The Resilient Propagation (Rprop) algorithm has been very popular for backpropagation training of multilayer feed-forward neural networks in various applications. The standard Rprop however encounters difficulties in the context of deep neural networks as typically happens with gradient-based learning algorithms. In this paper, we propose a modification of the Rprop that combines standard Rprop steps with a special drop out technique. We apply the method for training Deep Neural Networks as standalone components and in ensemble formulations. Results on the MNIST dataset show that the proposed modification alleviates standard Rprop's problems demonstrating improved learning speed and accuracy.

Gathering the most information by picking the least amount of data is a common task in experimental design or when exploring an unknown environment in reinforcement learning and robotics. A widely used measure for quantifying the information contained in some distribution of interest is its entropy. Greedily minimizing the expected entropy is therefore a standard method for choosing samples in order to gain strong beliefs about the underlying random variables. We show that this approach is prone to temporally getting stuck in local optima corresponding to wrongly biased beliefs. We suggest instead maximizing the expected cross entropy between old and new belief, which aims at challenging refutable beliefs and thereby avoids these local optima. We show that both criteria are closely related and that their difference can be traced back to the asymmetry of the Kullback-Leibler divergence. In illustrative examples as well as simulated and real-world experiments we demonstrate the advantage of cross entropy over simple entropy for practical applications.

Abstract--Nonnegative T ucker decomposition (NTD) is a powerful tool for the extraction of nonnegative parts-based and physically meaningful latent components from high-dimensional tensor data while preserving the natural multilinear structure of data. However, as the data tensor often has multiple modes and is large-scale, existing NTD algorithms suffer from a very high computational complexity in terms of both storage and computation time, which has been one major obstacle for practical applications of NTD. T o overcome these disadvantages, we show how low (multilinear) rank approximation (LRA) of tensors is able to significantly simplify the computation of the gradients of the cost function, upon which a family of efficient first-order NTD algorithms are developed. Besides dramatically reducing the storage complexity and running time, the new algorithms are quite flexible and robust to noise because any well-established LRA approaches can be applied. We also show how nonnegativity incorporating sparsity substantially improves the uniqueness property and partially alleviates the curse of dimensionality of the T ucker decompositions. Simulation results on synthetic and real-world data justify the validity and high efficiency of the proposed NTD algorithms. INDING information-rich and task-relevant variables hidden behind observation data is a fundamental task in data analysis and has been widely studied in the fields of signal and image processing and machine learning. Although the observation data can be very large, a much lower number of latent variables or components can capture the most significant features of the original data. Manuscript received ...This work was partially supported by the National Natural Science Foundation of China (grants U1201253), the Guangdong Province Natural Science Foundation (2014A030308009), the Guangdong Province Excellent Thesis Foundation (SYBZZXM201316), and the JSPS KAKENHI (26730125, 15K15955). Guoxu Zhou is with the School of Automation at Guangdong University of Technology, Guangzhou, China and the Laboratory for Advanced Brain Signal Processing, RIKEN Brain Science Institute, Wako-shi, Saitama, Japan. Andrzej Cichocki is with the Laboratory for Advanced Brain Signal Processing, RIKEN Brain Science Institute, Wako-shi, Saitama, Japan and with Systems Research Institute, Polish Academy of Science, Warsaw, Poland. Qibin Zhao is with the Laboratory for Advanced Brain Signal Processing, RIKEN Brain Science Institute, Japan. Shengli Xie is with the Faculty of Automation, Guangdong University of Technology, Guangzhou 510006, China. This important topic has been extensively studied in the last several decades, particularly witnessed by the great success of blind source separation (BSS) techniques [1].

This work is concerned with regular languages defined over large alphabets, either infinite or just too large to be expressed enumeratively. We define a generic model where transitions are labeled by elements of a finite partition of the alphabet. We then extend Angluin's L* algorithm for learning regular languages from examples for such automata. We have implemented this algorithm and we demonstrate its behavior where the alphabet is a subset of the natural or real numbers. We sketch the extension of the algorithm to a class of languages over partially ordered alphabets.

