arXiv subjects

Robert E. Kass

Publications and source records attributed to Robert E. Kass.

15 recordsLinked to original sources

arXiv2026

Simultaneous Inference in Multiple Matrix-Variate Graphs for High-Dimensional Neural Recordings

We study simultaneous inference for multiple matrix-variate Gaussian graphical models in high-dimensional settings. Such models arise when spatiotemporal data are collected across multiple sample groups or experimental sessions, where each group is characterized by its own graphical structure but shares common sparsity patterns. A central challenge is to conduct valid inference on collections of graph edges while efficiently borrowing strength across groups under both high-dimensionality and temporal dependence. We propose a unified framework that combines joint estimation via group penalized regression with a high-dimensional Gaussian approximation bootstrap to enable global testing of edge subsets of arbitrary size. The proposed procedure accommodates temporally dependent observations and avoids naive pooling across heterogeneous groups. We establish theoretical guarantees for the validity of the simultaneous tests under mild conditions on sample size, dimensionality, and non-stationary autoregressive temporal dependence, and show that the resulting tests are nearly optimal in terms of the testable region boundary. The method relies only on convex optimization and parametric bootstrap, making it computationally tractable. Simulation studies and a neural recording example illustrate the efficacy of the proposed approach.

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arXiv2025

Cross-Population Amplitude Coupling in High-Dimensional Oscillatory Neural Time Series

Neural oscillations have long been considered important markers of interaction across brain regions, yet identifying coordinated oscillatory activity from high-dimensional multiple-electrode recordings remains challenging. We sought to quantify time-varying covariation of oscillatory amplitudes across two brain regions, during a memory task, based on local field potentials recorded from 96 electrodes in each region. We extended Canonical Correlation Analysis (CCA) to multiple time series through the cross-correlation of latent time series. This, however, introduces a large number of possible lead-lag cross-correlations across the two regions. To manage that high dimensionality we developed rigorous statistical procedures aimed at finding a small number of dominant lead-lag effects. The method correctly identified ground truth structure in realistic simulation-based settings. When we used it to analyze local field potentials recorded from prefrontal cortex and visual area V4 we obtained highly plausible results. The new statistical methodology could also be applied to other slowly-varying high-dimensional time series.

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arXiv2025

Identifying interactions across brain areas while accounting for individual-neuron dynamics with a Transformer-based variational autoencoder

Advances in large-scale recording technologies now enable simultaneous measurements from multiple brain areas, offering new opportunities to study signal transmission across interacting components of neural circuits. However, neural responses exhibit substantial trial-to-trial variability, often driven by unobserved factors such as subtle changes in animal behavior or internal states. To prevent evolving background dynamics from contaminating identification of functional coupling, we developed a hybrid neural spike train model, GLM-Transformer, that incorporates flexible, deep latent variable models into a point process generalized linear model (GLM) having an interpretable component for cross-population interactions. A Transformer-based variational autoencoder captures nonstationary individual-neuron dynamics that vary across trials, while standard nonparametric regression GLM coupling terms provide estimates of directed interactions between neural populations. We incorporate a low-rank structure on population-to-population coupling effects to improve scalability. Across synthetic datasets and mechanistic simulations, GLM-Transformer recovers known coupling structure and remains robust to shared background fluctuations. When applied to the Allen Institute Visual Coding dataset, it identifies feedforward pathways consistent with established visual hierarchies. This work offers a step toward improved identification of neural population interactions, and contributes to ongoing efforts aimed at achieving interpretable results while harvesting the benefits of deep learning.

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arXiv2021

Cross-population coupling of neural activity based on Gaussian process current source densities

Because local field potentials (LFPs) arise from multiple sources in different spatial locations, they do not easily reveal coordinated activity across neural populations on a trial-to-trial basis. As we show here, however, once disparate source signals are decoupled, their trial-to-trial fluctuations become more accessible, and cross-population correlations become more apparent. To decouple sources we introduce a general framework for estimation of current source densities (CSDs). In this framework, the set of LFPs result from noise being added to the transform of the CSD by a biophysical forward model, while the CSD is considered to be the sum of a zero-mean, stationary, spatiotemporal Gaussian process, having fast and slow components, and a mean function, which is the sum of multiple time-varying functions distributed across space, each varying across trials. We derived biophysical forward models relevant to the data we analyzed. In simulation studies this approach improved identification of source signals compared to existing CSD estimation methods. Using data recorded from primate auditory cortex, we analyzed trial-to-trial fluctuations in both steady-state and task-evoked signals. We found cortical layer-specific phase coupling between two probes and showed that the same analysis applied directly to LFPs did not recover these patterns. We also found task-evoked CSDs to be correlated across probes, at specific cortical depths. Using data from Neuropixels probes in mouse visual areas, we again found evidence for depth-specific phase coupling of primary visual area and lateromedial area based on the CSDs.

