Approximate Bayesian Inference for Count Data Modeling

Bayesian inference allows to make conclusions based on some antecedents that depend on prior knowledge. It additionally allows to quantify uncertainty, which is important in Machine Learning in order to make better predictions and model interpretability. However, in real applications, we often deal with complicated models for which is unfeasible to perform full Bayesian inference. This thesis explores the use of approximate Bayesian inference for count data modeling using Expectation Propagation and Stochastic Expectation Propagation. In Chapter 2, we develop an expectation propagation approach to learn an EDCM finite mixture model. The EDCM distribution is an exponential approximation to the widely used Dirichlet Compound distribution and has shown to offer excellent modeling capabilities in the case of sparse count data. Chapter 3 develops an efficient generative mixture model of EMSD distributions. We use Stochastic Expectation Propagation, which reduces memory consumption, important characteristic when making inference in large datasets. Finally, Chapter 4 develops a probabilistic topic model using the generalized Dirichlet distribution (LGDA) in order to capture topic correlation while maintaining conjugacy. We make use of Expectation Propagation to approximate the posterior, resulting in a model that achieves more accurate inference compared to variational inference. We show that latent topics can be used as a proxy for improving supervised tasks

High-dimensional Sparse Count Data Clustering Using Finite Mixture Models

Due to the massive amount of available digital data, automating its analysis and modeling for different purposes and applications has become an urgent need. One of the most challenging tasks in machine learning is clustering, which is defined as the process of assigning observations sharing similar characteristics to subgroups. Such a task is significant, especially in implementing complex algorithms to deal with high-dimensional data. Thus, the advancement of computational power in statistical-based approaches is increasingly becoming an interesting and attractive research domain. Among the successful methods, mixture models have been widely acknowledged and successfully applied in numerous fields as they have been providing a convenient yet flexible formal setting for unsupervised and semi-supervised learning. An essential problem with these approaches is to develop a probabilistic model that represents the data well by taking into account its nature. Count data are widely used in machine learning and computer vision applications where an object, e.g., a text document or an image, can be represented by a vector corresponding to the appearance frequencies of words or visual words, respectively. Thus, they usually suffer from the well-known curse of dimensionality as objects are represented with high-dimensional and sparse vectors, i.e., a few thousand dimensions with a sparsity of 95 to 99%, which decline the performance of clustering algorithms dramatically. Moreover, count data systematically exhibit the burstiness and overdispersion phenomena, which both cannot be handled with a generic multinomial distribution, typically used to model count data, due to its dependency assumption. This thesis is constructed around six related manuscripts, in which we propose several approaches for high-dimensional sparse count data clustering via various mixture models based on hierarchical Bayesian modeling frameworks that have the ability to model the dependency of repetitive word occurrences. In such frameworks, a suitable distribution is used to introduce the prior information into the construction of the statistical model, based on a conjugate distribution to the multinomial, e.g. the Dirichlet, generalized Dirichlet, and the Beta-Liouville, which has numerous computational advantages. Thus, we proposed a novel model that we call the Multinomial Scaled Dirichlet (MSD) based on using the scaled Dirichlet as a prior to the multinomial to allow more modeling flexibility. Although these frameworks can model burstiness and overdispersion well, they share similar disadvantages making their estimation procedure is very inefficient when the collection size is large. To handle high-dimensionality, we considered two approaches. First, we derived close approximations to the distributions in a hierarchical structure to bring them to the exponential-family form aiming to combine the flexibility and efficiency of these models with the desirable statistical and computational properties of the exponential family of distributions, including sufficiency, which reduce the complexity and computational efforts especially for sparse and high-dimensional data. Second, we proposed a model-based unsupervised feature selection approach for count data to overcome several issues that may be caused by the high dimensionality of the feature space, such as over-fitting, low efficiency, and poor performance. Furthermore, we handled two significant aspects of mixture based clustering methods, namely, parameters estimation and performing model selection. We considered the Expectation-Maximization (EM) algorithm, which is a broadly applicable iterative algorithm for estimating the mixture model parameters, with incorporating several techniques to avoid its initialization dependency and poor local maxima. For model selection, we investigated different approaches to find the optimal number of components based on the Minimum Message Length (MML) philosophy. The effectiveness of our approaches is evaluated using challenging real-life applications, such as sentiment analysis, hate speech detection on Twitter, topic novelty detection, human interaction recognition in films and TV shows, facial expression recognition, face identification, and age estimation

Fully Bayesian Inference for Finite and Infinite Discrete Exponential Mixture Models

