We consider the problem of efficiently encoding a signal by transforming it to a new representation whose components are statistically independent. A widely studied linear solution, independent components analysis (ICA), exists for the case when the signal is generated as a linear transformation of independent non- Gaussian sources. Here, we examine a complementary case, in which the source is non-Gaussian but elliptically symmetric. In this case, no linear transform suffices to properly decompose the signal into independent components, but we show that a simple nonlinear transformation, which we call radial Gaussianization (RG), is able to remove all dependencies. We then demonstrate this methodology in the context of natural signal statistics. We first show that the joint distributions of bandpass filter responses, for both sound and images, are better described as elliptical than linearly transformed independent sources. Consistent with this, we demonstrate that the reduction in dependency achieved by applying RG to either pairs or blocks of bandpass filter responses is significantly greater than that achieved by PCA or ICA.

We present a new reinforcement-learning model for the role of the hippocampus in classical conditioning, focusing on the differences between trace and delay conditioning. In the model, all stimuli are represented both as unindividuated wholes and as a series of temporal elements with varying delays. These two stimulus representations interact, producing different patterns of learning in trace and delay conditioning. The model proposes that hippocampal lesions eliminate long-latency temporal elements, but preserve short-latency temporal elements. For trace conditioning, with no contiguity between stimulus and reward, these long-latency temporal elements are vital to learning adaptively timed responses. For delay conditioning, in contrast, the continued presence of the stimulus supports conditioned responding, and the short-latency elements suppress responding early in the stimulus. In accord with the empirical data, simulated hippocampal damage impairs trace conditioning, but not delay conditioning, at medium-length intervals. With longer intervals, learning is impaired in both procedures, and, with shorter intervals, in neither. In addition, the model makes novel predictions about the response topography with extended stimuli or post-training lesions. These results demonstrate how temporal contiguity, as in delay conditioning, changes the timing problem faced by animals, rendering it both easier and less susceptible to disruption by hippocampal lesions.

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.

Working memory is a central topic of cognitive neuroscience because it is critical for solving real world problems in which information from multiple temporally distant sources must be combined to generate appropriate behavior. However, an often neglected fact is that learning to use working memory effectively is itself a difficult problem. The Gating" framework is a collection of psychological models that show how dopamine can train the basal ganglia and prefrontal cortex to form useful working memory representations in certain types of problems. We bring together gating with ideas from machine learning about using finite memory systems in more general problems. Thus we present a normative Gating model that learns, by online temporal difference methods, to use working memory to maximize discounted future rewards in general partially observable settings. The model successfully solves a benchmark working memory problem, and exhibits limitations similar to those observed in human experiments. Moreover, the model introduces a concise, normative definition of high level cognitive concepts such as working memory and cognitive control in terms of maximizing discounted future rewards."

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.

Ranking is at the heart of many information retrieval applications. Unlike standard regression or classification, in which we predict outputs independently, in ranking, we are interested in predicting structured outputs so that misranking one object can significantly affect whether we correctly rank the other objects. In practice, the problem of ranking involves a large number of objects to be ranked and either approximate structured prediction methods are required, or assumptions of independence between object scores must be made in order to make the problem tractable. We present a probabilistic method for learning to rank using the graphical modelling framework of cumulative distribution networks (CDNs), where we can take into account the structure inherent to the problem of ranking by modelling the joint cumulative distribution functions (CDFs) over multiple pairwise preferences. We apply our framework to the problem of document retrieval in the case of the OHSUMED benchmark dataset. We will show that the RankNet, ListNet and ListMLE probabilistic models can be viewed as particular instances of CDNs and that our proposed framework allows for the exploration of a broad class of flexible structured loss functionals for ranking 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.

We develop a Bayesian sequential model for category learning. The sequential model updates two category parameters, the mean and the variance, over time. We define conjugate temporal priors to enable closed form solutions to be obtained. This model can be easily extended to supervised and unsupervised learning involving multiple categories. To model the spacing effect, we introduce a generic prior in the temporal updating stage to capture a learning preference, namely, less change for repetition and more change for variation. Finally, we show how this approach can be generalized to efficiently performmodel selection to decide whether observations are from one or multiple categories.

We present a theory of compositionality in stochastic optimal control, showing how task-optimal controllers can be constructed from certain primitives. The primitives are themselves feedback controllers pursuing their own agendas. They are mixed in proportion to how much progress they are making towards their agendas and how compatible their agendas are with the present task. The resulting composite control law is provably optimal when the problem belongs to a certain class. This class is rather general and yet has a number of unique properties - one of which is that the Bellman equation can be made linear even for non-linear or discrete dynamics. This gives rise to the compositionality developed here. In the special case of linear dynamics and Gaussian noise our framework yields analytical solutions (i.e. non-linear mixtures of linear-quadratic regulators) without requiring the final cost to be quadratic. More generally, a natural set of control primitives can be constructed by applying SVD to Greens function of the Bellman equation. We illustrate the theory in the context of human arm movements. The ideas of optimality and compositionality are both very prominent in the field of motor control, yet they are hard to reconcile. Our work makes this possible.