This thesis develops methods for causal inference and causal representation learning (CRL) in high-dimensional, time-varying data. The first contribution introduces the Causal Dynamic Variational Autoencoder (CDVAE), a model for estimating Individual Treatment Effects (ITEs) by capturing unobserved heterogeneity in treatment response driven by latent risk factors that affect only outcomes. CDVAE comes with theoretical guarantees on valid latent adjustment and generalization bounds for ITE error. Experiments on synthetic and real datasets show that CDVAE outperforms baselines, and that state-of-the-art models greatly improve when augmented with its latent substitutes, approaching oracle performance without access to true adjustment variables. The second contribution proposes an efficient framework for long-term counterfactual regression based on RNNs enhanced with Contrastive Predictive Coding (CPC) and InfoMax. It captures long-range dependencies under time-varying confounding while avoiding the computational cost of transformers, achieving state-of-the-art results and introducing CPC into causal inference. The third contribution advances CRL by addressing how latent causes manifest in observed variables. We introduce a model-agnostic interpretability layer based on the geometry of the decoder Jacobian. A sparse self-expression prior induces modular, possibly overlapping groups of observed features aligned with shared latent influences. We provide recovery guarantees in both disjoint and overlapping settings and show that meaningful latent-to-observed structure can be recovered without anchor features or single-parent assumptions. Scalable Jacobian-based regularization techniques are also developed.

We develop a flexible feature selection framework based on deep neural networks that approximately controls the false discovery rate (FDR), a measure of Type-I error. The method applies to architectures whose first layer is fully connected. From the second layer onward, it accommodates multilayer perceptrons (MLPs) of arbitrary width and depth, convolutional and recurrent networks, attention mechanisms, residual connections, and dropout. The procedure also accommodates stochastic gradient descent with data-independent initializations and learning rates. To the best of our knowledge, this is the first work to provide a theoretical guarantee of FDR control for feature selection within such a general deep learning setting. Our analysis is built upon a multi-index data-generating model and an asymptotic regime in which the feature dimension $n$ diverges faster than the latent dimension $q^{*}$, while the sample size, the number of training iterations, the network depth, and hidden layer widths are left unrestricted. Under this setting, we show that each coordinate of the gradient-based feature-importance vector admits a marginal normal approximation, thereby supporting the validity of asymptotic FDR control. As a theoretical limitation, we assume $\mathbf{B}$-right orthogonal invariance of the design matrix, and we discuss broader generalizations. We also present numerical experiments that underscore the theoretical findings.

We present a novel recurrent neural network architecture designed explicitly for day-ahead electricity price forecasting, aimed at improving short-term decision-making and operational management in energy systems. Our combined forecasting model embeds linear structures, such as expert models and Kalman filters, into recurrent networks, enabling efficient computation and enhanced interpretability. The design leverages the strengths of both linear and non-linear model structures, allowing it to capture all relevant stylised price characteristics in power markets, including calendar and autoregressive effects, as well as influences from load, renewable energy, and related fuel and carbon markets. For empirical testing, we use hourly data from the largest European electricity market spanning 2018 to 2025 in a comprehensive forecasting study, comparing our model against state-of-the-art approaches, particularly high-dimensional linear and neural network models. The proposed model achieves approximately 12% higher accuracy than leading benchmarks. We evaluate the contributions of the interpretable model components and conclude on the impact of combining linear and non-linear structures.

Boolean matrix factorization (BMF) approximates a given binary input matrix as the product of two smaller binary factors. Unlike binary matrix factorization based on standard arithmetic, BMF employs the Boolean OR and AND operations for the matrix product, which improves interpretability and reduces the approximation error. It is also used in role mining and computer vision. In this paper, we first propose algorithms for BMF that perform alternating optimization (AO) of the factor matrices, where each subproblem is solved via integer programming (IP). We then design different approaches to further enhance AO-based algorithms by selecting an optimal subset of rank-one factors from multiple runs. To address the scalability limits of IP-based methods, we introduce new greedy and local-search heuristics. We also construct a new C++ data structure for Boolean vectors and matrices that is significantly faster than existing ones and is of independent interest, allowing our heuristics to scale to large datasets. We illustrate the performance of all our proposed methods and compare them with the state of the art on various real datasets, both with and without missing data, including applications in topic modeling and imaging.

Suicide remains a leading cause of death in Western countries. As social media becomes central to daily life, digital footprints offer valuable insight into suicidal behavior. Focusing on individuals who attempted suicide while uploading videos to their channels, we investigate: How do linguistic patterns on YouTube reflect suicidal behavior, and how do these patterns align with or differ from expert knowledge? We examined linguistic changes around suicide attempts and compared individuals who attempted suicide while actively uploading to their channel with three control groups: those with prior attempts, those experiencing major life events, and matched individuals from the broader cohort. Applying complementary bottom-up, hybrid, and expert-driven approaches, we analyzed a novel longitudinal dataset of 181 suicide-attempt channels and 134 controls. In the bottom-up analysis, LLM-based topic-modeling identified 166 topics; five were linked to suicide attempts, two also showed attempt-related temporal changes (Mental Health Struggles, $OR = 1.74$; YouTube Engagement, $OR = 1.67$; $p < .01$). In the hybrid approach, clinical experts reviewed LLM-derived topics and flagged 19 as suicide-related. However, none showed significant effects beyond those identified bottom-up. YouTube Engagement, a platform-specific indicator, was not flagged, underscoring the value of bottom-up discovery. A top-down psychological assessment of suicide narratives revealed differing motivations: individuals describing prior attempts aimed to help others ($β=-1.69$, $p<.01$), whereas those attempted during the uploading period emphasized personal recovery ($β=1.08$, $p<.01$). By integrating these approaches, we offer a nuanced understanding of suicidality, bridging digital behavior and clinical insights.

