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.

Studying signal and noise properties of recorded neural data is critical in developing more efficient algorithms to recover the encoded information. Important issues exist in this research including the variant spectrum spans of neural spikes that make it difficult to choose a global optimal bandpass filter. Also, multiple sources produce aggregated noise that deviates from the conventional white Gaussian noise. In this work, the spectrum variability of spikes is addressed, based on which the concept of adaptive bandpass filter that fits the spectrum of individual spikes is proposed. Multiple noise sources have been studied through analytical models as well as empirical measurements. The dominant noise source is identified as neuron noise followed by interface noise of the electrode. This suggests that major efforts to reduce noise from electronics are not well spent. The measured noise from in vivo experiments shows a family of 1/f^{x} (x=1.5\pm 0.5) spectrum that can be reduced using noise shaping techniques. In summary, the methods of adaptive bandpass filtering and noise shaping together result in several dB signal-to-noise ratio (SNR) enhancement.

Multitask learning addressed the problem of learning related tasks whose information can be shared each other. Traditional problem usually deal with homogeneous tasks such as regression, classification individually. In this paper we consider the problem learning multiple related tasks where tasks consist of both continuous and discrete outputs from a common set of input variables that lie in a high-dimensional space. All of the tasks are related in the sense that they share the same set of relevant input variables, but the amount of influence of each input on different outputs may vary. We formulate this problem as a combination of linear regression and logistic regression and model the joint sparsity as L1/Linf and L1/L2-norm of the model parameters. Among several possible applications, our approach addresses an important open problem in genetic association mapping, where we are interested in discovering genetic markers that influence multiple correlated traits jointly. In our experiments, we demonstrate our method in the scenario of association mapping, using simulated and asthma data, and show that the algorithm can effectively recover the relevant inputs with respect to all of the tasks.

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.

By adding a spatial regularization kernel to a standard loss function formulation of the boosting problem, we develop a framework for spatially informed boosting. From this regularized loss framework we derive an efficient boosting algorithm that uses additional weights/priors on the base classifiers. We prove that the proposed algorithm exhibits a ``grouping effect, which encourages the selection of all spatially local, discriminative base classifiers. The algorithms primary advantage is in applications where the trained classifier is used to identify the spatial pattern of discriminative information, e.g. the voxel selection problem in fMRI. We demonstrate the algorithms performance on various data sets.

This paper is concerned with the consistency analysis on listwise ranking methods. Among various ranking methods, the listwise methods have competitive performances on benchmark datasets and are regarded as one of the state-of-the-art approaches. Most listwise ranking methods manage to optimize ranking on the whole list (permutation) of objects, however, in practical applications such as information retrieval, correct ranking at the top k positions is much more important. This paper aims to analyze whether existing listwise ranking methods are statistically consistent in the top-k setting. For this purpose, we define a top-k ranking framework, where the true loss (and thus the risks) are defined on the basis of top-k subgroup of permutations. This framework can include the permutation-level ranking framework proposed in previous work as a special case. Based on the new framework, we derive sufficient conditions for a listwise ranking method to be consistent with the top-k true loss, and show an effective way of modifying the surrogate loss functions in existing methods to satisfy these conditions. Experimental results show that after the modifications, the methods can work significantly better than their original versions.

Learning distance functions with side information plays a key role in many machine learning and data mining applications. Conventional approaches often assume a Mahalanobis distance function. These approaches are limited in two aspects: (i) they are computationally expensive (even infeasible) for high dimensional data because the size of the metric is in the square of dimensionality; (ii) they assume a fixed metric for the entire input space and therefore are unable to handle heterogeneous data. In this paper, we propose a novel scheme that learns nonlinear Bregman distance functions from side information using a non-parametric approach that is similar to support vector machines. The proposed scheme avoids the assumption of fixed metric because its local distance metric is implicitly derived from the Hessian matrix of a convex function that is used to generate the Bregman distance function. We present an efficient learning algorithm for the proposed scheme for distance function learning. The extensive experiments with semi-supervised clustering show the proposed technique (i) outperforms the state-of-the-art approaches for distance function learning, and (ii) is computationally efficient for high dimensional data.

There is a growing body of experimental evidence to suggest that the brain is capable of approximating optimal Bayesian inference in the face of noisy input stimuli. Despite this progress, the neural underpinnings of this computation are still poorly understood. In this paper we focus on the problem of Bayesian filtering of stochastic time series. In particular we introduce a novel neural network, derived from a line attractor architecture, whose dynamics map directly onto those of the Kalman Filter in the limit where the prediction error is small. When the prediction error is large we show that the network responds robustly to change-points in a way that is qualitatively compatible with the optimal Bayesian model. The model suggests ways in which probability distributions are encoded in the brain and makes a number of testable experimental predictions.

Across a wide range of cognitive tasks, recent experience influences behavior. For example, when individuals repeatedly perform a simple two-alternative forcedchoice task(2AFC), response latencies vary dramatically based on the immediately preceding trial sequence. These sequential effects have been interpreted as adaptation to the statistical structure of an uncertain, changing environment (e.g., Jones and Sieck, 2003; Mozer, Kinoshita, and Shettel, 2007; Yu and Cohen, 2008).The Dynamic Belief Model (DBM) (Yu and Cohen, 2008) explains sequential effects in 2AFC tasks as a rational consequence of a dynamic internal representation that tracks second-order statistics of the trial sequence (repetition rates) and predicts whether the upcoming trial will be a repetition or an alternation ofthe previous trial. Experimental results suggest that first-order statistics (base rates) also influence sequential effects. We propose a model that learns both first-and second-order sequence properties, each according to the basic principles ofthe DBM but under a unified inferential framework. This model, the Dynamic BeliefMixture Model (DBM2), obtains precise, parsimonious fits to data. Furthermore, the model predicts dissociations in behavioral (Maloney, Martello, Sahm, and Spillmann, 2005) and electrophysiological studies (Jentzsch and Sommer, 2002),supporting the psychological and neurobiological reality of its two components.

Large, relational factor graphs with structure defined by first-order logic or other languages give rise to notoriously difficult inference problems. Because unrolling the structure necessary to represent distributions over all hypotheses has exponential blow-up, solutions are often derived from MCMC. However, because of limitations in the design and parameterization of the jump function, these sampling-based methods suffer from local minima|the system must transition through lower-scoring configurations before arriving at a better MAP solution. This paper presents a new method of explicitly selecting fruitful downward jumps by leveraging reinforcement learning (RL). Rather than setting parameters to maximize the likelihood of the training data, parameters of the factor graph are treated as a log-linear function approximator and learned with temporal difference (TD); MAP inference is performed by executing the resulting policy on held out test data. Our method allows efficient gradient updates since only factors in the neighborhood of variables affected by an action need to be computed|we bypass the need to compute marginals entirely. Our method provides dramatic empirical success, producing new state-of-the-art results on a complex joint model of ontology alignment, with a 48\% reduction in error over state-of-the-art in that domain.