arXiv subjects

Tie-Yan Liu

Publications and source records attributed to Tie-Yan Liu.

At least 235 records · Page 13Linked to original sources

arXiv2017

Efficient Inexact Proximal Gradient Algorithm for Nonconvex Problems

The proximal gradient algorithm has been popularly used for convex optimization. Recently, it has also been extended for nonconvex problems, and the current state-of-the-art is the nonmonotone accelerated proximal gradient algorithm. However, it typically requires two exact proximal steps in each iteration, and can be inefficient when the proximal step is expensive. In this paper, we propose an efficient proximal gradient algorithm that requires only one inexact (and thus less expensive) proximal step in each iteration. Convergence to a critical point %of the nonconvex problem is still guaranteed and has a $O(1/k)$ convergence rate, which is the best rate for nonconvex problems with first-order methods. Experiments on a number of problems demonstrate that the proposed algorithm has comparable performance as the state-of-the-art, but is much faster.

math.OC↗

arXiv2017

Learning What Data to Learn

Machine learning is essentially the sciences of playing with data. An adaptive data selection strategy, enabling to dynamically choose different data at various training stages, can reach a more effective model in a more efficient way. In this paper, we propose a deep reinforcement learning framework, which we call \emph{\textbf{N}eural \textbf{D}ata \textbf{F}ilter} (\textbf{NDF}), to explore automatic and adaptive data selection in the training process. In particular, NDF takes advantage of a deep neural network to adaptively select and filter important data instances from a sequential stream of training data, such that the future accumulative reward (e.g., the convergence speed) is maximized. In contrast to previous studies in data selection that is mainly based on heuristic strategies, NDF is quite generic and thus can be widely suitable for many machine learning tasks. Taking neural network training with stochastic gradient descent (SGD) as an example, comprehensive experiments with respect to various neural network modeling (e.g., multi-layer perceptron networks, convolutional neural networks and recurrent neural networks) and several applications (e.g., image classification and text understanding) demonstrate that NDF powered SGD can achieve comparable accuracy with standard SGD process by using less data and fewer iterations.

cs.LG↗

arXiv2016

Randomized Mechanisms for Selling Reserved Instances in Cloud

Selling reserved instances (or virtual machines) is a basic service in cloud computing. In this paper, we consider a more flexible pricing model for instance reservation, in which a customer can propose the time length and number of resources of her request, while in today's industry, customers can only choose from several predefined reservation packages. Under this model, we design randomized mechanisms for customers coming online to optimize social welfare and providers' revenue. We first consider a simple case, where the requests from the customers do not vary too much in terms of both length and value density. We design a randomized mechanism that achieves a competitive ratio $\frac{1}{42}$ for both \emph{social welfare} and \emph{revenue}, which is a improvement as there is usually no revenue guarantee in previous works such as \cite{azar2015ec,wang2015selling}. This ratio can be improved up to $\frac{1}{11}$ when we impose a realistic constraint on the maximum number of resources used by each request. On the hardness side, we show an upper bound $\frac{1}{3}$ on competitive ratio for any randomized mechanism. We then extend our mechanism to the general case and achieve a competitive ratio $\frac{1}{42\log k\log T}$ for both social welfare and revenue, where $T$ is the ratio of the maximum request length to the minimum request length and $k$ is the ratio of the maximum request value density to the minimum request value density. This result outperforms the previous upper bound $\frac{1}{CkT}$ for deterministic mechanisms \cite{wang2015selling}. We also prove an upper bound $\frac{2}{\log 8kT}$ for any randomized mechanism. All the mechanisms we provide are in a greedy style. They are truthful and easy to be integrated into practical cloud systems.

