Image representation based on image bases provides a framework for understanding neural representation of visual perception. A recent fMRI study has shown that arbitrary contrast-defined visual images can be reconstructed from fMRI activity patterns using a combination of multi-scale local image bases. In the reconstruction model, the mapping from an fMRI activity pattern to the contrasts of the image bases was learned from measured fMRI responses to visual images. But the shapes of the images bases were fixed, and thus may not be optimal for reconstruction. Here, we propose a method to build a reconstruction model in which image bases are automatically extracted from the measured data. We constructed a probabilistic model that relates the fMRI activity space to the visual image space via a set of latent variables. The mapping from the latent variables to the visual image space can be regarded as a set of image bases. We found that spatially localized, multi-scale image bases were estimated near the fovea, and that the model using the estimated image bases was able to accurately reconstruct novel visual images. The proposed method provides a means to discover a novel functional mapping between stimuli and brain activity patterns.

We extend the concept of phase tuning, a ubiquitous mechanism among sensory neurons including motion and disparity selective neurons, to the motion contrast detection. We demonstrate that the motion contrast can be detected by phase shifts between mo tion neuronal responses in different spatial regions. By constructing the differential motion opponency in response to motions in two different spatial regions, varying motion contrasts can be detected, where similar motion is detected by zero phase shifts and differences in motion by nonzero phase shifts. The model can exhibit either enhancement or suppression of respons es by either different or similar motion in the surrounding. A primary advantage of the model is that the responses are selective to relative motion instead of absolute motion, which could model neurons found in neurop hysiological experiments responsible for motion pop-out detection.

The recent emergence of Graphics Processing Units (GPUs) as general-purpose parallel computing devices provides us with new opportunities to develop scalable learning methods for massive data. In this work, we consider the problem of parallelizing two inference methods on GPUs for latent Dirichlet Allocation (LDA) models, collapsed Gibbs sampling (CGS) and collapsed variational Bayesian (CVB). To address limited memory constraints on GPUs, we propose a novel data partitioning scheme that effectively reduces the memory cost. Furthermore, the partitioning scheme balances the computational cost on each multiprocessor and enables us to easily avoid memory access conflicts. We also use data streaming to handle extremely large datasets. Extensive experiments showed that our parallel inference methods consistently produced LDA models with the same predictive power as sequential training methods did but with 26x speedup for CGS and 196x speedup for CVB on a GPU with 30 multiprocessors; actually the speedup is almost linearly scalable with the number of multiprocessors available. The proposed partitioning scheme and data streaming can be easily ported to many other models in machine learning.

Learning a measure of similarity between pairs of objects is a fundamental problem in machine learning. It stands in the core of classification methods like kernel machines, and is particularly useful for applications like searching for images that are similar to a given image or finding videos that are relevant to a given video. In these tasks, users look for objects that are not only visually similar but also semantically related to a given object. Unfortunately, current approaches for learning similarity may not scale to large datasets with high dimensionality, especially when imposing metric constraints on the learned similarity. We describe OASIS, a method for learning pairwise similarity that is fast and scales linearly with the number of objects and the number of non-zero features. Scalability is achieved through online learning of a bilinear model over sparse representations using a large margin criterion and an efficient hinge loss cost. OASIS is accurate at a wide range of scales: on a standard benchmark with thousands of images, it is more precise than state-of-the-art methods, and faster by orders of magnitude. On 2 million images collected from the web, OASIS can be trained within 3 days on a single CPU. The non-metric similarities learned by OASIS can be transformed into metric similarities, achieving higher precisions than similarities that are learned as metrics in the first place. This suggests an approach for learning a metric from data that is larger by an order of magnitude than was handled before.

In this paper we study the problem of learning a low-dimensional (sparse) distance matrix. We propose a novel metric learning model which can simultaneously conduct dimension reduction and learn a distance matrix. The sparse representation involves a mixed-norm regularization which is non-convex. We then show that it can be equivalently formulated as a convex saddle (min-max) problem. From this saddle representation, we develop an efficient smooth optimization approach for sparse metric learning although the learning model is based on a non-differential loss function. This smooth optimization approach has an optimal convergence rate of $O(1 /\ell^2)$ for smooth problems where $\ell$ is the iteration number. Finally, we run experiments to validate the effectiveness and efficiency of our sparse metric learning model on various datasets.

