Many machine learning models, such as logistic regression (LR) and support vector machine (SVM), can be formulated as composite optimization problems. Recently, many distributed stochastic optimization (DSO) methods have been proposed to solve the large-scale composite optimization problems, which have shown better performance than traditional batch methods. However, most of these DSO methods might not be scalable enough. In this paper, we propose a novel DSO method, called scalable composite optimization for learning (SCOPE), and implement it on the fault-tolerant distributed platform Spark. SCOPE is both computation-efficient and communication-efficient. Theoretical analysis shows that SCOPE is convergent with linear convergence rate when the objective function is strongly convex. Furthermore, empirical results on real datasets show that SCOPE can outperform other state-of-the-art distributed learning methods on Spark, including both batch learning methods and DSO methods.

Learning multiple heterogeneous features from different data sources is challenging. One research topic is how to exploit and utilize the correlations among various features across multiple views with the aim of improving the performance of learning tasks, such as classification. In this paper, we propose a new multi-view feature learning algorithm that simultaneously analyzes features from different views. Compared to most of the existing subspace learning methods that only focus on exploiting a shared latent subspace, our algorithm not only learns individual information in each view but also captures feature correlations among multiple views by learning a shared component. By assuming that such a component is shared by all views, we simultaneously exploit the shared component and individual information of each view in a batch mode. Since the objective function is non-smooth and difficult to solve, we propose an efficient iterative algorithm for optimization with guaranteed convergence. Extensive experiments are conducted on several benchmark datasets. The results demonstrate that our proposed algorithm performs better than all the compared multi-view learning algorithms.

The k-fold cross-validation is commonly used to evaluate the effectiveness of SVMs with the selected hyper-parameters. It is known that the SVM k-fold cross-validation is expensive, since it requires training k SVMs. However, little work has explored reusing the h-th SVM for training the (h+1)-th SVM for improving the efficiency of k-fold cross-validation. In this paper, we propose three algorithms that reuse the h-th SVM for improving the efficiency of training the (h+1)-th SVM. Our key idea is to efficiently identify the support vectors and to accurately estimate their associated weights (also called alpha values) of the next SVM by using the previous SVM. Our experimental results show that our algorithms are several times faster than the k-fold cross-validation which does not make use of the previously trained SVM. Moreover, our algorithms produce the same results (hence same accuracy) as the k-fold cross-validation which does not make use of the previously trained SVM.

Correlation measures are a key element of statistics and machine learning, and essential for a wide range of data analysis tasks. Most existing correlation measures are for pairwise relationships, but real-world data can also exhibit complex multivariate correlations, involving three or more variables. We argue that multivariate correlation measures should be comparable, interpretable, scalable and unbiased. However, no existing measures satisfy all these requirements. In this paper, we propose an unbiased multivariate correlation measure, called UMC, which satisfies all the above criteria. UMC is a cumulative entropy based non-parametric multivariate correlation measure, which can capture both linear and non-linear correlations for groups of three or more variables. It employs a correction for chance using a statistical model of independence to address the issue of bias. UMC has high interpretability and we empirically show it outperforms state-of-the-art multivariate correlation measures in terms of statistical power, as well as for use in both subspace clustering and outlier detection tasks.

As a fundamental constituent of machine learning, domain adaptation generalizes a learning model from a source domain to a different (but related) target domain. In this paper, we focus on semi-supervised domain adaptation and explicitly extend the applied range of unlabeled target samples into the combination of distribution alignment and adaptive classifier learning. Specifically, our extension formulates the following aspects in a single optimization: 1) learning a cross-domain predictive model by developing the Fredholm integral based kernel prediction framework; 2) reducing the distribution difference between two domains; 3) exploring multiple kernels to induce an optimal learning space. Correspondingly, such an extension is distinguished with allowing for noise resiliency, facilitating knowledge transfer and analyzing diverse data characteristics. It is emphasized that we prove the differentiability of our formulation and present an effective optimization procedure based on the reduced gradient, guaranteeing rapid convergence. Comprehensive empirical studies verify the effectiveness of the proposed method.

