Semantic mapping (see (Nüchter and Hertzberg, 2008)) is a relatively new field in robotics which aims to give the robot a high-level, human-compatible, understanding of its environment in order to ease the integration of robots in daily environments, notably homes or workplaces. Such environments are usually composed of discrete places which correspond to different functions. For instance a house is usually made of different rooms and corridors used to move between them. Such places are called semantic places because they are defined in high-level human concepts as opposed to traditional low-level landmarks used in robot mapping. In this context, it's important for the robot to be able to recognize in which place or category of places it lies.

Bayesian optimization (Mockus et al., 1978) is a method for performing global optimization of unknown "black box" objectives that is particularly appropriate when objective function evaluations are expensive (in any sense, such as time or money). For example, consider a food company trying to design a low-calorie variant of a popular cookie. In this case, the design space is the space of possible recipes and might include several key parameters such as quantities of various ingredients and baking times. Each evaluation of a recipe entails computing (or perhaps actually measuring) the number of calories in the proposed cookie. Bayesian optimization can be used to propose new candidate recipes such that good results are found with few evaluations. Now suppose the company also wants to ensure the taste of the cookie is not compromised when calories are reduced. Therefore, for each proposed low-calorie recipe, they perform a taste test with sample customers. Because different people, or the same people at different times, have differing opinions about the taste of cookies, the company decides to require that at least 95% of test subjects must like the new cookie.

Communication costs, resulting from synchronization requirements during learning, can greatly slow down many parallel machine learning algorithms. In this paper, we present a parallel Markov chain Monte Carlo (MCMC) algorithm in which subsets of data are processed independently, with very little communication. First, we arbitrarily partition data onto multiple machines. Then, on each machine, any classical MCMC method (e.g., Gibbs sampling) may be used to draw samples from a posterior distribution given the data subset. Finally, the samples from each machine are combined to form samples from the full posterior. This embarrassingly parallel algorithm allows each machine to act independently on a subset of the data (without communication) until the final combination stage. We prove that our algorithm generates asymptotically exact samples and empirically demonstrate its ability to parallelize burn-in and sampling in several models.

We study trend filtering, a recently proposed tool of Kim et al. [SIAM Rev. 51 (2009) 339-360] for nonparametric regression. The trend filtering estimate is defined as the minimizer of a penalized least squares criterion, in which the penalty term sums the absolute $k$th order discrete derivatives over the input points. Perhaps not surprisingly, trend filtering estimates appear to have the structure of $k$th degree spline functions, with adaptively chosen knot points (we say ``appear'' here as trend filtering estimates are not really functions over continuous domains, and are only defined over the discrete set of inputs). This brings to mind comparisons to other nonparametric regression tools that also produce adaptive splines; in particular, we compare trend filtering to smoothing splines, which penalize the sum of squared derivatives across input points, and to locally adaptive regression splines [Ann. Statist. 25 (1997) 387-413], which penalize the total variation of the $k$th derivative. Empirically, we discover that trend filtering estimates adapt to the local level of smoothness much better than smoothing splines, and further, they exhibit a remarkable similarity to locally adaptive regression splines. We also provide theoretical support for these empirical findings; most notably, we prove that (with the right choice of tuning parameter) the trend filtering estimate converges to the true underlying function at the minimax rate for functions whose $k$th derivative is of bounded variation. This is done via an asymptotic pairing of trend filtering and locally adaptive regression splines, which have already been shown to converge at the minimax rate [Ann. Statist. 25 (1997) 387-413]. At the core of this argument is a new result tying together the fitted values of two lasso problems that share the same outcome vector, but have different predictor matrices.

Geographical location is vital to geospatial applications like local search and event detection. In this paper, we investigate and improve on the task of text-based geolocation prediction of Twitter users. Previous studies on this topic have typically assumed that geographical references (e.g., gazetteer terms, dialectal words) in a text are indicative of its authors location. However, these references are often buried in informal, ungrammatical, and multilingual data, and are therefore non-trivial to identify and exploit. We present an integrated geolocation prediction framework and investigate what factors impact on prediction accuracy. First, we evaluate a range of feature selection methods to obtain location indicative words. We then evaluate the impact of non-geotagged tweets, language, and user-declared metadata on geolocation prediction. In addition, we evaluate the impact of temporal variance on model generalisation, and discuss how users differ in terms of their geolocatability. We achieve state-of-the-art results for the text-based Twitter user geolocation task, and also provide the most extensive exploration of the task to date. Our findings provide valuable insights into the design of robust, practical text-based geolocation prediction systems.

