We revisit the problem of robust principal component analysis with features acting as prior side information. To this aim, a novel, elegant, non-convex optimization approach is proposed to decompose a given observation matrix into a low-rank core and the corresponding sparse residual. Rigorous theoretical analysis of the proposed algorithm results in exact recovery guarantees with low computational complexity. Aptly designed synthetic experiments demonstrate that our method is the first to wholly harness the power of non-convexity over convexity in terms of both recoverability and speed. That is, the proposed non-convex approach is more accurate and faster compared to the best available algorithms for the problem under study. Two real-world applications, namely image classification and face denoising further exemplify the practical superiority of the proposed method.

It is expensive and difficult to precisely annotate objects with multiple labels. Instead, in many real tasks, annotators may roughly assign each object with a set of candidate labels. The candidate set contains at least one but unknown number of ground-truth labels, and is usually adulterated with some irrelevant labels. In this paper, we formalize such problems as a new learning framework called partial multi-label learning (PML). To solve the PML problem, a confidence value is maintained for each candidate label to estimate how likely it is a ground-truth label of the instance. On one hand, the relevance ordering of labels on each instance is optimized by minimizing a rank loss weighted by the confidences; on the other hand, the confidence values are optimized by further exploiting structure information in feature and label spaces.Experimental results on various datasets show that the proposed approach is effective for solving PML problems.

This paper proposes a cooperative learning algorithm to train both the undirected energy-based model and the directed latent variable model jointly. The learning algorithm interweaves the maximum likelihood algorithms for learning the two models, and each iteration consists of the following two steps: (1) Modified contrastive divergence for energy-based model: The learning of the energy-based model is based on the contrastive divergence, but the finite-step MCMC sampling of the model is initialized from the synthesized examples generated by the latent variable model instead of being initialized from the observed examples. (2) MCMC teaching of the latent variable model: The learning of the latent variable model is based on how the MCMC in (1) changes the initial synthesized examples generated by the latent variable model, where the latent variables that generate the initial synthesized examples are known so that the learning is essentially supervised. Our experiments show that the cooperative learning algorithm can learn realistic models of images.

We study bilinear embedding models for the task of multi-relational link prediction and knowledge graph completion. Bilinear models belong to the most basic models for this task, they are comparably efficient to train and use, and they can provide good prediction performance. The main goal of this paper is to explore the expressiveness of and the connections between various bilinear models proposed in the literature. In particular, a substantial number of models can be represented as bilinear models with certain additional constraints enforced on the embeddings. We explore whether or not these constraints lead to universal models, which can in principle represent every set of relations, and whether or not there are subsumption relationships between various models. We report results of an independent experimental study that evaluates recent bilinear models in a common experimental setup. Finally, we provide evidence that relation-level ensembles of multiple bilinear models can achieve state-of-the-art prediction performance.

Temporal data clustering is a challenging task. Existing methods usually explore data self-representation strategy, which may hinder the clustering performance in insufficient or corrupted data scenarios. In real-world applications, we are easily accessible to a large amount of related labeled data. To this end, we propose a novel transferable subspace clustering approach by exploring useful information from relevant source data to enhance clustering performance in target temporal data. We manage to transform the original data into a shared low-dimensional and distinctive feature space by jointly seeking an effective domain-invariant projection. In this way, the well-labeled source knowledge can help obtain a more discriminative target representation. Moreover, a graph regularizer is designed to incorporate temporal information to preserve more sequence knowledge into the learned representation. Extensive experiments based on three human motion datasets illustrate that our approach is able to outperform state-of-the-art temporal data clustering methods.

Bayesian optimization (BayesOpt) is a derivative-free approach for sequentially optimizing stochastic black-box functions. Standard BayesOpt, which has shown many successes in machine learning applications, assumes a finite dimensional domain which often is a parametric space. The parameter space is defined by the features used in the function approximations which are often selected manually. Therefore, the performance of BayesOpt inevitably depends on the quality of chosen features. This paper proposes a new Bayesian optimization framework that is able to optimize directly on the domain of function spaces. The resulting framework, Bayesian Functional Optimization (BFO), not only extends the application domains of BayesOpt to functional optimization problems but also relaxes the performance dependency on the chosen parameter space. We model the domain of functions as a reproducing kernel Hilbert space (RKHS), and use the notion of Gaussian processes on a real separable Hilbert space. As a result, we are able to define traditional improvement-based (PI and EI) and optimistic acquisition functions (UCB) as functionals. We propose to optimize the acquisition functionals using analytic functional gradients that are also proved to be functions in a RKHS. We evaluate BFO in three typical functional optimization tasks: i) a synthetic functional optimization problem, ii) optimizing activation functions for a multi-layer perceptron neural network, and iii) a reinforcement learning task whose policies are modeled in RKHS.

