Spectral graph partitioning methods have received significant attention from both practitioners and theorists in computer science. Some notable studies have been carried out regarding the behavior of these methods for infinitely large sample size (von Luxburg et al., 2008; Rohe et al., 2011), which provide sufficient confidence to practitioners about the effectiveness of these methods. On the other hand, recent developments in computer vision have led to a plethora of applications, where the model deals with multi-way affinity relations and can be posed as uniform hypergraphs. Inthis paper, we view these models as random m-uniform hypergraphs and establish the consistency of spectral algorithm in this general setting. We develop aplanted partition model or stochastic blockmodel for such problems using higher order tensors, present a spectral technique suited for the purpose and study its large sample behavior. The analysis reveals that the algorithm is consistent for m-uniform hypergraphs for larger values of m, and also the rate of convergence improves for increasing m. Our result provides the first theoretical evidence that establishes the importance of m-way affinities.

Latent Dirichlet allocation (LDA) is a popular generative model of various objects such as texts and images, where an object is expressed as a mixture of latent topics. In this paper, we theoretically investigate variational Bayesian (VB) learning in LDA. More specifically, we analytically derive the leading term of the VB free energy under an asymptotic setup, and show that there exist transition thresholds in Dirichlet hyperparameters around which the sparsity-inducing behavior drastically changes. Then we further theoretically reveal the notable phenomenon that VB tends to induce weaker sparsity than MAP in the LDA model, which is opposed to other models. We experimentally demonstrate the practical validity of our asymptotic theory on real-world Last.FM music data.

We introduce a new multi-task framework, in which $K$ online learners are sharing a single annotator with limited bandwidth. On each round, each of the $K$ learners receives an input, and makes a prediction about the label of that input. Then, a shared (stochastic) mechanism decides which of the $K$ inputs will be annotated. The learner that receives the feedback (label) may update its prediction rule, and we proceed to the next round. We develop an online algorithm for multi-task binary classification that learns in this setting, and bound its performance in the worst-case setting. Additionally, we show that our algorithm can be used to solve two bandits problems: contextual bandits, and dueling bandits with context, both allowed to decouple exploration and exploitation. Empirical study with OCR data, vowel prediction (VJ project) and document classification, shows that our algorithm outperforms other algorithms, one of which uses uniform allocation, and essentially makes more (accuracy) for the same labour of the annotator.

We propose a new active learning algorithm for parametric linear regression with random design. We provide finite sample convergence guarantees for general distributions in the misspecified model. This is the first active learner for this setting that provably can improve over passive learning. Unlike other learning settings (such as classification), in regression the passive learning rate of O(1/epsilon) cannot in general be improved upon. Nonetheless, the so-called `constant' in the rate of convergence, which is characterized by a distribution-dependent risk, can be improved in many cases. For a given distribution, achieving the optimal risk requires prior knowledge of the distribution. Following the stratification technique advocated in Monte-Carlo function integration, our active learner approaches a the optimal risk using piecewise constant approximations.

Patch-based methods have been widely used for noise reduction in recent years. In this paper, we propose a general statistical aggregation method which combines image patches denoised with several commonly-used algorithms. We show that weakly denoised versions of the input image obtained with standard methods, can serve to compute an efficient patch-based aggregated estimator. In our approach, we evaluate the Stein's Unbiased Risk Estimator (SURE) of each denoised candidate imagepatch and use this information to compute the exponential weighted aggregation (EWA) estimator. The aggregation method is flexible enough to combine anystandard denoising algorithm and has an interpretation with Gibbs distribution. Thedenoising algorithm (PEWA) is based on a MCMC sampling and is able to produce results that are comparable to the current state-of-the-art.