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arXiv2019

Torus Graphs for Multivariate Phase Coupling Analysis

Angular measurements are often modeled as circular random variables, where there are natural circular analogues of moments, including correlation. Because a product of circles is a torus, a d-dimensional vector of circular random variables lies on a d-dimensional torus. For such vectors we present here a class of graphical models, which we call torus graphs, based on the full exponential family with pairwise interactions. The topological distinction between a torus and Euclidean space has several important consequences. Our development was motivated by the problem of identifying phase coupling among oscillatory signals recorded from multiple electrodes in the brain: oscillatory phases across electrodes might tend to advance or recede together, indicating coordination across brain areas. The data analyzed here consisted of 24 phase angles measured repeatedly across 840 experimental trials (replications) during a memory task, where the electrodes were in 4 distinct brain regions, all known to be active while memories are being stored or retrieved. In realistic numerical simulations, we found that a standard pairwise assessment, known as phase locking value, is unable to describe multivariate phase interactions, but that torus graphs can accurately identify conditional associations. Torus graphs generalize several more restrictive approaches that have appeared in various scientific literatures, and produced intuitive results in the data we analyzed. Torus graphs thus unify multivariate analysis of circular data and present fertile territory for future research.

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arXiv2017

A Sequential Scheme for Large Scale Bayesian Multiple Testing

The problem of large scale multiple testing arises in many contexts, including testing for pairwise interaction among large numbers of neurons. With advances in technologies, it has become common to record from hundreds of neurons simultaneously, and this number is growing quickly, so that the number of pairwise tests can be very large. It is important to control the rate at which false positives occur. In addition, there is sometimes information that affects the probability of a positive result for any given pair. In the case of neurons, they are more likely to have correlated activity when they are close together, and when they respond similarly to various stimuli. Recently a method was developed to control false positives when covariate information, such as distances between pairs of neurons, is available. This method, however, relies on computationally-intensive Markov Chain Monte Carlo (MCMC). Here we develop an alternative, based on Sequential Monte Carlo, which scales well with the size of the dataset. This scheme considers data items sequentially, with relevant probabilities being updated at each step. Simulation experiments demonstrate that the proposed algorithm delivers results as accurately as the previous MCMC method with only a single pass through the data. We illustrate the method by using it to analyze neural recordings from extrastriate cortex in a macaque monkey.

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arXiv2017

Efficient and accurate extraction of in vivo calcium signals from microendoscopic video data

In vivo calcium imaging through microscopes has enabled deep brain imaging of previously inaccessible neuronal populations within the brains of freely moving subjects. However, microendoscopic data suffer from high levels of background fluorescence as well as an increased potential for overlapping neuronal signals. Previous methods fail in identifying neurons and demixing their temporal activity because the cellular signals are often submerged in the large fluctuating background. Here we develop an efficient method to extract cellular signals with minimal influence from the background. We model the background with two realistic components: (1) one models the constant baseline and slow trends of each pixel, and (2) the other models the fast fluctuations from out-of-focus signals and is therefore constrained to have low spatial-frequency structure. This decomposition avoids cellular signals being absorbed into the background term. After subtracting the background approximated with this model, we use Constrained Nonnegative Matrix Factorization (CNMF, Pnevmatikakis et al. (2016)) to better demix neural signals and get their denoised and deconvolved temporal activity. We validate our method on simulated and experimental data, where it shows fast, reliable, and high quality signal extraction under a wide variety of imaging parameters.

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arXiv2015

Estimating Learning Effects: A Short-Time Fourier Transform Regression Model for MEG Source Localization

Magnetoencephalography (MEG) has a high temporal resolution well-suited for studying perceptual learning. However, to identify where learning happens in the brain, one needs to ap- ply source localization techniques to project MEG sensor data into brain space. Previous source localization methods, such as the short-time Fourier transform (STFT) method by Gramfort et al.([Gramfort et al., 2013]) produced intriguing results, but they were not designed to incor- porate trial-by-trial learning effects. Here we modify the approach in [Gramfort et al., 2013] to produce an STFT-based source localization method (STFT-R) that includes an additional regression of the STFT components on covariates such as the behavioral learning curve. We also exploit a hierarchical L 21 penalty to induce structured sparsity of STFT components and to emphasize signals from regions of interest (ROIs) that are selected according to prior knowl- edge. In reconstructing the ROI source signals from simulated data, STFT-R achieved smaller errors than a two-step method using the popular minimum-norm estimate (MNE), and in a real-world human learning experiment, STFT-R yielded more interpretable results about what time-frequency components of the ROI signals were correlated with learning.