cs.GT↗

arXiv2016

A Communication-Efficient Parallel Algorithm for Decision Tree

Decision tree (and its extensions such as Gradient Boosting Decision Trees and Random Forest) is a widely used machine learning algorithm, due to its practical effectiveness and model interpretability. With the emergence of big data, there is an increasing need to parallelize the training process of decision tree. However, most existing attempts along this line suffer from high communication costs. In this paper, we propose a new algorithm, called \emph{Parallel Voting Decision Tree (PV-Tree)}, to tackle this challenge. After partitioning the training data onto a number of (e.g., $M$) machines, this algorithm performs both local voting and global voting in each iteration. For local voting, the top-$k$ attributes are selected from each machine according to its local data. Then, globally top-$2k$ attributes are determined by a majority voting among these local candidates. Finally, the full-grained histograms of the globally top-$2k$ attributes are collected from local machines in order to identify the best (most informative) attribute and its split point. PV-Tree can achieve a very low communication cost (independent of the total number of attributes) and thus can scale out very well. Furthermore, theoretical analysis shows that this algorithm can learn a near optimal decision tree, since it can find the best attribute with a large probability. Our experiments on real-world datasets show that PV-Tree significantly outperforms the existing parallel decision tree algorithms in the trade-off between accuracy and efficiency.

cs.LG↗

arXiv2016

Dual Learning for Machine Translation

While neural machine translation (NMT) is making good progress in the past two years, tens of millions of bilingual sentence pairs are needed for its training. However, human labeling is very costly. To tackle this training data bottleneck, we develop a dual-learning mechanism, which can enable an NMT system to automatically learn from unlabeled data through a dual-learning game. This mechanism is inspired by the following observation: any machine translation task has a dual task, e.g., English-to-French translation (primal) versus French-to-English translation (dual); the primal and dual tasks can form a closed loop, and generate informative feedback signals to train the translation models, even if without the involvement of a human labeler. In the dual-learning mechanism, we use one agent to represent the model for the primal task and the other agent to represent the model for the dual task, then ask them to teach each other through a reinforcement learning process. Based on the feedback signals generated during this process (e.g., the language-model likelihood of the output of a model, and the reconstruction error of the original sentence after the primal and dual translations), we can iteratively update the two models until convergence (e.g., using the policy gradient methods). We call the corresponding approach to neural machine translation \emph{dual-NMT}. Experiments show that dual-NMT works very well on English$\leftrightarrow$French translation; especially, by learning from monolingual data (with 10% bilingual data for warm start), it achieves a comparable accuracy to NMT trained from the full bilingual data for the French-to-English translation task.

cs.CL↗

arXiv2016

LightRNN: Memory and Computation-Efficient Recurrent Neural Networks

Recurrent neural networks (RNNs) have achieved state-of-the-art performances in many natural language processing tasks, such as language modeling and machine translation. However, when the vocabulary is large, the RNN model will become very big (e.g., possibly beyond the memory capacity of a GPU device) and its training will become very inefficient. In this work, we propose a novel technique to tackle this challenge. The key idea is to use 2-Component (2C) shared embedding for word representations. We allocate every word in the vocabulary into a table, each row of which is associated with a vector, and each column associated with another vector. Depending on its position in the table, a word is jointly represented by two components: a row vector and a column vector. Since the words in the same row share the row vector and the words in the same column share the column vector, we only need $2 \sqrt{|V|}$ vectors to represent a vocabulary of $|V|$ unique words, which are far less than the $|V|$ vectors required by existing approaches. Based on the 2-Component shared embedding, we design a new RNN algorithm and evaluate it using the language modeling task on several benchmark datasets. The results show that our algorithm significantly reduces the model size and speeds up the training process, without sacrifice of accuracy (it achieves similar, if not better, perplexity as compared to state-of-the-art language models). Remarkably, on the One-Billion-Word benchmark Dataset, our algorithm achieves comparable perplexity to previous language models, whilst reducing the model size by a factor of 40-100, and speeding up the training process by a factor of 2. We name our proposed algorithm \emph{LightRNN} to reflect its very small model size and very high training speed.