Gaussian graphical models (GGMs) are widely used for statistical modeling, because of ease of inference and the ubiquitous use of the normal distribution in practical approximations. However, they are also known for their limited modeling abilities, due to the Gaussian assumption. In this paper, we introduce a novel variant of GGMs, which relaxes the Gaussian restriction and yet admits efficient inference. Specifically, we impose a bipartite structure on the GGM and govern the hidden variables by truncated normal distributions. The nonlinearity of the model is revealed by its connection to rectified linear unit (ReLU) neural networks. Meanwhile, thanks to the bipartite structure and appealing properties of truncated normals, we are able to train the models efficiently using contrastive divergence. We consider three output constructs, accounting for real-valued, binary and count data. We further extend the model to deep constructions and show that deep models can be used for unsupervised pre-training of rectifier neural networks. Extensive experimental results are provided to validate the proposed models and demonstrate their superiority over competing models.

Large-scale clustering has been widely used in many applications, and has received much attention. Most existing clustering methods suffer from both expensive computation and memory costs when applied to large-scale datasets. In this paper, we propose a novel clustering method, dubbed compressed k-means (CKM), for fast large-scale clustering. Specifically, high-dimensional data are compressed into short binary codes, which are well suited for fast clustering. CKM enjoys two key benefits: 1) storage can be significantly reduced by representing data points as binary codes; 2) distance computation is very efficient using Hamming metric between binary codes. We propose to jointly learn binary codes and clusters within one framework. Extensive experimental results on four large-scale datasets, including two million-scale datasets demonstrate that CKM outperforms the state-of-the-art large-scale clustering methods in terms of both computation and memory cost, while achieving comparable clustering accuracy.

Feature selection aims to select a small subset from the high-dimensional features which can lead to better learning performance, lower computational complexity, and better model readability. The class imbalance problem has been neglected by traditional feature selection methods, therefore the selected features will be biased towards the majority classes. Because of the superiority of F-measure to accuracy for imbalanced data, we propose to use F-measure as the performance measure for feature selection algorithms. As a pseudo-linear function, the optimization of F-measure can be achieved by minimizing the total costs. In this paper, we present a novel cost-sensitive feature selection (CSFS) method which optimizes F-measure instead of accuracy to take class imbalance issue into account. The features will be selected according to optimal F-measure classifier after solving a series of cost-sensitive feature selection sub-problems. The features selected by our method will fully represent the characteristics of not only majority classes, but also minority classes. Extensive experimental results conducted on synthetic, multi-class and multi-label datasets validate the efficiency and significance of our feature selection method.

Predictive models deployed in the real world may assign incorrect labels to instances with high confidence. Such errors or unknown unknowns are rooted in model incompleteness, and typically arise because of the mismatch between training data and the cases encountered at test time. As the models are blind to such errors, input from an oracle is needed to identify these failures. In this paper, we formulate and address the problem of informed discovery of unknown unknowns of any given predictive model where unknown unknowns occur due to systematic biases in the training data.We propose a model-agnostic methodology which uses feedback from an oracle to both identify unknown unknowns and to intelligently guide the discovery. We employ a two-phase approach which first organizes the data into multiple partitions based on the feature similarity of instances and the confidence scores assigned by the predictive model, and then utilizes an explore-exploit strategy for discovering unknown unknowns across these partitions. We demonstrate the efficacy of our framework by varying the underlying causes of unknown unknowns across various applications. To the best of our knowledge, this paper presents the first algorithmic approach to the problem of discovering unknown unknowns of predictive models.

We propose an algorithm for enumerating solutions to the Lasso regression problem.In ordinary Lasso regression, one global optimum is obtained and the resulting features are interpreted as task-relevant features.However, this can overlook possibly relevant features not selected by the Lasso.With the proposed method, we can enumerate many possible feature sets for human inspection, thus recording all the important features.We prove that by enumerating solutions, we can recover a true feature set exactly under less restrictive conditions compared with the ordinary Lasso.We confirm our theoretical results also in numerical simulations.Finally, in the gene expression and the text data, we demonstrate that the proposed method can enumerate a wide variety of meaningful feature sets, which are overlooked by the global optima.