Manifold regularization is a commonly used technique in semi-supervised learning. It enforces the classification rule to be smooth with respect to the data-manifold. Here, we derive sample complexity bounds based on pseudo-dimension for models that add a convex data dependent regularization term to a supervised learning process, as is in particular done in Manifold regularization. We then compare the bound for those semi-supervised methods to purely supervised methods, and discuss a setting in which the semi-supervised method can only have a constant improvement, ignoring logarithmic terms. By viewing Manifold regularization as a kernel method we then derive Rademacher bounds which allow for a distribution dependent analysis. Finally we illustrate that these bounds may be useful for choosing an appropriate manifold regularization parameter in situations with very sparsely labeled data.@en

Learning performance can show non-monotonic behavior. That is, more data does not necessarily lead to better models, even on average. We propose three algorithms that take a supervised learning model and make it perform more monotone. We prove consistency and monotonicity with high probability, and evaluate the algorithms on scenarios where non-monotone behaviour occurs. Our proposed algorithm MT_HT makes less than 1% non-monotone decisions on MNIST while staying competitive in terms of error rate compared to several baselines. Our code is available at https://github.com/tomviering/monotone.

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Large text corpora used for creating word embeddings (vectors which represent word meanings) often contain stereotypical gender biases. As a result, such unwanted biases will typically also be present in word embeddings derived from such corpora and downstream applications in the field of natural language processing (NLP). To minimize the effect of gender bias in these settings, more insight is needed when it comes to where and how biases manifest themselves in the text corpora employed. This paper contributes by showing how gender bias in word embeddings from Wikipedia has developed over time. Quantifying the gender bias over time shows that art related words have become more female biased. Family and science words have stereotypical biases towards respectively female and male words. These biases seem to have decreased since 2006, but these changes are not more extreme than those seen in random sets of words. Career related words are more strongly associated with male than with female, this difference has only become smaller in recently written articles. These developments provide additional understanding of what can be done to make Wikipedia more gender neutral and how important time of writing can be when considering biases in word embeddings trained from Wikipedia or from other text corpora.@en

Plotting a learner’s average performance against the number of training samples results in a learning curve. Studying such curves on one or more data sets is a way to get to a better understanding of the generalization properties of this learner. The behavior of learning curves is, however, not very well understood and can display (for most researchers) quite unexpected behavior. Our work introduces the formal notion of risk monotonicity, which asks the risk to not deteriorate with increasing training set sizes in expectation over the training samples. We then present the surprising result that various standard learners, specifically those that minimize the empirical risk, can act nonmonotonically irrespective of the training sample size. We provide a theoretical underpinning for specific instantiations from classification, regression, and density estimation. Altogether, the proposed monotonicity notion opens up a whole new direction of research. @en

Active learning algorithms propose what data should be labeled given a pool of unlabeled data. Instead of selecting randomly what data to annotate, active learning strategies aim to select data so as to get a good predictive model with as little labeled samples as possible. Single-shot batch active learners select all samples to be labeled in a single step, before any labels are observed.We study single-shot active learners that minimize generalization bounds to select a representative sample, such as the maximum mean discrepancy (MMD) active learner.We prove that a related bound, the discrepancy, provides a tighter worst-case bound. We study these bounds probabilistically, which inspires us to introduce a novel bound, the nuclear discrepancy (ND). The ND bound is tighter for the expected loss under optimistic probabilistic assumptions. Our experiments show that the MMD active learner performs better than the discrepancy in terms of the mean squared error, indicating that tighter worst case bounds do not imply better active learning performance. The proposed active learner improves significantly upon the MMD and discrepancy in the realizable setting and a similar trend is observed in the agnostic setting, showing the benefits of a probabilistic approach to active learning. Our study highlights that assumptions underlying generalization bounds can be equally important as bound-tightness, when it comes to active learning performance. Code for reproducing our experimental results can be found at https://github.com/tomviering/ NuclearDiscrepancy. @en