Mixture Models in Generative Adversarial Networks

Feb 02, 2018

Karim Said Barsim, Lirong Yang, Bin Yang

In this paper, we propose a multi-generator extension to the adversarial training framework, in which the objective of each generator is to represent a unique component of a target mixture distribution. In the training phase, the generators cooperate to represent, as a mixture, the target distribution while maintaining distinct manifolds. As opposed to traditional generative models, inference from a particular generator after training resembles selective sampling from a unique component in the target distribution. We demonstrate the feasibility of the proposed architecture both analytically and with basic Multi-Layer Perceptron (MLP) models trained on the MNIST dataset.
Feb 02, 2018

Karim Said Barsim, Lirong Yang, Bin Yang

* 5pages, 3 figures

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Multi-Scale Attention with Dense Encoder for Handwritten Mathematical Expression Recognition

Jan 31, 2018

Jianshu Zhang, Jun Du, Lirong Dai

Handwritten mathematical expression recognition is a challenging problem due to the complicated two-dimensional structures, ambiguous handwriting input and variant scales of handwritten math symbols. To settle this problem, we utilize the attention based encoder-decoder model that recognizes mathematical expression images from two-dimensional layouts to one-dimensional LaTeX strings. We improve the encoder by employing densely connected convolutional networks as they can strengthen feature extraction and facilitate gradient propagation especially on a small training set. We also present a novel multi-scale attention model which is employed to deal with the recognition of math symbols in different scales and save the fine-grained details that will be dropped by pooling operations. Validated on the CROHME competition task, the proposed method significantly outperforms the state-of-the-art methods with an expression recognition accuracy of 52.8% on CROHME 2014 and 50.1% on CROHME 2016, by only using the official training dataset.
Jan 31, 2018

Jianshu Zhang, Jun Du, Lirong Dai

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A GRU-based Encoder-Decoder Approach with Attention for Online Handwritten Mathematical Expression Recognition

Dec 04, 2017

Jianshu Zhang, Jun Du, Lirong Dai

In this study, we present a novel end-to-end approach based on the encoder-decoder framework with the attention mechanism for online handwritten mathematical expression recognition (OHMER). First, the input two-dimensional ink trajectory information of handwritten expression is encoded via the gated recurrent unit based recurrent neural network (GRU-RNN). Then the decoder is also implemented by the GRU-RNN with a coverage-based attention model. The proposed approach can simultaneously accomplish the symbol recognition and structural analysis to output a character sequence in LaTeX format. Validated on the CROHME 2014 competition task, our approach significantly outperforms the state-of-the-art with an expression recognition accuracy of 52.43% by only using the official training dataset. Furthermore, the alignments between the input trajectories of handwritten expressions and the output LaTeX sequences are visualized by the attention mechanism to show the effectiveness of the proposed method.
Dec 04, 2017

Jianshu Zhang, Jun Du, Lirong Dai

* Accepted by ICDAR 2017 conference

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In this paper we address the identifiability and efficient learning problems of finite mixtures of Plackett-Luce models for rank data. We prove that for any $k\geq 2$, the mixture of $k$ Plackett-Luce models for no more than $2k-1$ alternatives is non-identifiable and this bound is tight for $k=2$. For generic identifiability, we prove that the mixture of $k$ Plackett-Luce models over $m$ alternatives is generically identifiable if $k\leq\lfloor\frac {m-2} 2\rfloor!$. We also propose an efficient generalized method of moments (GMM) algorithm to learn the mixture of two Plackett-Luce models and show that the algorithm is consistent. Our experiments show that our GMM algorithm is significantly faster than the EMM algorithm by Gormley and Murphy (2008), while achieving competitive statistical efficiency.

