Alzheimer’s disease is the leading cause of dementia worldwide, and its accurate diagnosis is essential for the effectiveness of the therapies currently available. Deep learning methods applied to neuroimaging data have shown promise for this task, but most multimodal approaches assume that all modalities are available for every subject, an assumption that rarely holds in clinical practice or even in research cohorts such as ADNI, where FDG-PET is far less common than MRI. This thesis develops a multimodal framework for the three-class classification of subjects into cognitively normal, mild cognitive impairment and Alzheimer’s disease, which is natively robust to missing modalities. We formulate a Product-of-Experts model in which MRI and FDG- PET each contribute a Gaussian expert to a shared latent representation of the brain state, allowing predictions to be made from either modality alone or from both, always through the same classifier and without imputing the missing modality. Since different modality-availability patterns induce different latent-input regimes for this shared classifier, we further investigate two regularization strategies: a meta-learned regularizer, inspired by domain-generalization methods, and a Kullback-Leibler term that encourages the unimodal and multimodal latent distributions to remain compatible. Experiments on ADNI data show that jointly training the model with a standard supervised objective does not by itself improve over dedicated single-modality baselines, and that the latent representations induced by different modality subsets are clearly separated. Both regularizers improve on this basic model, with the meta-learned regularizer providing the most consistent gains across the three inference pathways. In the multimodal setting, the proposed model reaches a balanced accuracy comparable to that of a recent state-of-the-art transformer-based method, while using roughly two orders of magnitude fewer trainable parameters and remaining usable when one modality is absent at inference time. ... Read more

This thesis develops a mathematical and computational framework for demand sensing in supply chain management, addressing the dual challenges of forecast accuracy and hierarchical coherence. This work was carried out during a graduate internship at Dassault Systèmes. Modern retail demand is shaped by vertical aggregation constraints, horizontal product interactions, and temporal dependencies influenced by external drivers. Traditional approaches (classical time series, machine learning, and reconciliation heuristics) treat these aspects separately and struggle to deliver coherent and accurate forecasts at scale.

The thesis first establishes a theoretical foundation for multi-product demand forecasting. Forecasting is formalized as a supervised learning problem on probability spaces, introducing the multi-product demand process and a general forecast operator that unifies local versus global modeling, recursive versus direct horizons, and alternative loss functions. Hierarchical forecasting is expressed in compact linear algebraic form, showing how classical heuristics and optimal reconciliation (MinT/OLS) can be understood as projections onto the coherent subspace.

Building on this, the thesis introduces a graph-based extension of the framework. By embedding time series into relational graphs, Graph Neural Networks (GNNs) capture vertical, horizontal, and temporal dependencies within a unified model. An end-to-end forecasting pipeline is proposed, combining graph construction, feature extraction with external covariates, GNN encoding, and forecast generation, with coherence ensured through bottom-up construction, regularization penalties, or post-hoc reconciliation.

Empirical evaluation on the M5 dataset demonstrates the practical implications. Incorporating external drivers consistently improves accuracy across models and aggregation levels. Machine learning models, particularly gradient boosting, outperform classical baselines at granular levels, though the latter remain competitive at higher aggregations. The proposed Hierarchical Graph Network (HGN) achieves competitive results, with particular benefits at intermediate levels where both hierarchical and cross-series relations are most informative. A comparison of local versus global training highlights the trade-off between accuracy and computational efficiency.

The findings underscore three insights for practice: external drivers require robust data infrastructure, hybrid local–global modeling offers balanced accuracy and efficiency, and reconciliation remains essential to guarantee coherence. Overall, the thesis demonstrates how integrating hierarchical structure, external signals, and graph-based learning advances both the theory and practice of demand sensing in modern supply chains. ... Read more

Suppose that we want to infer the effect of a treatment on a certain outcome, where both the treatment and outcome are influenced by other variables. It has been well-established that in the linear setting, in case we know beforehand which of these other variables are instrumental (for the effect of the treatment on the outcome), we can infer the treatment effect in a consis-tent sense. This thesis analyses 3 methods that deals with the issue of unknown instrumental variables (IVs) and functional relationships in different ways to infer the treatment effect. The first method, Causal Inference with Invalid Instruments (CIII), assumes that we have a linear setting and a set with potential instrumental variables for whom a majority or plurality rule holds to obtain a robust confidence interval for the treatment effect. The second method, Anchor Regression (AR), only assumes a linear setting. By mediating between different meth-ods, the AR-estimator turns out the be robust to changes in the distribution of the sampled data. Lastly, Two Stage Curvature Identification (TSCI), does not require a linear setting or information on the IVs. Instead, it relies on the difference in functional form between the effect of the variables on the treatment and the effect of the variables on the outcome for consistent estimation and asymptotic normality. TSCI also provides a test for IV presence in the non-linear setting. In this thesis, I will explain the workings of these 3 methods, analyse their theoretical foundation and do simulation studies. Based on these analyses, I make several additions and suggestions to expand the theoretical scope and improve practical efficacy.3
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