Narendra-Shapiro (NS) algorithms are bandit-type algorithms that have been introduced in the sixties (with a view to applications in Psychology or learning automata), whose convergence has been intensively studied in the stochastic algorithm literature. In this paper, we adress the following question: are the Narendra-Shapiro (NS) bandit algorithms competitive from a \textit{regret} point of view? In our main result, we show that some competitive bounds can be obtained for such algorithms in their penalized version (introduced in \cite{Lamberton_Pages}). More precisely, up to an over-penalization modification, the pseudo-regret $\bar{R}_n$ related to the penalized two-armed bandit algorithm is uniformly bounded by $C \sqrt{n}$ (where $C$ is made explicit in the paper). \noindent We also generalize existing convergence and rates of convergence results to the multi-armed case of the over-penalized bandit algorithm, including the convergence toward the invariant measure of a Piecewise Deterministic Markov Process (PDMP) after a suitable renormalization. Finally, ergodic properties of this PDMP are given in the multi-armed case.

Asynchronous distributed stochastic gradient descent methods have trouble converging because of stale gradients. A gradient update sent to a parameter server by a client is stale if the parameters used to calculate that gradient have since been updated on the server. Approaches have been proposed to circumvent this problem that quantify staleness in terms of the number of elapsed updates. In this work, we propose a novel method that quantifies staleness in terms of moving averages of gradient statistics. We show that this method outperforms previous methods with respect to convergence speed and scalability to many clients. We also discuss how an extension to this method can be used to dramatically reduce bandwidth costs in a distributed training context. In particular, our method allows reduction of total bandwidth usage by a factor of 5 with little impact on cost convergence. We also describe (and link to) a software library that we have used to simulate these algorithms deterministically on a single machine.

Slow feature analysis (SFA) is an unsupervised-learning algorithm that extracts slowly varying features from a multi-dimensional time series. A supervised extension to SFA for classification and regression is graph-based SFA (GSFA). GSFA is based on the preservation of similarities, which are specified by a graph structure derived from the labels. It has been shown that hierarchical GSFA (HGSFA) allows learning from images and other high-dimensional data. The feature space spanned by HGSFA is complex due to the composition of the nonlinearities of the nodes in the network. However, we show that the network discards useful information prematurely before it reaches higher nodes, resulting in suboptimal global slowness and an under-exploited feature space. To counteract these problems, we propose an extension called hierarchical information-preserving GSFA (HiGSFA), where information preservation complements the slowness-maximization goal. We build a 10-layer HiGSFA network to estimate human age from facial photographs of the MORPH-II database, achieving a mean absolute error of 3.50 years, improving the state-of-the-art performance. HiGSFA and HGSFA support multiple-labels and offer a rich feature space, feed-forward training, and linear complexity in the number of samples and dimensions. Furthermore, HiGSFA outperforms HGSFA in terms of feature slowness, estimation accuracy and input reconstruction, giving rise to a promising hierarchical supervised-learning approach.

A new nonparametric approach for system identification has been recently proposed where the impulse response is modeled as the realization of a zero-mean Gaussian process whose covariance (kernel) has to be estimated from data. In this scheme, quality of the estimates crucially depends on the parametrization of the covariance of the Gaussian process. A family of kernels that have been shown to be particularly effective in the system identification framework is the family of Diagonal/Correlated (DC) kernels. Maximum entropy properties of a related family of kernels, the Tuned/Correlated (TC) kernels, have been recently pointed out in the literature. In this paper we show that maximum entropy properties indeed extend to the whole family of DC kernels. The maximum entropy interpretation can be exploited in conjunction with results on matrix completion problems in the graphical models literature to shed light on the structure of the DC kernel. In particular, we prove that the DC kernel admits a closed-form factorization, inverse and determinant. These results can be exploited both to improve the numerical stability and to reduce the computational complexity associated with the computation of the DC estimator.

In many classification problems a classifier should be robust to small variations in the input vector. This is a desired property not only for particular transformations, such as translation and rotation in image classification problems, but also for all others for which the change is small enough to retain the object perceptually indistinguishable. We propose two extensions of the backpropagation algorithm that train a neural network to be robust to variations in the feature vector. While the first of them enforces robustness of the loss function to all variations, the second method trains the predictions to be robust to a particular variation which changes the loss function the most. The second methods demonstrates better results, but is slightly slower. We analytically compare the proposed algorithm with two the most similar approaches (Tangent BP and Adversarial Training), and propose their fast versions. In the experimental part we perform comparison of all algorithms in terms of classification accuracy and robustness to noise on MNIST and CIFAR-10 datasets. Additionally we analyze how the performance of the proposed algorithm depends on the dataset size and data augmentation.