We present a supervised-learning algorithm from graph data (a set of graphs) for arbitrary twice-differentiable loss functions and sparse linear models over all possible subgraph features. To date, it has been shown that under all possible subgraph features, several types of sparse learning, such as Adaboost, LPBoost, LARS/LASSO, and sparse PLS regression, can be performed. Particularly emphasis is placed on simultaneous learning of relevant features from an infinite set of candidates. We first generalize techniques used in all these preceding studies to derive an unifying bounding technique for arbitrary separable functions. We then carefully use this bounding to make block coordinate gradient descent feasible over infinite subgraph features, resulting in a fast converging algorithm that can solve a wider class of sparse learning problems over graph data. We also empirically study the differences from the existing approaches in convergence property, selected subgraph features, and search-space sizes. We further discuss several unnoticed issues in sparse learning over all possible subgraph features.

The minimum message length(MML) principle[7] is an information theoretic criterion that links data compression with statistical inference [6]. It has a number of useful properties and it has close connections with Kolmogorov complexity [8]. Using the MML principle to construct estimators is known to be NPhard in general [4] so it is common to use approximations in practice [6]. The term'strict minimum message length' (SMML) is used for the exact MML criterion, to distinguish it from the various approximations. The only known algorithm for calculating an SMML estimator is Farr's algorithm [4] which applies to data taking values in a finite set which is (in some sense) 1-dimensional. A method for calculating SMML estimators for 1-dimensional exponential families with continuous sufficient statistics was also recently given in [3]. However, calculating SMML estimators for higher-dimensional data is still a difficult problem.

In the synthesis model signals are represented as a sparse combinations of atoms from a dictionary. Dictionary learning describes the acquisition process of the underlying dictionary for a given set of training samples. While ideally this would be achieved by optimizing the expectation of the factors over the underlying distribution of the training data, in practice the necessary information about the distribution is not available. Therefore, in real world applications it is achieved by minimizing an empirical average over the available samples. The main goal of this paper is to provide a sample complexity estimate that controls to what extent the empirical average deviates from the cost function. This estimate then provides a suitable estimate to the accuracy of the representation of the learned dictionary. The presented approach exemplifies the general results proposed by the authors in Sample Complexity of Dictionary Learning and other Matrix Factorizations, Gribonval et al. and gives more concrete bounds of the sample complexity of dictionary learning. We cover a variety of sparsity measures employed in the learning procedure.

In big data image/video analytics, we encounter the problem of learning an overcomplete dictionary for sparse representation from a large training dataset, which can not be processed at once because of storage and computational constraints. To tackle the problem of dictionary learning in such scenarios, we propose an algorithm for parallel dictionary learning. The fundamental idea behind the algorithm is to learn a sparse representation in two phases. In the first phase, the whole training dataset is partitioned into small non-overlapping subsets, and a dictionary is trained independently on each small database. In the second phase, the dictionaries are merged to form a global dictionary. We show that the proposed algorithm is efficient in its usage of memory and computational complexity, and performs on par with the standard learning strategy operating on the entire data at a time. As an application, we consider the problem of image denoising. We present a comparative analysis of our algorithm with the standard learning techniques, that use the entire database at a time, in terms of training and denoising performance. We observe that the split-and-merge algorithm results in a remarkable reduction of training time, without significantly affecting the denoising performance.

We consider the problem of minimizing the sum of two convex functions: one is the average of a large number of smooth component functions, and the other is a general convex function that admits a simple proximal mapping. We assume the whole objective function is strongly convex. Such problems often arise in machine learning, known as regularized empirical risk minimization. We propose and analyze a new proximal stochastic gradient method, which uses a multi-stage scheme to progressively reduce the variance of the stochastic gradient. While each iteration of this algorithm has similar cost as the classical stochastic gradient method (or incremental gradient method), we show that the expected objective value converges to the optimum at a geometric rate. The overall complexity of this method is much lower than both the proximal full gradient method and the standard proximal stochastic gradient method.