The conditional average treatment effect (CATE) is widely used in personalized medicine to inform therapeutic decisions. However, state-of-the-art methods for CATE estimation (so-called meta-learners) often perform poorly in the presence of low overlap. In this work, we introduce a new approach to tackle this issue and improve the performance of existing meta-learners in the low-overlap regions. Specifically, we introduce Overlap-Adaptive Regularization (OAR) that regularizes target models proportionally to overlap weights so that, informally, the regularization is higher in regions with low overlap. To the best of our knowledge, our OAR is the first approach to leverage overlap weights in the regularization terms of the meta-learners. Our OAR approach is flexible and works with any existing CATE meta-learner: we demonstrate how OAR can be applied to both parametric and non-parametric second-stage models. Furthermore, we propose debiased versions of our OAR that preserve the Neyman-orthogonality of existing meta-learners and thus ensure more robust inference. Through a series of (semi-)synthetic experiments, we demonstrate that our OAR significantly improves CATE estimation in low-overlap settings in comparison to constant regularization.

Multi-View Representation Learning (MVRL) aims to learn a unified representation of an object from multi-view data.Deep Canonical Correlation Analysis (DCCA) and its variants share simple formulations and demonstrate state-of-the-art performance. However, with extensive experiments, we observe the issue of model collapse, i.e., the performance of DCCA-based methods will drop drastically when training proceeds. The model collapse issue could significantly hinder the wide adoption of DCCA-based methods because it is challenging to decide when to early stop. To this end, we develop NR-DCCA, which is equipped with a novel noise regularization approach to prevent model collapse. Theoretical analysis shows that the Correlation Invariant Property is the key to preventing model collapse, and our noise regularization forces the neural network to possess such a property.

We introduce CaloFlow, a fast detector simulation framework based on normalizing flows. For the first time, we demonstrate that normalizing flows can reproduce many-channel calorimeter showers with extremely high fidelity, providing a fresh alternative to computationally expensive GEANT4 simulations, as well as other state-of-the-art fast simulation frameworks based on GANs and VAEs. Besides the usual histograms of physical features and images of calorimeter showers, we introduce a new metric for judging the quality of generative modeling: the performance of a classifier trained to differentiate real from generated images. We show that GAN-generated images can be identified by the classifier with nearly 100% accuracy, while images generated from CaloFlow are better able to fool the classifier. More broadly, normalizing flows offer several advantages compared to other state-of-the-art approaches (GANs and VAEs), including: tractable likelihoods; stable and convergent training; and principled model selection. Normalizing flows also provide a bijective mapping between data and the latent space, which could have other applications beyond simulation, for example, to detector unfolding.

Modelling statistical relationships beyond the conditional mean is crucial in many settings. Conditional density estimation (CDE) aims to learn the full conditional probability density from data. Though highly expressive, neural network based CDE models can suffer from severe over-fitting when trained with the maximum likelihood objective. Due to the inherent structure of such models, classical regularization approaches in the parameter space are rendered ineffective. To address this issue, we develop a model-agnostic noise regularization method for CDE that adds random perturbations to the data during training. We demonstrate that the proposed approach corresponds to a smoothness regularization and prove its asymptotic consistency. In our experiments, noise regularization significantly and consistently outperforms other regularization methods across seven data sets and three CDE models. The effectiveness of noise regularization makes neural network based CDE the preferable method over previous non- and semi-parametric approaches, even when training data is scarce.

Given a set of empirical observations, conditional density estimation aims to capture the statistical relationship between a conditional variable $\mathbf{x}$ and a dependent variable $\mathbf{y}$ by modeling their conditional probability $p(\mathbf{y}|\mathbf{x})$. The paper develops best practices for conditional density estimation for finance applications with neural networks, grounded on mathematical insights and empirical evaluations. In particular, we introduce a noise regularization and data normalization scheme, alleviating problems with over-fitting, initialization and hyper-parameter sensitivity of such estimators. We compare our proposed methodology with popular semi- and non-parametric density estimators, underpin its effectiveness in various benchmarks on simulated and Euro Stoxx 50 data and show its superior performance. Our methodology allows to obtain high-quality estimators for statistical expectations of higher moments, quantiles and non-linear return transformations, with very little assumptions about the return dynamic.