We derive a convex optimization problem for the task of segmenting sequential data, which explicitly treats presence of outliers. We describe two algorithms for solving this problem, one exact and one a top-down novel approach, and we derive a consistency results for the case of two segments and no outliers. Robustness to outliers is evaluated on two real-world tasks related to speech segmentation. Our algorithms outperform baseline segmentation algorithms.

In multi-label learning, an example is represented by a descriptive feature associated with several labels. Simply considering labels as independent or correlated is crude; it would be beneficial to define and exploit the causality between multiple labels. For example, an image label 'lake' implies the label 'water', but not vice versa. Since the original features are a disorderly mixture of the properties originating from different labels, it is intuitive to factorize these raw features to clearly represent each individual label and its causality relationship.Following the large-margin principle, we propose an effective approach to discover the causal features of multiple labels, thus revealing the causality between labels from the perspective of feature. We show theoretically that the proposed approach is a tight approximation of the empirical multi-label classification error, and the causality revealed strengthens the consistency of the algorithm. Extensive experimentations using synthetic and real-world data demonstrate that the proposed algorithm effectively discovers label causality, generates causal features, and improves multi-label learning.

Active learning is a subfield of machine learning that has been successfully used in many applications including text classification and bioinformatics. One of the fundamental branches of active learning is query synthesis, where the learning agent constructs artificial queries from scratch in order to reveal sensitive information about the true decision boundary. Nevertheless, the existing literature on membership query synthesis has focused on finite concept classes with a limited extension to real-world applications. In this paper, we present an efficient spectral algorithm for membership query synthesis for halfspaces, whose sample complexity is experimentally shown to be near-optimal. At each iteration, the algorithm consists of two steps. First, a convex optimization problem is solved that provides an approximate characterization of the version space. Second, a principal component is extracted, which yields a synthetic query that shrinks the version space exponentially fast. Unlike traditional methods in active learning, the proposed method can be readily extended into the batch setting by solving for the top k eigenvectors in the second step. Experimentally, it exhibits a significant improvement over traditional approaches such as uncertainty sampling and representative sampling. For example, to learn a halfspace in the Euclidean plane with 25 dimensions and an estimation error of 1E-4, the proposed algorithm uses less than 3% of the number of queries required by uncertainty sampling.

Canonical correlation analysis (CCA) and maximum margin output coding (MMOC) methods have shown promising results for multi-label prediction, where each instance is associated with multiple labels. However, these methods require an expensive decoding procedure to recover the multiple labels of each testing instance. The testing complexity becomes unacceptable when there are many labels. To avoid decoding completely, we present a novel large margin metric learning paradigm for multi-label prediction. In particular, the proposed method learns a distance metric to discover label dependency such that instances with very different multiple labels will be moved far away. To handle many labels, we present an accelerated proximal gradient procedure to speed up the learning process. Comprehensive experiments demonstrate that our proposed method is significantly faster than CCA and MMOC in terms of both training and testing complexities. Moreover, our method achieves superior prediction performance compared with state-of-the-art methods.

We consider a budgeted variant of the problem of learning from expert advice with N experts. Each queried expert incurs a cost and there is a given budget B on the total cost of experts that can be queried in any prediction round. We provide an online learning algorithm for this setting with regret after T prediction rounds bounded by O(sqrt(C log(N)T/B)), where C is the total cost of all experts. We complement this upper bound with a nearly matching lower bound Omega(sqrt(CT/B)) on the regret of any algorithm for this problem. We also provide experimental validation of our algorithm.

Utilizing attributes for visual recognition has attracted increasingly interest because attributes can effectively bridge the semantic gap between low-level visual features and high-level semantic labels. In this paper, we propose a novel method for learning predictable and discriminative attributes. Specifically, we require the learned attributes can be reliably predicted from visual features, and discover the inherent discriminative structure of data. In addition, we propose to exploit the intra-category locality of data to overcome the intra-category variance in visual data. We conduct extensive experiments on Animals with Attributes (AwA) and Caltech256 datasets, and the results demonstrate that the proposed method achieves state-of-the-art performance.

We present a probabilistic model for tensor decomposition where one or more tensor modes may have side-information about the mode entities in form of their features and/or their adjacency network. We consider a Bayesian approach based on the Canonical PARAFAC (CP) decomposition and enrich this single-layer decomposition approach with a two-layer decomposition. The second layer fits a factor model for each layer-one factor matrix and models the factor matrix via the mode entities' features and/or the network between the mode entities. The second-layer decomposition of each factor matrix also learns a binary latent representation for the entities of that mode, which can be useful in its own right. Our model can handle both continuous as well as binary tensor observations. Another appealing aspect of our model is the simplicity of the model inference, with easy-to-sample Gibbs updates. We demonstrate the results of our model on several benchmarks datasets, consisting of both real and binary tensors.

Covariate shift correction allows one to perform supervised learning even when the distribution of the covariates on the training set does not match that on the test set. This is achieved by re-weighting observations. Such a strategy removes bias, potentially at the expense of greatly increased variance. We propose a simple strategy for removing bias while retaining small variance. It uses a biased, low variance estimate as a prior and corrects the final estimate relative to the prior. We prove that this yields an efficient estimator and demonstrate good experimental performance.

Innovative methods have been developed for diagnosis, activity monitoring, and state estimation that achieve high accuracy through the use of stochastic models involving hybrid discrete and continuous behaviors. A key bottleneck is the automated acquisition of these hybrid models, and recent methods have focused predominantly on Jump Markov processes and piecewise autoregressive models. In this paper, we present a novel algorithm capable of performing unsupervised learning of guarded Probabilistic Hybrid Automata (PHA) models, which extends prior work by allowing stochastic discrete mode transitions in a hybrid system to have a functional dependence on its continuous state. Our experiments indicate that guarded PHA models can yield significant performance improvements when used by hybrid state estimators, particularly when diagnosing the true discrete mode of the system, without any noticeable impact on their real-time performance.

Spectral clustering is a fundamental technique in the field of data mining and information processing. Most existing spectral clustering algorithms integrate dimensionality reduction into the clustering process assisted by manifold learning in the original space. However, the manifold in reduced-dimensional subspace is likely to exhibit altered properties in contrast with the original space. Thus, applying manifold information obtained from the original space to the clustering process in a low-dimensional subspace is prone to inferior performance. Aiming to address this issue, we propose a novel convex algorithm that mines the manifold structure in the low-dimensional subspace. In addition, our unified learning process makes the manifold learning particularly tailored for the clustering. Compared with other related methods, the proposed algorithm results in more structured clustering result. To validate the efficacy of the proposed algorithm, we perform extensive experiments on several benchmark datasets in comparison with some state-of-the-art clustering approaches. The experimental results demonstrate that the proposed algorithm has quite promising clustering performance.