arXiv subjects

Christopher J. Rozell

Publications and source records attributed to Christopher J. Rozell.

At least 19 recordsLinked to original sources

arXiv2026

Subspace Learning with Interval-Censored Likelihoods for Dequantizing Percept PC LFP Snapshots

Implanted neurostimulators that sense local field potentials now enable chronic electrophysiology based biomarker tracking in patients at home. The Medtronic Percept PC, the only commercially available sensing-enabled deep brain stimulation (DBS) device, stores spectral amplitudes as 16-bit integers at approximately 0.1 $μ$V per bit (quantum $q \approx 0.11$ $μ$Vp). At frequencies where the true amplitude spans only a few quantization levels, consecutive bins round to the same stored value. Standard spectral parameterization (FOOOF, fitting oscillations and one over f), which separates periodic peaks from the aperiodic 1/f activity, treats every value as exact and fits oscillatory peaks to these plateaus. Because these spectra feed clinical biomarker pipelines and spectral foundation models for symptom decoding, spurious peaks can corrupt downstream inference. Across 9,438 spectra from 14 hemispheres in 7 subcallosal cingulate DBS patients, 20.6% of peaks detected at [2, 45] Hz have no match in ground truth synthesized by quantizing clean in-clinic BrainSense recordings, while aggregate beta band power and the aperiodic exponent are preserved. We formalize dequantization as interval-censored subspace estimation and compare five classes of correction methods. Quantized probabilistic PCA is the only tested method that reduces the spurious rate (20.6% to 18.3%) while preserving true peak detection and keeping noise floor RMSE below $q/\sqrt{12}$.

eess.SP↗

arXiv2026

Self-Supervised Dynamical System Representations for Physiological Time-Series

The effectiveness of self-supervised learning (SSL) for physiological time series depends on the ability of a pretraining objective to preserve information about the underlying physiological state while filtering out unrelated noise. However, existing strategies are limited due to reliance on heuristic principles or poorly constrained generative tasks. To address this limitation, we propose a pretraining framework that exploits the information structure of a dynamical systems generative model across multiple time-series. This framework reveals our key insight that class identity can be efficiently captured by extracting information about the generative variables related to the system parameters shared across similar time series samples, while noise unique to individual samples should be discarded. Building on this insight, we propose PULSE, a cross-reconstruction-based pretraining objective for physiological time series datasets that explicitly extracts system information while discarding non-transferrable sample-specific ones. We establish theory that provides sufficient conditions for the system information to be recovered, and empirically validate it using a synthetic dynamical systems experiment. Furthermore, we apply our method to diverse real-world datasets, demonstrating that PULSE learns representations that can broadly distinguish semantic classes, increase label efficiency, and improve transfer learning.

cs.LG↗

arXiv2026

Beyond Labels: Information-Efficient Human-in-the-Loop Learning using Ranking and Selection Queries

Integrating human expertise into machine learning systems often reduces the role of experts to labeling oracles, a paradigm that limits the amount of information exchanged and fails to capture the nuances of human judgment. We address this challenge by developing a human-in-the-loop framework to learn binary classifiers with rich query types, consisting of item ranking and exemplar selection. We first introduce probabilistic human response models for these rich queries motivated by the relationship experimentally observed between the perceived implicit score of an item and its distance to the unknown classifier. Using these models, we then design active learning algorithms that leverage the rich queries to increase the information gained per interaction. We provide theoretical bounds on sample complexity and develop a tractable and computationally efficient variational approximation. Through experiments with simulated annotators derived from crowdsourced word-sentiment and image-aesthetic datasets, we demonstrate significant reductions on sample complexity. We further extend active learning strategies to select queries that maximize information rate, explicitly balancing informational value against annotation cost. This algorithm in the word sentiment classification task reduces learning time by more than 57\% compared to traditional label-only active learning.

cs.HC↗

arXiv2026

Stable Filtering for Efficient Dimensionality Reduction of Streaming Manifold Data

