We present Confidence-Based Autonomy (CBA), an interactive algorithm for policy learning from demonstration. The CBA algorithm consists of two components which take advantage of the complimentary abilities of humans and computer agents. The first component, Confident Execution, enables the agent to identify states in which demonstration is required, to request a demonstration from the human teacher and to learn a policy based on the acquired data. The algorithm selects demonstrations based on a measure of action selection confidence, and our results show that using Confident Execution the agent requires fewer demonstrations to learn the policy than when demonstrations are selected by a human teacher. The second algorithmic component, Corrective Demonstration, enables the teacher to correct any mistakes made by the agent through additional demonstrations in order to improve the policy and future task performance. CBA and its individual components are compared and evaluated in a complex simulated driving domain. The complete CBA algorithm results in the best overall learning performance, successfully reproducing the behavior of the teacher while balancing the tradeoff between number of demonstrations and number of incorrect actions during learning.

We develop a technique for deriving data-dependent error bounds for transductive learning algorithms based on transductive Rademacher complexity. Our technique is based on a novel general error bound for transduction in terms of transductive Rademacher complexity, together with a novel bounding technique for Rademacher averages for particular algorithms, in terms of their "unlabeled-labeled" representation. This technique is relevant to many advanced graph-based transductive algorithms and we demonstrate its effectiveness by deriving error bounds to three well known algorithms. Finally, we present a new PAC-Bayesian bound for mixtures of transductive algorithms based on our Rademacher bounds.

We present an efficient algorithm for the inference of stochastic block models in large networks. The algorithm can be used as an optimized Markov chain Monte Carlo (MCMC) method, with a fast mixing time and a much reduced susceptibility to getting trapped in metastable states, or as a greedy agglomerative heuristic, with an almost linear $O(N\ln^2N)$ complexity, where $N$ is the number of nodes in the network, independent on the number of blocks being inferred. We show that the heuristic is capable of delivering results which are indistinguishable from the more exact and numerically expensive MCMC method in many artificial and empirical networks, despite being much faster. The method is entirely unbiased towards any specific mixing pattern, and in particular it does not favor assortative community structures.

A set of probabilistic predictions is well calibrated if the events that are predicted to occur with probability p do in fact occur about p fraction of the time. Well calibrated predictions are particularly important when machine learning models are used in decision analysis. This paper presents two new non-parametric methods for calibrating outputs of binary classification models: a method based on the Bayes optimal selection and a method based on the Bayesian model averaging. The advantage of these methods is that they are independent of the algorithm used to learn a predictive model, and they can be applied in a post-processing step, after the model is learned. This makes them applicable to a wide variety of machine learning models and methods. These calibration methods, as well as other methods, are tested on a variety of datasets in terms of both discrimination and calibration performance. The results show the methods either outperform or are comparable in performance to the state-of-the-art calibration methods.

We assume data sampled from a mixture of d-dimensional linear subspaces with spherically symmetric distributions within each subspace and an additional outlier component with spherically symmetric distribution within the ambient space (for simplicity we may assume that all distributions are uniform on their corresponding unit spheres). We also assume mixture weights for the different components. We say that one of the underlying subspaces of the model is most significant if its mixture weight is higher than the sum of the mixture weights of all other subspaces. We study the recovery of the most significant subspace by minimizing the lp-averaged distances of data points from d-dimensional subspaces, where p>0. Unlike other lp minimization problems, this minimization is non-convex for all p>0 and thus requires different methods for its analysis. We show that if 01 and there is more than one underlying subspace, then with overwhelming probability the most significant subspace cannot be recovered or nearly recovered. This last result does not require spherically symmetric outliers.

Accurate time series prediction over long future horizons is challenging and of great interest to both practitioners and academics. As a well-known intelligent algorithm, the standard formulation of Support Vector Regression (SVR) could be taken for multi-step-ahead time series prediction, only relying either on iterated strategy or direct strategy. This study proposes a novel multiple-step-ahead time series prediction approach which employs multiple-output support vector regression (M-SVR) with multiple-input multiple-output (MIMO) prediction strategy. In addition, the rank of three leading prediction strategies with SVR is comparatively examined, providing practical implications on the selection of the prediction strategy for multi-step-ahead forecasting while taking SVR as modeling technique. The proposed approach is validated with the simulated and real datasets. The quantitative and comprehensive assessments are performed on the basis of the prediction accuracy and computational cost. The results indicate that: 1) the M-SVR using MIMO strategy achieves the best accurate forecasts with accredited computational load, 2) the standard SVR using direct strategy achieves the second best accurate forecasts, but with the most expensive computational cost, and 3) the standard SVR using iterated strategy is the worst in terms of prediction accuracy, but with the least computational cost.

It is the main goal of this paper to propose a novel method to perform matrix completion on-line. Motivated by a wide variety of applications, ranging from the design of recommender systems to sensor network localization through seismic data reconstruction, we consider the matrix completion problem when entries of the matrix of interest are observed gradually. Precisely, we place ourselves in the situation where the predictive rule should be refined incrementally, rather than recomputed from scratch each time the sample of observed entries increases. The extension of existing matrix completion methods to the sequential prediction context is indeed a major issue in the Big Data era, and yet little addressed in the literature. The algorithm promoted in this article builds upon the Soft Impute approach introduced in Mazumder et al. (2010). The major novelty essentially arises from the use of a randomised technique for both computing and updating the Singular Value Decomposition (SVD) involved in the algorithm. Though of disarming simplicity, the method proposed turns out to be very efficient, while requiring reduced computations. Several numerical experiments based on real datasets illustrating its performance are displayed, together with preliminary results giving it a theoretical basis.

The least absolute shrinkage and selection operator (lasso) and ridge regression produce usually different estimates although input, loss function and parameterization of the penalty are identical. In this paper we look for ridge and lasso models with identical solution set. It turns out, that the lasso model with shrink vector $\lambda$ and a quadratic penalized model with shrink matrix as outer product of $\lambda$ with itself are equivalent, in the sense that they have equal solutions. To achieve this, we have to restrict the estimates to be positive. This doesn't limit the area of application since we can easily decompose every estimate in a positive and negative part. The resulting problem can be solved with a non negative least square algorithm. Beside this quadratic penalized model, an augmented regression model with positive bounded estimates is developed which is also equivalent to the lasso model, but is probably faster to solve.

A new shrinkage-based construction is developed for a compressible vector $\boldsymbol{x}\in\mathbb{R}^n$, for cases in which the components of $\xv$ are naturally associated with a tree structure. Important examples are when $\xv$ corresponds to the coefficients of a wavelet or block-DCT representation of data. The method we consider in detail, and for which numerical results are presented, is based on increments of a gamma process. However, we demonstrate that the general framework is appropriate for many other types of shrinkage priors, all within the L\'{e}vy process family, with the gamma process a special case. Bayesian inference is carried out by approximating the posterior with samples from an MCMC algorithm, as well as by constructing a heuristic variational approximation to the posterior. We also consider expectation-maximization (EM) for a MAP (point) solution. State-of-the-art results are manifested for compressive sensing and denoising applications, the latter with spiky (non-Gaussian) noise.

This paper provides a new unimodality test with application in hierarchical clustering methods. The proposed method denoted by signature test (Sigtest), transforms the data based on its statistics. The transformed data has much smaller variation compared to the original data and can be evaluated in a simple proposed unimodality test. Compared with the existing unimodality tests, Sigtest is more accurate in detecting the overlapped clusters and has a much less computational complexity. Simulation results demonstrate the efficiency of this statistic test for both real and synthetic data sets.