Large sparse datasets are common in many real-world applications. Linear SVM has been shown to be very efficient for classifying such datasets. However, it is still unknown how data sparseness would affect its convergence behavior. To study this problem in a systematic manner, we propose a novel approach to generate large and sparse data from real-world datasets, using statistical inference and the data sampling process in the PAC framework. We first study the convergence behavior of linear SVM experimentally, and make several observations, useful for real-world applications. We then offer theoretical proofs for our observations by studying the Bayes risk and PAC bound. Our experiment and theoretic results are valuable for learning large sparse datasets with linear SVM.

This paper studies active posterior estimation in a Bayesian setting when the likelihood is expensive to evaluate. Existing techniques for posterior estimation are based on generating samples representative of the posterior. Such methods do not consider efficiency in terms of likelihood evaluations. In order to be query efficient we treat posterior estimation in an active regression framework.  We propose two myopic query strategies to choose where to evaluate the likelihood and implement them using Gaussian processes. Via experiments on a series of synthetic and real examples we demonstrate that our approach is significantly more query efficient than existing techniques and other heuristics for posterior estimation.

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.

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.

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.

This paper studies an interesting problem: is it possible to predict the crowd opinion about a movie before the movie is actually released? The crowd opinion is here expressed by the distribution of ratings given by a sufficient amount of people. Consequently, the pre-release crowd opinion prediction can be regarded as a Label Distribution Learning (LDL) problem. In order to solve this problem, a Label Distribution Support Vector Regressor (LDSVR) is proposed in this paper. The basic idea of LDSVR is to fit a sigmoid function to each component of the label distribution simultaneously by a multi-output support vector machine. Experimental results show that LDSVR can accurately predict peoples’s rating distribution about a movie just based on the pre-release metadata of the movie.

Hierarchical Reinforcement Learning (HRL) outperforms many ‘flat’ Reinforcement Learning (RL) algorithms in some application domains. However, HRL may need longer time to obtain the optimal policy because of its large action space. Potential Based Reward Shaping (PBRS) has been widely used to incorporate heuristics into flat RL algorithms so as to reduce their exploration. In this paper, we investigate the integration of PBRS and HRL, and propose a new algorithm: PBRS-MAXQ-0. We prove that under certain conditions, PBRS-MAXQ-0 is guaranteed to converge. Empirical results show that PBRS-MAXQ-0 significantly outperforms MAXQ-0 given good heuristics, and can converge even when given misleading heuristics.

Deep neural networks (DNNs) show very strong performance on many machine learning problems, but they are very sensitive to the setting of their hyperparameters. Automated hyperparameter optimization methods have recently been shown to yield settings competitive with those found by human experts, but their widespread adoption is hampered by the fact that they require more computational resources than human experts. Humans have one advantage: when they evaluate a poor hyperparameter setting they can quickly detect (after a few SGD steps) that the resulting network performs poorly and terminate the corresponding evaluation to save time. Here, we mimic this early termination of bad runs based on a probabilistic model that extrapolates performance from the first part of a learning curve. Experiments with different neural network architectures show that our resulting approach speeds up state-of-the-art hyperparameter optimization methods for DNNs roughly twofold, enabling them to find DNN settings that yield better performance than those chosen by human experts.

Recent researches on transfer learning exploit deep structures for discriminative feature representation to tackle cross-domain disparity. However, few of them are able to joint feature learning and knowledge transfer in a unified deep framework. In this paper, we develop a novel approach, called Deep Low-Rank Coding (DLRC), for transfer learning. Specifically, discriminative low-rank coding is achieved in the guidance of an iterative supervised structure term for each single layer. In this way, both marginal and conditional distributions between two domains intend to be mitigated. In addition, a marginalized denoising feature transformation is employed to guarantee the learned single-layer low-rank coding to be robust despite of corruptions or noises. Finally, by stacking multiple layers of low-rank codings, we manage to learn robust cross-domain features from coarse to fine. Experimental results on several benchmarks have demonstrated the effectiveness of our proposed algorithm on facilitating the recognition performance for the target domain.

Solving multi-manifolds clustering problems that include delineating and resolving multiple intersections is a very challenging problem. In this paper we propose a novel procedure for clustering intersecting multi-manifolds and delineating junctions in high dimensional spaces. We propose to explicitly and directly resolve ambiguities near the intersections by using 2 properties: One is the position of the data points in the vicinity of the detected intersection; the other is the reliable estimation of the tangent spaces away from the intersections. We experiment with our method on a wide range of geometrically complex settings of convoluted intersecting manifolds, on which we demon- strate higher clustering performance than the state of the art. This includes tackling challenging geometric structures such as when the tangent spaces at the intersections points are not orthogonal.