* 26 pages, 2 figures; remove (incorrectly) generated date; add summary to section 6

* 26 pages, 2 figures; remove (incorrectly) generated date; add summary to section 6

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Possible and Necessary Allocations via Sequential Mechanisms

Dec 06, 2014

Haris Aziz, Toby Walsh, Lirong Xia

A simple mechanism for allocating indivisible resources is sequential allocation in which agents take turns to pick items. We focus on possible and necessary allocation problems, checking whether allocations of a given form occur in some or all mechanisms for several commonly used classes of sequential allocation mechanisms. In particular, we consider whether a given agent receives a given item, a set of items, or a subset of items for five natural classes of sequential allocation mechanisms: balanced, recursively balanced, balanced alternating, strictly alternating and all policies. We identify characterizations of allocations produced balanced, recursively balanced, balanced alternating policies and strictly alternating policies respectively, which extend the well-known characterization by Brams and King [2005] for policies without restrictions. In addition, we examine the computational complexity of possible and necessary allocation problems for these classes.
Dec 06, 2014

Haris Aziz, Toby Walsh, Lirong Xia

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We propose a simple method for combining together voting rules that performs a run-off between the different winners of each voting rule. We prove that this combinator has several good properties. For instance, even if just one of the base voting rules has a desirable property like Condorcet consistency, the combination inherits this property. In addition, we prove that combining voting rules together in this way can make finding a manipulation more computationally difficult. Finally, we study the impact of this combinator on approximation methods that find close to optimal manipulations.

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Dominating Manipulations in Voting with Partial Information

Jun 27, 2011

Vincent Conitzer, Toby Walsh, Lirong Xia

We consider manipulation problems when the manipulator only has partial information about the votes of the nonmanipulators. Such partial information is described by an information set, which is the set of profiles of the nonmanipulators that are indistinguishable to the manipulator. Given such an information set, a dominating manipulation is a non-truthful vote that the manipulator can cast which makes the winner at least as preferable (and sometimes more preferable) as the winner when the manipulator votes truthfully. When the manipulator has full information, computing whether or not there exists a dominating manipulation is in P for many common voting rules (by known results). We show that when the manipulator has no information, there is no dominating manipulation for many common voting rules. When the manipulator's information is represented by partial orders and only a small portion of the preferences are unknown, computing a dominating manipulation is NP-hard for many common voting rules. Our results thus throw light on whether we can prevent strategic behavior by limiting information about the votes of other voters.
Jun 27, 2011

Vincent Conitzer, Toby Walsh, Lirong Xia

* 7 pages by arxiv pdflatex, 1 figure. The 6-page version has the same content and will be published in Proceedings of the Twenty-Fifth AAAI Conference on Artificial Intelligence (AAAI-11)

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Nanson's and Baldwin's voting rules select a winner by successively eliminating candidates with low Borda scores. We show that these rules have a number of desirable computational properties. In particular, with unweighted votes, it is NP-hard to manipulate either rule with one manipulator, whilst with weighted votes, it is NP-hard to manipulate either rule with a small number of candidates and a coalition of manipulators. As only a couple of other voting rules are known to be NP-hard to manipulate with a single manipulator, Nanson's and Baldwin's rules appear to be particularly resistant to manipulation from a theoretical perspective. We also propose a number of approximation methods for manipulating these two rules. Experiments demonstrate that both rules are often difficult to manipulate in practice. These results suggest that elimination style voting rules deserve further study.

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Probabilistic Automata for Computing with Words

Apr 23, 2006

Yongzhi Cao, Lirong Xia, Mingsheng Ying

Usually, probabilistic automata and probabilistic grammars have crisp symbols as inputs, which can be viewed as the formal models of computing with values. In this paper, we first introduce probabilistic automata and probabilistic grammars for computing with (some special) words in a probabilistic framework, where the words are interpreted as probabilistic distributions or possibility distributions over a set of crisp symbols. By probabilistic conditioning, we then establish a retraction principle from computing with words to computing with values for handling crisp inputs and a generalized extension principle from computing with words to computing with all words for handling arbitrary inputs. These principles show that computing with values and computing with all words can be respectively implemented by computing with some special words. To compare the transition probabilities of two near inputs, we also examine some analytical properties of the transition probability functions of generalized extensions. Moreover, the retractions and the generalized extensions are shown to be equivalence-preserving. Finally, we clarify some relationships among the retractions, the generalized extensions, and the extensions studied recently by Qiu and Wang.
Apr 23, 2006

