arXiv subjects

Joshua T. Vogelstein

Publications and source records attributed to Joshua T. Vogelstein.

100 records · Page 6Linked to original sources

arXiv2013

Bayesian crack detection in ultra high resolution multimodal images of paintings

The preservation of our cultural heritage is of paramount importance. Thanks to recent developments in digital acquisition techniques, powerful image analysis algorithms are developed which can be useful non-invasive tools to assist in the restoration and preservation of art. In this paper we propose a semi-supervised crack detection method that can be used for high-dimensional acquisitions of paintings coming from different modalities. Our dataset consists of a recently acquired collection of images of the Ghent Altarpiece (1432), one of Northern Europe's most important art masterpieces. Our goal is to build a classifier that is able to discern crack pixels from the background consisting of non-crack pixels, making optimal use of the information that is provided by each modality. To accomplish this we employ a recently developed non-parametric Bayesian classifier, that uses tensor factorizations to characterize any conditional probability. A prior is placed on the parameters of the factorization such that every possible interaction between predictors is allowed while still identifying a sparse subset among these predictors. The proposed Bayesian classifier, which we will refer to as conditional Bayesian tensor factorization or CBTF, is assessed by visually comparing classification results with the Random Forest (RF) algorithm.

cs.CV↗

arXiv2013

DELTACON: A Principled Massive-Graph Similarity Function

How much did a network change since yesterday? How different is the wiring between Bob's brain (a left-handed male) and Alice's brain (a right-handed female)? Graph similarity with known node correspondence, i.e. the detection of changes in the connectivity of graphs, arises in numerous settings. In this work, we formally state the axioms and desired properties of the graph similarity functions, and evaluate when state-of-the-art methods fail to detect crucial connectivity changes in graphs. We propose DeltaCon, a principled, intuitive, and scalable algorithm that assesses the similarity between two graphs on the same nodes (e.g. employees of a company, customers of a mobile carrier). Experiments on various synthetic and real graphs showcase the advantages of our method over existing similarity measures. Finally, we employ DeltaCon to real applications: (a) we classify people to groups of high and low creativity based on their brain connectivity graphs, and (b) do temporal anomaly detection in the who-emails-whom Enron graph.

cs.SI↗

arXiv2012

Shuffled Graph Classification: Theory and Connectome Applications

We develop a formalism to address statistical pattern recognition of graph valued data. Of particular interest is the case of all graphs having the same number of uniquely labeled vertices. When the vertex labels are latent, such graphs are called shuffled graphs. Our formalism provides insight to trivially answer a number of open statistical questions including: (i) under what conditions does shuffling the vertices degrade classification performance and (ii) do universally consistent graph classifiers exist? The answers to these questions lead to practical heuristic algorithms with state-of-the-art finite sample performance, in agreement with our theoretical asymptotics.

q-bio.QM↗

arXiv2012

Consistent adjacency-spectral partitioning for the stochastic block model when the model parameters are unknown

For random graphs distributed according to a stochastic block model, we consider the inferential task of partioning vertices into blocks using spectral techniques. Spectral partioning using the normalized Laplacian and the adjacency matrix have both been shown to be consistent as the number of vertices tend to infinity. Importantly, both procedures require that the number of blocks and the rank of the communication probability matrix are known, even as the rest of the parameters may be unknown. In this article, we prove that the (suitably modified) adjacency-spectral partitioning procedure, requiring only an upper bound on the rank of the communication probability matrix, is consistent. Indeed, this result demonstrates a robustness to model mis-specification; an overestimate of the rank may impose a moderate performance penalty, but the procedure is still consistent. Furthermore, we extend this procedure to the setting where adjacencies may have multiple modalities and we allow for either directed or undirected graphs.

stat.ME↗

arXiv2012

Graph Classification using Signal-Subgraphs: Applications in Statistical Connectomics

This manuscript considers the following "graph classification" question: given a collection of graphs and associated classes, how can one predict the class of a newly observed graph? To address this question we propose a statistical model for graph/class pairs. This model naturally leads to a set of estimators to identify the class-conditional signal, or "signal-subgraph," defined as the collection of edges that are probabilistically different between the classes. The estimators admit classifiers which are asymptotically optimal and efficient, but differ by their assumption about the "coherency" of the signal-subgraph (coherency is the extent to which the signal-edges "stick together" around a common subset of vertices). Via simulation, the best estimator is shown to be not just a function of the coherency of the model, but also the number of training samples. These estimators are employed to address a contemporary neuroscience question: can we classify "connectomes" (brain-graphs) according to sex? The answer is yes, and significantly better than all benchmark algorithms considered. Synthetic data analysis demonstrates that even when the model is correct, given the relatively small number of training samples, the estimated signal-subgraph should be taken with a grain of salt. We conclude by discussing several possible extensions.

