Many learning tasks, such as cross-validation, parameter search, or leave-one-out analysis, involve multiple instances of similar problems, each instance sharing a large part of learning data with the others. We introduce a robust framework for solving multiple square-root LASSO problems, based on a sketch of the learning data that uses low-rank approximations. Our approach allows a dramatic reduction in computational effort, in effect reducing the number of observations from $m$ (the number of observations to start with) to $k$ (the number of singular values retained in the low-rank model), while not sacrificing---sometimes even improving---the statistical performance. Theoretical analysis, as well as numerical experiments on both synthetic and real data, illustrate the efficiency of the method in large scale applications.

When digitizing a print bilingual dictionary, whether via optical character recognition or manual entry, it is inevitable that errors are introduced into the electronic version that is created. We investigate automating the process of detecting errors in an XML representation of a digitized print dictionary using a hybrid approach that combines rule-based, feature-based, and language model-based methods. We investigate combining methods and show that using random forests is a promising approach. We find that in isolation, unsupervised methods rival the performance of supervised methods. Random forests typically require training data so we investigate how we can apply random forests to combine individual base methods that are themselves unsupervised without requiring large amounts of training data. Experiments reveal empirically that a relatively small amount of data is sufficient and can potentially be further reduced through specific selection criteria.

In this paper, an ensemble-based method for the screening of diabetic retinopathy (DR) is proposed. This approach is based on features extracted from the output of several retinal image processing algorithms, such as image-level (quality assessment, pre-screening, AM/FM), lesion-specific (microaneurysms, exudates) and anatomical (macula, optic disc) components. The actual decision about the presence of the disease is then made by an ensemble of machine learning classifiers. We have tested our approach on the publicly available Messidor database, where 90% sensitivity, 91% specificity and 90% accuracy and 0.989 AUC are achieved in a disease/no-disease setting. These results are highly competitive in this field and suggest that retinal image processing is a valid approach for automatic DR screening.

In various situations one is given only the predictions of multiple classifiers over a large unlabeled test data. This scenario raises the following questions: Without any labeled data and without any a-priori knowledge about the reliability of these different classifiers, is it possible to consistently and computationally efficiently estimate their accuracies? Furthermore, also in a completely unsupervised manner, can one construct a more accurate unsupervised ensemble classifier? In this paper, focusing on the binary case, we present simple, computationally efficient algorithms to solve these questions. Furthermore, under standard classifier independence assumptions, we prove our methods are consistent and study their asymptotic error. Our approach is spectral, based on the fact that the off-diagonal entries of the classifiers' covariance matrix and 3-d tensor are rank-one. We illustrate the competitive performance of our algorithms via extensive experiments on both artificial and real datasets.

One of the most fundamental problems in causal inference is the estimation of a causal effect when variables are confounded. This is difficult in an observational study, because one has no direct evidence that all confounders have been adjusted for. We introduce a novel approach for estimating causal effects that exploits observational conditional independencies to suggest "weak" paths in a unknown causal graph. The widely used faithfulness condition of Spirtes et al. is relaxed to allow for varying degrees of "path cancellations" that imply conditional independencies but do not rule out the existence of confounding causal paths. The outcome is a posterior distribution over bounds on the average causal effect via a linear programming approach and Bayesian inference. We claim this approach should be used in regular practice along with other default tools in observational studies.

We give a comprehensive theoretical characterization of a nonparametric estimator for the $L_2^2$ divergence between two continuous distributions. We first bound the rate of convergence of our estimator, showing that it is $\sqrt{n}$-consistent provided the densities are sufficiently smooth. In this smooth regime, we then show that our estimator is asymptotically normal, construct asymptotic confidence intervals, and establish a Berry-Ess\'{e}en style inequality characterizing the rate of convergence to normality. We also show that this estimator is minimax optimal.

Reliable microaneurysm detection in digital fundus images is still an open issue in medical image processing. We propose an ensemble-based framework to improve microaneurysm detection. Unlike the well-known approach of considering the output of multiple classifiers, we propose a combination of internal components of microaneurysm detectors, namely preprocessing methods and candidate extractors. We have evaluated our approach for microaneurysm detection in an online competition, where this algorithm is currently ranked as first and also on two other databases. Since microaneurysm detection is decisive in diabetic retinopathy grading, we also tested the proposed method for this task on the publicly available Messidor database, where a promising AUC 0.90 with 0.01 uncertainty is achieved in a 'DR/non-DR'-type classification based on the presence or absence of the microaneurysms.

We demonstrate that any physical object, as long as its volume is conserved when coupled with suitable operations, provides a sophisticated decision-making capability. We consider the problem of finding, as accurately and quickly as possible, the most profitable option from a set of options that gives stochastic rewards. These decisions are made as dictated by a physical object, which is moved in a manner similar to the fluctuations of a rigid body in a tug-of-war game. Our analytical calculations validate statistical reasons why our method exhibits higher efficiency than conventional algorithms.

Reinforcement learning agents have traditionally been evaluated on small toy problems. With advances in computing power and the advent of the Arcade Learning Environment, it is now possible to evaluate algorithms on diverse and difficult problems within a consistent framework. We discuss some challenges posed by the arcade learning environment which do not manifest in simpler environments. We then provide a comparison of model-free, linear learning algorithms on this challenging problem set.

We introduce a method to learn a hierarchy of successively more abstract representations of complex data based on optimizing an information-theoretic objective. Intuitively, the optimization searches for a set of latent factors that best explain the correlations in the data as measured by multivariate mutual information. The method is unsupervised, requires no model assumptions, and scales linearly with the number of variables which makes it an attractive approach for very high dimensional systems. We demonstrate that Correlation Explanation (CorEx) automatically discovers meaningful structure for data from diverse sources including personality tests, DNA, and human language.