We propose a new algorithm to learn a dictionary for reconstructing and sparsely encoding signals from measurements without phase. Specifically, we consider the task of estimating a two-dimensional image from squared-magnitude measurements of a complex-valued linear transformation of the original image. Several recent phase retrieval algorithms exploit underlying sparsity of the unknown signal in order to improve recovery performance. In this work, we consider such a sparse signal prior in the context of phase retrieval, when the sparsifying dictionary is not known in advance. Our algorithm jointly reconstructs the unknown signal - possibly corrupted by noise - and learns a dictionary such that each patch of the estimated image can be sparsely represented. Numerical experiments demonstrate that our approach can obtain significantly better reconstructions for phase retrieval problems with noise than methods that cannot exploit such "hidden" sparsity. Moreover, on the theoretical side, we provide a convergence result for our method.

In accessibility tests for digital preservation, over time we experience drifts of localized and labelled content in statistical models of evolving semantics represented as a vector field. This articulates the need to detect, measure, interpret and model outcomes of knowledge dynamics. To this end we employ a high-performance machine learning algorithm for the training of extremely large emergent self-organizing maps for exploratory data analysis. The working hypothesis we present here is that the dynamics of semantic drifts can be modeled on a relaxed version of Newtonian mechanics called social mechanics. By using term distances as a measure of semantic relatedness vs. their PageRank values indicating social importance and applied as variable `term mass', gravitation as a metaphor to express changes in the semantic content of a vector field lends a new perspective for experimentation. From `term gravitation' over time, one can compute its generating potential whose fluctuations manifest modifications in pairwise term similarity vs. social importance, thereby updating Osgood's semantic differential. The dataset examined is the public catalog metadata of Tate Galleries, London.

This paper studies the classification of high-dimensional Gaussian signals from low-dimensional noisy, linear measurements. In particular, it provides upper bounds (sufficient conditions) on the number of measurements required to drive the probability of misclassification to zero in the low-noise regime, both for random measurements and designed ones. Such bounds reveal two important operational regimes that are a function of the characteristics of the source: i) when the number of classes is less than or equal to the dimension of the space spanned by signals in each class, reliable classification is possible in the low-noise regime by using a one-vs-all measurement design; ii) when the dimension of the spaces spanned by signals in each class is lower than the number of classes, reliable classification is guaranteed in the low-noise regime by using a simple random measurement design. Simulation results both with synthetic and real data show that our analysis is sharp, in the sense that it is able to gauge the number of measurements required to drive the misclassification probability to zero in the low-noise regime.

We develop a unified and systematic framework for performing online nonnegative matrix factorization under a wide variety of important divergences. The online nature of our algorithm makes it particularly amenable to large-scale data. We prove that the sequence of learned dictionaries converges almost surely to the set of critical points of the expected loss function. We do so by leveraging the theory of stochastic approximations and projected dynamical systems. This result substantially generalizes the previous results obtained only for the squared-$\ell_2$ loss. Moreover, the novel techniques involved in our analysis open new avenues for analyzing similar matrix factorization problems. The computational efficiency and the quality of the learned dictionary of our algorithm are verified empirically on both synthetic and real datasets. In particular, on the tasks of topic learning, shadow removal and image denoising, our algorithm achieves superior trade-offs between the quality of learned dictionary and running time over the batch and other online NMF algorithms.

COCO is a platform for Comparing Continuous Optimizers in a black-box setting. It aims at automatizing the tedious and repetitive task of benchmarking numerical optimization algorithms to the greatest possible extent. We present the rationals behind the development of the platform as a general proposition for a guideline towards better benchmarking. We detail underlying fundamental concepts of COCO such as its definition of a problem, the idea of instances, the relevance of target values, and runtime as central performance measure. Finally, we give a quick overview of the basic code structure and the available test suites.