Yongzhi Cao, Lirong Xia, Mingsheng Ying

* 35 pages; 3 figures

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Deep Neural Network Embeddings with Gating Mechanisms for Text-Independent Speaker Verification

Apr 04, 2019

Lanhua You, Wu Guo, Lirong Dai, Jun Du

In this paper, gating mechanisms are applied in deep neural network (DNN) training for x-vector-based text-independent speaker verification. First, a gated convolution neural network (GCNN) is employed for modeling the frame-level embedding layers. Compared with the time-delay DNN (TDNN), the GCNN can obtain more expressive frame-level representations through carefully designed memory cell and gating mechanisms. Moreover, we propose a novel gated-attention statistics pooling strategy in which the attention scores are shared with the output gate. The gated-attention statistics pooling combines both gating and attention mechanisms into one framework; therefore, we can capture more useful information in the temporal pooling layer. Experiments are carried out using the NIST SRE16 and SRE18 evaluation datasets. The results demonstrate the effectiveness of the GCNN and show that the proposed gated-attention statistics pooling can further improve the performance.
Apr 04, 2019

Lanhua You, Wu Guo, Lirong Dai, Jun Du

* 5 pages, 3 figures, submitted to INTERSPEECH 2019

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This paper studies a stylized, yet natural, learning-to-rank problem and points out the critical incorrectness of a widely used nearest neighbor algorithm. We consider a model with $n$ agents (users) $\{x_i\}_{i \in [n]}$ and $m$ alternatives (items) $\{y_j\}_{j \in [m]}$, each of which is associated with a latent feature vector. Agents rank items nondeterministically according to the Plackett-Luce model, where the higher the utility of an item to the agent, the more likely this item will be ranked high by the agent. Our goal is to find neighbors of an arbitrary agent or alternative in the latent space. We first show that the Kendall-tau distance based kNN produces incorrect results in our model. Next, we fix the problem by introducing a new algorithm with features constructed from "global information" of the data matrix. Our approach is in sharp contrast to most existing feature engineering methods. Finally, we design another new algorithm identifying similar alternatives. The construction of alternative features can be done using "local information," highlighting the algorithmic difference between finding similar agents and similar alternatives.

* 10 pages' main document and 10 pages' supplementary documents

* 10 pages' main document and 10 pages' supplementary documents

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Stochastic Sequential Neural Networks with Structured Inference

May 24, 2017

Hao Liu, Haoli Bai, Lirong He, Zenglin Xu

Unsupervised structure learning in high-dimensional time series data has attracted a lot of research interests. For example, segmenting and labelling high dimensional time series can be helpful in behavior understanding and medical diagnosis. Recent advances in generative sequential modeling have suggested to combine recurrent neural networks with state space models (e.g., Hidden Markov Models). This combination can model not only the long term dependency in sequential data, but also the uncertainty included in the hidden states. Inheriting these advantages of stochastic neural sequential models, we propose a structured and stochastic sequential neural network, which models both the long-term dependencies via recurrent neural networks and the uncertainty in the segmentation and labels via discrete random variables. For accurate and efficient inference, we present a bi-directional inference network by reparamterizing the categorical segmentation and labels with the recent proposed Gumbel-Softmax approximation and resort to the Stochastic Gradient Variational Bayes. We evaluate the proposed model in a number of tasks, including speech modeling, automatic segmentation and labeling in behavior understanding, and sequential multi-objects recognition. Experimental results have demonstrated that our proposed model can achieve significant improvement over the state-of-the-art methods.
May 24, 2017

Hao Liu, Haoli Bai, Lirong He, Zenglin Xu

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Radical analysis network for zero-shot learning in printed Chinese character recognition

