We consider a distributed learning setup where a network of agents sequentially access realizations of a set of random variables with unknown distributions. The network objective is to find a parametrized distribution that best describes their joint observations in the sense of the Kullback-Leibler divergence. Apart from recent efforts in the literature, we analyze the case of countably many hypotheses and the case of a continuum of hypotheses. We provide non-asymptotic bounds for the concentration rate of the agents' beliefs around the correct hypothesis in terms of the number of agents, the network parameters, and the learning abilities of the agents. Additionally, we provide a novel motivation for a general set of distributed Non-Bayesian update rules as instances of the distributed stochastic mirror descent algorithm.

I introduce and analyse an anytime version of the Optimally Confident UCB (OCUCB) algorithm designed for minimising the cumulative regret in finite-armed stochastic bandits with subgaussian noise. The new algorithm is simple, intuitive (in hindsight) and comes with the strongest finite-time regret guarantees for a horizon-free algorithm so far. I also show a finite-time lower bound that nearly matches the upper bound.

Working on the daily closing prices and logreturns, in this paper we deal with the use of Hidden Markov Models (HMMs) to forecast the price of the EUR/USD Futures. The aim of our work is to understand how the HMMs describe different financial time series depending on their structure. Subsequently, we analyse the forecasting methods exposed in the previous literature, putting on evidence their pros and cons.

Subspace clustering methods based on $\ell_1$, $\ell_2$ or nuclear norm regularization have become very popular due to their simplicity, theoretical guarantees and empirical success. However, the choice of the regularizer can greatly impact both theory and practice. For instance, $\ell_1$ regularization is guaranteed to give a subspace-preserving affinity (i.e., there are no connections between points from different subspaces) under broad conditions (e.g., arbitrary subspaces and corrupted data). However, it requires solving a large scale convex optimization problem. On the other hand, $\ell_2$ and nuclear norm regularization provide efficient closed form solutions, but require very strong assumptions to guarantee a subspace-preserving affinity, e.g., independent subspaces and uncorrupted data. In this paper we study a subspace clustering method based on orthogonal matching pursuit. We show that the method is both computationally efficient and guaranteed to give a subspace-preserving affinity under broad conditions. Experiments on synthetic data verify our theoretical analysis, and applications in handwritten digit and face clustering show that our approach achieves the best trade off between accuracy and efficiency.

This study suggests a new prediction model for chaotic time series inspired by the brain emotional learning of mammals. We describe the structure and function of this model, which is referred to as BELPM (Brain Emotional Learning-Based Prediction Model). Structurally, the model mimics the connection between the regions of the limbic system, and functionally it uses weighted k nearest neighbors to imitate the roles of those regions. The learning algorithm of BELPM is defined using steepest descent (SD) and the least square estimator (LSE). Two benchmark chaotic time series, Lorenz and Henon, have been used to evaluate the performance of BELPM. The obtained results have been compared with those of other prediction methods. The results show that BELPM has the capability to achieve a reasonable accuracy for long-term prediction of chaotic time series, using a limited amount of training data and a reasonably low computational time.

We show how to adjust the coefficient of determination ($R^2$) when used for measuring predictive accuracy via leave-one-out cross-validation.

With the recent popularity of graphical clustering methods, there has been an increased focus on the information between samples. We show how learning cluster structure using edge features naturally and simultaneously determines the most likely number of clusters and addresses data scale issues. These results are particularly useful in instances where (a) there are a large number of clusters and (b) we have some labeled edges. Applications in this domain include image segmentation, community discovery and entity resolution. Our model is an extension of the planted partition model and our solution uses results of correlation clustering, which achieves a partition O(log(n))-close to the log-likelihood of the true clustering.

A new method for the unsupervised learning of sparse representations using autoencoders is proposed and implemented by ordering the output of the hidden units by their activation value and progressively reconstructing the input in this order. This can be done efficiently in parallel with the use of cumulative sums and sorting only slightly increasing the computational costs. Minimizing the difference of this progressive reconstruction with respect to the input can be seen as minimizing the number of active output units required for the reconstruction of the input. The model thus learns to reconstruct optimally using the least number of active output units. This leads to high sparsity without the need for extra hyperparameters, the amount of sparsity is instead implicitly learned by minimizing this progressive reconstruction error. Results of the trained model are given for patches of the CIFAR10 dataset, showing rapid convergence of features and extremely sparse output activations while maintaining a minimal reconstruction error and showing extreme robustness to overfitting. Additionally the reconstruction as function of number of active units is presented which shows the autoencoder learns a rank order code over the input where the highest ranked units correspond to the highest decrease in reconstruction error.

We present the recent advances along with an error analysis of the IBM speaker recognition system for conversational speech. Some of the key advancements that contribute to our system include: a nearest-neighbor discriminant analysis (NDA) approach (as opposed to LDA) for intersession variability compensation in the i-vector space, the application of speaker and channel-adapted features derived from an automatic speech recognition (ASR) system for speaker recognition, and the use of a DNN acoustic model with a very large number of output units ( 10k senones) to compute the frame-level soft alignments required in the i-vector estimation process. We evaluate these techniques on the NIST 2010 SRE extended core conditions (C1-C9), as well as the 10sec-10sec condition. To our knowledge, results achieved by our system represent the best performances published to date on these conditions. For example, on the extended tel-tel condition (C5) the system achieves an EER of 0.59%. To garner further understanding of the remaining errors (on C5), we examine the recordings associated with the low scoring target trials, where various issues are identified for the problematic recordings/trials. Interestingly, it is observed that correcting the pathological recordings not only improves the scores for the target trials but also for the nontarget trials.

Controlled interventions provide the most direct source of information for learning causal effects. In particular, a dose-response curve can be learned by varying the treatment level and observing the corresponding outcomes. However, interventions can be expensive and time-consuming. Observational data, where the treatment is not controlled by a known mechanism, is sometimes available. Under some strong assumptions, observational data allows for the estimation of dose-response curves. Estimating such curves nonparametrically is hard: sample sizes for controlled interventions may be small, while in the observational case a large number of measured confounders may need to be marginalized. In this paper, we introduce a hierarchical Gaussian process prior that constructs a distribution over the dose-response curve by learning from observational data, and reshapes the distribution with a nonparametric affine transform learned from controlled interventions. This function composition from different sources is shown to speed-up learning, which we demonstrate with a thorough sensitivity analysis and an application to modeling the effect of therapy on cognitive skills of premature infants.