Gaussian Processes (GPs) provide an extremely powerful mechanism to model a variety of problems but incur an O(N 3 ) complexity in the number of data samples. Common approximation methods rely on what are often termed inducing points but still typically incur an O(NM 2 ) complexity in the data and corresponding inducing points. Using Random Fourier Feature (RFF) maps, we overcome this by transforming the problem into a Bayesian Linear Regression formulation upon which we apply a Bayesian Variational treatment that also allows learning the corresponding kernel hyperparameters, likelihood and noise parameters. In this paper we introduce an alternative method using Fourier series to obtain spectral representations of common kernels, in particular for periodic warpings, which surprisingly have a convergent, non-random form using special functions, requiring fewer spectral features to approximate their corresponding kernel to high accuracy. Using this, we can fuse the Random Fourier Feature spectral representations of common kernels with their periodic counterparts to show how they can more effectively and expressively learn patterns in time-series for both interpolation and extrapolation. This method combines robustness, scalability and equally importantly, interpretability through a symbolic declarative grammar that is both functionally and humanly intuitive — a property that is crucial for explainable decision making. Using probabilistic programming and Variational Inference we are able to efficiently optimise over these rich functional representations. We show significantly improved Gram matrix approximation errors, and also demonstrate the method in several time-series problems comparing other commonly used approaches such as recurrent neural networks.

To deal with the low qualities of web workers in crowdsourcing, many unsupervised label aggregation methods have been investigated but most of them provide inconsistent performance. In this paper, we explore the learning from crowds with selective verification problem. In addition to the noisy responses from the crowds, it also collects the ground truths for a well-chosen subset of tasks as the reference, then aggregates the redundant responses based on the patterns provided by both the supervised and unsupervised signal. To improve the labeling efficiency, we propose the EBM selecting strategy for choosing the verification subset, which is based on the loss error minimization. Specifically, we first establish the expected loss error given the semi-supervised learning estimate, then find the subset that minimizes this selecting criterion. We do extensive empirical comparisons on both synthetic and real-world datasets to show the benefits of this new learning setting as well as our proposal.

With the advent of multi-view data, multi-view learning (MVL) has become an important research direction in machine learning. It is usually expected that multi-view algorithms can obtain better performance than that of merely using a single view. However, previous researches have pointed out that sometimes the utilization of multiple views may even deteriorate the performance. This will be a stumbling block for the practical use of MVL in real applications, especially for tasks requiring high dependability. Thus, it is eager to design reliable multi-view approaches, such that their performance is never degenerated by exploiting multiple views.This issue is vital but rarely studied. In this paper, we focus on clustering and propose the Reliable Multi-View Clustering (RMVC) method. Based on several candidate multi-view clusterings, RMVC maximizes the worst-case performance gain against the best single view clustering, which is equivalently expressed as no label information available. Specifically, employing the squared χ 2 distance for clustering comparison makes the formulation of RMVC easy to solve, and an efficient strategy is proposed for optimization. Theoretically, it can be proved that the performance of RMVC will never be significantly decreased under some assumption. Experimental results on a number of data sets demonstrate that the proposed method can effectively improve the reliability of multi-view clustering.

Lifelong learning intends to learn new consecutive tasks depending on previously accumulated experiences, i.e., knowledge library. However, the knowledge among different new coming tasks are imbalance. Therefore, in this paper, we try to mimic an effective "human cognition" strategy by actively sorting the importance of new tasks in the process of unknown-to-known and selecting to learn the important tasks with more information preferentially. To achieve this, we consider to assess the importance of the new coming task, i.e., unknown or not, as an outlier detection issue, and design a hierarchical dictionary learning model consisting of two-level task descriptors to sparse reconstruct each task with the l0 norm constraint. The new coming tasks are sorted depending on the sparse reconstruction score in descending order, and the task with high reconstruction score will be permitted to pass, where this mechanism is called as "watchdog." Next, the knowledge library of the lifelong learning framework encode the selected task by transferring previous knowledge, and then can also update itself with knowledge from both previously learned task and current task automatically. For model optimization, the alternating direction method is employed to solve our model and converges to a fixed point. Extensive experiments on both benchmark datasets and our own dataset demonstrate the effectiveness of our proposed model especially in task selection and dictionary learning.