cs.CL↗

arXiv2016

Generalization Error Bounds for Optimization Algorithms via Stability

Many machine learning tasks can be formulated as Regularized Empirical Risk Minimization (R-ERM), and solved by optimization algorithms such as gradient descent (GD), stochastic gradient descent (SGD), and stochastic variance reduction (SVRG). Conventional analysis on these optimization algorithms focuses on their convergence rates during the training process, however, people in the machine learning community may care more about the generalization performance of the learned model on unseen test data. In this paper, we investigate on this issue, by using stability as a tool. In particular, we decompose the generalization error for R-ERM, and derive its upper bound for both convex and non-convex cases. In convex cases, we prove that the generalization error can be bounded by the convergence rate of the optimization algorithm and the stability of the R-ERM process, both in expectation (in the order of $\mathcal{O}((1/n)+\mathbb{E}ρ(T))$, where $ρ(T)$ is the convergence error and $T$ is the number of iterations) and in high probability (in the order of $\mathcal{O}\left(\frac{\log{1/δ}}{\sqrt{n}}+ρ(T)\right)$ with probability $1-δ$). For non-convex cases, we can also obtain a similar expected generalization error bound. Our theorems indicate that 1) along with the training process, the generalization error will decrease for all the optimization algorithms under our investigation; 2) Comparatively speaking, SVRG has better generalization ability than GD and SGD. We have conducted experiments on both convex and non-convex problems, and the experimental results verify our theoretical findings.

stat.ML↗

arXiv2016

Asynchronous Stochastic Proximal Optimization Algorithms with Variance Reduction

Regularized empirical risk minimization (R-ERM) is an important branch of machine learning, since it constrains the capacity of the hypothesis space and guarantees the generalization ability of the learning algorithm. Two classic proximal optimization algorithms, i.e., proximal stochastic gradient descent (ProxSGD) and proximal stochastic coordinate descent (ProxSCD) have been widely used to solve the R-ERM problem. Recently, variance reduction technique was proposed to improve ProxSGD and ProxSCD, and the corresponding ProxSVRG and ProxSVRCD have better convergence rate. These proximal algorithms with variance reduction technique have also achieved great success in applications at small and moderate scales. However, in order to solve large-scale R-ERM problems and make more practical impacts, the parallel version of these algorithms are sorely needed. In this paper, we propose asynchronous ProxSVRG (Async-ProxSVRG) and asynchronous ProxSVRCD (Async-ProxSVRCD) algorithms, and prove that Async-ProxSVRG can achieve near linear speedup when the training data is sparse, while Async-ProxSVRCD can achieve near linear speedup regardless of the sparse condition, as long as the number of block partitions are appropriately set. We have conducted experiments on a regularized logistic regression task. The results verified our theoretical findings and demonstrated the practical efficiency of the asynchronous stochastic proximal algorithms with variance reduction.

cs.LG↗

arXiv2016

Solving Verbal Comprehension Questions in IQ Test by Knowledge-Powered Word Embedding

Intelligence Quotient (IQ) Test is a set of standardized questions designed to evaluate human intelligence. Verbal comprehension questions appear very frequently in IQ tests, which measure human's verbal ability including the understanding of the words with multiple senses, the synonyms and antonyms, and the analogies among words. In this work, we explore whether such tests can be solved automatically by artificial intelligence technologies, especially the deep learning technologies that are recently developed and successfully applied in a number of fields. However, we found that the task was quite challenging, and simply applying existing technologies (e.g., word embedding) could not achieve a good performance, mainly due to the multiple senses of words and the complex relations among words. To tackle these challenges, we propose a novel framework consisting of three components. First, we build a classifier to recognize the specific type of a verbal question (e.g., analogy, classification, synonym, or antonym). Second, we obtain distributed representations of words and relations by leveraging a novel word embedding method that considers the multi-sense nature of words and the relational knowledge among words (or their senses) contained in dictionaries. Third, for each type of questions, we propose a specific solver based on the obtained distributed word representations and relation representations. Experimental results have shown that the proposed framework can not only outperform existing methods for solving verbal comprehension questions but also exceed the average performance of the Amazon Mechanical Turk workers involved in the study. The results indicate that with appropriate uses of the deep learning technologies we might be a further step closer to the human intelligence.

cs.CL↗

arXiv2016

Sentence Level Recurrent Topic Model: Letting Topics Speak for Themselves

We propose Sentence Level Recurrent Topic Model (SLRTM), a new topic model that assumes the generation of each word within a sentence to depend on both the topic of the sentence and the whole history of its preceding words in the sentence. Different from conventional topic models that largely ignore the sequential order of words or their topic coherence, SLRTM gives full characterization to them by using a Recurrent Neural Networks (RNN) based framework. Experimental results have shown that SLRTM outperforms several strong baselines on various tasks. Furthermore, SLRTM can automatically generate sentences given a topic (i.e., topics to sentences), which is a key technology for real world applications such as personalized short text conversation.

