The study of representations invariant to common transformations of the data is important to learning. Most techniques have focused on local approximate invariance implemented within expensive optimization frameworks lacking explicit theoretical guarantees. In this paper, we study kernels that are invariant to the unitary group while having theoretical guarantees in addressing practical issues such as (1) unavailability of transformed versions of labelled data and (2) not observing all transformations. We present a theoretically motivated alternate approach to the invariant kernel SVM. Unlike previous approaches to the invariant SVM, the proposed formulation solves both issues mentioned. We also present a kernel extension of a recent technique to extract linear unitary-group invariant features addressing both issues and extend some guarantees regarding invariance and stability. We present experiments on the UCI ML datasets to illustrate and validate our methods.

Parallel sentences are a relatively scarce but extremely useful resource for many applications including cross-lingual retrieval and statistical machine translation. This research explores our new methodologies for mining such data from previously obtained comparable corpora. The task is highly practical since non-parallel multilingual data exist in far greater quantities than parallel corpora, but parallel sentences are a much more useful resource. Here we propose a web crawling method for building subject-aligned comparable corpora from e.g. Wikipedia dumps and Euronews web page. The improvements in machine translation are shown on Polish-English language pair for various text domains. We also tested another method of building parallel corpora based on comparable corpora data. It lets automatically broad existing corpus of sentences from subject of corpora based on analogies between them.

Martin Jaggi Dept. of Computer Science ETH Zürich, Switzerland The Frank-Wolfe (FW) optimization algorithm has lately regained popularity thanks in particular to its ability to nicely handle the structured constraints appearing in machine learning applications. However, its convergence rate is known to be slow (sublinear) when the solution lies at the boundary. A simple lessknown fix is to add the possibility to take'away steps' during optimization, an operation that importantly does not require a feasibility oracle. In this paper, we highlight and clarify several variants of the Frank-Wolfe optimization algorithm that have been successfully applied in practice: away-steps FW, pairwise FW, fully-corrective FW and Wolfe's minimum norm point algorithm, and prove for the first time that they all enjoy global linear convergence, under a weaker condition than strong convexity of the objective. The constant in the convergence rate has an elegant interpretation as the product of the (classical) condition number of the function with a novel geometric quantity that plays the role of a'condition number' of the constraint set. We provide pointers to where these algorithms have made a difference in practice, in particular with the flow polytope, the marginal polytope and the base polytope for submodular optimization. The Frank-Wolfe algorithm [9] (also known as conditional gradient) is one of the earliest existing methods for constrained convex optimization, and has seen an impressive revival recently due to its nice properties compared to projected or proximal gradient methods, in particular for sparse optimization and machine learning applications. On the other hand, the classical projected gradient and proximal methods have been known to exhibit a very nice adaptive acceleration property, namely that the the convergence rate becomes linear for strongly convex objective, i.e. that the optimization error of the same algorithm after t iterations will decrease geometrically with O((1 ρ)

Cricket betting is a multi-billion dollar market. Therefore, there is a strong incentive for models that can predict the outcomes of games and beat the odds provided by bookers. The aim of this study was to investigate to what degree it is possible to predict the outcome of cricket matches. The target competition was the English twenty over county cricket cup. The original features alongside engineered features gave rise to more than 500 team and player statistics. The models were optimized firstly with team features only and then both team and player features. The performance of the models was tested over individual seasons from 2009 to 2014 having been trained over previous season data in each case. The optimal model was a simple prediction method combined with complex hierarchical features and was shown to significantly outperform a gambling industry benchmark.

The random forest algorithm, proposed by L. Breiman in 2001, has been extremely successful as a general-purpose classification and regression method. The approach, which combines several randomized decision trees and aggregates their predictions by averaging, has shown excellent performance in settings where the number of variables is much larger than the number of observations. Moreover, it is versatile enough to be applied to large-scale problems, is easily adapted to various ad-hoc learning tasks, and returns measures of variable importance. The present article reviews the most recent theoretical and methodological developments for random forests. Emphasis is placed on the mathematical forces driving the algorithm, with special attention given to the selection of parameters, the resampling mechanism, and variable importance measures. This review is intended to provide non-experts easy access to the main ideas.

