Regularized empirical risk minimization including support vector machines plays an important role in machine learning theory. In this paper regularized pairwise learning (RPL) methods based on kernels will be investigated. One example is regularized minimization of the error entropy loss which has recently attracted quite some interest from the viewpoint of consistency and learning rates. This paper shows that such RPL methods have additionally good statistical robustness properties, if the loss function and the kernel are chosen appropriately. We treat two cases of particular interest: (i) a bounded and non-convex loss function and (ii) an unbounded convex loss function satisfying a certain Lipschitz type condition.

In an earlier work we have used the Triangular Fuzzy Numbers (TFNs)as an assessment tool of student skills.This approach led to an approximate linguistic characterization of the students' overall performance, but it was not proved to be sufficient in all cases for comparing the performance of two different student groups, since tywo TFNs are not always comparable. In the present paper we complete the above fuzzy assessment approach by presenting a defuzzification method of TFNS based on the Center of Gravity (COG) technique, which enables the required comparison. In addition we extend our results by using the Trapezoidal Fuzzy Numbers (TpFNs) too, which are a generalization of the TFNs, for student assessment and we present suitable examples illustrating our new results in practice.

Data-efficient reinforcement learning (RL) in continuous state-action spaces using very high-dimensional observations remains a key challenge in developing fully autonomous systems. We consider a particularly important instance of this challenge, the pixels-to-torques problem, where an RL agent learns a closed-loop control policy ("torques") from pixel information only. We introduce a data-efficient, model-based reinforcement learning algorithm that learns such a closed-loop policy directly from pixel information. The key ingredient is a deep dynamical model for learning a low-dimensional feature embedding of images jointly with a predictive model in this low-dimensional feature space. Joint learning is crucial for long-term predictions, which lie at the core of the adaptive nonlinear model predictive control strategy that we use for closed-loop control. Compared to state-of-the-art RL methods for continuous states and actions, our approach learns quickly, scales to high-dimensional state spaces, is lightweight and an important step toward fully autonomous end-to-end learning from pixels to torques.

We compare and contrast two approaches to validating a trained classifier while using all in-sample data for training. One is simultaneous validation over an organized set of hypotheses (SVOOSH), the well-known method that began with VC theory. The other is withhold and gap (WAG). WAG withholds a validation set, trains a holdout classifier on the remaining data, uses the validation data to validate that classifier, then adds the rate of disagreement between the holdout classifier and one trained using all in-sample data, which is an upper bound on the difference in error rates. We show that complex hypothesis classes and limited training data can make WAG a favorable alternative.

Currently, Markov-Gibbs random field (MGRF) image models which include high-order interactions are almost always built by modelling responses of a stack of local linear filters. Actual interaction structure is specified implicitly by the filter coefficients. In contrast, we learn an explicit high-order MGRF structure by considering the learning process in terms of general exponential family distributions nested over base models, so that potentials added later can build on previous ones. We relatively rapidly add new features by skipping over the costly optimisation of parameters. We introduce the use of local binary patterns as features in MGRF texture models, and generalise them by learning offsets to the surrounding pixels. These prove effective as high-order features, and are fast to compute. Several schemes for selecting high-order features by composition or search of a small subclass are compared. Additionally we present a simple modification of the maximum likelihood as a texture modelling-specific objective function which aims to improve generalisation by local windowing of statistics. The proposed method was experimentally evaluated by learning high-order MGRF models for a broad selection of complex textures and then performing texture synthesis, and succeeded on much of the continuum from stochastic through irregularly structured to near-regular textures. Learning interaction structure is very beneficial for textures with large-scale structure, although those with complex irregular structure still provide difficulties. The texture models were also quantitatively evaluated on two tasks and found to be competitive with other works: grading of synthesised textures by a panel of observers; and comparison against several recent MGRF models by evaluation on a constrained inpainting task.