cs.LG↗

arXiv2015

On the Depth of Deep Neural Networks: A Theoretical View

People believe that depth plays an important role in success of deep neural networks (DNN). However, this belief lacks solid theoretical justifications as far as we know. We investigate role of depth from perspective of margin bound. In margin bound, expected error is upper bounded by empirical margin error plus Rademacher Average (RA) based capacity term. First, we derive an upper bound for RA of DNN, and show that it increases with increasing depth. This indicates negative impact of depth on test performance. Second, we show that deeper networks tend to have larger representation power (measured by Betti numbers based complexity) than shallower networks in multi-class setting, and thus can lead to smaller empirical margin error. This implies positive impact of depth. The combination of these two results shows that for DNN with restricted number of hidden units, increasing depth is not always good since there is a tradeoff between positive and negative impacts. These results inspire us to seek alternative ways to achieve positive impact of depth, e.g., imposing margin-based penalty terms to cross entropy loss so as to reduce empirical margin error without increasing depth. Our experiments show that in this way, we achieve significantly better test performance.

cs.LG↗

arXiv2015

Learning Better Word Embedding by Asymmetric Low-Rank Projection of Knowledge Graph

Word embedding, which refers to low-dimensional dense vector representations of natural words, has demonstrated its power in many natural language processing tasks. However, it may suffer from the inaccurate and incomplete information contained in the free text corpus as training data. To tackle this challenge, there have been quite a few works that leverage knowledge graphs as an additional information source to improve the quality of word embedding. Although these works have achieved certain success, they have neglected some important facts about knowledge graphs: (i) many relationships in knowledge graphs are \emph{many-to-one}, \emph{one-to-many} or even \emph{many-to-many}, rather than simply \emph{one-to-one}; (ii) most head entities and tail entities in knowledge graphs come from very different semantic spaces. To address these issues, in this paper, we propose a new algorithm named ProjectNet. ProjecNet models the relationships between head and tail entities after transforming them with different low-rank projection matrices. The low-rank projection can allow non \emph{one-to-one} relationships between entities, while different projection matrices for head and tail entities allow them to originate in different semantic spaces. The experimental results demonstrate that ProjectNet yields more accurate word embedding than previous works, thus leads to clear improvements in various natural language processing tasks.

cs.CL↗

arXiv2015

Thompson Sampling for Budgeted Multi-armed Bandits

Thompson sampling is one of the earliest randomized algorithms for multi-armed bandits (MAB). In this paper, we extend the Thompson sampling to Budgeted MAB, where there is random cost for pulling an arm and the total cost is constrained by a budget. We start with the case of Bernoulli bandits, in which the random rewards (costs) of an arm are independently sampled from a Bernoulli distribution. To implement the Thompson sampling algorithm in this case, at each round, we sample two numbers from the posterior distributions of the reward and cost for each arm, obtain their ratio, select the arm with the maximum ratio, and then update the posterior distributions. We prove that the distribution-dependent regret bound of this algorithm is $O(\ln B)$, where $B$ denotes the budget. By introducing a Bernoulli trial, we further extend this algorithm to the setting that the rewards (costs) are drawn from general distributions, and prove that its regret bound remains almost the same. Our simulation results demonstrate the effectiveness of the proposed algorithm.

cs.LG↗

arXiv2014

LightLDA: Big Topic Models on Modest Compute Clusters

When building large-scale machine learning (ML) programs, such as big topic models or deep neural nets, one usually assumes such tasks can only be attempted with industrial-sized clusters with thousands of nodes, which are out of reach for most practitioners or academic researchers. We consider this challenge in the context of topic modeling on web-scale corpora, and show that with a modest cluster of as few as 8 machines, we can train a topic model with 1 million topics and a 1-million-word vocabulary (for a total of 1 trillion parameters), on a document collection with 200 billion tokens -- a scale not yet reported even with thousands of machines. Our major contributions include: 1) a new, highly efficient O(1) Metropolis-Hastings sampling algorithm, whose running cost is (surprisingly) agnostic of model size, and empirically converges nearly an order of magnitude faster than current state-of-the-art Gibbs samplers; 2) a structure-aware model-parallel scheme, which leverages dependencies within the topic model, yielding a sampling strategy that is frugal on machine memory and network communication; 3) a differential data-structure for model storage, which uses separate data structures for high- and low-frequency words to allow extremely large models to fit in memory, while maintaining high inference speed; and 4) a bounded asynchronous data-parallel scheme, which allows efficient distributed processing of massive data via a parameter server. Our distribution strategy is an instance of the model-and-data-parallel programming model underlying the Petuum framework for general distributed ML, and was implemented on top of the Petuum open-source system. We provide experimental evidence showing how this development puts massive models within reach on a small cluster while still enjoying proportional time cost reductions with increasing cluster size, in comparison with alternative options.

