40 research outputs found

    Flexible Bayesian Dynamic Modeling of Correlation and Covariance Matrices

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    Modeling correlation (and covariance) matrices can be challenging due to the positive-definiteness constraint and potential high-dimensionality. Our approach is to decompose the covariance matrix into the correlation and variance matrices and propose a novel Bayesian framework based on modeling the correlations as products of unit vectors. By specifying a wide range of distributions on a sphere (e.g. the squared-Dirichlet distribution), the proposed approach induces flexible prior distributions for covariance matrices (that go beyond the commonly used inverse-Wishart prior). For modeling real-life spatio-temporal processes with complex dependence structures, we extend our method to dynamic cases and introduce unit-vector Gaussian process priors in order to capture the evolution of correlation among components of a multivariate time series. To handle the intractability of the resulting posterior, we introduce the adaptive Δ\Delta-Spherical Hamiltonian Monte Carlo. We demonstrate the validity and flexibility of our proposed framework in a simulation study of periodic processes and an analysis of rat's local field potential activity in a complex sequence memory task.Comment: 49 pages, 15 figure

    Nonspatial sequence coding in CA1 neurons

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    The hippocampus is critical to the memory for sequences of events, a defining feature of episodic memory. However, the fundamental neuronal mechanisms underlying this capacity remain elusive. While considerable research indicates hippocampal neurons can represent sequences of locations, direct evidence of coding for the memory of sequential relationships among nonspatial events remains lacking. To address this important issue, we recorded neural activity in CA1 as rats performed a hippocampus-dependent sequencememory task. Briefly, the task involves the presentation of repeated sequences of odors at a single port and requires rats to identify each item as “in sequence” or “out of sequence”. We report that, while the animals’ location and behavior remained constant, hippocampal activity differed depending on the temporal context of items—in this case, whether they were presented in or out of sequence. Some neurons showed this effect across items or sequence positions (general sequence cells), while others exhibited selectivity for specific conjunctions of item and sequence position information (conjunctive sequence cells) or for specific probe types (probe-specific sequence cells). We also found that the temporal context of individual trials could be accurately decoded from the activity of neuronal ensembles, that sequence coding at the single-cell and ensemble level was linked to sequence memory performance, and that slow-gamma oscillations (20–40 Hz) were more strongly modulated by temporal context and performance than theta oscillations (4–12 Hz). These findings provide compelling evidence that sequence coding extends beyond the domain of spatial trajectories and is thus a fundamental function of the hippocampus

    The neurobiology of memory based predictions

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    Recent findings indicate that, in humans, the hippocampal memory system is involved in the capacity to imagine the future as well as remember the past. Other studies have suggested that animals may also have the capacity to recall the past and plan for the future. Here, we will consider data that bridge between these sets of findings by assessing the role of the hippocampus in memory and prediction in rats. We will argue that animals have the capacity for recollection and that the hippocampus plays a central and selective role in binding information in the service of recollective memory. Then we will consider examples of transitive inference, a paradigm that requires the integration of overlapping memories and flexible use of the resulting relational memory networks for generating predictions in novel situations. Our data show that animals have the capacity for transitive inference and that the hippocampus plays a central role in the ability to predict outcomes of events that have not yet occurred

    The hippocampus and disambiguation of overlapping sequences.

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    Recent models of hippocampal function emphasize its potential role in disambiguating sequences of events that compose distinct episodic memories. In this study, rats were trained to distinguish two overlapping sequences of odor choices. The capacity to disambiguate the sequences was measured by the critical odor choice after the overlapping elements of the sequences. When the sequences were presented in rapid alternation, damage to the hippocampus, produced either by infusions of the neurotoxin ibotenic acid or by radiofrequency current, produced a severe deficit, although animals with radiofrequency lesions relearned the task. When the sequences were presented spaced apart and in random order, animals with radiofrequency hippocampal lesions could perform the task. However, they failed when a memory delay was imposed before the critical choice. These findings support the hypothesis that the hippocampus is involved in representing sequences of nonspatial events, particularly when interference between the sequences is high or when animals must remember across a substantial delay preceding items in a current sequence

    A hierarchical bayesian model for differential connectivity in multi-trial brain signals

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    There is a strong interest in the neuroscience community to measure brain connectivity and develop methods that can differentiate connectivity across patient groups and across different experimental stimuli. The development of such statistical tools is critical to understand the dynamics of functional relationships among brain structures supporting memory encoding and retrieval. However, the challenge comes from the need to incorporate within-condition similarity with between-conditions heterogeneity in modeling connectivity, as well as how to provide a natural way to conduct trial- and condition-level inference on effective connectivity. A Bayesian hierarchical vector autoregressive (BH-VAR) model is proposed to characterize brain connectivity and infer differences in connectivity across conditions. Within-condition connectivity similarity and between-conditions connectivity heterogeneity are accounted for by the priors on trial-specific models. In addition to the fully Bayesian framework, an alternative two-stage computation approach is also proposed which still allows straightforward uncertainty quantification of between-trial conditions via MCMC posterior sampling, but provides a fast approximate procedure for the estimation of trial-specific VAR parameters. A novel aspect of the approach is the use of a frequency-specific measure, partial directed coherence (PDC), to characterize effective connectivity under the Bayesian framework. More specifically, PDC allows inferring directionality and explaining the extent to which the present oscillatory activity at a certain frequency in a sender channel influences the future oscillatory activity in a specific receiver channel relative to all possible receivers in the brain network. The proposed model is applied to a large electrophysiological dataset collected as rats performed a complex sequence memory task. This unique dataset includes local field potentials (LFPs) activity recorded from an array of electrodes across hippocampal region CA1 while animals were presented with multiple trials from two main conditions. The proposed modeling approach provided novel insights into hippocampal connectivity during memory performance. Specifically, it separated CA1 into two functional units, a lateral and a medial segment, each showing stronger functional connectivity to itself than to the other. This approach also revealed that information primarily flowed in a lateral-to-medial direction across trials (within-condition), and suggested this effect was stronger on one trial condition than the other (between-conditions effect). Collectively, these results indicate that the proposed model is a promising approach to quantify the variation of functional connectivity, both within- and between-conditions, and thus should have broad applications in neuroscience research
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