Fully supervised learning demands tight supervision of large amounts of data, a supervision that can be quite costly to acquire and constrains the scope of applications. To overcome this bottleneck, the machine learning community is seeking to incorporate weaker sources of information in the learning framework. In this paper, we address those limitations through partial labelling: e.g., giving only partial ordering when learning user preferences over items, or providing the label "flower" for a picture of Arum Lilies 1, instead of spending a consequent amount of time to find the exact taxonomy. Partial labelling has been studied in the context of classification Cour et al. (2011); Nguyen and Caruana (2008), multilabelling Yu et al. (2014), ranking Hüllermeier et al. (2008); Korba et al. (2018), as well as segmentation Verbeek and Triggs (2008); Papandreou et al. (2015), however a generic framework is still missing. Such a framework is a crucial step towards understanding how to learn from weaker sources of information, and widening the spectrum of machine learning beyond rigid applications of supervised learning. Some interesting directions are provided by Cid-Sueiro et al. (2014); van Rooyen and Williamson (2017), to recover the information lost in a corrupt acquisition of labels. Yet, they assume that the corruption process is known, which is a strong requirement that we want to relax. In this paper, we make the following contributions: - We provide a principled framework to solve the problem of learning with partial labelling, via structured prediction. This approach naturally leads to a variational framework built on the infimum loss.

Uncertainty estimation is important for ensuring safety and robustness of AI systems, especially for high-risk applications. While much progress has recently been made in this area, most research has focused on un-structured prediction, such as image classification and regression tasks. However, while task-specific forms of confidence score estimation have been investigated by the speech and machine translation communities, limited work has investigated general uncertainty estimation approaches for structured prediction. Thus, this work aims to investigate uncertainty estimation for structured prediction tasks within a single unified and interpretable probabilistic ensemble-based framework. We consider uncertainty estimation for sequence data at the token-level and complete sequence-level, provide interpretations for, and applications of, various measures of uncertainty and discuss the challenges associated with obtaining them. This work also explores the practical challenges associated with obtaining uncertainty estimates for structured predictions tasks and provides baselines for token-level error detection, sequence-level prediction rejection, and sequence-level out-of-domain input detection using ensembles of auto-regressive transformer models trained on the WMT'14 English-French and WMT'17 English-German translation and LibriSpeech speech recognition datasets.

The success of Artificial Intelligence (AI) should be largely attributed to the accessibility of abundant data. However, this is not exactly the case in reality, where it is common for developers in industry to face insufficient, incomplete and isolated data. Consequently, federated learning was proposed to alleviate such challenges by allowing multiple parties to collaboratively build machine learning models without explicitly sharing their data and in the meantime, preserve data privacy. However, existing algorithms of federated learning mainly focus on examples where, either the data do not require explicit labeling, or all data are labeled. Yet in reality, we are often confronted with the case that labeling data itself is costly and there is no sufficient supply of labeled data. While such issues are commonly solved by semi-supervised learning, to the best of knowledge, no existing effort has been put to federated semi-supervised learning. In this survey, we briefly summarize prevalent semi-supervised algorithms and make a brief prospect into federated semi-supervised learning, including possible methodologies, settings and challenges.

Machine learning systems must adapt to data distributions that evolve over time, in applications ranging from sensor networks and self-driving car perception modules to brain-machine interfaces. We consider gradual domain adaptation, where the goal is to adapt an initial classifier trained on a source domain given only unlabeled data that shifts gradually in distribution towards a target domain. We prove the first non-vacuous upper bound on the error of self-training with gradual shifts, under settings where directly adapting to the target domain can result in unbounded error. The theoretical analysis leads to algorithmic insights, highlighting that regularization and label sharpening are essential even when we have infinite data, and suggesting that self-training works particularly well for shifts with small Wasserstein-infinity distance. Leveraging the gradual shift structure leads to higher accuracies on a rotating MNIST dataset and a realistic Portraits dataset.

Methods for taking into account external knowledge in Machine Learning models have the potential to address outstanding issues in data-driven AI methods, such as improving safety and fairness, and can simplify training in the presence of scarce data. We propose a simple, but effective, method for injecting constraints at training time in supervised learning, based on decomposition and bi-level optimization: a master step is in charge of enforcing the constraints, while a learner step takes care of training the model. The process leads to approximate constraint satisfaction. The method is applicable to any ML approach for which the concept of label (or target) is well defined (most regression and classification scenarios), and allows to reuse existing training algorithms with no modifications. We require no assumption on the constraints, although their properties affect the shape and complexity of the master problem. Convergence guarantees are hard to provide, but we found that the approach performs well on ML tasks with fairness constraints and on classical datasets with synthetic constraints.

