In this paper we show that a large class of Latent variable models, such as Mixed Membership Stochastic Block(MMSB) Models, Topic Models, and Adversarial Clustering, can be unified through a geometric perspective, replacing model specific assumptions and algorithms for individual models. The geometric perspective leads to the formulation: \emph{find a latent $k-$ polytope $K$ in ${\bf R}^d$ given $n$ data points, each obtained by perturbing a latent point in $K$}. This problem does not seem to have been considered in the literature. The most important contribution of this paper is to show that the latent $k-$polytope problem admits an efficient algorithm under deterministic assumptions which naturally hold in Latent variable models considered in this paper. ur algorithm runs in time $O^*(k\; \mbox{nnz})$ matching the best running time of algorithms in special cases considered here and is better when the data is sparse, as is the case in applications. An important novelty of the algorithm is the introduction of \emph{subset smoothed polytope}, $K'$, the convex hull of the ${n\choose \delta n}$ points obtained by averaging all $\delta n$ subsets of the data points, for a given $\delta \in (0,1)$. We show that $K$ and $K'$ are close in Hausdroff distance. Among the consequences of our algorithm are the following: (a) MMSB Models and Topic Models: the first quasi-input-sparsity time algorithm for parameter estimation for $k \in O^*(1)$, (b) Adversarial Clustering: In $k-$means, if, an adversary is allowed to move many data points from each cluster an arbitrary amount towards the convex hull of the centers of other clusters, our algorithm still estimates cluster centers well.
In the last decades, philosophers have begun using empirical data for conceptual analysis, but corpus-based conceptual analysis has so far failed to develop, in part because of the absence of reliable methods to automatically detect concepts in textual data. Previous attempts have shown that topic models can constitute efficient concept detection heuristics, but while they leverage the syntagmatic relations in a corpus, they fail to exploit paradigmatic relations, and thus probably fail to model concepts accurately. In this article, we show that using a topic model that models concepts on a space of word embeddings (Hu and Tsujii, 2016) can lead to significant increases in concept detection performance, as well as enable the target concept to be expressed in more flexible ways using word vectors.
Topic models provide a useful method for dimensionality reduction and exploratory data analysis in large text corpora. Most approaches to topic model inference have been based on a maximum likelihood objective. Efficient algorithms exist that approximate this objective, but they have no provable guarantees. Recently, algorithms have been introduced that provide provable bounds, but these algorithms are not practical because they are inefficient and not robust to violations of model assumptions. In this paper we present an algorithm for topic model inference that is both provable and practical. The algorithm produces results comparable to the best MCMC implementations while running orders of magnitude faster.
Topic Modeling is an approach used for automatic comprehension and classification of data in a variety of settings, and perhaps the canonical application is in uncovering thematic structure in a corpus of documents. A number of foundational works both in machine learning and in theory have suggested a probabilistic model for documents, whereby documents arise as a convex combination of (i.e. distribution on) a small number of topic vectors, each topic vector being a distribution on words (i.e. a vector of word-frequencies). Similar models have since been used in a variety of application areas; the Latent Dirichlet Allocation or LDA model of Blei et al. is especially popular. Theoretical studies of topic modeling focus on learning the model's parameters assuming the data is actually generated from it. Existing approaches for the most part rely on Singular Value Decomposition(SVD), and consequently have one of two limitations: these works need to either assume that each document contains only one topic, or else can only recover the span of the topic vectors instead of the topic vectors themselves. This paper formally justifies Nonnegative Matrix Factorization(NMF) as a main tool in this context, which is an analog of SVD where all vectors are nonnegative. Using this tool we give the first polynomial-time algorithm for learning topic models without the above two limitations. The algorithm uses a fairly mild assumption about the underlying topic matrix called separability, which is usually found to hold in real-life data. A compelling feature of our algorithm is that it generalizes to models that incorporate topic-topic correlations, such as the Correlated Topic Model and the Pachinko Allocation Model. We hope that this paper will motivate further theoretical results that use NMF as a replacement for SVD - just as NMF has come to replace SVD in many applications.