Mar 29, 2018

Jianshu Zhang, Yixing Zhu, Jun Du, Lirong Dai

Chinese characters have a huge set of character categories, more than 20,000 and the number is still increasing as more and more novel characters continue being created. However, the enormous characters can be decomposed into a compact set of about 500 fundamental and structural radicals. This paper introduces a novel radical analysis network (RAN) to recognize printed Chinese characters by identifying radicals and analyzing two-dimensional spatial structures among them. The proposed RAN first extracts visual features from input by employing convolutional neural networks as an encoder. Then a decoder based on recurrent neural networks is employed, aiming at generating captions of Chinese characters by detecting radicals and two-dimensional structures through a spatial attention mechanism. The manner of treating a Chinese character as a composition of radicals rather than a single character class largely reduces the size of vocabulary and enables RAN to possess the ability of recognizing unseen Chinese character classes, namely zero-shot learning.
Mar 29, 2018

Jianshu Zhang, Yixing Zhu, Jun Du, Lirong Dai

* Accepted by ICME2018

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Deep-FSMN for Large Vocabulary Continuous Speech Recognition

Mar 04, 2018

Shiliang Zhang, Ming Lei, Zhijie Yan, Lirong Dai

In this paper, we present an improved feedforward sequential memory networks (FSMN) architecture, namely Deep-FSMN (DFSMN), by introducing skip connections between memory blocks in adjacent layers. These skip connections enable the information flow across different layers and thus alleviate the gradient vanishing problem when building very deep structure. As a result, DFSMN significantly benefits from these skip connections and deep structure. We have compared the performance of DFSMN to BLSTM both with and without lower frame rate (LFR) on several large speech recognition tasks, including English and Mandarin. Experimental results shown that DFSMN can consistently outperform BLSTM with dramatic gain, especially trained with LFR using CD-Phone as modeling units. In the 2000 hours Fisher (FSH) task, the proposed DFSMN can achieve a word error rate of 9.4% by purely using the cross-entropy criterion and decoding with a 3-gram language model, which achieves a 1.5% absolute improvement compared to the BLSTM. In a 20000 hours Mandarin recognition task, the LFR trained DFSMN can achieve more than 20% relative improvement compared to the LFR trained BLSTM. Moreover, we can easily design the lookahead filter order of the memory blocks in DFSMN to control the latency for real-time applications.
Mar 04, 2018

Shiliang Zhang, Ming Lei, Zhijie Yan, Lirong Dai

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Trajectory-based Radical Analysis Network for Online Handwritten Chinese Character Recognition

Jan 22, 2018

Jianshu Zhang, Yixing Zhu, Jun Du, Lirong Dai

Recently, great progress has been made for online handwritten Chinese character recognition due to the emergence of deep learning techniques. However, previous research mostly treated each Chinese character as one class without explicitly considering its inherent structure, namely the radical components with complicated geometry. In this study, we propose a novel trajectory-based radical analysis network (TRAN) to firstly identify radicals and analyze two-dimensional structures among radicals simultaneously, then recognize Chinese characters by generating captions of them based on the analysis of their internal radicals. The proposed TRAN employs recurrent neural networks (RNNs) as both an encoder and a decoder. The RNN encoder makes full use of online information by directly transforming handwriting trajectory into high-level features. The RNN decoder aims at generating the caption by detecting radicals and spatial structures through an attention model. The manner of treating a Chinese character as a two-dimensional composition of radicals can reduce the size of vocabulary and enable TRAN to possess the capability of recognizing unseen Chinese character classes, only if the corresponding radicals have been seen. Evaluated on CASIA-OLHWDB database, the proposed approach significantly outperforms the state-of-the-art whole-character modeling approach with a relative character error rate (CER) reduction of 10%. Meanwhile, for the case of recognition of 500 unseen Chinese characters, TRAN can achieve a character accuracy of about 60% while the traditional whole-character method has no capability to handle them.
Jan 22, 2018

Jianshu Zhang, Yixing Zhu, Jun Du, Lirong Dai

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