arXiv subjects

Bruno M. Jedynak

Publications and source records attributed to Bruno M. Jedynak.

6 recordsLinked to original sources

arXiv2026

Time Series Classification through Diffeomorphic Time Warping (DiffTW)

Time series classification involves learning a mapping from a continuous, temporally ordered sequence of real-valued observations to discrete response variables, like class labels. This task is fundamental in domains, including health monitoring, where temporal structure is critical for prediction. Dynamic Time Warping (DTW) is a standard technique for measuring similarity between sequences varying in time or speed. However, DTW is restricted to discrete point matching. Moving beyond pairwise alignment, we propose a theoretical framework learning mappings between real-valued functions. These mappings approximate the flow associated with the characteristic curves of a linear transport equation with a space-dependent velocity field, providing a diffeomorphic transformation between time series. Using the method of characteristics, we transform this partial differential equation into ordinary differential equations (ODEs) modeling system dynamics. The objective function to learn these ODEs derives from the fundamental theorem of calculus. To enable flexible, expressive representations of the velocity field, we utilize reproducing kernel Hilbert spaces and optimal control methods. Our method, Diffeomorphic Time Warping (DiffTW), provides a theoretically grounded dissimilarity measure. Using a 1-nearest neighbor classifier, DiffTW outperforms unconstrained DTW on 39 of 85 datasets with 3 ties; however, constrained DTW outperforms DiffTW on 48 of 85 datasets with 5 ties.

stat.ML↗

arXiv2023

Learning nonparametric ordinary differential equations from noisy data

Learning nonparametric systems of Ordinary Differential Equations (ODEs) dot x = f(t,x) from noisy data is an emerging machine learning topic. We use the well-developed theory of Reproducing Kernel Hilbert Spaces (RKHS) to define candidates for f for which the solution of the ODE exists and is unique. Learning f consists of solving a constrained optimization problem in an RKHS. We propose a penalty method that iteratively uses the Representer theorem and Euler approximations to provide a numerical solution. We prove a generalization bound for the L2 distance between x and its estimator and provide experimental comparisons with the state-of-the-art.

stat.ML↗

arXiv2020

Unstructured Primary Outcome in Randomized Controlled Trials

The primary outcome of Randomized clinical Trials (RCTs) are typically dichotomous, continuous, multivariate continuous, or time-to-event. However, what if this outcome is unstructured, e.g., a list of variables of mixed types, longitudinal sequences, images, audio recordings, etc. When the outcome is unstructured it is unclear how to assess RCT success and how to compute sample size. We show that kernel methods offer natural extensions to traditional biostatistics methods. We demonstrate our approach with the measurements of computer usage in a cohort of aging participants, some of which will become cognitively impaired. Simulations as well as a real data experiment show the superiority of the proposed approach compared to the standard in this situation: generalized mixed effect models.

stat.ME↗

arXiv2018

Topology guaranteed segmentation of the human retina from OCT using convolutional neural networks

Optical coherence tomography (OCT) is a noninvasive imaging modality which can be used to obtain depth images of the retina. The changing layer thicknesses can thus be quantified by analyzing these OCT images, moreover these changes have been shown to correlate with disease progression in multiple sclerosis. Recent automated retinal layer segmentation tools use machine learning methods to perform pixel-wise labeling and graph methods to guarantee the layer hierarchy or topology. However, graph parameters like distance and smoothness constraints must be experimentally assigned by retinal region and pathology, thus degrading the flexibility and time efficiency of the whole framework. In this paper, we develop cascaded deep networks to provide a topologically correct segmentation of the retinal layers in a single feed forward propagation. The first network (S-Net) performs pixel-wise labeling and the second regression network (R-Net) takes the topologically unconstrained S-Net results and outputs layer thicknesses for each layer and each position. Relu activation is used as the final operation of the R-Net which guarantees non-negativity of the output layer thickness. Since the segmentation boundary position is acquired by summing up the corresponding non-negative layer thicknesses, the layer ordering (i.e., topology) of the reconstructed boundaries is guaranteed even at the fovea where the distances between boundaries can be zero. The R-Net is trained using simulated masks and thus can be generalized to provide topology guaranteed segmentation for other layered structures. This deep network has achieved comparable mean absolute boundary error (2.82 μm) to state-of-the-art graph methods (2.83 μm).

cs.CV↗

arXiv2016

A multivariate nonlinear mixed effects model for longitudinal image analysis: Application to amyloid imaging

It is important to characterize the temporal trajectories of disease-related biomarkers in order to monitor progression and identify potential points of intervention. This is especially important for neurodegenerative diseases, as therapeutic intervention is most likely to be effective in the preclinical disease stages prior to significant neuronal damage. Longitudinal neuroimaging allows for the measurement of structural, functional, and metabolic integrity of the brain over time at the level of voxels. However, commonly used longitudinal analysis approaches, such as linear mixed effects models, do not account for the fact that individuals enter a study at various disease stages and progress at different rates, and generally consider each voxelwise measure independently. We propose a multivariate nonlinear mixed effects model for estimating the trajectories of voxelwise neuroimaging biomarkers from longitudinal data that accounts for such differences across individuals. The method involves the prediction of a progression score for each visit based on a collective analysis of voxelwise biomarker data within an expectation-maximization framework that efficiently handles large amounts of measurements and variable number of visits per individual, and accounts for spatial correlations among voxels. This score allows individuals with similar progressions to be aligned and analyzed together, which enables the construction of a trajectory of brain changes as a function of an underlying progression or disease stage. Application of our method to studying images of beta-amyloid deposition, a hallmark of preclinical Alzheimer's disease, suggests that precuneus is the earliest cortical region to accumulate amyloid. The proposed method can be applied to other types of longitudinal imaging data, including metabolism, blood flow, tau, and structural imaging-derived measures.

stat.ME↗

arXiv2015

Probabilistic Group Testing under Sum Observations: A Parallelizable 2-Approximation for Entropy Loss

We consider the problem of group testing with sum observations and noiseless answers, in which we aim to locate multiple objects by querying the number of objects in each of a sequence of chosen sets. We study a probabilistic setting with entropy loss, in which we assume a joint Bayesian prior density on the locations of the objects and seek to choose the sets queried to minimize the expected entropy of the Bayesian posterior distribution after a fixed number of questions. We present a new non-adaptive policy, called the dyadic policy, show it is optimal among non-adaptive policies, and is within a factor of two of optimal among adaptive policies. This policy is quick to compute, its nonadaptive nature makes it easy to parallelize, and our bounds show it performs well even when compared with adaptive policies. We also study an adaptive greedy policy, which maximizes the one-step expected reduction in entropy, and show that it performs at least as well as the dyadic policy, offering greater query efficiency but reduced parallelism. Numerical experiments demonstrate that both procedures outperform a divide-and-conquer benchmark policy from the literature, called sequential bifurcation, and show how these procedures may be applied in a stylized computer vision problem.

cs.IT↗