Masters Degrees (Applied Mathematics)


Recent Submissions

Now showing 1 - 5 of 52
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    Bayesian forecasting of stock returns using simultaneous graphical dynamic linear models
    (Stellenbosch : Stellenbosch University, 2022-12) Kyakutwika, Nelson; Bartlett, Bruce; Becker, Ronnie; Stellenbosch University. Faculty of Science. Dept. of Applied Mathematics.
    ENGLISH ABSTRACT: Cross-series dependencies are crucial in obtaining accurate forecasts when forecast- ing a multivariate time series. Simultaneous Graphical Dynamic Linear Models (SGDLMs) are Bayesian models that elegantly capture cross-series dependencies. This study aims to forecast returns of a 40-dimensional time series of stock data using SGDLMs. The SGDLM approach involves constructing a customised dy- namic linear model (DLM) for each univariate time series. Every day, the DLMs are recoupled using importance sampling and decoupled using mean-field varia- tional Bayes. We summarise the standard theory on DLMs to set the foundation for studying SGDLMs. We discuss the structure of SGDLMs in detail and give de- tailed explanations of the proofs of the formulae involved. Our analyses are run on a CPU-based computer; an illustration of the intensity of the computations is given. We give an insight into the efficacy of the recoupling/decoupling techniques. Our results suggest that SGDLMs forecast the stock data accurately and respond to market gyrations nicely.
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    Semi-supervised learning in computer vision
    (Stellenbosch : Stellenbosch University, 2022-12) Louw, Christiaan; Brink, Willie; Stellenbosch University. Faculty of Science. Dept. of Applied Mathematics.
    ENGLISH ABSTRACT: Deep learning models have proven to be successful at tasks such as image classification. A major drawback of supervised learning is the need for large labelled datasets to obtain good classification accuracy. This can be a bar rier to those in resource-constrained environments wanting to implement a classification model in a previously unexplored field. Recent advancements in unsupervised learning methods, such as contrastive learning, have made it viable to perform representation learning without labels, which when com bined with supervised learning on relatively small labelled datasets can lead to state-of-the-art performance on image classification tasks. We study this technique, called semi-supervised learning, and provide an in vestigation into three semi-supervised learning frameworks. Our work starts by discussing the implementations of the SimCLR, SimSiam and FixMatch frameworks. We compare the results of each framework on the CIFAR-10 and STL-10 datasets in label-scarce scenarios and show that: (1) all frameworks outperform a purely supervised learning baseline when the number of labels is reduced, (2) the improvement in performance of the frameworks over the su pervised baseline increases as the number of available labels is decreased and (3) in most cases, the semi-supervised learning frameworks are able to match or outperform the supervised baseline with 10% as many labels. We also investigate the performance of the SimCLR and SimSiam framework on class-imbalanced versions of the CIFAR-10 and STL-10 datasets, and find that: (1) the improvements over the supervised learning baseline is less sub stantial than in the results with fewer overall, but balanced, class labels, and (2) with basic oversampling implemented the results are significantly improved, with the semi-supervised learning frameworks benefiting the most. The results in this thesis indicate that unsupervised representation learning can indeed lower the number of labelled images required for successful image classification by a significant degree. We also show that each of the frameworks considered in this work serves this function well.
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    Low-resource image captioning
    (Stellenbosch : Stellenbosch University, 2022-12) Du Plessis, Mikkel; Brink, Willie; Stellenbosch University. Faculty of Science. Dept. of Applied Mathematics.
