In many real world applications, labeled data are usually expensive to get, while there may be a large amount of unlabeled data. To reduce the labeling cost, active learning attempts to discover the most informative data points for labeling. Recently, Optimal Experimental Design (OED) techniques have attracted an increasing amount of attention. OED is concerned with the design of experiments that minimizes variances of a parameterized model. Typical design criteria include D-, A-, and E-optimality. However, all these criteria are based on an ordinary linear regression model which aims to minimize the empirical error whereas the geometrical structure of the data space is not well respected. In this paper, we propose a novel optimal experimental design approach for active learning, called Laplacian G-Optimal Design (LapGOD), which considers both discriminating and geometrical structures. By using Laplacian Regularized Least Squares which incorporates manifold regularization into linear regression, our proposed algorithm selects those data points that minimizes the maximum variance of the predicted values on the data manifold. We also extend our algorithm to nonlinear case by using kernel trick. The experimental results on various image databases have shown that our proposed LapGOD active learning algorithm can significantly enhance the classification accuracy if the selected data points are used as training data.

We present an interactive learning method that enables a user to iteratively refine a regression model. The user examines the output of the model, visualized as the vertical axis of a 2D scatterplot, and provides corrections by repositioning individual data instances to the correct output level. Each repositioned data instance acts as a control point for altering the learned model, using the geometry underlying the data. We capture the underlying structure of the data as a manifold, on which we compute a set of basis functions as the foundation for learning. Our results show that manifold-based interactive learning improves performance monotonically with each correction, outperforming alternative approaches.

This paper proposes a novel robust sparse representation method, called the two-stage sparse representation (TSR), for robust recognition on a large-scale database. Based on the divide and conquer strategy, TSR divides the procedure of robust recognition into outlier detection stage and recognition stage. In the first stage, a weighted linear regression is used to learn a metric in which noise and outliers in image pixels are detected. In the second stage, based on the learnt metric, the large-scale dataset is firstly filtered into a small set according to the nearest neighbor criterion. Then a sparse representation is computed by the non-negative least squares technique. The sparse solution is unique and can be optimized efficiently. The extensive numerical experiments on several public databases demonstrate that the proposed TSR approach generally obtains better classification accuracy than the state of the art Sparse Representation Classification (SRC). At the same time, by using the TSR, a significant reduction of computational cost is reached by over fifty times in comparison with the SRC, which enables the TSR to be deployed more suitably for large-scale dataset.

We propose Dirichlet Process mixtures of Generalized Linear Models (DP-GLM), a new method of nonparametric regression that accommodates continuous and categorical inputs, and responses that can be modeled by a generalized linear model. We prove conditions for the asymptotic unbiasedness of the DP-GLM regression mean function estimate. We also give examples for when those conditions hold, including models for compactly supported continuous distributions and a model with continuous covariates and categorical response. We empirically analyze the properties of the DP-GLM and why it provides better results than existing Dirichlet process mixture regression models. We evaluate DP-GLM on several data sets, comparing it to modern methods of nonparametric regression like CART, Bayesian trees and Gaussian processes. Compared to existing techniques, the DP-GLM provides a single model (and corresponding inference algorithms) that performs well in many regression settings.

We consider the problem of predicting as well as the best linear combination of d given functions in least squares regression, and variants of this problem including constraints on the parameters of the linear combination. When the input distribution is known, there already exists an algorithm having an expected excess risk of order d/n, where n is the size of the training data. Without this strong assumption, standard results often contain a multiplicative log n factor, and require some additional assumptions like uniform boundedness of the d-dimensional input representation and exponential moments of the output. This work provides new risk bounds for the ridge estimator and the ordinary least squares estimator, and their variants. It also provides shrinkage procedures with convergence rate d/n (i.e., without the logarithmic factor) in expectation and in deviations, under various assumptions. The key common surprising factor of these results is the absence of exponential moment condition on the output distribution while achieving exponential deviations. All risk bounds are obtained through a PAC-Bayesian analysis on truncated differences of losses. Finally, we show that some of these results are not particular to the least squares loss, but can be generalized to similar strongly convex loss functions.

