This empirical study is mainly devoted to comparing four tree-based boosting algorithms: mart, abc-mart, robust logitboost, and abc-logitboost, for multi-class classification on a variety of publicly available datasets. Some of those datasets have been thoroughly tested in prior studies using a broad range of classification algorithms including SVM, neural nets, and deep learning. In terms of the empirical classification errors, our experiment results demonstrate: 1. Abc-mart considerably improves mart. 2. Abc-logitboost considerably improves (robust) logitboost. 3. Robust) logitboost} considerably improves mart on most datasets. 4. Abc-logitboost considerably improves abc-mart on most datasets. 5. These four boosting algorithms (especially abc-logitboost) outperform SVM on many datasets. 6. Compared to the best deep learning methods, these four boosting algorithms (especially abc-logitboost) are competitive.

This paper describes the approach taken to the XML Mining track at INEX 2008 by a group at the Queensland University of Technology. We introduce the K-tree clustering algorithm in an Information Retrieval context by adapting it for document clustering. Many large scale problems exist in document clustering. K-tree scales well with large inputs due to its low complexity. It offers promising results both in terms of efficiency and quality. Document classification was completed using Support Vector Machines.

We introduce K-tree in an information retrieval context. It is an efficient approximation of the k-means clustering algorithm. Unlike k-means it forms a hierarchy of clusters. It has been extended to address issues with sparse representations. We compare performance and quality to CLUTO using document collections. The K-tree has a low time complexity that is suitable for large document collections. This tree structure allows for efficient disk based implementations where space requirements exceed that of main memory.

Vector quantization(VQ) is a lossy data compression technique from signal processing, which is restricted to feature vectors and therefore inapplicable for combinatorial structures. This contribution presents a theoretical foundation of graph quantization (GQ) that extends VQ to the domain of attributed graphs. We present the necessary Lloyd-Max conditions for optimality of a graph quantizer and consistency results for optimal GQ design based on empirical distortion measures and stochastic optimization. These results statistically justify existing clustering algorithms in the domain of graphs. The proposed approach provides a template of how to link structural pattern recognition methods other than GQ to statistical pattern recognition.

The problem of learning tree-structured Gaussian graphical models from independent and identically distributed (i.i.d.) samples is considered. The influence of the tree structure and the parameters of the Gaussian distribution on the learning rate as the number of samples increases is discussed. Specifically, the error exponent corresponding to the event that the estimated tree structure differs from the actual unknown tree structure of the distribution is analyzed. Finding the error exponent reduces to a least-squares problem in the very noisy learning regime. In this regime, it is shown that the extremal tree structure that minimizes the error exponent is the star for any fixed set of correlation coefficients on the edges of the tree. If the magnitudes of all the correlation coefficients are less than 0.63, it is also shown that the tree structure that maximizes the error exponent is the Markov chain. In other words, the star and the chain graphs represent the hardest and the easiest structures to learn in the class of tree-structured Gaussian graphical models. This result can also be intuitively explained by correlation decay: pairs of nodes which are far apart, in terms of graph distance, are unlikely to be mistaken as edges by the maximum-likelihood estimator in the asymptotic regime.

This paper addresses the problem of identifying a lower dimensional space where observed data can be sparsely represented. This under-complete dictionary learning task can be formulated as a blind separation problem of sparse sources linearly mixed with an unknown orthogonal mixing matrix. This issue is formulated in a Bayesian framework. First, the unknown sparse sources are modeled as Bernoulli-Gaussian processes. To promote sparsity, a weighted mixture of an atom at zero and a Gaussian distribution is proposed as prior distribution for the unobserved sources. A non-informative prior distribution defined on an appropriate Stiefel manifold is elected for the mixing matrix. The Bayesian inference on the unknown parameters is conducted using a Markov chain Monte Carlo (MCMC) method. A partially collapsed Gibbs sampler is designed to generate samples asymptotically distributed according to the joint posterior distribution of the unknown model parameters and hyperparameters. These samples are then used to approximate the joint maximum a posteriori estimator of the sources and mixing matrix. Simulations conducted on synthetic data are reported to illustrate the performance of the method for recovering sparse representations. An application to sparse coding on under-complete dictionary is finally investigated.