    ENGLISH ABSTRACT: Image captioning combines computer vision and natural language processing, and aims to automatically generate a short natural language phrase that describes relationships between objects and context within a given image. As the field of deep learning evolves, several approaches have produced impressive models and generally follow an encoder-decoder architecture. An encoder is utilised for visual cues and a textual decoder to produce a final caption. This can create a challenging gap between visual and textual representations, and makes the training of image captioning models resource intensive. Consequently, recent image captioning models have relied on a steady increase of training set size, computing requirements and training times. This thesis explores the viability of two model architectures for the task of image captioning in a low-resource scenario. We focus specifically on models that can be trained on a single consumer-level GPU in under 5 hours, using only a few thousand images. Our first model is a conventional image captioning model with a pre-trained convolutional neural network as the encoder, followed by an attention mechanism, and an LSTM as the decoder. Our second model utilises a Transformer in the encoder and the decoder. Additionally, we propose three auxiliary techniques that aim to extract more information from images and training captions with only marginal computational overhead. Firstly, we address the typical sparseness in object and scene representation by taking advantage of top-down and bottom-up features, in order to present the decoder with richer visual information and context. Secondly, we suppress semantically unlikely caption candidates during the decoder’s beam search procedure through the inclusion of a language model. Thirdly, we enhance the expressiveness of the model by augmenting training captions with a paraphrase generator. We find that the Transformer-based architecture is superior under low-data circumstances. Through a combination of all proposed methods applied, we achieve state-of-the-art performance on the Flickr8k test set and surpass existing recurrent-based methods. To further validate the generalisability of our models, we train on small, randomly sampled subsets of the MS COCO dataset and achieve competitive test scores compared to existing models trained on the full dataset.
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    Fruit detection in an orchard using deep learning approaches
    (Stellenbosch : Stellenbosch University, 2022-04) Koech, Kiprono Elijah; Bah, Bubacarr; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences (Applied Mathematics)
    ENGLISH ABSTRACT: Over the last few years, we have witnessed rapid advancement in technology in different fields: communication, transport security, finance, and medicine. Agriculture is no exception. Today, agriculture is practised with sophisticated technologies such as satellite imaging, soil and water sensors, weather tracking, and robots. Fruit detection is a critical process in robot harvesting and yield estimation. With the rise in deep learning, state-of-the-art object detectors have been developed. In this paper, we deploy two state-of-the-art model detectors; namely, Mask Region-based CNN (Mask R-CNN), and You Only Look Once (YOLOv5), in the context of fruit detection. The training data are orchard images of apples and mangoes taken under natural outdoor conditions. The images are taken under varied illumination conditions to ensure that the models learn rich features allowing them to generalize well in a new dataset. Ablation studies are presented to understand how the two models compare in terms of accuracy and speed at inference time. We also investigated the significance of transfer learning in such an application. In particular, we considered weight initialization using ImageNet, COCO, and weights from models trained on a di erent orchard dataset. As a post-processing step, we implemented ensemble techniques on the detection results of the two models. Mask R-CNN and YOLOv5 attained an F1 score of 93% on mangoes datasets and 88% on apple images, and ensembling led to an up to 3% increase in F1 score.
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    The Impact of peptide flanking residues on predicting peptide-MHC-II binding interactions using convolutional Neural Networks
    (Stellenbosch : Stellenbosch University, 2022-04) Daumas, Tshenolo Thato Eustacia; Bah, Bubacarr; Degoot, Abdoelnaser M.; Ndifon, Wilfred; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences (Applied Mathematics)
    ENGLISH ABSTRACT: Major histocompatibility complex class II (MHC-II) is one of three classes of MHC molecules and is located on the surface of professional antigen presenting cells. MHC-II molecules present antigenic peptides derived from pathogens that cause infection, for recognition by CD4+ T lymphocytes. MHC-II molecules are critical components of the chain of intercellular interactions required for the adaptive im- mune response to be launched successfully, as this chain is thought to begin with the binding of antigenic peptides by MHC-II molecules. While considerable progress in computational efforts have been made towards un- derstanding peptide-MHC interactions for classes I and II, the case for peptide- MHC-II remains challenging due to MHC-II molecules being highly polymorphic and having open-ended binding grooves. Consequently, MHC-II molecules interact with peptides of varying lengths; therefore, the role that peptide flanking residues (PFRs) play in peptide-MHC-II binding interactions must be considered. We pro- pose an allele-specific convolutional neural network model that simulates binding interactions between peptides and MHC-II molecules that also incorporates PFR information in the input. Deep learning models for peptide-MHC-II interactions that have been published, such as the allele-specific model, NetMHCII and the transallelic model NetMHCI- Ipan have demonstrated encouraging predictive performance. When compared, our proposed CNN model outperformed the latest version of the model, NetMHCII-2.3 across all MHC-II alleles considered with mean AUC value of 0.951 as compared with 0.822 for NetMHCII-3.2. Furthermore, we analysed the impact that PFRs have on modelling peptide-MHC-II binding interactions and laid the foundations of de- veloping a transallelic model based on the CNN model.