We consider the matrix completion problem of recovering a structured matrix from noisy and partial measurements. Recent works have proposed tractable estimators with strong statistical guarantees for the case where the underlying matrix is low--rank, and the measurements consist of a subset, either of the exact individual entries, or of the entries perturbed by additive Gaussian noise, which is thus implicitly suited for thin--tailed continuous data. Arguably, common applications of matrix completion require estimators for (a) heterogeneous data--types, such as skewed--continuous, count, binary, etc., (b) for heterogeneous noise models (beyond Gaussian), which capture varied uncertainty in the measurements, and (c) heterogeneous structural constraints beyond low--rank, such as block--sparsity, or a superposition structure of low--rank plus elementwise sparseness, among others. In this paper, we provide a vastly unified framework for generalized matrix completion by considering a matrix completion setting wherein the matrix entries are sampled from any member of the rich family of exponential family distributions; and impose general structural constraints on the underlying matrix, as captured by a general regularizer $\mathcal{R}(.)$. We propose a simple convex regularized $M$--estimator for the generalized framework, and provide a unified and novel statistical analysis for this general class of estimators. We finally corroborate our theoretical results on simulated datasets.

Models for recommender systems use latent factors to explain the preferences and behaviors of users with respect to a set of items (e.g., movies, books, academic papers). Typically, the latent factors are assumed to be static and, given these factors, the observed preferences and behaviors of users are assumed to be generated without order. These assumptions limit the explorative and predictive capabilities of such models, since users' interests and item popularity may evolve over time. To address this, we propose dPF, a dynamic matrix factorization model based on the recent Poisson factorization model for recommendations. dPF models the time evolving latent factors with a Kalman filter and the actions with Poisson distributions. We derive a scalable variational inference algorithm to infer the latent factors. Finally, we demonstrate dPF on 10 years of user click data from arXiv.org, one of the largest repository of scientific papers and a formidable source of information about the behavior of scientists. Empirically we show performance improvement over both static and, more recently proposed, dynamic recommendation models. We also provide a thorough exploration of the inferred posteriors over the latent variables.

The group membership prediction (GMP) problem involves predicting whether or not a collection of instances share a certain semantic property. For instance, in kinship verification given a collection of images, the goal is to predict whether or not they share a {\it familial} relationship. In this context we propose a novel probability model and introduce latent {\em view-specific} and {\em view-shared} random variables to jointly account for the view-specific appearance and cross-view similarities among data instances. Our model posits that data from each view is independent conditioned on the shared variables. This postulate leads to a parametric probability model that decomposes group membership likelihood into a tensor product of data-independent parameters and data-dependent factors. We propose learning the data-independent parameters in a discriminative way with bilinear classifiers, and test our prediction algorithm on challenging visual recognition tasks such as multi-camera person re-identification and kinship verification. On most benchmark datasets, our method can significantly outperform the current state-of-the-art.

Tree structures are ubiquitous in data across many domains, and many datasets are naturally modelled by unobserved tree structures. In this paper, first we review the theory of random fragmentation processes [Bertoin, 2006], and a number of existing methods for modelling trees, including the popular nested Chinese restaurant process (nCRP). Then we define a general class of probability distributions over trees: the Dirichlet fragmentation process (DFP) through a novel combination of the theory of Dirichlet processes and random fragmentation processes. This DFP presents a stick-breaking construction, and relates to the nCRP in the same way the Dirichlet process relates to the Chinese restaurant process. Furthermore, we develop a novel hierarchical mixture model with the DFP, and empirically compare the new model to similar models in machine learning. Experiments show the DFP mixture model to be convincingly better than existing state-of-the-art approaches for hierarchical clustering and density modelling. The process of random fragmentation is common to many areas, such as the degradation of large polymer chains in chemistry, or the evolution of phylogenetic trees in biology. An elegant mathematical tool for describing such phenomena is the fragmentation process (FP) [Bertoin, 2006]. As a concrete example of a FP, consider a stick of unit length.

Traditional Kalman filter (KF) is derived under the well-known minimum mean square error (MMSE) criterion, which is optimal under Gaussian assumption. However, when the signals are non-Gaussian, especially when the system is disturbed by some heavy-tailed impulsive noises, the performance of KF will deteriorate seriously. To improve the robustness of KF against impulsive noises, we propose in this work a new Kalman filter, called the maximum correntropy Kalman filter (MCKF), which adopts the robust maximum correntropy criterion (MCC) as the optimality criterion, instead of using the MMSE. Similar to the traditional KF, the state mean and covariance matrix propagation equations are used to give prior estimations of the state and covariance matrix in MCKF. A novel fixed-point algorithm is then used to update the posterior estimations. A sufficient condition that guarantees the convergence of the fixed-point algorithm is given. Illustration examples are presented to demonstrate the effectiveness and robustness of the new algorithm.

We study the restless bandit associated with an extremely simple scalar Kalman filter model in discrete time. Under certain assumptions, we prove that the problem is indexable in the sense that the Whittle index is a non-decreasing function of the relevant belief state. In spite of the long history of this problem, this appears to be the first such proof. We use results about Schur-convexity and mechanical words, which are particular binary strings intimately related to palindromes.