arXiv subjects

Nicholas Marco

Publications and source records attributed to Nicholas Marco.

6 recordsLinked to original sources

arXiv2026

Adaptive Generalized Elliptical Slice Sampling

A central challenge in gradient-free MCMC is designing algorithms that simultaneously bypass manual tuning, scale efficiently with dimension, and adapt to local target geometry. While adaptive strategies can auto-tune generic frameworks like random walk Metropolis, they offer slow, linear-order scaling of mixing times with dimension. Elliptical slice sampling (ESS) offers a promising alternative: it is tuning-free, adjusts to local geometry, and can achieve nearly dimension-free scaling under favorable conditions. However, its efficiency degrades rapidly if there is a mismatch between the target distribution and the distribution used to generate the ellipse-defining auxiliary variables, precluding its use in high-dimensional settings. We demonstrate that a careful synthesis of ESS and diminishing adaptation directly resolves these bottlenecks. The resulting adaptive generalized elliptical slice sampler (AGESS) self-corrects from a slow-mixing to a fast-mixing regime, while preserving ergodicity across a wide variety of target densities satisfying mild regularity conditions. The algorithm's utility is demonstrated across a broad collection of challenging applications, including generalized regression, deep Gaussian process surrogate modeling, and high-dimensional sparse regression. Together, our theoretical results and the case studies give evidence of the efficiency and robustness of AGESS across target distributions that are non-elliptical, non-differentiable, multi-modal, or high-dimensional.

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arXiv2026

Mixed Membership Models for Multilevel Functional Data

Mixed membership models extend classical clustering by substituting the notion of uncertain membership with the notion of mixed membership. In particular, these models allow each observation to partially belong to multiple pure membership classes. We discuss mixed membership models for functional data by extending the framework to multilevel functional observations. We show how the classical multivariate Karhunen-Loeve decomposition can be translated into a simple hierarchical model for scalable and flexible expressivity of the underlying stochastic processes. The identifiability of partial membership structures is aided by the definition of a hierarchical repulsive prior on the unitary simplex. Our work is motivated and illustrated by applications to a study on functional brain imaging through electroencephalography (EEG) of children with autism spectrum disorder (ASD).

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arXiv2024

Covariate Adjusted Functional Mixed Membership Models

Mixed membership models are a flexible class of probabilistic data representations used for unsupervised and semi-supervised learning, allowing each observation to partially belong to multiple clusters or features. In this manuscript, we extend the framework of functional mixed membership models to allow for covariate-dependent adjustments. The proposed model utilizes a multivariate Karhunen-Lo\`eve decomposition, which allows for a scalable and flexible model. Within this framework, we establish a set of sufficient conditions ensuring the identifiability of the mean, covariance, and allocation structure up to a permutation of the labels. This manuscript is primarily motivated by studies on functional brain imaging through electroencephalography (EEG) of children with autism spectrum disorder (ASD). Specifically, we are interested in characterizing the heterogeneity of alpha oscillations for typically developing (TD) children and children with ASD. Since alpha oscillations are known to change as children develop, we aim to characterize the heterogeneity of alpha oscillations conditionally on the age of the child. Using the proposed framework, we were able to gain novel information on the developmental trajectories of alpha oscillations for children with ASD and how the developmental trajectories differ between TD children and children with ASD.

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arXiv2024

Modeling Neural Switching via Drift-Diffusion Models

Neural encoding is a field in neuroscience that focuses on characterizing how information from stimuli is encoded in the spiking activity of neurons. When more than one stimulus is present, a theory known as multiplexing posits that neurons temporally switch between encoding various stimuli, creating a fluctuating firing pattern. Here, we propose a new statistical framework to analyze rate fluctuations and discern whether neurons employ multiplexing as a means of encoding multiple stimuli. We adopt a mechanistic approach to modeling multiplexing by constructing a non-Markovian endogenous state-space model. Specifically, we posit that multiplexing arises from competition between the stimuli, which are modeled as latent drift-diffusion processes. We propose a new MCMC algorithm for conducting posterior inference on similar types of state-space models, where typical state-space MCMC methods fail due to strong dependence between the parameters. In addition, we develop alternative models that represent a wide class of alternative encoding theories and perform model comparison using WAIC to determine whether the data suggest the occurrence multiplexing over alternative theories of neural encoding. Using the proposed framework, we provide evidence of multiplexing within the inferior colliculus and novel insight into the switching dynamics.

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arXiv2022

Flexible Regularized Estimation in High-Dimensional Mixed Membership Models

Mixed membership models are an extension of finite mixture models, where each observation can partially belong to more than one mixture component. A probabilistic framework for mixed membership models of high-dimensional continuous data is proposed with a focus on scalability and interpretability. The novel probabilistic representation of mixed membership is based on convex combinations of dependent multivariate Gaussian random vectors. In this setting, scalability is ensured through approximations of a tensor covariance structure through multivariate eigen-approximations with adaptive regularization imposed through shrinkage priors. Conditional weak posterior consistency is established on an unconstrained model, allowing for a simple posterior sampling scheme while keeping many of the desired theoretical properties of our model. The model is motivated by two biomedical case studies: a case study on functional brain imaging of children with autism spectrum disorder (ASD) and a case study on gene expression data from breast cancer tissue. These applications highlight how the typical assumption made in cluster analysis, that each observation comes from one homogeneous subgroup, may often be restrictive in several applications, leading to unnatural interpretations of data features.

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arXiv2022

Functional Mixed Membership Models

Mixed membership models, or partial membership models, are a flexible unsupervised learning method that allows each observation to belong to multiple clusters. In this paper, we propose a Bayesian mixed membership model for functional data. By using the multivariate Karhunen-Lo\`eve theorem, we are able to derive a scalable representation of Gaussian processes that maintains data-driven learning of the covariance structure. Within this framework, we establish conditional posterior consistency given a known feature allocation matrix. Compared to previous work on mixed membership models, our proposal allows for increased modeling flexibility, with the benefit of a directly interpretable mean and covariance structure. Our work is motivated by studies in functional brain imaging through electroencephalography (EEG) of children with autism spectrum disorder (ASD). In this context, our work formalizes the clinical notion of "spectrum" in terms of feature membership proportions.

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