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Register a new userCombinatorial Topic Models using Small-Variance Asymptotics
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Added by
Ke Jiang
Publication date
2016
fields
Informatics Engineering
and research's language is
English
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Topic models have emerged as fundamental tools in unsupervised machine learning. Most modern topic modeling algorithms take a probabilistic view and derive inference algorithms based on Latent Dirichlet Allocation (LDA) or its variants. In contrast, we study topic modeling as a combinatorial optimization problem, and propose a new objective function derived from LDA by passing to the small-variance limit. We minimize the derived objective by using ideas from combinatorial optimization, which results in a new, fast, and high-quality topic modeling algorithm. In particular, we show that our results are competitive with popular LDA-based topic modeling approaches, and also discuss the (dis)similarities between our approach and its probabilistic counterparts.
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Topic models are widely used unsupervised models capable of learning topics - weighted lists of words and documents - from large collections of text documents. When topic models are used for discovery of topics in text collections, a question that arises naturally is how well the model-induced topics correspond to topics of interest to the analyst. In this paper we revisit and extend a so far neglected approach to topic model evaluation based on measuring topic coverage - computationally matching model topics with a set of reference topics that models are expected to uncover. The approach is well suited for analyzing models performance in topic discovery and for large-scale analysis of both topic models and measures of model quality. We propose new measures of coverage and evaluate, in a series of experiments, different types of topic models on two distinct text domains for which interest for topic discovery exists. The experiments include evaluation of model quality, analysis of coverage of distinct topic categories, and the analysis of the relationship between coverage and other methods of topic model evaluation. The paper contributes a new supervised measure of coverage, and the first unsupervised measure of coverage. The supervised measure achieves topic matching accuracy close to human agreement. The unsupervised measure correlates highly with the supervised one (Spearmans $rho geq 0.95$). Other contributions include insights into both topic models and different methods of model evaluation, and the datasets and code for facilitating future research on topic coverage.
Small variance asymptotics is emerging as a useful technique for inference in large scale Bayesian non-parametric mixture models. This paper analyses the online learning of robot manipulation tasks with Bayesian non-parametric mixture models under small variance asymptotics. The analysis yields a scalable online sequence clustering (SOSC) algorithm that is non-parametric in the number of clusters and the subspace dimension of each cluster. SOSC groups the new datapoint in its low dimensional subspace by online inference in a non-parametric mixture of probabilistic principal component analyzers (MPPCA) based on Dirichlet process, and captures the state transition and state duration information online in a hidden semi-Markov model (HSMM) based on hierarchical Dirichlet process. A task-parameterized formulation of our approach autonomously adapts the model to changing environmental situations during manipulation. We apply the algorithm in a teleoperation setting to recognize the intention of the operator and remotely adjust the movement of the robot using the learned model. The generative model is used to synthesize both time-independent and time-dependent behaviours by relying on the principles of shared and autonomous control. Experiments with the Baxter robot yield parsimonious clusters that adapt online with new demonstrations and assist the operator in performing remote manipulation tasks.
The learning rate warmup heuristic achieves remarkable success in stabilizing training, accelerating convergence and improving generalization for adaptive stochastic optimization algorithms like RMSprop and Adam. Here, we study its mechanism in details. Pursuing the theory behind warmup, we identify a problem of the adaptive learning rate (i.e., it has problematically large variance in the early stage), suggest warmup works as a variance reduction technique, and provide both empirical and theoretical evidence to verify our hypothesis. We further propose RAdam, a new variant of Adam, by introducing a term to rectify the variance of the adaptive learning rate. Extensive experimental results on image classification, language modeling, and neural machine translation verify our intuition and demonstrate the effectiveness and robustness of our proposed method. All implementations are available at: https://github.com/LiyuanLucasLiu/RAdam.
Traditional Relational Topic Models provide a way to discover the hidden topics from a document network. Many theoretical and practical tasks, such as dimensional reduction, document clustering, link prediction, benefit from this revealed knowledge. However, existing relational topic models are based on an assumption that the number of hidden topics is known in advance, and this is impractical in many real-world applications. Therefore, in order to relax this assumption, we propose a nonparametric relational topic model in this paper. Instead of using fixed-dimensional probability distributions in its generative model, we use stochastic processes. Specifically, a gamma process is assigned to each document, which represents the topic interest of this document. Although this method provides an elegant solution, it brings additional challenges when mathematically modeling the inherent network structure of typical document network, i.e., two spatially closer documents tend to have more similar topics. Furthermore, we require that the topics are shared by all the documents. In order to resolve these challenges, we use a subsampling strategy to assign each document a different gamma process from the global gamma process, and the subsampling probabilities of documents are assigned with a Markov Random Field constraint that inherits the document network structure. Through the designed posterior inference algorithm, we can discover the hidden topics and its number simultaneously. Experimental results on both synthetic and real-world network datasets demonstrate the capabilities of learning the hidden topics and, more importantly, the number of topics.
The simplicial condition and other stronger conditions that imply it have recently played a central role in developing polynomial time algorithms with provable asymptotic consistency and sample complexity guarantees for topic estimation in separable topic models. Of these algorithms, those that rely solely on the simplicial condition are impractical while the practical ones need stronger conditions. In this paper, we demonstrate, for the first time, that the simplicial condition is a fundamental, algorithm-independent, information-theoretic necessary condition for consistent separable topic estimation. Furthermore, under solely the simplicial condition, we present a practical quadratic-complexity algorithm based on random projections which consistently detects all novel words of all topics using only up to second-order empirical word moments. This algorithm is amenable to distributed implementation making it attractive for big-data scenarios involving a network of large distributed databases.
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