I introduce an algorithm for estimating parameters from multidimensional data based on forward modelling. In contrast to many machine learning approaches it avoids fitting an inverse model and the problems associated with this. The algorithm makes explicit use of the sensitivities of the data to the parameters, with the goal of better treating parameters which only have a weak impact on the data. The forward modelling approach provides uncertainty (full covariance) estimates in the predicted parameters as well as a goodness-of-fit for observations. I demonstrate the algorithm, ILIUM, with the estimation of stellar astrophysical parameters (APs) from simulations of the low resolution spectrophotometry to be obtained by Gaia. The AP accuracy is competitive with that obtained by a support vector machine. For example, for zero extinction stars covering a wide range of metallicity, surface gravity and temperature, ILIUM can estimate Teff to an accuracy of 0.3% at G=15 and to 4% for (lower signal-to-noise ratio) spectra at G=20. [Fe/H] and logg can be estimated to accuracies of 0.1-0.4dex for stars with G<=18.5. If extinction varies a priori over a wide range (Av=0-10mag), then Teff and Av can be estimated quite accurately (3-4% and 0.1-0.2mag respectively at G=15), but there is a strong and ubiquitous degeneracy in these parameters which limits our ability to estimate either accurately at faint magnitudes. Using the forward model we can map these degeneracies (in advance), and thus provide a complete probability distribution over solutions. (Abridged)

We consider the problem of reconstructing a low rank matrix from noisy observations of a subset of its entries. This task has applications in statistical learning, computer vision, and signal processing. In these contexts, "noise" generically refers to any contribution to the data that is not captured by the low-rank model. In most applications, the noise level is large compared to the underlying signal and it is important to avoid overfitting. In order to tackle this problem, we define a regularized cost function well suited for spectral reconstruction methods. Within a random noise model, and in the large system limit, we prove that the resulting accuracy undergoes a phase transition depending on the noise level and on the fraction of observed entries. The cost function can be minimized using OPTSPACE (a manifold gradient descent algorithm). Numerical simulations show that this approach is competitive with state-of-the-art alternatives.

Probabilistic topic models (and their extensions) have become popular as models of latent structures in collections of text documents or images. These models are usually treated as generative models and trained using maximum likelihood estimation, an approach which may be suboptimal in the context of an overall classification problem. In this paper, we describe DiscLDA, a discriminative learning framework for such models as Latent Dirichlet Allocation (LDA) in the setting of dimensionality reduction with supervised side information. In DiscLDA, a class-dependent linear transformation is introduced on the topic mixture proportions. This parameter is estimated by maximizing the conditional likelihood using Monte Carlo EM. By using the transformed topic mixture proportions as a new representation of documents, we obtain a supervised dimensionality reduction algorithm that uncovers the latent structure in a document collection while preserving predictive power for the task of classification. We compare the predictive power of the latent structure of DiscLDA with unsupervised LDA on the 20 Newsgroup ocument classification task.

A score function induced by a generative model of the data can provide a feature vectorof a fixed dimension for each data sample. Data samples themselves may be of differing lengths (e.g., speech segments, or other sequence data), but as a score function is based on the properties of the data generation process, it produces a fixed-length vector in a highly informative space, typically referred to as a "score space". Discriminative classifiers have been shown to achieve higher performance in appropriately chosen score spaces than is achievable by either the corresponding generative likelihood-based classifiers, or the discriminative classifiers usingstandard feature extractors. In this paper, we present a novel score space that exploits the free energy associated with a generative model. The resulting freeenergy score space (FESS) takes into account latent structure of the data at various levels, and can be trivially shown to lead to classification performance that at least matches the performance of the free energy classifier based on the same generative model, and the same factorization of the posterior. We also show that in several typical vision and computational biology applications the classifiers optimized in FESS outperform the corresponding pure generative approaches, as well as a number of previous approaches to combining discriminating and generative models.