A standard assumption in deep learning is that the inductive bias introduced by a neural network architecture must persist from training through inference. The architecture you train with is the architecture you deploy. This assumption constrains the community from selecting architectures that may have desirable efficiency or design properties due to difficulties with optimization. We challenge this assumption with Network of Theseus (NoT), a method for progressively converting a trained, or even untrained, guide network architecture part-by-part into an entirely different target network architecture while preserving the performance of the guide network. At each stage, components in the guide network architecture are incrementally replaced with target architecture modules and aligned via representational similarity metrics. This procedure largely preserves the functionality of the guide network even under substantial architectural changes-for example, converting a convolutional network into a multilayer perceptron, or GPT-2 into a recurrent neural network. By decoupling optimization from deployment, NoT expands the space of viable inference-time architectures, opening opportunities for better accuracy-efficiency tradeoffs and enabling more directed exploration of the architectural design space.

While methods exist for aligning flow matching models--a popular and effective class of generative models--with human preferences, existing approaches fail to achieve both adaptation efficiency and probabilistically sound prior preservation. In this work, we leverage the theory of optimal control and propose VGG-Flow, a gradient-matching-based method for finetuning pretrained flow matching models. The key idea behind this algorithm is that the optimal difference between the finetuned velocity field and the pretrained one should be matched with the gradient field of a value function. This method not only incorporates first-order information from the reward model but also benefits from heuristic initialization of the value function to enable fast adaptation. Empirically, we show on a popular text-to-image flow matching model, Stable Diffusion 3, that our method can finetune flow matching models under limited computational budgets while achieving effective and prior-preserving alignment.

However, in infants and young children, accurate segmentation is challenging due to development and imaging constraints. Pediatric brain MRI is notoriously difficult to acquire, with inconsistent availability of imaging modalities, substantial non-head anatomy in the field of view, and frequent motion artifacts. This has led to specialized segmentation models that are often limited to specific image types or narrow age groups, or that are fragile for more variable images such as those acquired clinically. We address this method fragmentation with BabySeg, a deep learning brain segmentation framework for infants and young children that supports diverse MRI protocols, including repeat scans and image types unavailable during training. Our approach builds on recent domain randomization techniques, which synthesize training images far beyond realistic bounds to promote dataset shift invariance. We also describe a mechanism that enables models to flexibly pool and interact features from any number of input scans. We demonstrate state-of-the-art performance that matches or exceeds the accuracy of several existing methods for various age cohorts and input configurations using a single model, in a fraction of the runtime required by many existing tools.

Long context reasoning in large language models (LLMs) has demonstrated enhancement of their cognitive capabilities via chain-of-thought (CoT) inference. Training such models is usually done via reinforcement learning with verifiable rewards (RLVR) in reasoning based problems, like math and programming. However, RLVR is limited by several bottlenecks, such as, lack of dense reward, and inadequate sample efficiency. As a result, it requires significant compute resources in post-training phase. To overcome these limitations, in this work, we propose \textbf{Semantic Soft Bootstrapping (SSB)}, a self-distillation technique, in which the same base language model plays the role of both teacher and student, but receives different semantic contexts about the correctness of its outcome at training time. The model is first prompted with a math problem and several rollouts are generated. From them, the correct and most common incorrect response are filtered, and then provided to the model in context to produce a more robust, step-by-step explanation with a verified final answer. This pipeline automatically curates a paired teacher-student training set from raw problem-answer data, without any human intervention. This generation process also produces a sequence of logits, which is what the student model tries to match in the training phase just from the bare question alone. In our experiment, Qwen2.5-3B-Instruct on GSM8K dataset via parameter-efficient fine-tuning. We then tested its accuracy on MATH500, and AIME2024 benchmarks. Our experiments show a jump of 10.6%, and 10% improvements in accuracy, respectively, over group relative policy optimization (GRPO), which is a commonly used RLVR algorithm. Our code is available at https://github.com/purbeshmitra/semantic-soft-bootstrapping, and the model, curated dataset is available at https://huggingface.co/purbeshmitra/semantic-soft-bootstrapping.

Structure-based drug design (SBDD) focuses on designing small-molecule ligands that bind to specific protein pockets. Computational methods are integral in modern SBDD workflows and often make use of virtual screening methods via docking or pharmacophore search. Modern generative modeling approaches have focused on improving novel ligand discovery by enabling de novo design. In this work, we recognize that these tasks share a common structure and can therefore be represented as different instantiations of a consistent generative modeling framework. We propose a unified approach in OMTRA, a multi-modal flow matching model that flexibly performs many tasks relevant to SBDD, including some with no analogue in conventional workflows. Additionally, we curate a dataset of 500M 3D molecular conformers, complementing protein-ligand data and expanding the chemical diversity available for training. OMTRA obtains state of the art performance on pocket-conditioned de novo design and docking; however, the effects of large-scale pretraining and multi-task training are modest. All code, trained models, and dataset for reproducing this work are available at https://github.com/gnina/OMTRA