Artificial Intelligence (AI) can potentially transform the industry, enhancing the production process and minimizing manual, repetitive tasks. Accordingly, the synergy between high-performance computing and powerful mathematical models enables the application of sophisticated data analysis procedures like Machine Learning. However, challenges exist regarding effective, efficient, and flexible processing to generate valuable knowledge. Consequently, this work comprehensively describes industrial challenges where AI can be exploited, focusing on the dairy industry. The conclusions presented can help researchers apply novel approaches for cattle monitoring and farmers by proposing advanced technological solutions to their needs.

Recent works have demonstrated the potential of Graph Neural Networks (GNN) for network intrusion detection. Despite their advantages, a significant gap persists between real-world scenarios, where detection speed is critical, and existing proposals, which operate on large graphs representing several hours of traffic. This gap results in unrealistic operational conditions and impractical detection delays. Moreover, existing models do not generalize well across different networks, hampering their deployment in production environments. To address these issues, we introduce PPTGNN, a practical spatio-temporal GNN for intrusion detection. PPTGNN enables near real-time predictions, while better capturing the spatio-temporal dynamics of network attacks. PPTGNN employs self-supervised pre-training for improved performance and reduced dependency on labeled data. We evaluate PPTGNN on three public datasets and show that it significantly outperforms state-of-the-art models, such as E-ResGAT and E-GraphSAGE, with an average accuracy improvement of 10.38%. Finally, we show that a pre-trained PPTGNN can easily be fine-tuned to unseen networks with minimal labeled examples. This highlights the potential of PPTGNN as a general, large-scale pre-trained model that can effectively operate in diverse network environments.

To enhance the robustness of the Light Gradient Boosting Machine (LightGBM) algorithm for image classification, a topological data analysis (TDA)-based robustness optimization algorithm for LightGBM, TDA-LightGBM, is proposed to address the interference of noise on image classification. Initially, the method partitions the feature engineering process into two streams: pixel feature stream and topological feature stream for feature extraction respectively. Subsequently, these pixel and topological features are amalgamated into a comprehensive feature vector, serving as the input for LightGBM in image classification tasks. This fusion of features not only encompasses traditional feature engineering methodologies but also harnesses topological structure information to more accurately encapsulate the intrinsic features of the image. The objective is to surmount challenges related to unstable feature extraction and diminished classification accuracy induced by data noise in conventional image processing. Experimental findings substantiate that TDA-LightGBM achieves a 3% accuracy improvement over LightGBM on the SOCOFing dataset across five classification tasks under noisy conditions. In noise-free scenarios, TDA-LightGBM exhibits a 0.5% accuracy enhancement over LightGBM on two classification tasks, achieving a remarkable accuracy of 99.8%. Furthermore, the method elevates the classification accuracy of the Ultrasound Breast Images for Breast Cancer dataset and the Masked CASIA WebFace dataset by 6% and 15%, respectively, surpassing LightGBM in the presence of noise. These empirical results underscore the efficacy of the TDA-LightGBM approach in fortifying the robustness of LightGBM by integrating topological features, thereby augmenting the performance of image classification tasks amidst data perturbations.

Self-attention is key to the remarkable success of transformers in sequence modeling tasks including many applications in natural language processing and computer vision. Like neural network layers, these attention mechanisms are often developed by heuristics and experience. To provide a principled framework for constructing attention layers in transformers, we show that the self-attention corresponds to the support vector expansion derived from a support vector regression problem, whose primal formulation has the form of a neural network layer. Using our framework, we derive popular attention layers used in practice and propose two new attentions: 1) the Batch Normalized Attention (Attention-BN) derived from the batch normalization layer and 2) the Attention with Scaled Head (Attention-SH) derived from using less training data to fit the SVR model. We empirically demonstrate the advantages of the Attention-BN and Attention-SH in reducing head redundancy, increasing the model's accuracy, and improving the model's efficiency in a variety of practical applications including image and time-series classification.