We introduce a dynamic generative model, Bayesian allocation model (BAM), which establishes explicit connections between nonnegative tensor factorization (NTF), graphical models of discrete probability distributions and their Bayesian extensions, and the topic models such as the latent Dirichlet allocation. BAM is based on a Poisson process, whose events are marked by using a Bayesian network, where the conditional probability tables of this network are then integrated out analytically. We show that the resulting marginal process turns out to be a Polya urn, an integer valued self-reinforcing process. This urn processes, which we name a Polya-Bayes process, obey certain conditional independence properties that provide further insight about the nature of NTF. These insights also let us develop space efficient simulation algorithms that respect the potential sparsity of data: we propose a class of sequential importance sampling algorithms for computing NTF and approximating their marginal likelihood, which would be useful for model selection. The resulting methods can also be viewed as a model scoring method for topic models and discrete Bayesian networks with hidden variables. The new algorithms have favourable properties in the sparse data regime when contrasted with variational algorithms that become more accurate when the total sum of the elements of the observed tensor goes to infinity. We illustrate the performance on several examples and numerically study the behaviour of the algorithms for various data regimes.
Scientific documents rely on both mathematics and text to communicate ideas. Inspired by the topical correspondence between mathematical equations and word contexts observed in scientific texts, we propose a novel topic model that jointly generates mathematical equations and their surrounding text (TopicEq). Using an extension of the correlated topic model, the context is generated from a mixture of latent topics, and the equation is generated by an RNN that depends on the latent topic activations. To experiment with this model, we create a corpus of 400K equation-context pairs extracted from a range of scientific articles from arXiv, and fit the model using a variational autoencoder approach. Experimental results show that this joint model significantly outperforms existing topic models and equation models for scientific texts. Moreover, we qualitatively show that the model effectively captures the relationship between topics and mathematics, enabling novel applications such as topic-aware equation generation, equation topic inference, and topic-aware alignment of mathematical symbols and words.
Aspect-based Opinion Summary (AOS), consisting of aspect discovery and sentiment classification steps, has recently been emerging as one of the most crucial data mining tasks in e-commerce systems. Along this direction, the LDA-based model is considered as a notably suitable approach, since this model offers both topic modeling and sentiment classification. However, unlike traditional topic modeling, in the context of aspect discovery it is often required some initial seed words, whose prior knowledge is not easy to be incorporated into LDA models. Moreover, LDA approaches rely on sampling methods, which need to load the whole corpus into memory, making them hardly scalable. In this research, we study an alternative approach for AOS problem, based on Autoencoding Variational Inference (AVI). Firstly, we introduce the Autoencoding Variational Inference for Aspect Discovery (AVIAD) model, which extends the previous work of Autoencoding Variational Inference for Topic Models (AVITM) to embed prior knowledge of seed words. This work includes enhancement of the previous AVI architecture and also modification of the loss function. Ultimately, we present the Autoencoding Variational Inference for Joint Sentiment/Topic (AVIJST) model. In this model, we substantially extend the AVI model to support the JST model, which performs topic modeling for corresponding sentiment. The experimental results show that our proposed models enjoy higher topic coherent, faster convergence time and better accuracy on sentiment classification, as compared to their LDA-based counterparts.
Topic models are in widespread use in natural language processing and beyond. Here, we propose a new framework for the evaluation of probabilistic topic modeling algorithms based on synthetic corpora containing an unambiguously defined ground truth topic structure. The major innovation of our approach is the ability to quantify the agreement between the planted and inferred topic structures by comparing the assigned topic labels at the level of the tokens. In experiments, our approach yields novel insights about the relative strengths of topic models as corpus characteristics vary, and the first evidence of an "undetectable phase" for topic models when the planted structure is weak. We also establish the practical relevance of the insights gained for synthetic corpora by predicting the performance of topic modeling algorithms in classification tasks in real-world corpora.
This paper proposes Dirichlet Variational Autoencoder (DirVAE) using a Dirichlet prior for a continuous latent variable that exhibits the characteristic of the categorical probabilities. To infer the parameters of DirVAE, we utilize the stochastic gradient method by approximating the Gamma distribution, which is a component of the Dirichlet distribution, with the inverse Gamma CDF approximation. Additionally, we reshape the component collapsing issue by investigating two problem sources, which are decoder weight collapsing and latent value collapsing, and we show that DirVAE has no component collapsing; while Gaussian VAE exhibits the decoder weight collapsing and Stick-Breaking VAE shows the latent value collapsing. The experimental results show that 1) DirVAE models the latent representation result with the best log-likelihood compared to the baselines; and 2) DirVAE produces more interpretable latent values with no collapsing issues which the baseline models suffer from. Also, we show that the learned latent representation from the DirVAE achieves the best classification accuracy in the semi-supervised and the supervised classification tasks on MNIST, OMNIGLOT, and SVHN compared to the baseline VAEs. Finally, we demonstrated that the DirVAE augmented topic models show better performances in most cases.
