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In the standard machine learning framework, training data is assumed to be fully supervised. However, collecting fully labelled data is not always easy. Due to cost, time, effort or other types of constraints, requiring the whole data to be labelled can be difficult in many applications, whereas collecting unlabelled data can be relatively easy. Therefore, paradigms that enable learning from unlabelled and/or partially labelled data have been growing recently in machine learning. The focus of this thesis is to provide algorithms that enable weakly annotating unlabelled parts of data not provided in the standard supervised setting consisting of an instance-label pair for each sample, then learning from weakly as well as strongly labelled data. More specifically, the bulk of the thesis aims at finding solutions for data that come in the form of bags or groups of instances where available information about the labels is at the bag level only. This is the form of the electromyographic (EMG) data, which represent the main application of the thesis. Electromyographic (EMG) data can be used to diagnose muscles as either normal or suffering from a neuromuscular disease. Muscles can be classified into one of three labels; normal, myopathic or neurogenic. Each muscle consists of motor units (MUs). Equivalently, an EMG signal detected from a muscle consists of motor unit potential trains (MUPTs). This data is an example of partially labelled data where instances (MUs) are grouped in bags (muscles) and labels are provided for bags but not for instances. First, we introduce and investigate a weakly supervised learning paradigm that aims at improving classification performance by using a spectral graph-theoretic approach to weakly annotate unlabelled instances before classification. The spectral graph-theoretic phase of this paradigm groups unlabelled data instances using similarity graph models. Two new similarity graph models are introduced as well in this paradigm. This paradigm improves overall bag accuracy for EMG datasets. Second, generative modelling approaches for multiple-instance learning (MIL) are presented. We introduce and analyse a variety of model structures and components of these generative models and believe it can serve as a methodological guide to other MIL tasks of similar form. This approach improves overall bag accuracy, especially for low-dimensional bags-of-instances datasets like EMG datasets. MIL generative models provide an example of models where probability distributions need to be represented compactly and efficiently, especially when number of variables of a certain model is large. Sum-product networks (SPNs) represent a relatively new class of deep probabilistic models that aims at providing a compact and tractable representation of a probability distribution. SPNs are used to model the joint distribution of instance features in the MIL generative models. An SPN whose structure is learnt by a structure learning algorithm introduced in this thesis leads to improved bag accuracy for higher-dimensional datasets.

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