Causal models provide rich descriptions of complex systems as sets of mechanisms by which each variable is influenced by its direct causes. They support reasoning about manipulating parts of the system and thus hold promise for addressing some of the open challenges of artificial intelligence (AI), such as planning, transferring knowledge in changing environments, or robustness to distribution shifts. However, a key obstacle to more widespread use of causal models in AI is the requirement that the relevant variables be specified a priori, which is typically not the case for the high-dimensional, unstructured data processed by modern AI systems. At the same time, machine learning (ML) has proven quite successful at automatically extracting useful and compact representations of such complex data. Causal representation learning (CRL) aims to combine the core strengths of ML and causality by learning representations in the form of latent variables endowed with causal model semantics. In this thesis, we study and present new results for different CRL settings. A central theme is the question of identifiability: Given infinite data, when are representations satisfying the same learning objective guaranteed to be equivalent? This is an important prerequisite for CRL, as it formally characterises if and when a learning task is, at least in principle, feasible. Since learning causal models, even without a representation learning component, is notoriously difficult, we require additional assumptions on the model class or rich data beyond the classical i.i.d. setting. By partially characterising identifiability for different settings, this thesis investigates what is possible for CRL without direct supervision, and thus contributes to its theoretical foundations. Ideally, the developed insights can help inform data collection practices or inspire the design of new practical estimation methods.

We provide a novel dimension-free uniform concentration bound for the empirical risk function of constrained logistic regression. Our bound yields a milder sufficient condition for a uniform law of large numbers than conditions derived by the Rademacher complexity argument and McDiarmid's inequality. The derivation is based on the PAC-Bayes approach with second-order expansion and Rademacher-complexity-based bounds for the residual term of the expansion.

Pairwise dot-product self-attention is key to the success of transformers that achieve state-of-the-art performance across a variety of applications in language and vision. This dot-product self-attention computes attention weights among the input tokens using Euclidean distance, which makes the model prone to representation collapse and vulnerable to contaminated samples. In this paper, we propose using a Mahalanobis distance metric for computing the attention weights to stretch the underlying feature space in directions of high contextual relevance. In particular, we define a hyper-ellipsoidal neighborhood around each query to increase the attention weights of the tokens lying in the contextually important directions. We term this novel class of attention Elliptical Attention. Our Elliptical Attention provides two benefits: 1) reducing representation collapse and 2) enhancing the model's robustness as the Elliptical Attention pays more attention to contextually relevant information rather than focusing on some small subset of informative features. We empirically demonstrate the advantages of Elliptical Attention over the baseline dot-product attention and state-of-the-art attention methods on various practical tasks, including object classification, image segmentation, and language modeling across different data modalities.

Patchwork learning arises as a new and challenging data collection paradigm where both samples and features are observed in fragmented subsets. Due to technological limits, measurement expense, or multimodal data integration, such patchwork data structures are frequently seen in neuroscience, healthcare, and genomics, among others. Instead of analyzing each data patch separately, it is highly desirable to extract comprehensive knowledge from the whole data set. In this work, we focus on the clustering problem in patchwork learning, aiming at discovering clusters amongst all samples even when some are never jointly observed for any feature. We propose a novel spectral clustering method called Cluster Quilting, consisting of (i) patch ordering that exploits the overlapping structure amongst all patches, (ii) patchwise SVD, (iii) sequential linear mapping of top singular vectors for patch overlaps, followed by (iv) k-means on the combined and weighted singular vectors. Under a sub-Gaussian mixture model, we establish theoretical guarantees via a non-asymptotic misclustering rate bound that reflects both properties of the patch-wise observation regime as well as the clustering signal and noise dependencies. We also validate our Cluster Quilting algorithm through extensive empirical studies on both simulated and real data sets in neuroscience and genomics, where it discovers more accurate and scientifically more plausible clusters than other approaches.

We introduce a new method to jointly reduce the dimension of the input and output space of a high-dimensional function. Choosing a reduced input subspace influences which output subspace is relevant and vice versa. Conventional methods focus on reducing either the input or output space, even though both are often reduced simultaneously in practice. Our coupled approach naturally supports goal-oriented dimension reduction, where either an input or output quantity of interest is prescribed. We consider, in particular, goal-oriented sensor placement and goal-oriented sensitivity analysis, which can be viewed as dimension reduction where the most important output or, respectively, input components are chosen. Both applications present difficult combinatorial optimization problems with expensive objectives such as the expected information gain and Sobol indices. By optimizing gradient-based bounds, we can determine the most informative sensors and most sensitive parameters as the largest diagonal entries of some diagnostic matrices, thus bypassing the combinatorial optimization and objective evaluation.

We examine the continuous-time counterpart of mirror descent, namely mirror flow, on classification problems which are linearly separable. Such problems are minimised `at infinity' and have many possible solutions; we study which solution is preferred by the algorithm depending on the mirror potential. For exponential tailed losses and under mild assumptions on the potential, we show that the iterates converge in direction towards a $\phi_\infty$-maximum margin classifier. The function $\phi_\infty$ is the $\textit{horizon function}$ of the mirror potential and characterises its shape `at infinity'. When the potential is separable, a simple formula allows to compute this function. We analyse several examples of potentials and provide numerical experiments highlighting our results.