Supervised learning with large-scale data usually leads to complex optimization problems, especially for classification tasks with multiple classes. Stochastic sub gradient methods can enable efficient learning with a large number of samples for classification techniques that minimize the average loss over the training samples. However, recent techniques, such as minimax risk classifiers (MRCs), minimize the maximum expected loss and are not amenable to stochastic sub gradient methods. In this paper, we present a learning algorithm based on the combination of constraint and column generation that enables efficient learning of MRCs with large-scale data for classification tasks with multiple classes. Experiments on multiple benchmark datasets show that the proposed algorithm provides upto a 10x speedup for general large-scale data and around a 100x speedup with a sizeable number of classes.

Abstract The use of crowdsourcing for annotating data has become a popular and cheap alternative to expert labelling. As a consequence, an aggregation task is required to combine the different labels provided and agree on a single one per example. Most aggregation techniques, including the simple and robust majority voting—to select the label with the largest number of votes—disregard the descriptive information provided by the explanatory variable. In this paper, we propose domain-aware voting, an extension of majority voting which incorporates the descriptive variable and the rest of the instances of the dataset for aggregating the label of every instance. The experimental results with simulated and real-world crowdsourced data suggest that domain-aware voting is a competitive alternative to majority voting, especially when a part of the dataset is unlabelled. We elaborate on practical criteria for the use of domain-aware voting.

In recent years we have seen a handful of work on inference algorithms over non-stationary data streams. Given their flexibility, Bayesian non-parametric models are a good candidate for these scenarios. However, reliable streaming inference under the concept drift phenomenon is still an open problem for these models. In this work, we propose a variational inference algorithm for Dirichlet process mixture models. Our proposal deals with the concept drift by including an exponential forgetting over the prior global parameters. Our algorithm allows to adapt the learned model to the concept drifts automatically. We perform experiments in both synthetic and real data, showing that the proposed model outperforms state-of-the-art variational methods in density estimation, clustering and parameter tracking.

Abstract Statistical tests are a powerful set of tools when applied correctly, but unfortunately the extended misuse of them has caused great concern. Among many other applications, they are used in the detection of biomarkers so as to use the resulting p-values as a reference with which the candidate biomarkers are ranked. Although statistical tests can be used to rank, they have not been designed for that use. Moreover, there is no need to compute any p-value to build a ranking of candidate biomarkers. Those two facts raise the question of whether or not alternative methods which are not based on the computation of statistical tests that match or improve their performances can be proposed. In this paper, we propose two alternative methods to statistical tests. In addition, we propose an evaluation framework to assess both statistical tests and alternative methods in terms of both the performance and the reproducibility. The results indicate that there are alternative methods that can match or surpass methods based on statistical tests in terms of the reproducibility when processing real data, while maintaining a similar performance when dealing with synthetic data. The main conclusion is that there is room for the proposal of such alternative methods.

The$K$-means algorithm is one of the most popular clustering methods. However, it is a well-known fact that its performance, in terms of quality of the obtained solution and computational load, highly depends upon its initialization phase. For this reason, different initialization techniques have been developed throughout the years to enable its fast convergence to competitive solutions. In this sense, it is common practice to re-start the$K$-means algorithm several times via one of these techniques and keep the solution with the lowest error. Unfortunately, such a choice is still likely to be a poor approximation of the optimal set of centroids. In this article, we introduce a cheap Split-Merge step that can be used to re-start the$K$-means algorithm after reaching a fixed point. Under some settings, one can show that this approach reduces the error of the given fixed point without requiring any further iteration of the$K$-means algorithm. Moreover, experimental results show that this strategy is able to generate approximations with an associated error that is hard to reach for different multi-start methods, such as multi-start Forgy$K$-means,$K$-means++ and Hartigan$K$-means, while also computing a lower amount of distances than the previous algorithms.

Nowadays, streaming data analysis has become a relevant area of research in machine learning. Most of the data streams available are unlabeled, and thus it is necessary to develop specific clustering techniques that take into account the particularities of the streaming data. In streaming data scenarios, the data is composed of an increasing sequence of batches of samples where the concept drift phenomenon may occur. In this work, we formally define the streaming K -means (SKM) problem, which implies a restart of the error function when a concept drift occurs. An approximated error function that does not rely on concept drift detection is proposed. We prove that such a surrogate is a good approximation of the SKM error. Then, we introduce an algorithm to deal with SKM problem by minimizing the surrogate error function each time a new batch arrives. Alternative initialization criteria are presented and theoretically analyzed for streaming data scenarios. Among them, we develop and analyze theoretically two initialization methods that search for the best trade-off between the importance that is given to the past and the current batches. The experiments show that the proposed algorithm with, the proposed initialization criteria, obtain the best results when dealing with the SKM problem without requiring to detect when concept drift takes place.