Exponential Family Hybrid Semi-Supervised Learning

We present an approach to semi-supervised learning based on an exponential family characterization. Our approach generalizes previous work on coupled priors for hybrid generative/discriminative models. Our model is more flexible and natural than previous approaches. Experimental results on several data sets show that our approach also performs better in practice.Comment: 6 pages, 3 figure

Action classification using a discriminative multilevel HDP-HMM

We classify human actions occurring in depth image sequences using features based on skeletal joint positions. The action classes are represented by a multi-level Hierarchical Dirichlet Process – Hidden Markov Model (HDP-HMM). The non-parametric HDP-HMM allows the inference of hidden states automatically from training data. The model parameters of each class are formulated as transformations from a shared base distribution, thus promoting the use of unlabelled examples during training and borrowing information across action classes. Further, the parameters are learnt in a discriminative way. We use a normalized gamma process representation of HDP and margin based likelihood functions for this purpose. We sample parameters from the complex posterior distribution induced by our discriminative likelihood function using elliptical slice sampling. Experiments with two different datasets show that action class models learnt using our technique produce good classification results

Statistical Analysis of Spherical Data: Clustering, Feature Selection and Applications

In the light of interdisciplinary applications, data to be studied and analyzed have witnessed a growth in volume and change in their intrinsic structure and type. In other words, in practice the diversity of resources generating objects have imposed several challenges for decision maker to determine informative data in terms of time, model capability, scalability and knowledge discovery. Thus, it is highly desirable to be able to extract patterns of interest that support the decision of data management. Clustering, among other machine learning approaches, is an important data engineering technique that empowers the automatic discovery of similar object’s clusters and the consequent assignment of new unseen objects to appropriate clusters. In this context, the majority of current research does not completely address the true structure and nature of data for particular application at hand. In contrast to most previous research, our proposed work focuses on the modeling and classification of spherical data that are naturally generated in many data mining and knowledge discovery applications. Thus, in this thesis we propose several estimation and feature selection frameworks based on Langevin distribution which are devoted to spherical patterns in offline and online settings. In this thesis, we first formulate a unified probabilistic framework, where we build probabilistic kernels based on Fisher score and information divergences from finite Langevin mixture for Support Vector Machine. We are motivated by the fact that the blending of generative and discriminative approaches has prevailed by exploring and adopting distinct characteristic of each approach toward constructing a complementary system combining the best of both. Due to the high demand to construct compact and accurate statistical models that are automatically adjustable to dynamic changes, next in this thesis, we propose probabilistic frameworks for high-dimensional spherical data modeling based on finite Langevin mixtures that allow simultaneous clustering and feature selection in offline and online settings. To this end, we adopted finite mixture models which have long been heavily relied on deterministic learning approaches such as maximum likelihood estimation. Despite their successful utilization in wide spectrum of areas, these approaches have several drawbacks as we will discuss in this thesis. An alternative approach is the adoption of Bayesian inference that naturally addresses data uncertainty while ensuring good generalization. To address this issue, we also propose a Bayesian approach for finite Langevin mixture model estimation and selection. When data change dynamically and grow drastically, finite mixture is not always a feasible solution. In contrast with previous approaches, which suppose an unknown finite number of mixture components, we finally propose a nonparametric Bayesian approach which assumes an infinite number of components. We further enhance our model by simultaneously detecting informative features in the process of clustering. Through extensive empirical experiments, we demonstrate the merits of the proposed learning frameworks on diverse high dimensional datasets and challenging real-world applications

Finite Bivariate and Multivariate Beta Mixture Models Learning and Applications

Finite mixture models have been revealed to provide flexibility for data clustering. They have demonstrated high competence and potential to capture hidden structure in data. Modern technological progresses, growing volumes and varieties of generated data, revolutionized computers and other related factors are contributing to produce large scale data. This fact enhances the significance of finding reliable and adaptable models which can analyze bigger, more complex data to identify latent patterns, deliver faster and more accurate results and make decisions with minimal human interaction. Adopting the finest and most accurate distribution that appropriately represents the mixture components is critical. The most widely adopted generative model has been the Gaussian mixture. In numerous real-world applications, however, when the nature and structure of data are non-Gaussian, this modelling fails. One of the other crucial issues when using mixtures is determination of the model complexity or number of mixture components. Minimum message length (MML) is one of the main techniques in frequentist frameworks to tackle this challenging issue. In this work, we have designed and implemented a finite mixture model, using the bivariate and multivariate Beta distributions for cluster analysis and demonstrated its flexibility in describing the intrinsic characteristics of the observed data. In addition, we have applied our estimation and model selection algorithms to synthetic and real datasets. Most importantly, we considered interesting applications such as in image segmentation, software modules defect prediction, spam detection and occupancy estimation in smart buildings

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