Many areas in science and engineering now have access to technologies that enable the rapid collection of overwhelming data volumes. While these datasets are vital for understanding phenomena from physical to biological and social systems, the sheer magnitude of the data makes even simple storage, transmission, and basic processing highly challenging. To enable efficient and accurate execution of these data processing tasks, we require new dimensionality reduction tools that 1) do not need expensive, time-consuming training, and 2) preserve the underlying geometry of the data that has the information required to understand the measured system. Specifically, the geometry to be preserved is that induced by the fact that in many applications, streaming high-dimensional data evolves on a low-dimensional attractor manifold. Importantly, we may not know the exact structure of this manifold a priori. To solve these challenges, we present randomized filtering (RF), which leverages a specific instantiation of randomized dimensionality reduction to provably preserve non-linear manifold structure in the embedded space while remaining data-independent and computationally efficient. In this work we build on the rich theoretical promise of randomized dimensionality reduction to develop RF as a real, practical approach. We introduce novel methods, analysis, and experimental verification to illuminate the practicality of RF in diverse scientific applications, including several simulated and real-data examples that showcase the tangible benefits of RF.

eess.SP↗

arXiv2024

Probabilistic Decomposed Linear Dynamical Systems for Robust Discovery of Latent Neural Dynamics

Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve according to simple locally linear dynamics. However, existing methods for latent variable estimation are not robust to dynamical noise and system nonlinearity due to noise-sensitive inference procedures and limited model formulations. This can lead to inconsistent results on signals with similar dynamics, limiting the model's ability to provide scientific insight. In this work, we address these limitations and propose a probabilistic approach to latent variable estimation in decomposed models that improves robustness against dynamical noise. Additionally, we introduce an extended latent dynamics model to improve robustness against system nonlinearities. We evaluate our approach on several synthetic dynamical systems, including an empirically-derived brain-computer interface experiment, and demonstrate more accurate latent variable inference in nonlinear systems with diverse noise conditions. Furthermore, we apply our method to a real-world clinical neurophysiology dataset, illustrating the ability to identify interpretable and coherent structure where previous models cannot.

stat.ML↗

arXiv2023

Manifold Contrastive Learning with Variational Lie Group Operators

Self-supervised learning of deep neural networks has become a prevalent paradigm for learning representations that transfer to a variety of downstream tasks. Similar to proposed models of the ventral stream of biological vision, it is observed that these networks lead to a separation of category manifolds in the representations of the penultimate layer. Although this observation matches the manifold hypothesis of representation learning, current self-supervised approaches are limited in their ability to explicitly model this manifold. Indeed, current approaches often only apply augmentations from a pre-specified set of "positive pairs" during learning. In this work, we propose a contrastive learning approach that directly models the latent manifold using Lie group operators parameterized by coefficients with a sparsity-promoting prior. A variational distribution over these coefficients provides a generative model of the manifold, with samples which provide feature augmentations applicable both during contrastive training and downstream tasks. Additionally, learned coefficient distributions provide a quantification of which transformations are most likely at each point on the manifold while preserving identity. We demonstrate benefits in self-supervised benchmarks for image datasets, as well as a downstream semi-supervised task. In the former case, we demonstrate that the proposed methods can effectively apply manifold feature augmentations and improve learning both with and without a projection head. In the latter case, we demonstrate that feature augmentations sampled from learned Lie group operators can improve classification performance when using few labels.

cs.LG↗

arXiv2023

Decomposed Linear Dynamical Systems (dLDS) for learning the latent components of neural dynamics

Learning interpretable representations of neural dynamics at a population level is a crucial first step to understanding how observed neural activity relates to perception and behavior. Models of neural dynamics often focus on either low-dimensional projections of neural activity, or on learning dynamical systems that explicitly relate to the neural state over time. We discuss how these two approaches are interrelated by considering dynamical systems as representative of flows on a low-dimensional manifold. Building on this concept, we propose a new decomposed dynamical system model that represents complex non-stationary and nonlinear dynamics of time series data as a sparse combination of simpler, more interpretable components. Our model is trained through a dictionary learning procedure, where we leverage recent results in tracking sparse vectors over time. The decomposed nature of the dynamics is more expressive than previous switched approaches for a given number of parameters and enables modeling of overlapping and non-stationary dynamics. In both continuous-time and discrete-time instructional examples we demonstrate that our model can well approximate the original system, learn efficient representations, and capture smooth transitions between dynamical modes, focusing on intuitive low-dimensional non-stationary linear and nonlinear systems. Furthermore, we highlight our model's ability to efficiently capture and demix population dynamics generated from multiple independent subnetworks, a task that is computationally impractical for switched models. Finally, we apply our model to neural "full brain" recordings of C. elegans data, illustrating a diversity of dynamics that is obscured when classified into discrete states.

