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.

Toponym resolution, or grounding names of places to their actual locations, is an important problem in analysis of both historical corpora and present-day news and web content. Recent approaches have shifted from rule-based spatial minimization methods to machine learned classifiers that use features of the text surrounding a toponym. Such methods have been shown to be highly effective, but they crucially rely on gazetteers and are unable to handle unknown place names or locations. We address this limitation by modeling the geographic distributions of words over the earth's surface: we calculate the geographic profile of each word based on local spatial statistics over a set of geo-referenced language models. These geo-profiles can be further refined by combining in-domain data with background statistics from Wikipedia. Our resolver computes the overlap of all geo-profiles in a given text span; without using a gazetteer, it performs on par with existing classifiers. When combined with a gazetteer, it achieves state-of-the-art performance for two standard toponym resolution corpora (TR-CoNLL and Civil War). Furthermore, it dramatically improves recall when toponyms are identified by named entity recognizers, which often (correctly) find non-standard variants of toponyms.

Advice giving has been long explored in artificial intelligence to build robust learning algorithms. We consider advice giving in relational domains where the noise is systematic. The advice is provided as logical statements that are then explicitly considered by the learning algorithm at every update. Our empirical evidence proves that human advice can effectively accelerate learning in noisy structured domains where so far humans have been merely used as labelers or as designers of initial structure of the model.

Most typical statistical and machine learning approaches to time series modeling optimize a single-step prediction error. In multiple-step simulation, the learned model is iteratively applied, feeding through the previous output as its new input. Any such predictor however, inevitably introduces errors, and these compounding errors change the input distribution for future prediction steps, breaking the train-test i.i.d assumption common in supervised learning. We present an approach that reuses training data to make a no-regret learner robust to errors made during multi-step prediction. Our insight is to formulate the problem as imitation learning; the training data serves as a "demonstrator" by providing corrections for the errors made during multi-step prediction. By this reduction of multi-step time series prediction to imitation learning, we establish theoretically a strong performance guarantee on the relation between training error and the multi-step prediction error. We present experimental results of our method, DaD, and show significant improvement over the traditional approach in two notably different domains, dynamic system modeling and video texture prediction.

Curriculum learning (CL) or self-paced learning (SPL) represents a recently proposed learning regime inspired by the learning process of humans and animals that gradually proceeds from easy to more complex samples in training. The two methods share a similar conceptual learning paradigm, but differ in specific learning schemes. In CL, the curriculum is predetermined by prior knowledge, and remain fixed thereafter. Therefore, this type of method heavily relies on the quality of prior knowledge while ignoring feedback about the learner. In SPL, the curriculum is dynamically determined to adjust to the learning pace of the leaner. However, SPL is unable to deal with prior knowledge, rendering it prone to overfitting. In this paper, we discover the missing link between CL and SPL, and propose a unified framework named self-paced curriculum leaning (SPCL). SPCL is formulated as a concise optimization problem that takes into account both prior knowledge known before training and the learning progress during training. In comparison to human education, SPCL is analogous to "instructor-student-collaborative" learning mode, as opposed to "instructor-driven" in CL or "student-driven" in SPL. Empirically, we show that the advantage of SPCL on two tasks.

We consider the problem of embedding entities and relations of knowledge bases into low-dimensional continuous vector spaces (distributed representations). Unlike most existing approaches, which are primarily efficient for modelling pairwise relations between entities, we attempt to explicitly model both pairwise relations and long-range interactions between entities, by interpreting them as linear operators on the low-dimensional embeddings of the entities. Therefore, in this paper we introduces Path-Ranking to capture the long-range interactions of knowledge graph and at the same time preserve the pairwise relations of knowledge graph; we call it 'structured embedding via pairwise relation and long-range interactions' (referred to as SePLi). Comparing with the-state-of-the-art models, SePLi achieves better performances of embeddings.

Locality preserving projection (LPP) is an effective dimensionality reduction method based on manifold learning, which is defined over the graph weighted squared L2-norm distances in the projected subspace. Since squared L2-norm distance is prone to outliers, it is desirable to develop a robust LPP method. In this paper, motivated by existing studies that improve the robustness of statistical learning models via L1-norm or not-squared L2-norm formulations, we propose a robust LPP (rLPP) formulation to minimize the p-th order of the L2-norm distances, which can better tolerate large outlying data samples because it suppress the introduced biased more than the L1-norm or not squared L2-norm minimizations. However, solving the formulated objective is very challenging because it not only non-smooth but also non-convex. As an important theoretical contribution of this work, we systematically derive an efficient iterative algorithm to solve the general p-th order L2-norm minimization problem, which, to the best of our knowledge, is solved for the first time in literature. Extensive empirical evaluations on the proposed rLPP method have been performed, in which our new method outperforms the related state-of-the-art methods in a variety of experimental settings and demonstrate its effectiveness in seeking better subspaces on both noiseless and noisy data.

In Kernel-based Learning the targeted phenomenon is summarized by a set of explanatory examples derived from the training set. When the model size grows with the complexity of the task, such approaches are so computationally demanding that the adoption of comprehensive models is not always viable.In this paper, a general framework aimed at minimizing this problem is proposed: multiple classifiers are stratified and dynamically invoked according to increasing levels of complexity corresponding to incrementally more expressive representation spaces.Computationally expensive inferences are thus adopted only when the classification at lower levels is too uncertain over an individual instance. The application of complex functions is thus avoided where possible, with a significant reduction of the overall costs. The proposed strategy has been integrated within two well-known algorithms: Support Vector Machines and Passive-Aggressive Online classifier.A significant cost reduction (up to 90%), with a negligible performance drop, is observed against two Natural Language Processing tasks, i.e. Question Classification and Sentiment Analysis in Twitter.