We study the linear subspace fitting problem in the overparameterized setting, where the estimated subspace can perfectly interpolate the training examples. Our scope includes the least-squares solutions to subspace fitting tasks with varying levels of supervision in the training data (i.e., the proportion of input-output examples of the desired low-dimensional mapping) and orthonormality of the vectors defining the learned operator. This flexible family of problems connects standard, unsupervised subspace fitting that enforces strict orthonormality with a corresponding regression task that is fully supervised and does not constrain the linear operator structure. This class of problems is defined over a supervision-orthonormality plane, where each coordinate induces a problem instance with a unique pair of supervision level and softness of orthonormality constraints. We explore this plane and show that the generalization errors of the corresponding subspace fitting problems follow double descent trends as the settings become more supervised and less orthonormally constrained.

Positive-unlabeled (PU) learning trains a binary classifier using only positive and unlabeled data. A common simplifying assumption is that the positive data is representative of the target positive class. This assumption is often violated in practice due to time variation, domain shift, or adversarial concept drift. This paper shows that PU learning is possible even with arbitrarily non-representative positive data when provided unlabeled datasets from the source and target distributions. Our key insight is that only the negative class's distribution need be fixed. We propose two methods to learn under such arbitrary positive bias. The first couples negative-unlabeled (NU) learning with unlabeled-unlabeled (UU) learning while the other uses a novel recursive risk estimator robust to positive shift. Experimental results demonstrate our methods' effectiveness across numerous real-world datasets and forms of positive data bias, including disjoint positive class-conditional supports.

The quality of a graph is determined jointly by three key factors of the graph: nodes, edges and similarity measure (or edge weights), and is very crucial to the success of graph-based semi-supervised learning (SSL) approaches. Recently, dynamic graph, which means part/all its factors are dynamically updated during the training process, has demonstrated to be promising for graph-based semi-supervised learning. However, existing approaches only update part of the three factors and keep the rest manually specified during the learning stage. In this paper, we propose a novel graph-based semi-supervised learning approach to optimize all three factors simultaneously in an end-to-end learning fashion. To this end, we concatenate two neural networks (feature network and similarity network) together to learn the categorical label and semantic similarity, respectively, and train the networks to minimize a unified SSL objective function. We also introduce an extended graph Laplacian regularization term to increase training efficiency. Extensive experiments on several benchmark datasets demonstrate the effectiveness of our approach.

In a supervised learning setting, we have a yardstick or plumbline to judge how well we are doing: the response itself. A frequent question in biological and biomedical applications is whether a property of interest (say, disease type, cell type, the prognosis of a patient) can be "predicted", given one or more other properties, called the predictors. Often we are motivated by a situation in which the property to be predicted is unknown (it lies in the future, or is hard to measure), while the predictors are known. The crucial point is that we learn the prediction rule from a set of training data in which the property of interest is also known. Once we have the rule, we can either apply it to new data, and make actual predictions of unknown outcomes; or we can dissect the rule with the aim of better understanding the underlying biology. Compared to unsupervised learning and what we have seen in Chapters 5, 7 and 9, where we do not know what we are looking for or how to decide whether our result is "right", we are on much more solid ground with supervised learning: the objective is clearly stated, and there are straightforward criteria to measure how well we are doing. The central issues in supervised learning151151 Sometimes the term statistical learning is used, more or less exchangeably. Or did our rule indeed pick up some of the pertinent patterns in the system being studied, which will also apply to yet unseen new data? An example for overfitting: two regression lines are fit to data in the \((x, y)\)-plane (black points). We can think of such a line as a rule that predicts the \(y\)-value, given an \(x\)-value. Both lines are smooth, but the fits differ in what is called their bandwidth, which intuitively can be interpreted their stiffness. The blue line seems overly keen to follow minor wiggles in the data, while the orange line captures the general trend but is less detailed. The effective number of parameters needed to describe the blue line is much higher than for the orange line. Also, if we were to obtain additional data, it is likely that the blue line would do a worse job than the orange line in modeling the new data. We'll formalize these concepts –training error and test set error– later in this chapter. Although exemplified here with line fitting, the concept applies more generally to prediction models. See exemplary applications that motivate the use of supervised learning methods.

As a newly emerging unsupervised learning paradigm, self-supervised learning (SSL) recently gained widespread attention, which usually introduces a pretext task without manual annotation of data. With its help, SSL effectively learns the feature representation beneficial for downstream tasks. Thus the pretext task plays a key role. However, the study of its design, especially its essence currently is still open. In this paper, we borrow a multi-view perspective to decouple a class of popular pretext tasks into a combination of view data augmentation (VDA) and view label classification (VLC), where we attempt to explore the essence of such pretext task while providing some insights into its design. Specifically, a simple multi-view learning framework is specially designed (SSL-MV), which assists the feature learning of downstream tasks (original view) through the same tasks on the augmented views. SSL-MV focuses on VDA while abandons VLC, empirically uncovering that it is VDA rather than generally considered VLC that dominates the performance of such SSL. Additionally, thanks to replacing VLC with VDA tasks, SSL-MV also enables an integrated inference combining the predictions from the augmented views, further improving the performance. Experiments on several benchmark datasets demonstrate its advantages.