stat.ML↗

arXiv2023

PrefGen: Preference Guided Image Generation with Relative Attributes

Deep generative models have the capacity to render high fidelity images of content like human faces. Recently, there has been substantial progress in conditionally generating images with specific quantitative attributes, like the emotion conveyed by one's face. These methods typically require a user to explicitly quantify the desired intensity of a visual attribute. A limitation of this method is that many attributes, like how "angry" a human face looks, are difficult for a user to precisely quantify. However, a user would be able to reliably say which of two faces seems "angrier". Following this premise, we develop the $\textit{PrefGen}$ system, which allows users to control the relative attributes of generated images by presenting them with simple paired comparison queries of the form "do you prefer image $a$ or image $b$?" Using information from a sequence of query responses, we can estimate user preferences over a set of image attributes and perform preference-guided image editing and generation. Furthermore, to make preference localization feasible and efficient, we apply an active query selection strategy. We demonstrate the success of this approach using a StyleGAN2 generator on the task of human face editing. Additionally, we demonstrate how our approach can be combined with CLIP, allowing a user to edit the relative intensity of attributes specified by text prompts. Code at https://github.com/helblazer811/PrefGen.

cs.CV↗

arXiv2022

Variational Sparse Coding with Learned Thresholding

Sparse coding strategies have been lauded for their parsimonious representations of data that leverage low dimensional structure. However, inference of these codes typically relies on an optimization procedure with poor computational scaling in high-dimensional problems. For example, sparse inference in the representations learned in the high-dimensional intermediary layers of deep neural networks (DNNs) requires an iterative minimization to be performed at each training step. As such, recent, quick methods in variational inference have been proposed to infer sparse codes by learning a distribution over the codes with a DNN. In this work, we propose a new approach to variational sparse coding that allows us to learn sparse distributions by thresholding samples, avoiding the use of problematic relaxations. We first evaluate and analyze our method by training a linear generator, showing that it has superior performance, statistical efficiency, and gradient estimation compared to other sparse distributions. We then compare to a standard variational autoencoder using a DNN generator on the Fashion MNIST and CelebA datasets

cs.LG↗

arXiv2021

Late fusion of machine learning models using passively captured interpersonal social interactions and motion from smartphones predicts decompensation in heart failure

Objective: Worldwide, heart failure (HF) is a major cause of morbidity and mortality and one of the leading causes of hospitalization. Early detection of HF symptoms and pro-active management may reduce adverse events. Approach: Twenty-eight participants were monitored using a smartphone app after discharge from hospitals, and each clinical event during the enrollment (N=110 clinical events) was recorded. Motion, social, location, and clinical survey data collected via the smartphone-based monitoring system were used to develop and validate an algorithm for predicting or classifying HF decompensation events (hospitalizations or clinic visit) versus clinic monitoring visits in which they were determined to be compensated or stable. Models based on single modality as well as early and late fusion approaches combining patient-reported outcomes and passive smartphone data were evaluated. Results: The highest AUCPr for classifying decompensation with a late fusion approach was 0.80 using leave one subject out cross-validation. Significance: Passively collected data from smartphones, especially when combined with weekly patient-reported outcomes, may reflect behavioral and physiological changes due to HF and thus could enable prediction of HF decompensation.

