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.

SVM in advance, and this limits their applications to largescale problems. To address this issue, several methods for Support vector machines (SVMs) play a very dominant selecting a set of basis vectors are proposed. They include role in data classification due to their good sampling from the training set in the Nystrom method generalization performance. However, they suffer [Williams and Seeger, 2001] and variants of the Incomplete from the high computational complexity in the Cholesky factorization [Bach and Jordan, 2005], core vector classification phase when there are a considerable machine (CVM) [Tsang et al., 2005], relevance vector machine number of support vectors (SVs). Then it is desirable (RVM)[Tipping, 2001], and relevance units machine to design efficient algorithms in the classification (RUM)[Gao and Zhang, 2009]. Wu et al. [Wu et al., 2006] phase to deal with the datasets of realtime add one constraint on the number of basis vectors to the standard pattern recognition systems. To this end, we SVM optimization problem, and then solve this modified propose a novel classifier called HMLSVMs (Hierarchical nonconvex problem to build sparse kernel learning algorithms Mixing Linear Support Vector Machines) (SKLA). Joachims and Yu [Joachims and Yu, 2009] in this paper, which has a hierarchical structure explore a new sparse kernel SVMs via cutting plane training, with a mixing linear SVMs classifier at each node called cutting-plane subspace pursuit (CPSP).Although and predicts the label of a sample using only a the above methods prunes the SVs and reduces computational few hyperplanes. We also give a generalization complexity in classification phase, when a new test sample is error bound for the class of locally linear SVMs introduced, they still need to compare it with these pruned (LLSVMs) based on the Rademacher theory, which SVs via kernel calculations to predict the label of the test ensures that overfitting can be effectively avoided.

The domain adaptation problem arises often in the field of sentiment classification. There are two distinct needs in domain adaptation, namely labeling adaptation and instance adaptation. Most of current research focuses on the former one, while neglects the latter one. In this work, we propose a joint approach, named feature ensemble plus sample selection (SS-FE), which takes both types of adaptation into account. A feature ensemble (FE) model is first proposed to learn a new labeling function in a feature re-weighting manner. Furthermore, a PCA-based sample selection (PCA-SS) method is proposed as an aid to FE for instance adaptation. Experimental results show that the proposed SS-FE approach could gain significant improvements, compared to individual FE and PCA-SS, due to its comprehensive consideration of both labeling adaptation and instance adaptation.

Feature noising is an effective mechanism on reducing the risk of overfitting. To avoid an explosive searching space, existing work typically assumes that all features share a single noise level, which is often cross-validated. In this paper, we present a Bayesian feature noising model that flexibly allows for dimension-specific or group-specific noise levels, and we derive a learning algorithm that adaptively updates these noise levels. Our adaptive rule is simple and interpretable, by drawing a direct connection to the fitness of each individual feature or feature group. Empirical results on various datasets demonstrate the effectiveness on avoiding extensive tuning and sometimes improving the performance due to its flexibility.

Distributed word representations have a rising interest in NLP community. Most of existing models assume only one vector for each individual word, which ignores polysemy and thus degrades their effectiveness for downstream tasks. To address this problem, some recent work adopts multi-prototype models to learn multiple embeddings per word type. In this paper, we distinguish the different senses of each word by their latent topics. We present a general architecture to learn the word and topic embeddings efficiently, which is an extension to the Skip-Gram model and can model the interaction between words and topics simultaneously. The experiments on the word similarity and text classification tasks show our model outperforms state-of-the-art methods.

Random feature mappings have been successfully used for approximating non-linear kernels to scaleup kernel methods. Some work aims at speeding up the feature mappings, but brings increasing variance of the approximation. In this paper, we propose a novel random feature mapping method that uses a signed Circulant Random Matrix (CRM) instead of an unstructured random matrix to project input data. The signed CRM has linear space complexity as the whole signed CRM can be recovered from one column of the CRM, and ensures loglin-ear time complexity to compute the feature mapping using the Fast Fourier Transform (FFT). Theoretically, we prove that approximating Gaussian kernel using our mapping method is unbiased and does not increase the variance. Experimentally, we demonstrate that our proposed mapping method is time and space efficient while retaining similar accuracies with state-of-the-art random feature mapping methods. Our proposed random feature mapping method can be implemented easily and make kernel methods scalable and practical for large scale training and predicting problems.

The rapidly growing of Location-based Social Networks (LBSNs) provides a vast amount of check-in data, which enables many services, e.g., point-of-interest (POI) recommendation. In this paper, we study the next new POI recommendation problem in which new POIs with respect to users' current location are to be recommended. The challenge lies in the difficulty in precisely learning users' sequential information and personalizing the recommendation model. To this end, we resort to the Metric Embedding method for the recommendation, which avoids drawbacks of the Matrix Factorization technique. We propose a personalized ranking metric embedding method (PRME) to model personalized check-in sequences. We further develop a PRME-G model, which integrates sequential information, individual preference, and geographical influence, to improve the recommendation performance. Experiments on two real-world LBSN datasets demonstrate that our new algorithm outperforms the state-of-the-art next POI recommendation methods.

We address an ensemble clustering problem, where reliable clusters are locally embedded in given multiple partitions. We propose a new nonnegative matrix factorization (NMF)-based method, in which locally reliable clusters are explicitly considered by using instance-wise weights over clusters. Our method factorizes the input cluster assignment matrix into two matrices H and W, which are optimized by iteratively 1) updating H and W while keeping the weight matrix constant and 2) updating the weight matrix while keeping H and W constant, alternatively. The weights in the second step were updated by solving a convex problem, which makes our algorithm significantly faster than existing NMF-based ensemble clustering methods. We empirically proved that our method outperformed a lot of cutting-edge ensemble clustering methods by using a variety of datasets.

The rapidly growing of Location-based Social Networks (LBSNs) provides a vast amount of check-in data, which enables many services, e.g., point-of-interest (POI) recommendation. In this paper, we study the next new POI recommendation problem in which new POIs with respect to users' current location are to be recommended. The challenge lies in the difficulty in precisely learning users' sequential information and personalizing the recommendation model. To this end, we resort to the Metric Embedding method for the recommendation, which avoids drawbacks of the Matrix Factorization technique. We propose a personalized ranking metric embedding method (PRME) to model personalized check-in sequences. We further develop a PRME-G model, which integrates sequential information, individual preference, and geographical influence, to improve the recommendation performance. Experiments on two real-world LBSN datasets demonstrate that our new algorithm outperforms the state-of-the-art next POI recommendation methods.

Principal component analysis (PCA) is an unsupervised method for learning low-dimensional features with orthogonal projections. Multilinear PCA methods extend PCA to deal with multidimensional data (tensors) directly via tensor-to-tensor projection or tensor-to-vector projection (TVP). However, under the TVP setting, it is difficult to develop an effective multilinear PCA method with the orthogonality constraint. This paper tackles this problem by proposing a novel Semi-Orthogonal Multilinear PCA (SO-MPCA) approach. SO-MPCA learns low-dimensional features directly from tensors via TVP by imposing the orthogonality constraint in only one mode. This formulation results in more captured variance and more learned features than full orthogonality. For better generalization, we further introduce a relaxed start (RS) strategy to get SO-MPCA-RS by fixing the starting projection vectors, which increases the bias and reduces the variance of the learning model. Experiments on both face (2D) and gait (3D) data demonstrate that SO-MPCA-RS outperforms other competing algorithms on the whole, and the relaxed start strategy is also effective for other TVP-based PCA methods.