stat.ML↗

arXiv2014

Generalization Analysis for Game-Theoretic Machine Learning

For Internet applications like sponsored search, cautions need to be taken when using machine learning to optimize their mechanisms (e.g., auction) since self-interested agents in these applications may change their behaviors (and thus the data distribution) in response to the mechanisms. To tackle this problem, a framework called game-theoretic machine learning (GTML) was recently proposed, which first learns a Markov behavior model to characterize agents' behaviors, and then learns the optimal mechanism by simulating agents' behavior changes in response to the mechanism. While GTML has demonstrated practical success, its generalization analysis is challenging because the behavior data are non-i.i.d. and dependent on the mechanism. To address this challenge, first, we decompose the generalization error for GTML into the behavior learning error and the mechanism learning error; second, for the behavior learning error, we obtain novel non-asymptotic error bounds for both parametric and non-parametric behavior learning methods; third, for the mechanism learning error, we derive a uniform convergence bound based on a new concept called nested covering number of the mechanism space and the generalization analysis techniques developed for mixing sequences. To the best of our knowledge, this is the first work on the generalization analysis of GTML, and we believe it has general implications to the theoretical analysis of other complicated machine learning problems.

cs.LG↗

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↗

arXiv2014

Sequential Click Prediction for Sponsored Search with Recurrent Neural Networks

Click prediction is one of the fundamental problems in sponsored search. Most of existing studies took advantage of machine learning approaches to predict ad click for each event of ad view independently. However, as observed in the real-world sponsored search system, user's behaviors on ads yield high dependency on how the user behaved along with the past time, especially in terms of what queries she submitted, what ads she clicked or ignored, and how long she spent on the landing pages of clicked ads, etc. Inspired by these observations, we introduce a novel framework based on Recurrent Neural Networks (RNN). Compared to traditional methods, this framework directly models the dependency on user's sequential behaviors into the click prediction process through the recurrent structure in RNN. Large scale evaluations on the click-through logs from a commercial search engine demonstrate that our approach can significantly improve the click prediction accuracy, compared to sequence-independent approaches.

cs.IR↗

arXiv2014

Agent Behavior Prediction and Its Generalization Analysis

Machine learning algorithms have been applied to predict agent behaviors in real-world dynamic systems, such as advertiser behaviors in sponsored search and worker behaviors in crowdsourcing. The behavior data in these systems are generated by live agents: once the systems change due to the adoption of the prediction models learnt from the behavior data, agents will observe and respond to these changes by changing their own behaviors accordingly. As a result, the behavior data will evolve and will not be identically and independently distributed, posing great challenges to the theoretical analysis on the machine learning algorithms for behavior prediction. To tackle this challenge, in this paper, we propose to use Markov Chain in Random Environments (MCRE) to describe the behavior data, and perform generalization analysis of the machine learning algorithms on its basis. Since the one-step transition probability matrix of MCRE depends on both previous states and the random environment, conventional techniques for generalization analysis cannot be directly applied. To address this issue, we propose a novel technique that transforms the original MCRE into a higher-dimensional time-homogeneous Markov chain. The new Markov chain involves more variables but is more regular, and thus easier to deal with. We prove the convergence of the new Markov chain when time approaches infinity. Then we prove a generalization bound for the machine learning algorithms on the behavior data generated by the new Markov chain, which depends on both the Markovian parameters and the covering number of the function class compounded by the loss function for behavior prediction and the behavior prediction model. To the best of our knowledge, this is the first work that performs the generalization analysis on data generated by complex processes in real-world dynamic systems.

cs.LG↗