ABSTRACT The objective of this paper is to investigate how noisy and incomplete observations can be integrated in the process of building a reduced-order model. This problematic arises in many scientific domains where there exists a need for accurate low-order descriptions of highly-complex phenomena, which can not be directly and/or deterministically observed. Within this context, the paper proposes a probabilistic framework for the construction of "POD-Galerkin" reduced-order models. Assuming a hidden Markov chain, the inference integrates the uncertainty of the hidden states relying on their posterior distribution. Simulations show the benefits obtained by exploiting the proposed framework. Index Terms-- Reduced-order modeling, POD-Galerkin projection, hidden Markov model, uncertainty, optic-flow. 1. INTRODUCTION In many fields of Sciences, one is interested in studying the spatiotemporal evolution of a state variable characterized by a differential equation.

This paper is about the asymptotic behavior of the Kalman filter [11]. The Kalman-Bucy filter merges predictions from a trusted model of the dynamics of the system with incoming measurements in order to get an accurate, real-time estimate of the unknown internal state of the system. The estimation relies on the computation of a positive semidefinite matrix P, the covariance of the estimation error. The difference equation verified by P is a discrete-time algebraic Riccati equation. Kalman showed that, for a linear time-invariant system, under detectability conditions, the Riccati equation converges to a fixed point, which is unique under certain stabilizability conditions ([10], see also [9]). The classical convergence analysis requires several steps, showing that the error covariance is upper bounded, that, with zero initial value, it is monotone increasing, so that it admits a limit, and then proving that the corresponding filter is stable and that the limit is the same for all initial covariances. In [4] Bougerol proposed a more geometric convergence analysis by showing that the discrete-time Riccati iteration is a contraction for the Riemannian metric associated to the cone of positive definite matrices. Other authors elaborated along these lines (see e.g.

The task of determining labels of all network nodes based on the knowledge about network structure and labels of some training subset of nodes is called the within-network classification. It may happen that none of the labels of the nodes is known and additionally there is no information about number of classes to which nodes can be assigned. In such a case a subset of nodes has to be selected for initial label acquisition. The question that arises is: "labels of which nodes should be collected and used for learning in order to provide the best classification accuracy for the whole network?". Active learning and inference is a practical framework to study this problem. A set of methods for active learning and inference for within network classification is proposed and validated. The utility score calculation for each node based on network structure is the first step in the process. The scores enable to rank the nodes. Based on the ranking, a set of nodes, for which the labels are acquired, is selected (e.g. by taking top or bottom N from the ranking). The new measure-neighbour methods proposed in the paper suggest not obtaining labels of nodes from the ranking but rather acquiring labels of their neighbours. The paper examines 29 distinct formulations of utility score and selection methods reporting their impact on the results of two collective classification algorithms: Iterative Classification Algorithm and Loopy Belief Propagation. We advocate that the accuracy of presented methods depends on the structural properties of the examined network. We claim that measure-neighbour methods will work better than the regular methods for networks with higher clustering coefficient and worse than regular methods for networks with low clustering coefficient. According to our hypothesis, based on clustering coefficient we are able to recommend appropriate active learning and inference method.

Two classes of gamma-ray bursts (GRBs), short and long, have been determined without any doubts, and are usually ascribed to different progenitors, yet these classes overlap for a variety of descriptive parameters. A subsample of 46 long and 22 short $Fermi$ GRBs with estimated Hurst Exponents (HEs), complemented by minimum variability time-scales (MVTS) and durations ($T_{90}$) is used to perform a supervised Machine Learning (ML) and Monte Carlo (MC) simulation using a Support Vector Machine (SVM) algorithm. It is found that while $T_{90}$ itself performs very well in distinguishing short and long GRBs, the overall success ratio is higher when the training set is complemented by MVTS and HE. These results may allow to introduce a new (non-linear) parameter that might provide less ambiguous classification of GRBs.

Gaussian process regression is a popular method for non-parametric probabilistic modeling of functions. The Gaussian process prior is characterized by so-called hyperparameters, which often have a large influence on the posterior model and can be difficult to tune. This work provides a method for numerical marginalization of the hyperparameters, relying on the rigorous framework of sequential Monte Carlo. Our method is well suited for online problems, and we demonstrate its ability to handle real-world problems with several dimensions and compare it to other marginalization methods. We also conclude that our proposed method is a competitive alternative to the commonly used point estimates maximizing the likelihood, both in terms of computational load and its ability to handle multimodal posteriors.