This paper investigates a new method for improving the learning algorithm of Mixture of Experts (ME) model using a hybrid of Modified Cuckoo Search (MCS) and Conjugate Gradient (CG) as a second order optimization technique. The CG technique is combined with Back-Propagation (BP) algorithm to yield a much more efficient learning algorithm for ME structure. In addition, the experts and gating networks in enhanced model are replaced by CG based Multi-Layer Perceptrons (MLPs) to provide faster and more accurate learning. The CG is considerably depends on initial weights of connections of Artificial Neural Network (ANN), so, a metaheuristic algorithm, the so-called Modified Cuckoo Search is applied in order to select the optimal weights. The performance of proposed method is compared with Gradient Decent Based ME (GDME) and Conjugate Gradient Based ME (CGME) in classification and regression problems. The experimental results show that hybrid MSC and CG based ME (MCS-CGME) has faster convergence and better performance in utilized benchmark data sets.

Under the heading of "Addressing the big data challenge", the European 7th Framework Programme sees the issue thus (see INFSO, 2012): "Recent industry reports detail how data volumes are growing at a faster rate than our ability to interpret and exploit them for innovative ICT applications, for decision support, planning, monitoring, control and interaction. This includes unstructured data types such as video, audio, images and free text as well as structured data types such as database records, sensor readings and 3D. While each of these types requires some specific form of processing and analytics, many of the general principles for managing and storing them at extreme scales are common across all of them." Analytics tool capability is called for, to address these burgeoning issues in the data intensive industries, to support "effective policy making and implementation" of public bodies resulting in "significant annual savings from 1 Big Data applications", and also to exploit open, linked data - "foster the reuse of public sector information and strengthen other open data activities linked to commercial exploitation." The "big data" marketplace is stated to be potentially worth approximately USD 600 billion. To address the challenges of search and discovery in massive and complex data sets and data flows, it is our contention in this work that we must move to an appropriate topology - to an appropriate framework such that computation is greatly facilitated. Our work is all about empowering those who are involved in data analytics, through clustering and related algorithms, to face these new challenges. Scalability and interactivity are two of the performance issues that follow directly from clustering algorithms, for search, retrieval and discovery, that are of linear computational complexity or better (logarithmic, or constant).

The problem of active diagnosis arises in several applications such as disease diagnosis, and fault diagnosis in computer networks, where the goal is to rapidly identify the binary states of a set of objects (e.g., faulty or working) by sequentially selecting, and observing, (noisy) responses to binary valued queries. Current algorithms in this area rely on loopy belief propagation for active query selection. These algorithms have an exponential time complexity, making them slow and even intractable in large networks. We propose a rank-based greedy algorithm that sequentially chooses queries such that the area under the ROC curve of the rank-based output is maximized. The AUC criterion allows us to make a simplifying assumption that significantly reduces the complexity of active query selection (from exponential to near quadratic), with little or no compromise on the performance quality.

We address the problem of learning the parameters in graphical models when inference is intractable. A common strategy in this case is to replace the partition function with its Bethe approximation. We show that there exists a regime of empirical marginals where such Bethe learning will fail. By failure we mean that the empirical marginals cannot be recovered from the approximated maximum likelihood parameters (i.e., moment matching is not achieved). We provide several conditions on empirical marginals that yield outer and inner bounds on the set of Bethe learnable marginals. An interesting implication of our results is that there exists a large class of marginals that cannot be obtained as stable fixed points of belief propagation. Taken together our results provide a novel approach to analyzing learning with Bethe approximations and highlight when it can be expected to work or fail.

Fisher score is one of the most widely used supervised feature selection methods. However, it selects each feature independently according to their scores under the Fisher criterion, which leads to a suboptimal subset of features. In this paper, we present a generalized Fisher score to jointly select features. It aims at finding an subset of features, which maximize the lower bound of traditional Fisher score. The resulting feature selection problem is a mixed integer programming, which can be reformulated as a quadratically constrained linear programming (QCLP). It is solved by cutting plane algorithm, in each iteration of which a multiple kernel learning problem is solved alternatively by multivariate ridge regression and projected gradient descent. Experiments on benchmark data sets indicate that the proposed method outperforms Fisher score as well as many other state-of-the-art feature selection methods.

We show that the Bregman divergence provides a rich framework to estimate unnormalized statistical models for continuous or discrete random variables, that is, models which do not integrate or sum to one, respectively. We prove that recent estimation methods such as noise-contrastive estimation, ratio matching, and score matching belong to the proposed framework, and explain their interconnection based on supervised learning. Further, we discuss the role of boosting in unsupervised learning.

We propose a method that infers whether linear relations between two high-dimensional variables X and Y are due to a causal influence from X to Y or from Y to X. The earlier proposed so-called Trace Method is extended to the regime where the dimension of the observed variables exceeds the sample size. Based on previous work, we postulate conditions that characterize a causal relation between X and Y. Moreover, we describe a statistical test and argue that both causal directions are typically rejected if there is a common cause. A full theoretical analysis is presented for the deterministic case but our approach seems to be valid for the noisy case, too, for which we additionally present an approach based on a sparsity constraint. The discussed method yields promising results for both simulated and real world data.

Such relaxations make STC amenable to: 1) directly control the sparsity of inferred representations by using sparsity-inducing regularizers; 2) be seamlessly integrated with a convex error function (e.g., SVM hinge loss) for supervised learning; and 3) be efficiently learned with a simply structured coordinate descent algorithm. Our results demonstrate the advantages of STC and supervised MedSTC on identifying topical meanings of words and improving classification accuracy and time efficiency.

A Support Vector Method for multivariate performance measures was recently introduced by Joachims (2005). The underlying optimization problem is currently solved using cutting plane methods such as SVM-Perf and BMRM. One can show that these algorithms converge to an eta accurate solution in O(1/Lambda*e) iterations, where lambda is the trade-off parameter between the regularizer and the loss function. We present a smoothing strategy for multivariate performance scores, in particular precision/recall break-even point and ROCArea. When combined with Nesterov's accelerated gradient algorithm our smoothing strategy yields an optimization algorithm which converges to an eta accurate solution in O(min{1/e,1/sqrt(lambda*e)}) iterations. Furthermore, the cost per iteration of our scheme is the same as that of SVM-Perf and BMRM. Empirical evaluation on a number of publicly available datasets shows that our method converges significantly faster than cutting plane methods without sacrificing generalization ability.

Conditional independence testing is an important problem, especially in Bayesian network learning and causal discovery. Due to the curse of dimensionality, testing for conditional independence of continuous variables is particularly challenging. We propose a Kernel-based Conditional Independence test (KCI-test), by constructing an appropriate test statistic and deriving its asymptotic distribution under the null hypothesis of conditional independence. The proposed method is computationally efficient and easy to implement. Experimental results show that it outperforms other methods, especially when the conditioning set is large or the sample size is not very large, in which case other methods encounter difficulties.