This dissertation investigates the use of one-sided classification algorithms in the application of separating hazardous chlorinated solvents from other materials, based on their Raman spectra. The experimentation is carried out using a new one-sided classification toolkit that was designed and developed from the ground up. In the one-sided classification paradigm, the objective is to separate elements of the target class from all outliers. These one-sided classifiers are generally chosen, in practice, when there is a deficiency of some sort in the training examples. Sometimes outlier examples can be rare, expensive to label, or even entirely absent. However, this author would like to note that they can be equally applicable when outlier examples are plentiful but nonetheless not statistically representative of the complete outlier concept. It is this scenario that is explicitly dealt with in this research work. In these circumstances, one-sided classifiers have been found to be more robust that conventional multi-class classifiers. The term "unexpected" outliers is introduced to represent outlier examples, encountered in the test set, that have been taken from a different distribution to the training set examples. These are examples that are a result of an inadequate representation of all possible outliers in the training set. It can often be impossible to fully characterise outlier examples given the fact that they can represent the immeasurable quantity of "everything else" that is not a target. The findings from this research have shown the potential drawbacks of using conventional multi-class classification algorithms when the test data come from a completely different distribution to that of the training samples.

More than 2,500 women have stripped naked on a beach in the Republic of Ireland to break the world record for the largest skinny dip.

Key to structured prediction is exploiting the problem structure to simplify the learning process. A major challenge arises when data exhibit a local structure (e.g., are made by "parts") that can be leveraged to better approximate the relation between (parts of) the input and (parts of) the output. Recent literature on signal processing, and in particular computer vision, has shown that capturing these aspects is indeed essential to achieve state-of-the-art performance. While such algorithms are typically derived on a case-by-case basis, in this work we propose the first theoretical framework to deal with part-based data from a general perspective. We derive a novel approach to deal with these problems and study its generalization properties within the setting of statistical learning theory. Our analysis is novel in that it explicitly quantifies the benefits of leveraging the part-based structure of the problem with respect to the learning rates of the proposed estimator.

Recently, generative adversarial networks and adversarial autoencoders have gained a lot of attention in machine learning community due to their exceptional performance in tasks such as digit classification and face recognition. They map the autoencoder's bottleneck layer output (termed as code vectors) to different noise Probability Distribution Functions (PDFs), that can be further regularized to cluster based on class information. In addition, they also allow a generation of synthetic samples by sampling the code vectors from the mapped PDFs. Inspired by these properties, we investigate the application of adversarial autoencoders to the domain of emotion recognition. Specifically, we conduct experiments on the following two aspects: (i) their ability to encode high dimensional feature vector representations for emotional utterances into a compressed space (with a minimal loss of emotion class discriminability in the compressed space), and (ii) their ability to regenerate synthetic samples in the original feature space, to be later used for purposes such as training emotion recognition classifiers. We demonstrate the promise of adversarial autoencoders with regards to these aspects on the Interactive Emotional Dyadic Motion Capture (IEMOCAP) corpus and present our analysis.

This paper draws a parallel between similarity-based categorisation models developed in cognitive psychology and the nearest neighbour classifier (1-NN) in machine learning. Conceived as a result of the historical rivalry between prototype theories (abstraction) and exemplar theories (memorisation), recent models of human categorisation seek a compromise in-between. Regarding the stimuli (entities to be categorised) as points in a metric space, machine learning offers a large collection of methods to select a small, representative and discriminative point set. These methods are known under various names: instance selection, data editing, prototype selection, prototype generation or prototype replacement. The nearest neighbour classifier is used with the selected reference set. Such a set can be interpreted as a data-driven categorisation model. We juxtapose the models from the two fields to enable cross-referencing. We believe that both machine learning and cognitive psychology can draw inspiration from the comparison and enrich their repertoire of similarity-based models.

Learning vector embeddings of complex networks is a powerful approach used to predict missing or unobserved edges in network data. However, an open challenge in this area is developing techniques that can reason about $\textit{subgraphs}$ in network data, which can involve the logical conjunction of several edge relationships. Here we introduce a framework to make predictions about conjunctive logical queries---i.e., subgraph relationships---on heterogeneous network data. In our approach, we embed network nodes in a low-dimensional space and represent logical operators as learned geometric operations (e.g., translation, rotation) in this embedding space. We prove that a small set of geometric operations are sufficient to represent conjunctive logical queries on a network, and we introduce a series of increasingly strong implementations of these operators. We demonstrate the utility of this framework in two application studies on networks with millions of edges: predicting unobserved subgraphs in a network of drug-gene-disease interactions and in a network of social interactions derived from a popular web forum. These experiments demonstrate how our framework can efficiently make logical predictions such as "what drugs are likely to target proteins involved with both diseases X and Y?" Together our results highlight how imposing logical structure can make network embeddings more useful for large-scale knowledge discovery.

For statistical learning, categorical variables in a table are usually considered as discrete entities and encoded separately to feature vectors, e.g., with one-hot encoding. "Dirty" non-curated data gives rise to categorical variables with a very high cardinality but redundancy: several categories reflect the same entity. In databases, this issue is typically solved with a deduplication step. We show that a simple approach that exposes the redundancy to the learning algorithm brings significant gains. We study a generalization of one-hot encoding, similarity encoding, that builds feature vectors from similarities across categories. We perform a thorough empirical validation on non-curated tables, a problem seldom studied in machine learning. Results on seven real-world datasets show that similarity encoding brings significant gains in prediction in comparison with known encoding methods for categories or strings, notably one-hot encoding and bag of character n-grams. We draw practical recommendations for encoding dirty categories: 3-gram similarity appears to be a good choice to capture morphological resemblance. For very high-cardinality, dimensionality reduction significantly reduces the computational cost with little loss in performance: random projections or choosing a subset of prototype categories still outperforms classic encoding approaches.

We introduce a new feature map for barcodes that arise in persistent homology computation. The main idea is to first realize each barcode as a path in a convenient vector space, and to then compute its path signature which takes values in the tensor algebra of that vector space. The composition of these two operations - barcode to path, path to tensor series - results in a feature map that has several desirable properties for statistical learning, such as universality and characteristicness, and achieves state-of-the-art results on common classification benchmarks.

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The representation power of similarity functions used in neural network-based graph embedding is considered. The inner product similarity (IPS) with feature vectors computed via neural networks is commonly used for representing the strength of association between two nodes. However, only a little work has been done on the representation capability of IPS. A very recent work shed light on the nature of IPS and reveals that IPS has the capability of approximating any positive definite (PD) similarities. However, a simple example demonstrates the fundamental limitation of IPS to approximate non-PD similarities. We then propose a novel model named Shifted IPS (SIPS) that approximates any Conditionally PD (CPD) similarities arbitrary well. CPD is a generalization of PD with many examples such as negative Poincare distance and negative Wasserstein distance, thus SIPS has a potential impact to significantly improve the applicability of graph embedding without taking great care in configuring the similarity function. Our numerical experiments demonstrate the SIPS's superiority over IPS. In theory, we further extend SIPS beyond CPD by considering the inner product in Minkowski space so that it approximates more general similarities.