Latent Representation Inference for the Biomedical Sciences Through the Lens of Deep Generative Modeling

Abstract

Real-world data typically have high ambient dimension and contain substantial temporal structure. However, despite this seemingly “high-dimensional” nature, many previous lines of work support the idea that these data lie instead in lower-dimensional manifolds embedded in high-dimensional spaces (Brahma et al., 2016; Fefferman et al., 2016; Whiteley et al., 2022). Perhaps not surprisingly, the same is also true for several biomedical data modalities of interest (e.g., biomedical images, neural population recordings, “omics” data). That is, even though most biomedical data have high ambient dimension and considerable temporal structure, there is strong evidence in support of the idea that they can be well represented in much lower dimensional spaces (Ebitz and Hayden, 2021; Gallego et al., 2017; Gerber et al., 2010; Humphries, 2021; T. M. Norman et al., 2019; Saxena and Cunningham, 2019).Additionally, recent technological advances have improved the resolution, diversity, andspeed of biomedical data acquisition, leading to a sheer explosion in the complexity and volume of data generated in major hospital and research centers (X. Yang et al., 2024). In this context, new modeling tools capable of efficiently learning compressed representations from such data, which can be leveraged to test new hypotheses and to develop new diagnostic, monitoring, and treatment paradigms have become all but essential to the progress of biomedical research.More specifically, there is a growing need for new modeling tools capable of inferring“compressed representations” that are particularly well-suited for biomedical research purposes. For instance, it might be desirable to learn compressed latent spaces that preserve the underlying dynamics of the original data, so that one may use these representations to probe the temporal evolution of biological processes of interest in health and disease states. As another example, it might be beneficial to estimate the error or uncertainty incurred when mapping data samples into the inferred latent space, so that practitioners can run statistical testing in latent space.In this context, modern deep generative modeling approaches have achieved great success in producing high-quality samples from all sorts of complex, real-world data modalities (e.g., video, audio, text, protein sequence and structure) (Ramesh et al., 2022; Rombach et al., 2022; K. E. Wu et al., 2024). However, despite their tremendous success as generative machines, most of such models fall short in learning latent representations of data that would be particularly well-suited to the needs of clinicians and biomedical researchers. For instance, by themselves, existing state-of-the-art diffusion-based models (DBMs; Ho et al., 2020; Sohl-Dickstein et al., 2015; Y. Song and Ermon, 2019; Y. Song, Sohl-Dickstein, et al., 2021) produce only uncompressed latent spaces, which are typically highly un-structured and un-informative, due to the incremental noise injection and mixing nature of such models.Therefore, there is a seeming disconnect between the design and inherent behaviorof existing state-of-the-art deep generative models and the widely supported “manifold hypothesis” of data, which considerably hinders the utilization of such models as powerful tools in experimental design, hypothesis testing, diagnostics, and treatment for biomedical science and clinical applications. In this dissertation, I present three new deep generative models capable of inferring compressed latent spaces satisfying several desired properties for biomedical science applications.Briefly, in Chapter 2 I present a new variant of the Variational Auto-Encoder (VAE;D. P. Kingma and Welling, 2014; Rezende et al., 2014) framework, which leverages a Generalized Additive Modeling (GAM; T. J. Hastie and Tibshirani, 1990) design, along with the flexibility of Gaussian Processes (GPs; Rasmussen and Nickisch, 2010) to model task-based brain functional magnetic resonance imaging (fMRI) data in an interpretable manner, while accounting for spatial auto-correlations present in these data, which are often ignored in existing analysis methods for fMRI (de Albuquerque et al., 2021).In Chapter 3, I propose a new flow model which leverages the existing probability flowODE (pfODE) view of DBMs (Y. Song, Sohl-Dickstein, et al., 2021) along with a previously proposed measure of intrinsic dimensionality called the Participation-Ratio (PR, P. Gao et al., 2017) to construct new “noising schedules” for DBMs, which allow practitioners to map data samples into a (potentially) compressed latent space of pre-specified dimensionality, while preserving local neighborhood structure and allowing for precise control and quantification of error incurred during latent space mapping (de Albuquerque & Pearson, 2024). In the same chapter I also highlight important connections between the proposed new model and the rapidly emerging literature on flow-matching approaches (Albergo et al., 2023; Lipman et al., 2023; X. Liu et al., 2023) to training continuous-time normalizing flow models (CTNFs; T. Q. Chen et al., 2018; Papamakarios et al., 2021; Rezende and Mohamed, 2015).In Chapter 4, I present a novel flow-matching based approach, which extends the framework proposed in Chapter 3 to yield a new model, capable of inferring a compressed latent representation of the data, while also capturing its intrinsic dynamics. This model is trained using a regularizer which enforces that the dynamics learned be preserved as we compress data into latent space. Importantly, this model retains the same latent space properties of the flow proposed in Chapter 3, namely neighborhood structure preservation and calibrated posterior inference. Finally, I discuss limitations of the proposed approaches, as well as new directions in deep generative model development and applications to biomedical science research problems.