Motivated by online advertising auctions, we consider repeated Vickrey auctions where goods of unknown value are sold sequentially and bidders only learn (potentially noisy) information about a good's value once it is purchased. We adopt an online learning approach with bandit feedback to model this problem and derive bidding strategies for two models: stochastic and adversarial. In the stochastic model, the observed values of the goods are random variables centered around the true value of the good. In this case, logarithmic regret is achievable when competing against well behaved adversaries. In the adversarial model, the goods need not be identical and we simply compare our performance against that of the best fixed bid in hindsight. We show that sublinear regret is also achievable in this case and prove matching minimax lower bounds. To our knowledge, this is the first complete set of strategies for bidders participating in auctions of this type.

The paradigm of multi-task learning is that one can achieve better generalization by learning tasks jointly and thus exploiting the similarity between the tasks rather than learning them independently of each other. While previously the relationship between tasks had to be user-defined in the form of an output kernel, recent approaches jointly learn the tasks and the output kernel. As the output kernel is a positive semidefinite matrix, the resulting optimization problems are not scalable in the number of tasks as an eigendecomposition is required in each step. Using the theory of positive semidefinite kernels we show in this paper that for a certain class of regularizers on the output kernel, the constraint of being positive semidefinite can be dropped as it is automatically satisfied for the relaxed problem. This leads to an unconstrained dual problem which can be solved efficiently. Experiments on several multi-task and multi-class data sets illustrate the efficacy of our approach in terms of computational efficiency as well as generalization performance.

Expectation propagation (EP) is a deterministic approximation algorithm that is often used to perform approximate Bayesian parameter learning. EP approximates the full intractable posterior distribution through a set of local approximations that are iteratively refined for each datapoint. EP can offer analytic and computational advantages over other approximations, such as Variational Inference (VI), and is the method of choice for a number of models. The local nature of EP appears to make it an ideal candidate for performing Bayesian learning on large models in large-scale dataset settings. However, EP has a crucial limitation in this context: the number of approximating factors needs to increase with the number of data-points, N, which often entails a prohibitively large memory overhead. This paper presents an extension to EP, called stochastic expectation propagation (SEP), that maintains a global posterior approximation (like VI) but updates it in a local way (like EP). Experiments on a number of canonical learning problems using synthetic and real-world datasets indicate that SEP performs almost as well as full EP, but reduces the memory consumption by a factor of $N$. SEP is therefore ideally suited to performing approximate Bayesian learning in the large model, large dataset setting.

Spoken language translation (SLT) has become very important in an increasingly globalized world. Machine translation (MT) for automatic speech recognition (ASR) systems is a major challenge of great interest. This research investigates that automatic sentence segmentation of speech that is important for enriching speech recognition output and for aiding downstream language processing. This article focuses on the automatic sentence segmentation of speech and improving MT results. We explore the problem of identifying sentence boundaries in the transcriptions produced by automatic speech recognition systems in the Polish language. We also experiment with reverse normalization of the recognized speech samples.

We propose a simple method to learn linear causal cyclic models in the presence of latent variables. The method relies on equilibrium data of the model recorded under a specific kind of interventions ("shift interventions"). The location and strength of these interventions do not have to be known and can be estimated from the data. Our method, called backShift, only uses second moments of the data and performs simple joint matrix diagonalization, applied to differences between covariance matrices. We give a sufficient and necessary condition for identifiability of the system, which is fulfilled almost surely under some quite general assumptions if and only if there are at least three distinct experimental settings, one of which can be pure observational data. We demonstrate the performance on some simulated data and applications in flow cytometry and financial time series. The code is made available as R-package backShift.