eess.SP↗

arXiv2021

Variational Autoencoder with Learned Latent Structure

The manifold hypothesis states that high-dimensional data can be modeled as lying on or near a low-dimensional, nonlinear manifold. Variational Autoencoders (VAEs) approximate this manifold by learning mappings from low-dimensional latent vectors to high-dimensional data while encouraging a global structure in the latent space through the use of a specified prior distribution. When this prior does not match the structure of the true data manifold, it can lead to a less accurate model of the data. To resolve this mismatch, we introduce the Variational Autoencoder with Learned Latent Structure (VAELLS) which incorporates a learnable manifold model into the latent space of a VAE. This enables us to learn the nonlinear manifold structure from the data and use that structure to define a prior in the latent space. The integration of a latent manifold model not only ensures that our prior is well-matched to the data, but also allows us to define generative transformation paths in the latent space and describe class manifolds with transformations stemming from examples of each class. We validate our model on examples with known latent structure and also demonstrate its capabilities on a real-world dataset.

stat.ML↗

arXiv2020

Efficient Tracking of Sparse Signals via an Earth Mover's Distance Dynamics Regularizer

Tracking algorithms such as the Kalman filter aim to improve inference performance by leveraging the temporal dynamics in streaming observations. However, the tracking regularizers are often based on the $\ell_p$-norm which cannot account for important geometrical relationships between neighboring signal elements. We propose a practical approach to using the earth mover's distance (EMD) via the earth mover's distance dynamic filtering (EMD-DF) algorithm for causally tracking time-varying sparse signals when there is a natural geometry to the coefficient space that should be respected (e.g., meaningful ordering). Specifically, this paper presents a new Beckmann formulation that dramatically reduces computational complexity, as well as an evaluation of the performance and complexity of the proposed approach in imaging and frequency tracking applications with real and simulated neurophysiology data.

eess.SP↗

arXiv2020

Parallel Unbalanced Optimal Transport Regularization for Large Scale Imaging Problems

The modeling of phenomenological structure is a crucial aspect in inverse imaging problems. One emerging modeling tool in computational imaging is the optimal transport framework. Its ability to model geometric displacements across an image's support gives it attractive qualities similar to those of optical flow methods which are effective at capturing visual motion, but are restricted to operate in significantly smaller state-spaces. Despite this advantage, two major drawbacks make it unsuitable for general deployment: (i) it suffers from exorbitant computational costs due to a quadratic optimization-variable complexity, and (ii) it has a mass-balancing assumption that limits applications with natural images. We tackle these issues simultaneously by proposing a novel formulation for an unbalanced optimal transport regularizer that has linear optimization-variable complexity. In addition, we present a general parallelizable proximal method for this regularizer, and demonstrate superior empirical performance on novel dynamical tracking applications in synthetic and real video.

eess.IV↗

arXiv2019

Sparse Bayesian Learning with Dynamic Filtering for Inference of Time-Varying Sparse Signals

Many signal processing applications require estimation of time-varying sparse signals, potentially with the knowledge of an imperfect dynamics model. In this paper, we propose an algorithm for dynamic filtering of time-varying sparse signals based on the sparse Bayesian learning (SBL) framework. The key idea underlying the algorithm, termed SBL-DF, is the incorporation of a signal prediction generated from a dynamics model and estimates of previous time steps into the hyperpriors of the SBL probability model. The proposed algorithm is robust to imperfect dynamics models (due to the propagation of dynamics information through higher-order statistics), robust to certain undesirable dictionary properties such as coherence (due to properties of the SBL framework), allows the use of arbitrary dynamics models, and requires the tuning of fewer parameters than many other dynamic filtering algorithms do. We also extend the fast marginal likelihood SBL inference procedure to the informative hyperprior setting to create a particularly efficient version of the SBL-DF algorithm. Numerical simulations show that SBL-DF converges much faster and to more accurate solutions than standard SBL and other dynamical filtering algorithms. In particular, we show that SBL-DF outperforms state of the art algorithms when the dictionary contains challenging structure such as coherence and column scaling, as is found in many practical applications.