We present Variational Aspect-based Latent Topic Allocation (VALTA), a family of autoencoding topic models that learn aspect-based representations of reviews. VALTA defines a user-item encoder that maps bag-of-words vectors for combined reviews associated with each paired user and item onto structured embeddings, which in turn define per-aspect topic weights. We model individual reviews in a structured manner by inferring an aspect assignment for each sentence in a given review, where the per-aspect topic weights obtained by the user-item encoder serve to define a mixture over topics, conditioned on the aspect. The result is an autoencoding neural topic model for reviews, which can be trained in a fully unsupervised manner to learn topics that are structured into aspects. Experimental evaluation on large number of datasets demonstrates that aspects are interpretable, yield higher coherence scores than non-structured autoencoding topic model variants, and can be utilized to perform aspect-based comparison and genre discovery.
In our work, we propose to represent HTM as a set of flat models, or layers, and a set of topical hierarchies, or edges. We suggest several quality measures for edges of hierarchical models, resembling those proposed for flat models. We conduct an assessment experimentation and show strong correlation between the proposed measures and human judgement on topical edge quality. We also introduce heterogeneous algorithm to build hierarchical topic models for heterogeneous data sources. We show how making certain adjustments to learning process helps to retain original structure of customized models while allowing for slight coherent modifications for new documents. We evaluate this approach using the proposed measures and show that the proposed heterogeneous algorithm significantly outperforms the baseline concat approach. Finally, we implement our own ESE called Rysearch, which demonstrates the potential of ARTM approach for visualizing large heterogeneous document collections.
Recently, considerable research effort has been devoted to developing deep architectures for topic models to learn topic structures. Although several deep models have been proposed to learn better topic proportions of documents, how to leverage the benefits of deep structures for learning word distributions of topics has not yet been rigorously studied. Here we propose a new multi-layer generative process on word distributions of topics, where each layer consists of a set of topics and each topic is drawn from a mixture of the topics of the layer above. As the topics in all layers can be directly interpreted by words, the proposed model is able to discover interpretable topic hierarchies. As a self-contained module, our model can be flexibly adapted to different kinds of topic models to improve their modelling accuracy and interpretability. Extensive experiments on text corpora demonstrate the advantages of the proposed model.
Topic models are widely used for thematic structure discovery in text. But traditional topic models often require dedicated inference procedures for specific tasks at hand. Also, they are not designed to generate word-level semantic representations. To address these limitations, we propose a topic modeling approach based on Generative Adversarial Nets (GANs), called Adversarial-neural Topic Model (ATM). The proposed ATM models topics with Dirichlet prior and employs a generator network to capture the semantic patterns among latent topics. Meanwhile, the generator could also produce word-level semantic representations. To illustrate the feasibility of porting ATM to tasks other than topic modeling, we apply ATM for open domain event extraction. Our experimental results on the two public corpora show that ATM generates more coherence topics, outperforming a number of competitive baselines. Moreover, ATM is able to extract meaningful events from news articles.
Electronic health records (EHR) are rich heterogeneous collection of patient health information, whose broad adoption provides great opportunities for systematic health data mining. However, heterogeneous EHR data types and biased ascertainment impose computational challenges. Here, we present mixEHR, an unsupervised generative model integrating collaborative filtering and latent topic models, which jointly models the discrete distributions of data observation bias and actual data using latent disease-topic distributions. We apply mixEHR on 12.8 million phenotypic observations from the MIMIC dataset, and use it to reveal latent disease topics, interpret EHR results, impute missing data, and predict mortality in intensive care units. Using both simulation and real data, we show that mixEHR outperforms previous methods and reveals meaningful multi-disease insights.
The top word list, i.e., the top-M words with highest marginal probability in a given topic, is the standard topic representation in topic models. Most of recent automatical topic labeling algorithms and popular topic quality metrics are based on it. However, we find, empirically, words in this type of top word list are not always representative. The objective of this paper is to find more representative top word lists for topics. To achieve this, we rerank the words in a given topic by further considering marginal probability on words over every other topic. The reranking list of top-M words is used to be a novel topic representation for topic models. We investigate three reranking methodologies, using (1) standard deviation weight, (2) standard deviation weight with topic size and (3) Chi Square \c{hi}2statistic selection. Experimental results on real world collections indicate that our representations can extract more representative words for topics, agreeing with human judgements.