stat.AP↗

arXiv2011

Magnetic Resonance Connectome Automated Pipeline

This manuscript presents a novel, tightly integrated pipeline for estimating a connectome, which is a comprehensive description of the neural circuits in the brain. The pipeline utilizes magnetic resonance imaging (MRI) data to produce a high-level estimate of the structural connectivity in the human brain. The Magnetic Resonance Connectome Automated Pipeline (MRCAP) is efficient and its modular construction allows researchers to modify algorithms to meet their specific requirements. The pipeline has been validated and over 200 connectomes have been processed and analyzed to date. This tool enables the prediction and assessment of various cognitive covariates, and this research is applicable to a variety of domains and applications. MRCAP will enable MR connectomes to be rapidly generated to ultimately help spur discoveries about the structure and function of the human brain.

q-bio.NC↗

arXiv2011

Optimizing the quantity/quality trade-off in connectome inference

We demonstrate a meaningful prospective power analysis for an (admittedly idealized) illustrative connectome inference task. Modeling neurons as vertices and synapses as edges in a simple random graph model, we optimize the trade-off between the number of (putative) edges identified and the accuracy of the edge identification procedure. We conclude that explicit analysis of the quantity/quality trade-off is imperative for optimal neuroscientific experimental design. In particular, more though more errorful edge identification can yield superior inferential performance.

q-bio.NC↗

arXiv2011

Are mental properties supervenient on brain properties?

The "mind-brain supervenience" conjecture suggests that all mental properties are derived from the physical properties of the brain. To address the question of whether the mind supervenes on the brain, we frame a supervenience hypothesis in rigorous statistical terms. Specifically, we propose a modified version of supervenience (called epsilon-supervenience) that is amenable to experimental investigation and statistical analysis. To illustrate this approach, we perform a thought experiment that illustrates how the probabilistic theory of pattern recognition can be used to make a one-sided determination of epsilon-supervenience. The physical property of the brain employed in this analysis is the graph describing brain connectivity (i.e., the brain-graph or connectome). epsilon-supervenience allows us to determine whether a particular mental property can be inferred from one's connectome to within any given positive misclassification rate, regardless of the relationship between the two. This may provide motivation for cross-disciplinary research between neuroscientists and statisticians.

q-bio.OT↗

arXiv2011

A Bayesian approach for inferring neuronal connectivity from calcium fluorescent imaging data

Deducing the structure of neural circuits is one of the central problems of modern neuroscience. Recently-introduced calcium fluorescent imaging methods permit experimentalists to observe network activity in large populations of neurons, but these techniques provide only indirect observations of neural spike trains, with limited time resolution and signal quality. In this work we present a Bayesian approach for inferring neural circuitry given this type of imaging data. We model the network activity in terms of a collection of coupled hidden Markov chains, with each chain corresponding to a single neuron in the network and the coupling between the chains reflecting the network's connectivity matrix. We derive a Monte Carlo Expectation--Maximization algorithm for fitting the model parameters; to obtain the sufficient statistics in a computationally-efficient manner, we introduce a specialized blockwise-Gibbs algorithm for sampling from the joint activity of all observed neurons given the observed fluorescence data. We perform large-scale simulations of randomly connected neuronal networks with biophysically realistic parameters and find that the proposed methods can accurately infer the connectivity in these networks given reasonable experimental and computational constraints. In addition, the estimation accuracy may be improved significantly by incorporating prior knowledge about the sparseness of connectivity in the network, via standard L$_1$ penalization methods.

stat.AP↗

arXiv2009

Fast non-negative deconvolution for spike train inference from population calcium imaging

Calcium imaging for observing spiking activity from large populations of neurons are quickly gaining popularity. While the raw data are fluorescence movies, the underlying spike trains are of interest. This work presents a fast non-negative deconvolution filter to infer the approximately most likely spike train for each neuron, given the fluorescence observations. This algorithm outperforms optimal linear deconvolution (Wiener filtering) on both simulated and biological data. The performance gains come from restricting the inferred spike trains to be positive (using an interior-point method), unlike the Wiener filter. The algorithm is fast enough that even when imaging over 100 neurons, inference can be performed on the set of all observed traces faster than real-time. Performing optimal spatial filtering on the images further refines the estimates. Importantly, all the parameters required to perform the inference can be estimated using only the fluorescence data, obviating the need to perform joint electrophysiological and imaging calibration experiments.

q-bio.QM↗