Count data often appears in natural language processing and computer vision applications. For example, in images and textual documents clustering, each image or text can be described by a histogram of visual words or text words. In real applications, these frequency vectors often show high-dimensional and sparsity nature. In this case, hierarchical Bayesian modeling frameworks show the ability to model the dependence of the word repetitive occurrences ’burstiness’. Moreover, approximating these models to exponential families is helpful to improve computing efficiency, especially when facing high-dimensional count data and large data sets. However, classical deterministic approaches such as expectation-maximization (EM) do not achieve good results in real-life complex applications. This thesis explores the use of a fully Bayesian inference for finite discrete exponential mixture models of Multinomial Generalized Dirichlet (EMGD), Multinomial Beta-Liouville (EMBL), Multinomial Scaled Dirichlet (EMSD), and Multinomial Shifted Scaled Dirichlet (EMSSD). Finite mixtures have already shown superior performance in real data sets clustering with EM approach. The proposed approaches in this thesis are based on Monte Carlo simulation technique of Gibbs sampling mixed with Metropolis-Hastings step, and we utilize exponential family conjugate prior information to construct the required posteriors relying on Bayesian theory. Furthermore, we also present the infinite models based on Dirichlet processes, which results in clustering algorithms that do not require the specification of the number of mixture components to be given in advance. The performance of our Bayesian approaches was tested in some challenging real-world applications concerning text sentiment analysis, fake news detection, and human face gender recognition

Efficient Computation of Log-likelihood Function in Clustering Overdispersed Count Data

In this work, we present an overdispersed count data clustering algorithm, which uses the mesh method for computing the log-likelihood function, of the multinomial Dirichlet, multinomial generalized Dirichlet, and multinomial Beta-Liouville distributions. Count data are often used in many areas such as information retrieval, data mining, and computer vision. The multinomial Dirichlet distribution (MDD) is one of the widely used methods of modeling multi-categorical count data with overdispersion. In recent works, the use of the mesh algorithm, which involves the approximation of the multinomial Dirichlet distribution's (MDD) log-likelihood function, based on the Bernoulli polynomials; has been proposed instead of using the traditional numerical computation of the log-likelihood function which either results in instability, or leads to long run times that make its use infeasible when modeling large-scale data. Therefore, we extend the mesh algorithm approach for computing the log likelihood function of more flexible distributions, namely multinomial generalized Dirichlet (MGD) and multinomial Beta-Liouville (MBL). A finite mixture model based on these distributions, is optimized by expectation maximization, and attempts to achieve a high accuracy for count data clustering. Through a set of experiments, the proposed approach shows its merits in two real-world clustering problems, that concern natural scenes categorization and facial expression recognition

Exploring the topical structure of short text through probability models : from tasks to fundamentals

