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A common belief in high-dimensional data analysis is that data are concentrated on a low-dimensional manifold. This motivates simultaneous dimension reduction and regression on manifolds. We provide an algorithm for learning gradients on…
Ensemble learning has had many successes in supervised learning, but it has been rare in unsupervised learning and dimensionality reduction. This study explores dimensionality reduction ensembles, using principal component analysis and…
The quest for simplification in physics drives the exploration of concise mathematical representations for complex systems. This Dissertation focuses on the concept of dimensionality reduction as a means to obtain low-dimensional…
We consider the optimization of an uncertain objective over continuous and multi-dimensional decision spaces in problems in which we are only provided with observational data. We propose a novel algorithmic framework that is tractable,…
Manifold learning is used for dimensionality reduction, with the goal of finding a projection subspace to increase and decrease the inter- and intraclass variances, respectively. However, a bottleneck for subspace learning methods often…
In this work, we study high-dimensional mean estimation under user-level differential privacy, and design an $(\varepsilon,\delta)$-differentially private mechanism using as few users as possible. In particular, we provide a nearly optimal…
The concept of personalised medicine in cancer therapy is becoming increasingly important. There already exist drugs administered specifically for patients with tumours presenting well-defined mutations. However, the field is still in its…
To make sense of the world our brains must analyze high-dimensional datasets streamed by our sensory organs. Because such analysis begins with dimensionality reduction, modelling early sensory processing requires biologically plausible…
Many problems within personalized medicine and digital health rely on the analysis of continuous-time functional biomarkers and other complex data structures emerging from high-resolution patient monitoring. In this context, this work…
We introduce a new framework for dimension reduction in the context of high-dimensional regression. Our proposal is to aggregate an ensemble of random projections, which have been carefully chosen based on the empirical regression…
Motivation: Gene selection has become a common task in most gene expression studies. The objective of such research is often to identify the smallest possible set of genes that can still achieve good predictive performance. The problem of…
We present a novel method to improve pharmacokinetics modeling, an essential step of drug development. Conventional models frequently fail to fully represent the intricacies of drug absorption and distribution, which limits their predictive…
A treatment regime is a function that maps individual patient information to a recommended treatment, hence explicitly incorporating the heterogeneity in need for treatment across individuals. Patient responses are dichotomous and can be…
Recent advances in diffusion and flow matching models have highlighted a shift in the preferred prediction target -- moving from noise ($\varepsilon$) and velocity (v) to direct data (x) prediction -- particularly in high-dimensional…
This paper proposes a novel kernel approach to linear dimension reduction for supervised learning. The purpose of the dimension reduction is to find directions in the input space to explain the output as effectively as possible. The…
We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems, which we call dynamical dimension reduction (DDR). In the DDR model, each point is evolved via a nonlinear flow towards…
We conduct a theoretical study of various solution methods for the adaptive fractionation problem. The two messages of this paper are: (i) dynamic programming (DP) is a useful framework for adaptive radiation therapy, particularly adaptive…
Personalized models are essential in digital health because individuals exhibit substantial physiological and behavioral heterogeneity. Yet personalization is limited by scarce and noisy user-specific data. Most existing methods rely on…
Personalized medicine has become an important part of medicine, for instance predicting individual drug responses based on genomic information. However, many current statistical methods are not tailored to this task, because they overlook…
We study the problem of learning to choose from m discrete treatment options (e.g., news item or medical drug) the one with best causal effect for a particular instance (e.g., user or patient) where the training data consists of passive…