arXiv subjects

Brendan Martin

Publications and source records attributed to Brendan Martin.

5 recordsLinked to original sources

arXiv2026

Spectral clustering of network time series via the sample covariance matrix

Spectral clustering for community detection is analysed in multivariate time series models whose dependence structure is determined by an unobserved stochastic blockmodel. We establish that spectral clustering of the sample covariance matrix achieves exact recovery of the underlying communities. The recovery rates depend explicitly on the network size, sample length, block separation, and degree of data dependence. This demonstrates that exact community recovery under a stochastic blockmodel is possible even when the adjacency matrix is unobserved. Our theory provides extensions of both classical and fine-grained matrix perturbation theory to the setting of dependent data, which may be of independent interest.

math.ST↗

arXiv2026

The LIRA-Ising Model: Estimating the boundaries of irregularly shaped X-ray sources

Mapping the boundary of an extended source is a key step in the study of its morphology. The background contamination and statistical fluctuations of typical astronomical images make this a challenging statistical task, particularly for X-ray images with low surface brightness. We develop a three-step Bayesian procedure to identify the boundaries of irregularly shaped sources. We first apply a Bayesian multiscale reconstruction algorithm known as LIRA to obtain posterior pixelwise probability distributions of the source intensity that properly account for known structures, astrophysical background, and the effect of the telescope point spread function. Next, we adopt an Ising model to group pixels with similar intensities into cohesive regions corresponding to background and source. Finally, the boundary is derived on the basis of the most likely aggregation of pixels into the source region. Because the overall model combines LIRA and the Ising model, we call it LIRA-Ising. We verify the proposed method using a set of simulation studies. We then apply it to the Chandra X-ray Observatory images of two high redshift quasars, PKS J1421-0643 and 0730+257, to determine the extent and morphology of X-ray jets. Our method shows a uniform X-ray surface brightness of PKS J1421-0643 jet, and identifies knotty structure in the X-ray jet of 0730+257.

astro-ph.IM↗

arXiv2025

Factor-Driven Network Informed Restricted Vector Autoregression

High-dimensional financial time series often exhibit complex dependence relations driven by both common market structures and latent connections among assets. To capture these characteristics, this paper proposes Factor-Driven Network Informed Restricted Vector Autoregression (FNIRVAR), a model for the common and idiosyncratic components of high-dimensional time series with an underlying unobserved network structure. The common component is modelled by a static factor model, which allows for strong cross-sectional dependence, whilst a network vector autoregressive process captures the residual co-movements due to the idiosyncratic component. An assortative stochastic block model underlies the network VAR, leading to groups of highly co-moving variables in the idiosyncratic component. For estimation, a two-step procedure is proposed, whereby the static factors are estimated via principal component analysis, followed by estimation of the network VAR parameters. The method is demonstrated in financial applications to daily returns, intraday returns, and FRED-MD macroeconomic variables. In all cases, the proposed method outperforms a static factor model, as well as a static factor plus LASSO-estimated sparse VAR model, in terms of forecasting and financial performance metrics.

stat.ME↗

arXiv2024

NIRVAR: Network Informed Restricted Vector Autoregression

High-dimensional panels of time series often arise in finance and macroeconomics, where co-movements within groups of panel components occur. Extracting these groupings from the data provides a coarse-grained description of the complex system in question and can inform subsequent prediction tasks. We develop a novel methodology to model such a panel as a restricted vector autoregressive process, where the coefficient matrix is the weighted adjacency matrix of a stochastic block model. This network time series model, which we call the Network Informed Restricted Vector Autoregression (NIRVAR) model, yields a coefficient matrix that has a sparse block-diagonal structure. We propose an estimation procedure that embeds each panel component in a low-dimensional latent space and clusters the embedded points to recover the blocks of the coefficient matrix. Crucially, the method allows for network-based time series modelling when the underlying network is unobserved. We derive the bias, consistency and asymptotic normality of the NIRVAR estimator. Simulation studies suggest that the NIRVAR estimated embedded points are Gaussian distributed around the ground truth latent positions. On three applications to finance, macroeconomics, and transportation systems, NIRVAR outperforms competing models in terms of prediction and provides interpretable results regarding group recovery.

stat.ME↗

arXiv2024

NOISe: Nuclei-Aware Osteoclast Instance Segmentation for Mouse-to-Human Domain Transfer

Osteoclast cell image analysis plays a key role in osteoporosis research, but it typically involves extensive manual image processing and hand annotations by a trained expert. In the last few years, a handful of machine learning approaches for osteoclast image analysis have been developed, but none have addressed the full instance segmentation task required to produce the same output as that of the human expert led process. Furthermore, none of the prior, fully automated algorithms have publicly available code, pretrained models, or annotated datasets, inhibiting reproduction and extension of their work. We present a new dataset with ~2*10^5 expert annotated mouse osteoclast masks, together with a deep learning instance segmentation method which works for both in vitro mouse osteoclast cells on plastic tissue culture plates and human osteoclast cells on bone chips. To our knowledge, this is the first work to automate the full osteoclast instance segmentation task. Our method achieves a performance of 0.82 mAP_0.5 (mean average precision at intersection-over-union threshold of 0.5) in cross validation for mouse osteoclasts. We present a novel nuclei-aware osteoclast instance segmentation training strategy (NOISe) based on the unique biology of osteoclasts, to improve the model's generalizability and boost the mAP_0.5 from 0.60 to 0.82 on human osteoclasts. We publish our annotated mouse osteoclast image dataset, instance segmentation models, and code at github.com/michaelwwan/noise to enable reproducibility and to provide a public tool to accelerate osteoporosis research.

cs.CV↗