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.

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.

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.

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.

We develop a structured output model for object category detection that explicitly accounts for alignment, multiple aspects and partial truncation in both training and inference. The model is formulated as large margin learning with latent variables and slack rescaling, and both training and inference are computationally efficient. We make the following contributions: (i) we note that extending the Structured Output Regression formulation of Blaschko and Lampert [1] to include a bias term significantly improves performance; (ii) that alignment (to account for small rotations andanisotropic scalings) can be included as a latent variable and efficiently determined and implemented; (iii) that the latent variable extends to multiple aspects (e.g.left facing, right facing, front) with the same formulation; and (iv), most significantly for performance, that truncated and truncated instances can be included in both training and inference with an explicit truncation mask. We demonstrate the method by training and testing on the PASCAL VOC 2007 data set - training includes the truncated examples, and in testing object instances are detected at multiple scales, alignments, and with significant truncations.

In the Gaussian process regression the observation model is commonly assumed to be Gaussian, which is convenient in computational perspective. However, the drawback is that the predictive accuracy of the model can be significantly compromised if the observations are contaminated by outliers. A robust observation model, such as the Student-t distribution, reduces the influence of outlying observations and improves the predictions. The problem, however, is the analytically intractable inference. In this work, we discuss the properties of a Gaussian process regression model with the Student-t likelihood and utilize the Laplace approximation for approximate inference. We compare our approach to a variational approximation and a Markov chain Monte Carlo scheme, which utilize the commonly used scale mixture representation of the Student-t distribution.

Recent work has led to the ability to perform space efficient, approximate counting over large vocabularies in a streaming context. Motivated by the existence of data structures of this type, we explore the computation of associativity scores, other- wise known as pointwise mutual information (PMI), in a streaming context. We give theoretical bounds showing the impracticality of perfect online PMI compu- tation, and detail an algorithm with high expected accuracy. Experiments on news articles show our approach gives high accuracy on real world data.

Learning to rank is a relatively new field of study, aiming to learn a ranking function from a set of training data with relevancy labels. The ranking algorithms are often evaluated using Information Retrieval measures, such as Normalized Discounted Cumulative Gain [1] and Mean Average Precision [2]. Until recently, most learning to rank algorithms were not using a loss function related to the above mentioned evaluation measures. The main difficulty in direct optimization of these measures is that they depend on the ranks of documents, not the numerical values output by the ranking function. We propose a probabilistic framework that addresses this challenge by optimizing the expectation of NDCG over all the possible permutations of documents. A relaxation strategy is used to approximate the average of NDCG over the space of permutation, and a bound optimization approach is proposed to make the computation efficient. Extensive experiments show that the proposed algorithm outperforms state-of-the-art ranking algorithms on several benchmark data sets.

We consider the problem of learning probabilistic models for complex relational structures between various types of objects. A model can help us "understand" a dataset of relational facts in at least two ways, by finding interpretable structure in the data, and by supporting predictions, or inferences about whether particular unobserved relations are likely to be true. Often there is a tradeoff between these two aims: cluster-based models yield more easily interpretable representations, while factorization-based approaches have given better predictive performance on large data sets. We introduce the Bayesian Clustered Tensor Factorization (BCTF) model, which embeds a factorized representation of relations in a nonparametric Bayesian clustering framework. Inference is fully Bayesian but scales well to large data sets. The model simultaneously discovers interpretable clusters and yields predictive performance that matches or beats previous probabilistic models for relational data.

Embeddings of probability measures into reproducing kernel Hilbert spaces have been proposed as a straightforward and practical means of representing and comparing probabilities.In particular, the distance between embeddings (the maximum mean discrepancy, or MMD) has several key advantages over many classical metrics on distributions, namely easy computability, fast convergence and low bias of finite sample estimates. An important requirement of the embedding RKHS is that it be characteristic: in this case, the MMD between two distributions is zero if and only if the distributions coincide. Three new results on the MMD are introduced inthe present study. First, it is established that MMD corresponds to the optimal risk of a kernel classifier, thus forming a natural link between the distance between distributions and their ease of classification. An important consequence is that a kernel must be characteristic to guarantee classifiability between distributions inthe RKHS.