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arXiv2014

False discovery rate regression: an application to neural synchrony detection in primary visual cortex

Many approaches for multiple testing begin with the assumption that all tests in a given study should be combined into a global false-discovery-rate analysis. But this may be inappropriate for many of today's large-scale screening problems, where auxiliary information about each test is often available, and where a combined analysis can lead to poorly calibrated error rates within different subsets of the experiment. To address this issue, we introduce an approach called false-discovery-rate regression that directly uses this auxiliary information to inform the outcome of each test. The method can be motivated by a two-groups model in which covariates are allowed to influence the local false discovery rate, or equivalently, the posterior probability that a given observation is a signal. This poses many subtle issues at the interface between inference and computation, and we investigate several variations of the overall approach. Simulation evidence suggests that: (1) when covariate effects are present, FDR regression improves power for a fixed false-discovery rate; and (2) when covariate effects are absent, the method is robust, in the sense that it does not lead to inflated error rates. We apply the method to neural recordings from primary visual cortex. The goal is to detect pairs of neurons that exhibit fine-time-scale interactions, in the sense that they fire together more often than expected due to chance. Our method detects roughly 50% more synchronous pairs versus a standard FDR-controlling analysis. The companion R package FDRreg implements all methods described in the paper.

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arXiv2011

Assessment of synchrony in multiple neural spike trains using loglinear point process models

Neural spike trains, which are sequences of very brief jumps in voltage across the cell membrane, were one of the motivating applications for the development of point process methodology. Early work required the assumption of stationarity, but contemporary experiments often use time-varying stimuli and produce time-varying neural responses. More recently, many statistical methods have been developed for nonstationary neural point process data. There has also been much interest in identifying synchrony, meaning events across two or more neurons that are nearly simultaneous at the time scale of the recordings. A natural statistical approach is to discretize time, using short time bins, and to introduce loglinear models for dependency among neurons, but previous use of loglinear modeling technology has assumed stationarity. We introduce a succinct yet powerful class of time-varying loglinear models by (a) allowing individual-neuron effects (main effects) to involve time-varying intensities; (b) also allowing the individual-neuron effects to involve autocovariation effects (history effects) due to past spiking, (c) assuming excess synchrony effects (interaction effects) do not depend on history, and (d) assuming all effects vary smoothly across time.

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arXiv2011

Statistical Inference: The Big Picture

Statistics has moved beyond the frequentist-Bayesian controversies of the past. Where does this leave our ability to interpret results? I suggest that a philosophy compatible with statistical practice, labeled here statistical pragmatism, serves as a foundation for inference. Statistical pragmatism is inclusive and emphasizes the assumptions that connect statistical models with observed data. I argue that introductory courses often mischaracterize the process of statistical inference and I propose an alternative "big picture" depiction.

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arXiv2011

Rejoinder

Rejoinder of "Statistical Inference: The Big Picture" by R. E. Kass [arXiv:1106.2895]

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arXiv2010

Comment: How Should Indirect Evidence Be Used?

Indirect evidence is crucial for successful statistical practice. Sometimes, however, it is better used informally. Future efforts should be directed toward understanding better the connection between statistical methods and scientific problems. [arXiv:1012.1161]

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arXiv2010

Approximate Methods for State-Space Models

State-space models provide an important body of techniques for analyzing time-series, but their use requires estimating unobserved states. The optimal estimate of the state is its conditional expectation given the observation histories, and computing this expectation is hard when there are nonlinearities. Existing filtering methods, including sequential Monte Carlo, tend to be either inaccurate or slow. In this paper, we study a nonlinear filter for nonlinear/non-Gaussian state-space models, which uses Laplace's method, an asymptotic series expansion, to approximate the state's conditional mean and variance, together with a Gaussian conditional distribution. This {\em Laplace-Gaussian filter} (LGF) gives fast, recursive, deterministic state estimates, with an error which is set by the stochastic characteristics of the model and is, we show, stable over time. We illustrate the estimation ability of the LGF by applying it to the problem of neural decoding and compare it to sequential Monte Carlo both in simulations and with real data. We find that the LGF can deliver superior results in a small fraction of the computing time.

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arXiv2008

Information In The Non-Stationary Case

Information estimates such as the ``direct method'' of Strong et al. (1998) sidestep the difficult problem of estimating the joint distribution of response and stimulus by instead estimating the difference between the marginal and conditional entropies of the response. While this is an effective estimation strategy, it tempts the practitioner to ignore the role of the stimulus and the meaning of mutual information. We show here that, as the number of trials increases indefinitely, the direct (or ``plug-in'') estimate of marginal entropy converges (with probability 1) to the entropy of the time-averaged conditional distribution of the response, and the direct estimate of the conditional entropy converges to the time-averaged entropy of the conditional distribution of the response. Under joint stationarity and ergodicity of the response and stimulus, the difference of these quantities converges to the mutual information. When the stimulus is deterministic or non-stationary the direct estimate of information no longer estimates mutual information, which is no longer meaningful, but it remains a measure of variability of the response distribution across time.

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