Learning graphical models with hidden variables can offer semantic insights to complex data and lead to salient structured predictors without relying on expensive, sometime unattainable fully annotated training data. While likelihood-based methods have been extensively explored, to our knowledge, learning structured prediction models with latent variables based on the max-margin principle remains largely an open problem. In this paper, we present a partially observed Maximum Entropy Discrimination Markov Network (PoMEN) model that attempts to combine the advantages of Bayesian and margin based paradigms for learning Markov networks from partially labeled data. PoMEN leads to an averaging prediction rule that resembles a Bayes predictor that is more robust to overfitting, but is also built on the desirable discriminative laws resemble those of the M$^3$N. We develop an EM-style algorithm utilizing existing convex optimization algorithms for M$^3$N as a subroutine. We demonstrate competent performance of PoMEN over existing methods on a real-world web data extraction task.

Kernel supervised learning methods can be unified by utilizing the tools from regularization theory. The duality between regularization and prior leads to interpreting regularization methods in terms of maximum a posteriori estimation and has motivated Bayesian interpretations of kernel methods. In this paper we pursue a Bayesian interpretation of sparsity in the kernel setting by making use of a mixture of a point-mass distribution and prior that we refer to as ``Silverman's g-prior.'' We provide a theoretical analysis of the posterior consistency of a Bayesian model choice procedure based on this prior. We also establish the asymptotic relationship between this procedure and the Bayesian information criterion.

We introduce a new interpretation of multiscale random fields (MSRFs) that admits efficient optimization in the framework of regular (single level) random fields (RFs). It is based on a new operator, called append, that combines sets of random variables (RVs) to single RVs. We assume that a MSRF can be decomposed into disjoint trees that link RVs at different pyramid levels. The append operator is then applied to map RVs in each tree structure to a single RV. We demonstrate the usefulness of the proposed approach on a challenging task involving grouping contours of target shapes in images. MSRFs provide a natural representation of multiscale contour models, which are needed in order to cope with unstable contour decompositions. The append operator allows us to find optimal image labels using the classical framework of relaxation labeling, Alternative methods like Markov Chain Monte Carlo (MCMC) could also be used.

Regularized Least Squares (RLS) algorithms have the ability to avoid over-fitting problems and to express solutions as kernel expansions. However, we observe that the current RLS algorithms cannot provide a satisfactory interpretation even on a constant function. On the other hand, while kernel-based algorithms have been developed in such a tendency that almost all learning algorithms are kernelized or being kernelized, a basic fact is often ignored: The learned function from the data and the kernel fits the data well, but may not be consistent with the kernel. Based on these considerations and on the intuition that a good kernel-based inductive function should be consistent with both the data and the kernel, a novel learning scheme is proposed. The advantages of this scheme lie in its corresponding Representer Theorem, its strong interpretation ability about what kind of functions should not be penalized, and its promising accuracy improvements shown in a number of experiments. Furthermore, we provide a detailed technical description about heat kernels, which serves as an example for the readers to apply similar techniques for other kernels. Our work provides a preliminary step in a new direction to explore the varying consistency between inductive functions and kernels under various distributions.

Stochastic Neighbor Embedding (SNE) has shown to be quite promising for data visualization. Currently, the most popular implementation, t-SNE, is restricted to a particular Student t-distribution as its embedding distribution. Moreover, it uses a gradient descent algorithm that may require users to tune parameters such as the learning step size, momentum, etc., in finding its optimum. In this paper, we propose the Heavy-tailed Symmetric Stochastic Neighbor Embedding (HSSNE) method, which is a generalization of the t-SNE to accommodate various heavy-tailed embedding similarity functions. With this generalization, we are presented with two difficulties. The first is how to select the best embedding similarity among all heavy-tailed functions and the second is how to optimize the objective function once the heave-tailed function has been selected. Our contributions then are: (1) we point out that various heavy-tailed embedding similarities can be characterized by their negative score functions. Based on this finding, we present a parameterized subset of similarity functions for choosing the best tail-heaviness for HSSNE; (2) we present a fixed-point optimization algorithm that can be applied to all heavy-tailed functions and does not require the user to set any parameters; and (3) we present two empirical studies, one for unsupervised visualization showing that our optimization algorithm runs as fast and as good as the best known t-SNE implementation and the other for semi-supervised visualization showing quantitative superiority using the homogeneity measure as well as qualitative advantage in cluster separation over t-SNE.