Local Linear embedding (LLE) is a popular dimension reduction method. In this paper, we first show LLE with nonnegative constraint is equivalent to the widely used Laplacian embedding. We further propose to iterate the two steps in LLE repeatedly to improve the results. Thirdly, we relax the kNN constraint of LLE and present a sparse similarity learning algorithm. The final Iterative LLE combines these three improvements. Extensive experiment results show that iterative LLE algorithm significantly improve both classification and clustering results.

Latent variable models for network data extract a summary of the relational structure underlying an observed network. The simplest possible models subdivide nodes of the network into clusters; the probability of a link between any two nodes then depends only on their cluster assignment. Currently available models can be classified by whether clusters are disjoint or are allowed to overlap. These models can explain a "flat" clustering structure. Hierarchical Bayesian models provide a natural approach to capture more complex dependencies. We propose a model in which objects are characterised by a latent feature vector. Each feature is itself partitioned into disjoint groups (subclusters), corresponding to a second layer of hierarchy. In experimental comparisons, the model achieves significantly improved predictive performance on social and biological link prediction tasks. The results indicate that models with a single layer hierarchy over-simplify real networks.

In this paper we address the following question: Can we approximately sample from a Bayesian posterior distribution if we are only allowed to touch a small mini-batch of data-items for every sample we generate?. An algorithm based on the Langevin equation with stochastic gradients (SGLD) was previously proposed to solve this, but its mixing rate was slow. By leveraging the Bayesian Central Limit Theorem, we extend the SGLD algorithm so that at high mixing rates it will sample from a normal approximation of the posterior, while for slow mixing rates it will mimic the behavior of SGLD with a pre-conditioner matrix. As a bonus, the proposed algorithm is reminiscent of Fisher scoring (with stochastic gradients) and as such an efficient optimizer during burn-in.

In this paper, a novel learning paradigm is presented to automatically identify groups of informative and correlated features from very high dimensions. Specifically, we explicitly incorporate correlation measures as constraints and then propose an efficient embedded feature selection method using recently developed cutting plane strategy. The benefits of the proposed algorithm are two-folds. First, it can identify the optimal discriminative and uncorrelated feature subset to the output labels, denoted here as Support Features, which brings about significant improvements in prediction performance over other state of the art feature selection methods considered in the paper. Second, during the learning process, the underlying group structures of correlated features associated with each support feature, denoted as Affiliated Features, can also be discovered without any additional cost. These affiliated features serve to improve the interpretations on the learning tasks. Extensive empirical studies on both synthetic and very high dimensional real-world datasets verify the validity and efficiency of the proposed method.

Discriminative linear models are a popular tool in machine learning. These can be generally divided into two types: The first is linear classifiers, such as support vector machines, which are well studied and provide state-of-the-art results. One shortcoming of these models is that their output (known as the 'margin') is not calibrated, and cannot be translated naturally into a distribution over the labels. Thus, it is difficult to incorporate such models as components of larger systems, unlike probabilistic based approaches. The second type of approach constructs class conditional distributions using a nonlinearity (e.g. log-linear models), but is occasionally worse in terms of classification error. We propose a supervised learning method which combines the best of both approaches. Specifically, our method provides a distribution over the labels, which is a linear function of the model parameters. As a consequence, differences between probabilities are linear functions, a property which most probabilistic models (e.g. log-linear) do not have. Our model assumes that classes correspond to linear subspaces (rather than to half spaces). Using a relaxed projection operator, we construct a measure which evaluates the degree to which a given vector 'belongs' to a subspace, resulting in a distribution over labels. Interestingly, this view is closely related to similar concepts in quantum detection theory. The resulting models can be trained either to maximize the margin or to optimize average likelihood measures. The corresponding optimization problems are semidefinite programs which can be solved efficiently. We illustrate the performance of our algorithm on real world datasets, and show that it outperforms 2nd order kernel methods.

We introduce a copula mixture model to perform dependency-seeking clustering when co-occurring samples from different data sources are available. The model takes advantage of the great flexibility offered by the copulas framework to extend mixtures of Canonical Correlation Analysis to multivariate data with arbitrary continuous marginal densities. We formulate our model as a non-parametric Bayesian mixture, while providing efficient MCMC inference. Experiments on synthetic and real data demonstrate that the increased flexibility of the copula mixture significantly improves the clustering and the interpretability of the results.

We consider the problem of object recognition with a large number of classes. In order to overcome the low amount of labeled examples available in this setting, we introduce a new feature learning and extraction procedure based on a factor model we call spike-and-slab sparse coding (S3C). Prior work on S3C has not prioritized the ability to exploit parallel architectures and scale S3C to the enormous problem sizes needed for object recognition. We present a novel inference procedure for appropriate for use with GPUs which allows us to dramatically increase both the training set size and the amount of latent factors that S3C may be trained with. We demonstrate that this approach improves upon the supervised learning capabilities of both sparse coding and the spike-and-slab Restricted Boltzmann Machine (ssRBM) on the CIFAR-10 dataset. We use the CIFAR-100 dataset to demonstrate that our method scales to large numbers of classes better than previous methods. Finally, we use our method to win the NIPS 2011 Workshop on Challenges In Learning Hierarchical Models? Transfer Learning Challenge.

In this paper we propose a unified framework for structured prediction with latent variables which includes hidden conditional random fields and latent structured support vector machines as special cases. We describe a local entropy approximation for this general formulation using duality, and derive an efficient message passing algorithm that is guaranteed to converge. We demonstrate its effectiveness in the tasks of image segmentation as well as 3D indoor scene understanding from single images, showing that our approach is superior to latent structured support vector machines and hidden conditional random fields.

We study the problem of unsupervised domain adaptation, which aims to adapt classifiers trained on a labeled source domain to an unlabeled target domain. Many existing approaches first learn domain-invariant features and then construct classifiers with them. We propose a novel approach that jointly learn the both. Specifically, while the method identifies a feature space where data in the source and the target domains are similarly distributed, it also learns the feature space discriminatively, optimizing an information-theoretic metric as an proxy to the expected misclassification error on the target domain. We show how this optimization can be effectively carried out with simple gradient-based methods and how hyperparameters can be cross-validated without demanding any labeled data from the target domain. Empirical studies on benchmark tasks of object recognition and sentiment analysis validated our modeling assumptions and demonstrated significant improvement of our method over competing ones in classification accuracies.

Learning invariant representations is an important problem in machine learning and pattern recognition. In this paper, we present a novel framework of transformation-invariant feature learning by incorporating linear transformations into the feature learning algorithms. For example, we present the transformation-invariant restricted Boltzmann machine that compactly represents data by its weights and their transformations, which achieves invariance of the feature representation via probabilistic max pooling. In addition, we show that our transformation-invariant feature learning framework can also be extended to other unsupervised learning methods, such as autoencoders or sparse coding. We evaluate our method on several image classification benchmark datasets, such as MNIST variations, CIFAR-10, and STL-10, and show competitive or superior classification performance when compared to the state-of-the-art. Furthermore, our method achieves state-of-the-art performance on phone classification tasks with the TIMIT dataset, which demonstrates wide applicability of our proposed algorithms to other domains.