85,401 research outputs found
Variational Elliptical Processes
We present elliptical processes, a family of non-parametric probabilistic
models that subsume Gaussian processes and Student's t processes. This
generalization includes a range of new heavy-tailed behaviors while retaining
computational tractability. Elliptical processes are based on a representation
of elliptical distributions as a continuous mixture of Gaussian distributions.
We parameterize this mixture distribution as a spline normalizing flow, which
we train using variational inference. The proposed form of the variational
posterior enables a sparse variational elliptical process applicable to
large-scale problems. We highlight advantages compared to Gaussian processes
through regression and classification experiments. Elliptical processes can
supersede Gaussian processes in several settings, including cases where the
likelihood is non-Gaussian or when accurate tail modeling is essential.Comment: 14 pages, 15 figures, appendix 9 page
Application of shifted delta cepstral features for GMM language identification
Spoken language identifcation (LID) in telephone speech signals is an important and difficult classification task. Language identifcation modules can be used as front end signal routers for multilanguage speech recognition or transcription devices. Gaussian Mixture Models (GMM\u27s) can be utilized to effectively model the distribution of feature vectors present in speech signals for classification. Common feature vectors used for speech processing include Linear Prediction (LP-CC), Mel-Frequency (MF-CC), and Perceptual Linear Prediction derived Cepstral coefficients (PLP-CC). This thesis compares and examines the recently proposed type of feature vector called the Shifted Delta Cepstral (SDC) coefficients. Utilization of the Shifted Delta Cepstral coefficients has been shown to improve language identification performance. This thesis explores the use of different types of shifted delta cepstral feature vectors for spoken language identification of telephone speech using a simple Gaussian Mixture Models based classifier for a 3-language task. The OGI Multi-language Telephone Speech Corpus is used to evaluate the system
Supervised Classification Using Finite Mixture Copula
Use of copula for statistical classification is recent and gaining popularity. For example, statistical classification using copula has been proposed for automatic character recognition, medical diagnostic and most recently in data mining. Classical discrimination rules assume normality. But in this data age time, this assumption is often questionable. In fact features of data could be a mixture of discrete and continues random variables. In this paper, mixture copula densities are used to model class conditional distributions. Such types of densities are useful when the marginal densities of the vector of features are not normally distributed and are of a mixed kind of variables. Authors have shown that such mixture models are very useful for uncovering hidden structures in the data, and used them for clustering in data mining. Under such mixture models, maximum likelihood estimation methods are not suitable and regular expectation maximization algorithm is inefficient and may not converge. A new estimation method is proposed to estimate such densities and build the classifier based on mixture finite Gaussian densities. Simulations are used to compare the performance of the copula based classifier with classical normal distribution based models, logistic regression based model and independent model cases. The method is also applied to a real data
Positive data clustering using finite inverted dirichlet mixture models
In this thesis we present an unsupervised algorithm for learning finite mixture models from multivariate positive data. Indeed, this kind of data appears naturally in many applications, yet it has not been adequately addressed in the past. This mixture model is based on the inverted Dirichlet distribution, which offers a good representation and modeling of positive non gaussian data. The proposed approach for estimating the parameters of an inverted Dirichlet mixture is based on the maximum likelihood (ML) using Newton Raphson method. We also develop an approach, based on the Minimum Message Length (MML) criterion, to select the optimal number of clusters to represent the data using such a mixture. Experimental results are presented using artificial histograms and real data sets. The challenging problem of software modules classification is investigated within the proposed statistical framework, also
Estimation of Single-Gaussian and Gaussian mixture models for pattern recognition
Single-Gaussian and Gaussian-Mixture Models are utilized in various
pattern recognition tasks. The model parameters are estimated usually via
Maximum Likelihood Estimation (MLE) with respect to available training data.
However, if only small amount of training data is available, the resulting model
will not generalize well. Loosely speaking, classification performance given an
unseen test set may be poor. In this paper, we propose a novel estimation technique
of the model variances. Once the variances were estimated using MLE,
they are multiplied by a scaling factor, which reflects the amount of uncertainty
present in the limited sample set. The optimal value of the scaling factor is based
on the Kullback-Leibler criterion and on the assumption that the training and test
sets are sampled from the same source distribution. In addition, in the case of
GMM, the proper number of components can be determined
Mixtures of Shifted Asymmetric Laplace Distributions
A mixture of shifted asymmetric Laplace distributions is introduced and used
for clustering and classification. A variant of the EM algorithm is developed
for parameter estimation by exploiting the relationship with the general
inverse Gaussian distribution. This approach is mathematically elegant and
relatively computationally straightforward. Our novel mixture modelling
approach is demonstrated on both simulated and real data to illustrate
clustering and classification applications. In these analyses, our mixture of
shifted asymmetric Laplace distributions performs favourably when compared to
the popular Gaussian approach. This work, which marks an important step in the
non-Gaussian model-based clustering and classification direction, concludes
with discussion as well as suggestions for future work
- …