In this article the package High-dimensional Metrics (\texttt{hdm}) is introduced. It is a collection of statistical methods for estimation and quantification of uncertainty in high-dimensional approximately sparse models. It focuses on providing confidence intervals and significance testing for (possibly many) low-dimensional subcomponents of the high-dimensional parameter vector. Efficient estimators and uniformly valid confidence intervals for regression coefficients on target variables (e.g., treatment or policy variable) in a high-dimensional approximately sparse regression model, for average treatment effect (ATE) and average treatment effect for the treated (ATET), as well for extensions of these parameters to the endogenous setting are provided. Theory grounded, data-driven methods for selecting the penalization parameter in Lasso regressions under heteroscedastic and non-Gaussian errors are implemented. Moreover, joint/ simultaneous confidence intervals for regression coefficients of a high-dimensional sparse regression are implemented. Data sets which have been used in the literature and might be useful for classroom demonstration and for testing new estimators are included.

This paper identifies a problem with the usual procedure for L2-regularization parameter estimation in a domain adaptation setting. In such a setting, there are differences between the distributions generating the training data (source domain) and the test data (target domain). The usual cross-validation procedure requires validation data, which can not be obtained from the unlabeled target data. The problem is that if one decides to use source validation data, the regularization parameter is underestimated. One possible solution is to scale the source validation data through importance weighting, but we show that this correction is not sufficient. We conclude the paper with an empirical analysis of the effect of several importance weight estimators on the estimation of the regularization parameter.

The Event Calculus is a temporal logic that has been used as a basis in event recognition applications, providing among others, direct connections to machine learning, via Inductive Logic Programming (ILP). We present an ILP system for online learning of Event Calculus theories. To allow for a single-pass learning strategy, we use the Hoeffding bound for evaluating clauses on a subset of the input stream. We employ a decoupling scheme of the Event Calculus axioms during the learning process, that allows to learn each clause in isolation. Moreover, we use abductive-inductive logic programming techniques to handle unobserved target predicates. We evaluate our approach on an activity recognition application and compare it to a number of batch learning techniques. We obtain results of comparable predicative accuracy with significant speed-ups in training time. We also outperform hand-crafted rules and match the performance of a sound incremental learner that can only operate on noise-free datasets. This paper is under consideration for acceptance in TPLP.

Many aspects of the design of efficient crowdsourcing processes, such as defining workers bonuses, fair prices and time limits of the tasks, involve knowledge of the likely duration of the task at hand. In this work we introduce a new timesensitive Bayesian aggregation method that simultaneously estimates a tasks duration and obtains reliable aggregations of crowdsourced judgments. Our method, called BCCTime, uses latent variables to represent the uncertainty about the workers completion time, the tasks duration and the workers accuracy. To relate the quality of a judgment to the time a worker spends on a task, our model assumes that each task is completed within a latent time window within which all workers with a propensity to genuinely attempt the labelling task (i.e., no spammers) are expected to submit their judgments. In contrast, workers with a lower propensity to valid labelling, such as spammers, bots or lazy labellers, are assumed to perform tasks considerably faster or slower than the time required by normal workers. Specifically, we use efficient message-passing Bayesian inference to learn approximate posterior probabilities of (i) the confusion matrix of each worker, (ii) the propensity to valid labelling of each worker, (iii) the unbiased duration of each task and (iv) the true label of each task. Using two real- world public datasets for entity linking tasks, we show that BCCTime produces up to 11% more accurate classifications and up to 100% more informative estimates of a tasks duration compared to stateoftheart methods.

Preterm births occur at an alarming rate of 10-15%. Preemies have a higher risk of infant mortality, developmental retardation and long-term disabilities. Predicting preterm birth is difficult, even for the most experienced clinicians. The most well-designed clinical study thus far reaches a modest sensitivity of 18.2-24.2% at specificity of 28.6-33.3%. We take a different approach by exploiting databases of normal hospital operations. We aims are twofold: (i) to derive an easy-to-use, interpretable prediction rule with quantified uncertainties, and (ii) to construct accurate classifiers for preterm birth prediction. Our approach is to automatically generate and select from hundreds (if not thousands) of possible predictors using stability-aware techniques. Derived from a large database of 15,814 women, our simplified prediction rule with only 10 items has sensitivity of 62.3% at specificity of 81.5%.