Recent technological advances have radically changed the way we communicate. Today’s communication has become ubiquitous and it has fostered the need for information that is easier to create, spread and consume. As a consequence, we have experienced the shortening of text messages in mediums ranging from electronic mailing, instant messaging to microblogging. Moreover, the ubiquity and fast-paced nature of these mediums have promoted their use for unthinkable tasks. For instance, reporting real-world events was classically carried out by news reporters, but, nowadays, most interesting events are first disclosed on social networks like Twitter by eyewitness through short text messages. As a result, the exploitation of the thematic content in short text has captured the interest of both research and industry. Topic models are a type of probability models that have traditionally been used to explore this thematic content, a.k.a. topics, in regular text. Most popular topic models fall into the sub-class of LVMs (Latent Variable Models), which include several latent variables at the corpus, document and word levels to summarise the topics at each level. However, classical LVM-based topic models struggle to learn semantically meaningful topics in short text because the lack of co-occurring words within a document hampers the estimation of the local latent variables at the document level. To overcome this limitation, pooling and hierarchical Bayesian strategies that leverage on contextual information have been essential to improve the quality of topics in short text. In this thesis, we study the problem of learning semantically meaningful and predictive representations of text in two distinct phases: • In the first phase, Part I, we investigate the use of LVM-based topic models for the specific task of event detection in Twitter. In this situation, the use of contextual information to pool tweets together comes naturally. Thus, we first extend an existing clustering algorithm for event detection to use the topics learned from pooled tweets. Then, we propose a probability model that integrates topic modelling and clustering to enable the flow of information between both components. • In the second phase, Part II and Part III, we challenge the use of local latent variables in LVMs, specially when the context of short messages is not available. First of all, we study the evaluation of the generalization capabilities of LVMs like PFA (Poisson Factor Analysis) and propose unbiased estimation methods to approximate it. With the most accurate method, we compare the generalization of chordal models without latent variables to that of PFA topic models in short and regular text collections. In summary, we demonstrate that by integrating clustering and topic modelling, the performance of event detection techniques in Twitter is improved due to the interaction between both components. Moreover, we develop several unbiased likelihood estimation methods for assessing the generalization of PFA and we empirically validate their accuracy in different document collections. Finally, we show that we can learn chordal models without latent variables in text through Chordalysis, and that they can be a competitive alternative to classical topic models, specially in short text.Els avenços tecnològics han canviat radicalment la forma que ens comuniquem. Avui en dia, la comunicació és ubiqua, la qual cosa fomenta l’ús de informació fàcil de crear, difondre i consumir. Com a resultat, hem experimentat l’escurçament dels missatges de text en diferents medis de comunicació, des del correu electrònic, a la missatgeria instantània, al microblogging. A més de la ubiqüitat, la naturalesa accelerada d’aquests medis ha promogut el seu ús per tasques fins ara inimaginables. Per exemple, el relat d’esdeveniments era clàssicament dut a terme per periodistes a peu de carrer, però, en l’actualitat, el successos més interessants es publiquen directament en xarxes socials com Twitter a través de missatges curts. Conseqüentment, l’explotació de la informació temàtica del text curt ha atret l'interès tant de la recerca com de la indústria. Els models temàtics (o topic models) són un tipus de models de probabilitat que tradicionalment s’han utilitzat per explotar la informació temàtica en documents de text. Els models més populars pertanyen al subgrup de models amb variables latents, els quals incorporen varies variables a nivell de corpus, document i paraula amb la finalitat de descriure el contingut temàtic a cada nivell. Tanmateix, aquests models tenen dificultats per aprendre la semàntica en documents curts degut a la manca de coocurrència en les paraules d’un mateix document, la qual cosa impedeix una correcta estimació de les variables locals. Per tal de solucionar aquesta limitació, l’agregació de missatges segons el context i l’ús d’estratègies jeràrquiques Bayesianes són essencials per millorar la qualitat dels temes apresos. En aquesta tesi, estudiem en dos fases el problema d’aprenentatge d’estructures semàntiques i predictives en documents de text: En la primera fase, Part I, investiguem l’ús de models temàtics amb variables latents per la detecció d’esdeveniments a Twitter. En aquest escenari, l’ús del context per agregar tweets sorgeix de forma natural. Per això, primer estenem un algorisme de clustering per detectar esdeveniments a partir dels temes apresos en els tweets agregats. I seguidament, proposem un nou model de probabilitat que integra el model temàtic i el de clustering per tal que la informació flueixi entre ambdós components. En la segona fase, Part II i Part III, qüestionem l’ús de variables latents locals en models per a text curt sense context. Primer de tot, estudiem com avaluar la capacitat de generalització d’un model amb variables latents com el PFA (Poisson Factor Analysis) a través del càlcul de la likelihood. Atès que aquest càlcul és computacionalment intractable, proposem diferents mètodes d estimació. Amb el mètode més acurat, comparem la generalització de models chordals sense variables latents amb la del models PFA, tant en text curt com estàndard. En resum, demostrem que integrant clustering i models temàtics, el rendiment de les tècniques de detecció d’esdeveniments a Twitter millora degut a la interacció entre ambdós components. A més a més, desenvolupem diferents mètodes d’estimació per avaluar la capacitat generalizadora dels models PFA i validem empíricament la seva exactitud en diverses col·leccions de text. Finalment, mostrem que podem aprendre models chordals sense variables latents en text a través de Chordalysis i que aquests models poden ser una bona alternativa als models temàtics clàssics, especialment en text curt.Postprint (published version

Producing power-law distributions and damping word frequencies with two-stage language models

Standard statistical models of language fail to capture one of the most striking properties of natural languages: the power-law distribution in the frequencies of word tokens. We present a framework for developing statisticalmodels that can generically produce power laws, breaking generativemodels into two stages. The first stage, the generator, can be any standard probabilistic model, while the second stage, the adaptor, transforms the word frequencies of this model to provide a closer match to natural language. We show that two commonly used Bayesian models, the Dirichlet-multinomial model and the Dirichlet process, can be viewed as special cases of our framework. We discuss two stochastic processes-the Chinese restaurant process and its two-parameter generalization based on the Pitman-Yor process-that can be used as adaptors in our framework to produce power-law distributions over word frequencies. We show that these adaptors justify common estimation procedures based on logarithmic or inverse-power transformations of empirical frequencies. In addition, taking the Pitman-Yor Chinese restaurant process as an adaptor justifies the appearance of type frequencies in formal analyses of natural language and improves the performance of a model for unsupervised learning of morphology.48 page(s