eess.SP↗

arXiv2019

Hierarchical Optimal Transport for Multimodal Distribution Alignment

In many machine learning applications, it is necessary to meaningfully aggregate, through alignment, different but related datasets. Optimal transport (OT)-based approaches pose alignment as a divergence minimization problem: the aim is to transform a source dataset to match a target dataset using the Wasserstein distance as a divergence measure. We introduce a hierarchical formulation of OT which leverages clustered structure in data to improve alignment in noisy, ambiguous, or multimodal settings. To solve this numerically, we propose a distributed ADMM algorithm that also exploits the Sinkhorn distance, thus it has an efficient computational complexity that scales quadratically with the size of the largest cluster. When the transformation between two datasets is unitary, we provide performance guarantees that describe when and how well aligned cluster correspondences can be recovered with our formulation, as well as provide worst-case dataset geometry for such a strategy. We apply this method to synthetic datasets that model data as mixtures of low-rank Gaussians and study the impact that different geometric properties of the data have on alignment. Next, we applied our approach to a neural decoding application where the goal is to predict movement directions and instantaneous velocities from populations of neurons in the macaque primary motor cortex. Our results demonstrate that when clustered structure exists in datasets, and is consistent across trials or time points, a hierarchical alignment strategy that leverages such structure can provide significant improvements in cross-domain alignment.

stat.ML↗

arXiv2019

Active embedding search via noisy paired comparisons

Suppose that we wish to estimate a user's preference vector $w$ from paired comparisons of the form "does user $w$ prefer item $p$ or item $q$?," where both the user and items are embedded in a low-dimensional Euclidean space with distances that reflect user and item similarities. Such observations arise in numerous settings, including psychometrics and psychology experiments, search tasks, advertising, and recommender systems. In such tasks, queries can be extremely costly and subject to varying levels of response noise; thus, we aim to actively choose pairs that are most informative given the results of previous comparisons. We provide new theoretical insights into the benefits and challenges of greedy information maximization in this setting, and develop two novel strategies that maximize lower bounds on information gain and are simpler to analyze and compute respectively. We use simulated responses from a real-world dataset to validate our strategies through their similar performance to greedy information maximization, and their superior preference estimation over state-of-the-art selection methods as well as random queries.

stat.ML↗

arXiv2017

Stabilizing Embedology: Geometry-Preserving Delay-Coordinate Maps

Delay-coordinate mapping is an effective and widely used technique for reconstructing and analyzing the dynamics of a nonlinear system based on time-series outputs. The efficacy of delay-coordinate mapping has long been supported by Takens' embedding theorem, which guarantees that delay-coordinate maps use the time-series output to provide a reconstruction of the hidden state space that is a one-to-one embedding of the system's attractor. While this topological guarantee ensures that distinct points in the reconstruction correspond to distinct points in the original state space, it does not characterize the quality of this embedding or illuminate how the specific parameters affect the reconstruction. In this paper, we extend Takens' result by establishing conditions under which delay-coordinate mapping is guaranteed to provide a stable embedding of a system's attractor. Beyond only preserving the attractor topology, a stable embedding preserves the attractor geometry by ensuring that distances between points in the state space are approximately preserved. In particular, we find that delay-coordinate mapping stably embeds an attractor of a dynamical system if the stable rank of the system is large enough to be proportional to the dimension of the attractor. The stable rank reflects the relation between the sampling interval and the number of delays in delay-coordinate mapping. Our theoretical findings give guidance to choosing system parameters, echoing the trade-off between irrelevancy and redundancy that has been heuristically investigated in the literature. Our initial result is stated for attractors that are smooth submanifolds of Euclidean space, with extensions provided for the case of strange attractors.

nlin.CD↗

arXiv2015

Re-Weighted l_1 Dynamic Filtering for Time-Varying Sparse Signal Estimation

Signal estimation from incomplete observations improves as more signal structure can be exploited in the inference process. Classic algorithms (e.g., Kalman filtering) have exploited strong dynamic structure for time-varying signals while modern work has often focused on exploiting low-dimensional signal structure (e.g., sparsity in a basis) for static signals. Few algorithms attempt to merge both static and dynamic structure to improve estimation for time-varying sparse signals (e.g., video). In this work we present a re-weighted l_1 dynamic filtering scheme for causal signal estimation that utilizes both sparsity assumptions and dynamic structure. Our algorithm leverages work on hierarchical Laplacian scale mixture models to create a dynamic probabilistic model. The resulting algorithm incorporates both dynamic and sparsity priors in the estimation procedure in a robust and efficient algorithm. We demonstrate the results in simulation using both synthetic and natural data.

math.ST↗