In this paper we consider the problem of learning an n x n Kernel matrix from m similarity matrices under general convex loss. Past research have extensively studied the m =1 case and have derived several algorithms which require sophisticated techniques like ACCP, SOCP, etc. The existing algorithms do not apply if one uses arbitrary losses and often can not handle m > 1 case. We present several provably convergent iterative algorithms, where each iteration requires either an SVM or a Multiple Kernel Learning (MKL) solver for m > 1 case. One of the major contributions of the paper is to extend the well known Mirror Descent(MD) framework to handle Cartesian product of psd matrices. This novel extension leads to an algorithm, called EMKL, which solves the problem in O(m^2 log n) iterations; in each iteration one solves an MKL involving m kernels and m eigen-decomposition of n x n matrices. By suitably defining a restriction on the objective function, a faster version of EMKL is proposed, called REKL, which avoids the eigen-decomposition. An alternative to both EMKL and REKL is also suggested which requires only an SVM solver. Experimental results on real world protein data set involving several similarity matrices illustrate the efficacy of the proposed algorithms.

A new algorithm for isotonic regression is presented based on recursively partitioning the solution space. We develop efficient methods for each partitioning subproblem through an equivalent representation as a network flow problem, and prove that this sequence of partitions converges to the global solution. These network flow problems can further be decomposed in order to solve very large problems. Success of isotonic regression in prediction and our algorithm's favorable computational properties are demonstrated through simulated examples as large as 2x10^5 variables and 10^7 constraints.

In this paper, we propose an efficient algorithm for estimating the natural policy gradient with parameter-based exploration; this algorithm samples directly in the parameter space. Unlike previous methods based on natural gradients, our algorithm calculates the natural policy gradient using the inverse of the exact Fisher information matrix. The computational cost of this algorithm is equal to that of conventional policy gradients whereas previous natural policy gradient methods have a prohibitive computational cost. Experimental results show that the proposed method outperforms several policy gradient methods.

In this paper we consider the fundamental problem of semi-supervised kernel function learning. We propose a general regularized framework for learning a kernel matrix, and then demonstrate an equivalence between our proposed kernel matrix learning framework and a general linear transformation learning problem. Our result shows that the learned kernel matrices parameterize a linear transformation kernel function and can be applied inductively to new data points. Furthermore, our result gives a constructive method for kernelizing most existing Mahalanobis metric learning formulations. To make our results practical for large-scale data, we modify our framework to limit the number of parameters in the optimization process. We also consider the problem of kernelized inductive dimensionality reduction in the semi-supervised setting. We introduce a novel method for this problem by considering a special case of our general kernel learning framework where we select the trace norm function as the regularizer. We empirically demonstrate that our framework learns useful kernel functions, improving the $k$-NN classification accuracy significantly in a variety of domains. Furthermore, our kernelized dimensionality reduction technique significantly reduces the dimensionality of the feature space while achieving competitive classification accuracies.

We propose a new probabilistic model for analyzing dynamic evolutions of relational data, such as additions, deletions and split & merge, of relation clusters like communities in social networks. Our proposed model abstracts observed time-varying object-object relationships into relationships between object clusters. We extend the infinite Hidden Markov model to follow dynamic and time-sensitive changes in the structure of the relational data and to estimate a number of clusters simultaneously. We show the usefulness of the model through experiments with synthetic and real-world data sets.

In this paper, we point out that there exist scaling and initialization problems in most existing multiple kernel learning (MKL) approaches, which employ the large margin principle to jointly learn both a kernel and an SVM classifier. The reason is that the margin itself can not well describe how good a kernel is due to the negligence of the scaling. We use the ratio between the margin and the radius of the minimum enclosing ball to measure the goodness of a kernel, and present a new minimization formulation for kernel learning. This formulation is invariant to scalings of learned kernels, and when learning linear combination of basis kernels it is also invariant to scalings of basis kernels and to the types (e.g., L1 or L2) of norm constraints on combination coefficients. We establish the differentiability of our formulation, and propose a gradient projection algorithm for kernel learning. Experiments show that our method significantly outperforms both SVM with the uniform combination of basis kernels and other state-of-art MKL approaches.

The present study investigates the impact of STD on the dynamics of a continuous attractor neural network (CANN) and its potential roles in neural information processing. We find that the network with STD can generate both static and traveling bumps, and STD enhances the performance of the network in tracking external inputs. In particular, we find that STD endows the network with slow-decaying plateau behaviors, namely, the network being initially stimulated to an active state will decay to silence very slowly in the time scale of STD rather than that of neural signaling. We argue that this provides a mechanism for neural systems to hold short-term memory easily and shut off persistent activities naturally.

In multi-instance learning, there are two kinds of prediction failure, i.e., false negative and false positive. Current research mainly focus on avoding the former. We attempt to utilize the geometric distribution of instances inside positive bags to avoid both the former and the latter. Based on kernel principal component analysis, we define a projection constraint for each positive bag to classify its constituent instances far away from the separating hyperplane while place positive instances and negative instances at opposite sides. We apply the Constrained Concave-Convex Procedure to solve the resulted problem. Empirical results demonstrate that our approach offers improved generalization performance.

We extend Latent Dirichlet Allocation (LDA) by explicitly allowing for the encoding of side information in the distribution over words. This results in a variety of new capabilities, such as improved estimates for infrequently occurring words, as well as the ability to leverage thesauri and dictionaries in order to boost topic cohesion within and across languages. We present experiments on multi-language topic synchronisation where dictionary information is used to bias corresponding words towards similar topics. Results indicate that our model substantially improves topic cohesion when compared to the standard LDA model.

Most active learning approaches select either informative or representative unlabeled instances to query their labels. Although several active learning algorithms have been proposed to combine the two criterions for query selection, they are usually ad hoc in finding unlabeled instances that are both informative and representative. We address this challenge by a principled approach, termed QUIRE, based on the min-max view of active learning. The proposed approach provides a systematic way for measuring and combining the informativeness and representativeness of an instance. Extensive experimental results show that the proposed QUIRE approach outperforms several state-of -the-art active learning approaches.