Accurate prediction of conversation topics can be a valuable signal for creating coherent and engaging dialog systems. In this work, we focus on context-aware topic classification methods for identifying topics in free-form human-chatbot dialogs. We extend previous work on neural topic classification and unsupervised topic keyword detection by incorporating conversational context and dialog act features. On annotated data, we show that incorporating context and dialog acts leads to relative gains in topic classification accuracy by 35% and on unsupervised keyword detection recall by 11% for conversational interactions where topics frequently span multiple utterances. We show that topical metrics such as topical depth is highly correlated with dialog evaluation metrics such as coherence and engagement implying that conversational topic models can predict user satisfaction. Our work for detecting conversation topics and keywords can be used to guide chatbots towards coherent dialog.
Probabilistic topic modeling is a popular choice as the first step of crosslingual tasks to enable knowledge transfer and extract multilingual features. While many multilingual topic models have been developed, their assumptions on the training corpus are quite varied, and it is not clear how well the models can be applied under various training conditions. In this paper, we systematically study the knowledge transfer mechanisms behind different multilingual topic models, and through a broad set of experiments with four models on ten languages, we provide empirical insights that can inform the selection and future development of multilingual topic models.
Probabilistic topic models are widely used to discover latent topics in document collections, while latent feature vector representations of words have been used to obtain high performance in many NLP tasks. In this paper, we extend two different Dirichlet multinomial topic models by incorporating latent feature vector representations of words trained on very large corpora to improve the word-topic mapping learnt on a smaller corpus. Experimental results show that by using information from the external corpora, our new models produce significant improvements on topic coherence, document clustering and document classification tasks, especially on datasets with few or short documents.
A high degree of topical diversity is often considered to be an important characteristic of interesting text documents. A recent proposal for measuring topical diversity identifies three distributions for assessing the diversity of documents: distributions of words within documents, words within topics, and topics within documents. Topic models play a central role in this approach and, hence, their quality is crucial to the efficacy of measuring topical diversity. The quality of topic models is affected by two causes: generality and impurity of topics. General topics only include common information of a background corpus and are assigned to most of the documents. Impure topics contain words that are not related to the topic. Impurity lowers the interpretability of topic models. Impure topics are likely to get assigned to documents erroneously. We propose a hierarchical re-estimation process aimed at removing generality and impurity. Our approach has three re-estimation components: (1) document re-estimation, which removes general words from the documents; (2) topic re-estimation, which re-estimates the distribution over words of each topic; and (3) topic assignment re-estimation, which re-estimates for each document its distributions over topics. For measuring topical diversity of text documents, our HiTR approach improves over the state-of-the-art measured on PubMed dataset.
We address two challenges of probabilistic topic modelling in order to better estimate the probability of a word in a given context, i.e., P(word|context): (1) No Language Structure in Context: Probabilistic topic models ignore word order by summarizing a given context as a "bag-of-word" and consequently the semantics of words in the context is lost. The LSTM-LM learns a vector-space representation of each word by accounting for word order in local collocation patterns and models complex characteristics of language (e.g., syntax and semantics), while the TM simultaneously learns a latent representation from the entire document and discovers the underlying thematic structure. We unite two complementary paradigms of learning the meaning of word occurrences by combining a TM (e.g., DocNADE) and a LM in a unified probabilistic framework, named as ctx-DocNADE. (2) Limited Context and/or Smaller training corpus of documents: In settings with a small number of word occurrences (i.e., lack of context) in short text or data sparsity in a corpus of few documents, the application of TMs is challenging. We address this challenge by incorporating external knowledge into neural autoregressive topic models via a language modelling approach: we use word embeddings as input of a LSTM-LM with the aim to improve the word-topic mapping on a smaller and/or short-text corpus. The proposed DocNADE extension is named as ctx-DocNADEe. We present novel neural autoregressive topic model variants coupled with neural LMs and embeddings priors that consistently outperform state-of-the-art generative TMs in terms of generalization (perplexity), interpretability (topic coherence) and applicability (retrieval and classification) over 6 long-text and 8 short-text datasets from diverse domains.