Region-specific linear models are widely used in practical applications because of their non-linear but highly interpretable model representations. One of the key challenges in their use is non-convexity in simultaneous optimization of regions and region-specific models. This paper proposes novel convex region-specific linear models, which we refer to as partition-wise linear models. Our key ideas are 1) assigning linear models not to regions but to partitions (region-specifiers) and representing region-specific linear models by linear combinations of partition-specific models, and 2) optimizing regions via partition selection from a large number of given partition candidates by means of convex structured regularizations. In addition to providing initialization-free globally-optimal solutions, our convex formulation makes it possible to derive a generalization bound and to use such advanced optimization techniques as proximal methods and decomposition of the proximal maps for sparsity-inducing regularizations. Experimental results demonstrate that our partition-wise linear models perform better than or are at least competitive with state-of-the-art region-specific or locally linear models.

In this paper, we propose a Generalized Unsupervised Manifold Alignment (GU-MA) method to build the connections between different but correlated datasets without any known correspondences. Based on the assumption that datasets of the same theme usually have similar manifold structures, GUMA is formulated into an explicit integer optimization problem considering the structure matching and preserving criteria, as well as the feature comparability of the corresponding points in the mutual embedding space. The main benefits of this model include: (1) simultaneous discovery and alignment of manifold structures; (2) fully unsupervised matchingwithout any pre-specified correspondences; (3) efficient iterative alignment without computations in all permutation cases. Experimental results on dataset matching and real-world applications demonstrate the effectiveness and the practicability of our manifold alignment method.

Persistent activity refers to the phenomenon that cortical neurons keep firing even after the stimulus triggering the initial neuronal responses is moved. Persistent activity is widely believed to be the substrate for a neural system retaining a memory trace of the stimulus information. In a conventional view, persistent activity is regarded as an attractor of the network dynamics, but it faces a challenge of how to be closed properly. Here, in contrast to the view of attractor, we consider that the stimulus information is encoded in a marginally unstable state of the network which decays very slowly and exhibits persistent firing for a prolonged duration. We propose a simple yet effective mechanism to achieve this goal, which utilizes the property of short-term plasticity (STP) of neuronal synapses. STP has two forms, short-term depression (STD) and short-term facilitation (STF), which have opposite effects on retaining neuronal responses. We find that by properly combining STF and STD, a neural system can hold persistent activity of graded lifetime, and that persistent activity fades away naturally without relying on an external drive. The implications of these results on neural information representation are discussed.

Discriminative dictionary learning (DL) has been widely studied in various pattern classification problems. Most of the existing DL methods aim to learn a synthesis dictionary to represent the input signal while enforcing the representation coefficients and/or representation residual to be discriminative. However, the $\ell_0$ or $\ell_1$-norm sparsity constraint on the representation coefficients adopted in many DL methods makes the training and testing phases time consuming. We propose a new discriminative DL framework, namely projective dictionary pair learning (DPL), which learns a synthesis dictionary and an analysis dictionary jointly to achieve the goal of signal representation and discrimination. Compared with conventional DL methods, the proposed DPL method can not only greatly reduce the time complexity in the training and testing phases, but also lead to very competitive accuracies in a variety of visual classification tasks.

In many classification problems, the input is represented as a set of features, e.g., the bag-of-words (BoW) representation of documents. Support vector machines (SVMs) are widely used tools for such classification problems. The performance of the SVMs is generally determined by whether kernel values between data points can be defined properly. However, SVMs for BoW representations have a major weakness in that the co-occurrence of different but semantically similar words cannot be reflected in the kernel calculation. To overcome the weakness, we propose a kernel-based discriminative classifier for BoW data, which we call the latent support measure machine (latent SMM). With the latent SMM, a latent vector is associated with each vocabulary term, and each document is represented as a distribution of the latent vectors for words appearing in the document. To represent the distributions efficiently, we use the kernel embeddings of distributions that hold high order moment information about distributions. Then the latent SMM finds a separating hyperplane that maximizes the margins between distributions of different classes while estimating latent vectors for words to improve the classification performance. In the experiments, we show that the latent SMM achieves state-of-the-art accuracy for BoW text classification, is robust with respect to its own hyper-parameters, and is useful to visualize words.