We consider the problem of feature-efficient prediction - a setting where features have costs and the learner is limited by a budget constraint on the total cost of the features it can examine in test time. We focus on solving this problem with boosting by optimizing the choice of base learners in the training phase and stopping the boosting process when the learner's budget runs out. We experimentally show that our method improves upon the boosting approach AdaBoostRS [Reyzin, 2011] and in many cases also outperforms the recent algorithm SpeedBoost [Grubb and Bagnell, 2012]. We provide a theoretical justication for our optimization method via the margin bound. We also experimentally show that our method outperforms pruned decision trees, a natural budgeted classifier.

We propose a scalable Gaussian process model for regression by applying a deep neural network as the feature-mapping function. We first pre-train the deep neural network with a stacked denoising auto-encoder in an unsupervised way. Then, we perform a Bayesian linear regression on the top layer of the pre-trained deep network. The resulting model, Deep-Neural-Network-based Gaussian Process (DNN-GP), can learn much more meaningful representation of the data by the finite-dimensional but deep-layered feature-mapping function. Unlike standard Gaussian processes, our model scales well with the size of the training set due to the avoidance of kernel matrix inversion. Moreover, we present a mixture of DNN-GPs to further improve the regression performance. For the experiments on three representative large datasets, our proposed models significantly outperform the state-of-the-art algorithms of Gaussian process regression.

The Laplacian matrix of a graph can be used in many areas of mathematical research and has a physical interpretation in various theories. However, there are a few open issues in the Laplacian graph construction: (i) Selecting the appropriate scale of analysis, (ii) Selecting the appropriate number of neighbors, (iii) Handling multiscale data, and, (iv) Dealing with noise and outliers. In this paper, we propose that the affinity between pairs of samples could be computed using sparse representation with proper constraints. This parameter free setting automatically produces the Laplacian graph, leads to significant reduction in computation cost and robustness to the outliers and noise. We further provide an efficient algorithm to solve the difficult optimization problem based on improvement of existing algorithms. To demonstrate our motivation, we conduct spectral clustering experiments with benchmark methods. Empirical experiments on 9 data sets demonstrate the effectiveness of our method.

Most approaches to causal discovery assume a fixed (or time-invariant) causal model; however, in practical situations, especially in neuroscience and economics, causal relations might be time-dependent for various reasons. This paper aims to identify the time-dependent causal relations from observational data. We consider general formulations for time-varying causal modeling on stochastic processes, which can also capture the causal influence from a certain type of unobserved confounders.  We focus on two issues: one is whether such a causal model, including the causal direction, is identifiable from observational data; the other is how to estimate such a model in a principled way. We show that under appropriate assumptions, the causal structure is identifiable according to our formulated model. We then propose a principled way for its estimation by extending Gaussian Process regression, which enables an automatic way to learn how the causal model changes over time. Experimental results on both artificial and real data demonstrate the practical usefulness of time-dependent causal modeling and the effectiveness of the proposed approach for estimation.

However, by being autonomous, structure of the policy, which is often critical for understanding these approaches have the problem of discovering the demonstration, is unobserved. We unnatural hierarchies, which may be difficult to interpret and formulate this problem as active learning of Probabilistic communicate to people. State-Dependent Grammars (PSDGs) from In this paper, we study the problem of learning policies demonstrations. Given a set of expert demonstrations, with hierarchical structure from demonstrations of a teacher our approach learns a hierarchical policy by whose policy is structured hierarchically, with natural applications actively selecting demonstrations and using queries to problems such as tutoring arithmetic, cooking, and to explicate their intentional structure at selected furniture assembly. A key challenge in this problem is that the points. Our contributions include a new algorithm demonstrations do not reveal the hierarchical task structure of for imitation learning of hierarchical policies and the teacher. Rather, only ground states and teacher actions are principled heuristics for the selection of demonstrations directly observable. This can lead to significant ambiguity in and queries.

The goal of subspace segmentation is to partition a set of data drawn from a union of subspace into their underlying subspaces. The performance of  spectral clustering based approaches heavily depends on learned data affinity matrices, which are usually constructed either directly from the raw data or from their computed representations. In this paper, we propose a novel method to simultaneously learn the representations of data and the affinity matrix of representation in a unified optimization framework. A novel Augmented Lagrangian Multiplier based algorithm is designed to effectively and efficiently seek the optimal solution of the problem. The experimental results on both synthetic and real data demonstrate the efficacy of the proposed method and its superior performance over the state-of-the-art alternatives.

Low rank matrix recovery has shown its importance as a theoretic foundation in many areas of information processing. Its solutions are usually obtained in batch mode that requires to load all the data into memory during processing, and thus are hardly applicable on large scale data. Moreover, a fraction of data may be severely contaminated by outliers, which makes accurate recovery significantly more challenging. This paper proposes a novel online robust low rank matrix recovery method to address these difficulties. In particular, we first introduce an online algorithm to solve the problem of low rank matrix completion. Then we move on to low rank matrix recovery from observations with intensive outliers. The outlier support is robustly estimated from a perspective of mixture model. Experiments on both synthetic and real data are conducted to demonstrate the efficacy of our method and show its superior performance over the state-of-the-arts.

Model selection is an important problem of cost-sensitive SVM (CS-SVM). Although using solution path to find global optimal parameters is a powerful method for model selection, it is a challenge to extend the framework to solve two regularization parameters of CS-SVM simultaneously. To overcome this challenge, we make three main steps in this paper. (i) A critical-regions-based bi-parameter space partition algorithm is proposed to present all piecewise linearities of CS-SVM. (ii) An invariant-regions-based bi-parameter space partition algorithm is further proposed to compute empirical errors for all parameter pairs. (iii) The global optimal solutions for K-fold cross validation are computed by superposing K invariant region based bi-parameter space partitions into one. The three steps constitute the model selection of CS-SVM which can find global optimal parameter pairs in K-fold cross validation. Experimental results on seven normal datsets and four imbalanced datasets, show that our proposed method has better generalization ability and than various kinds of grid search methods, however, with less running time.

A common way of attacking multi-label classification problems is by splitting it into a set of binary classification problems, then solving each problem independently using traditional single-label methods. Nevertheless, by learning classifiers separately the information about the relationship between labels tends to be neglected. Built on recent advances in structure learning in Ising Markov Random Fields (I-MRF), we propose a multi-label classification algorithm that explicitly estimate and incorporate label dependence into the classifiers learning process by means of a sparse convex multi-task learning formulation.Extensive experiments considering several existing multi-label algorithms indicate that the proposed method, while conceptually simple, outperforms the contenders in several datasets and performance metrics. Besides that, the conditional dependence graph encoded in the I-MRF provides a useful information that can be used in a posterior investigation regarding the reasons behind the relationship between labels.

In this paper we investigate the use of coactive learning in a multitask setting. In coactive learning, an expert presents the learner with a problem and the learner returns a candidate solution. The expert then improves on the solution if necessary and presents the improved solution to the learner. The goal for the learner is to learn to produce solutions which cannot be further improved by the expert while minimizing the average expert effort. In this paper, we consider the setting where there are multiple experts (tasks), and in each iteration one expert presents a problem to the learner. While the experts are expected to have different solution preferences, they are also assumed to share similarities, which should enable generalization across experts. We analyze several algorithms for this setting and derive bounds on the average expert effort during learning. Our main contribution is the balanced Perceptron algorithm, which is the first coactive learning algorithm that is both able to generalize across experts when possible, while also guaranteeing convergence to optimal solutions for individual experts. Our experiments in three domains confirm that this algorithm is effective in the multitask setting, compared to natural baselines.