In this paper, we propose an active perception method for recognizing object categories based on the multimodal hierarchical Dirichlet process (MHDP). The MHDP enables a robot to form object categories using multimodal information, e.g., visual, auditory, and haptic information, which can be observed by performing actions on an object. However, performing many actions on a target object requires a long time. In a real-time scenario, i.e., when the time is limited, the robot has to determine the set of actions that is most effective for recognizing a target object. We propose an MHDP-based active perception method that uses the information gain (IG) maximization criterion and lazy greedy algorithm. We show that the IG maximization criterion is optimal in the sense that the criterion is equivalent to a minimization of the expected Kullback--Leibler divergence between a final recognition state and the recognition state after the next set of actions. However, a straightforward calculation of IG is practically impossible. Therefore, we derive an efficient Monte Carlo approximation method for IG by making use of a property of the MHDP. We also show that the IG has submodular and non-decreasing properties as a set function because of the structure of the graphical model of the MHDP. Therefore, the IG maximization problem is reduced to a submodular maximization problem. This means that greedy and lazy greedy algorithms are effective and have a theoretical justification for their performance. We conducted an experiment using an upper-torso humanoid robot and a second one using synthetic data. The experimental results show that the method enables the robot to select a set of actions that allow it to recognize target objects quickly and accurately. The results support our theoretical outcomes.

Linguistic borrowing is the phenomenon of transferring linguistic constructions (lexical, phonological, morphological, and syntactic) from a donor language to a recipient language as a result of contacts between communities speaking different languages. Borrowed words are found in all languages, andin contrast to cognate relationshipsborrowing relationships may exist across unrelated languages (for example, about 40% of Swahilis vocabulary is borrowed from the unrelated language Arabic). In this work, we develop a model of morpho-phonological transformations across languages. Its features are based on universal constraints from Optimality Theory (OT), and we show that compared to several standardbut linguistically more naïvebaselines, our OT-inspired model obtains good performance at predicting donor forms from borrowed forms with only a few dozen training examples, making this a cost-effective strategy for sharing lexical information across languages. We demonstrate applications of the lexical borrowing model in machine translation, using resource-rich donor language to obtain translations of out-of-vocabulary loanwords in a lower resource language. Our framework obtains substantial improvements (up to 1.6 BLEU) over standard baselines.

We describe a hybridisation strategy whose objective is to integrate linguistic resources from shallow-transfer rule-based machine translation (RBMT) into phrase-based statistical machine translation (PBSMT). It basically consists of enriching the phrase table of a PBSMT system with bilingual phrase pairs matching transfer rules and dictionary entries from a shallow-transfer RBMT system. This new strategy takes advantage of how the linguistic resources are used by the RBMT system to segment the source-language sentences to be translated, and overcomes the limitations of existing hybrid approaches that treat the RBMT systems as a black box. Experimental results confirm that our approach delivers translations of higher quality than existing ones, and that it is specially useful when the parallel corpus available for training the SMT system is small or when translating out-of-domain texts that are well covered by the RBMT dictionaries. A combination of this approach with a recently proposed unsupervised shallow-transfer rule inference algorithm results in a significantly greater translation quality than that of a baseline PBSMT; in this case, the only hand-crafted resource used are the dictionaries commonly used in RBMT. Moreover, the translation quality achieved by the hybrid system built with automatically inferred rules is similar to that obtained by those built with hand-crafted rules.

This work formulates a novel song recommender system as a matrix completion problem that benefits from collaborative filtering through Non-negative Matrix Factorization (NMF) and content-based filtering via total variation (TV) on graphs. The graphs encode both playlist proximity information and song similarity, using a rich combination of audio, meta-data and social features. As we demonstrate, our hybrid recommendation system is very versatile and incorporates several well-known methods while outperforming them. Particularly, we show on real-world data that our model overcomes w.r.t. two evaluation metrics the recommendation of models solely based on low-rank information, graph-based information or a combination of both.

This report presents an algorithm for the solution of multiple kernel learning (MKL) problems with elastic-net constraints on the kernel weights. Please see Sun et al. (2013) and Yang et al. (2011) for a review on multiple kernel learning and its extensions. In particular Yang et al. (2011) introduced the generalized multiple kernel learning (GMKL) model where the kernel weights are subject to elastic-net constraints. While Xu et al. (2010) presents an elegant algorithm to solve MKL problems with L