We consider the empirical risk minimization problem for linear supervised learning, with regularization by structured sparsity-inducing norms. These are defined as sums of Euclidean norms on certain subsets of variables, extending the usual $\ell_1$-norm and the group $\ell_1$-norm by allowing the subsets to overlap. This leads to a specific set of allowed nonzero patterns for the solutions of such problems. We first explore the relationship between the groups defining the norm and the resulting nonzero patterns, providing both forward and backward algorithms to go back and forth from groups to patterns. This allows the design of norms adapted to specific prior knowledge expressed in terms of nonzero patterns. We also present an efficient active set algorithm, and analyze the consistency of variable selection for least-squares linear regression in low and high-dimensional settings.

We consider the problem of learning a structured multi-task regression, where the output consists of multiple responses that are related by a graph and the correlated response variables are dependent on the common inputs in a sparse but synergistic manner. Previous methods such as l1/l2-regularized multi-task regression assume that all of the output variables are equally related to the inputs, although in many real-world problems, outputs are related in a complex manner. In this paper, we propose graph-guided fused lasso (GFlasso) for structured multi-task regression that exploits the graph structure over the output variables. We introduce a novel penalty function based on fusion penalty to encourage highly correlated outputs to share a common set of relevant inputs. In addition, we propose a simple yet efficient proximal-gradient method for optimizing GFlasso that can also be applied to any optimization problems with a convex smooth loss and the general class of fusion penalty defined on arbitrary graph structures. By exploiting the structure of the non-smooth ''fusion penalty'', our method achieves a faster convergence rate than the standard first-order method, sub-gradient method, and is significantly more scalable than the widely adopted second-order cone-programming and quadratic-programming formulations. In addition, we provide an analysis of the consistency property of the GFlasso model. Experimental results not only demonstrate the superiority of GFlasso over the standard lasso but also show the efficiency and scalability of our proximal-gradient method.

But whereas in the general Rwandan populace males tend Despite the increasing ubiquity of mobile phones in the developing to be much better educated (76.3% of males are literate, but world, remarkably little is known about the structure only 64.7% of females), among mobile phone users it is the and demographics of the mobile phone market. While a women who achieve higher levels of education: the median few qualitative studies have detailed social norms of phone woman completes secondary school, while the median man use in specific communities (Donner 2007; Burrell 2009), does not (t 4.79). Table 1 shows a few statistics on asset and a handful of quantitative researchers have begun to analyze ownership, with associated sampling error.

To tackle the vocabulary problem in conversational systems, previous work has applied unsupervised learning approaches on co-occurring speech and eye gaze during interaction to automatically acquire new words. Although these approaches have shown promise, several issues related to human language behavior and human-machine conversation have not been addressed. First, psycholinguistic studies have shown certain temporal regularities between human eye movement and language production. While these regularities can potentially guide the acquisition process, they have not been incorporated in the previous unsupervised approaches. Second, conversational systems generally have an existing knowledge base about the domain and vocabulary. While the existing knowledge can potentially help bootstrap and constrain the acquired new words, it has not been incorporated in the previous models. Third, eye gaze could serve different functions in human-machine conversation. Some gaze streams may not be closely coupled with speech stream, and thus are potentially detrimental to word acquisition. Automated recognition of closely-coupled speech-gaze streams based on conversation context is important. To address these issues, we developed new approaches that incorporate user language behavior, domain knowledge, and conversation context in word acquisition. We evaluated these approaches in the context of situated dialogue in a virtual world. Our experimental results have shown that incorporating the above three types of contextual information significantly improves word acquisition performance.

We study online social networks in which relationships can be either positive (indicating relations such as friendship) or negative (indicating relations such as opposition or antagonism). Such a mix of positive and negative links arise in a variety of online settings; we study datasets from Epinions, Slashdot and Wikipedia. We find that the signs of links in the underlying social networks can be predicted with high accuracy, using models that generalize across this diverse range of sites. These models provide insight into some of the fundamental principles that drive the formation of signed links in networks, shedding light on theories of balance and status from social psychology; they also suggest social computing applications by which the attitude of one user toward another can be estimated from evidence provided by their relationships with other members of the surrounding social network.