21,855 research outputs found
Can we identify non-stationary dynamics of trial-to-trial variability?"
Identifying sources of the apparent variability in non-stationary scenarios is a fundamental problem in many biological data analysis settings. For instance, neurophysiological responses to the same task often vary from each repetition of the same experiment (trial) to the next. The origin and functional role of this observed variability is one of the fundamental questions in neuroscience. The nature of such trial-to-trial dynamics however remains largely elusive to current data analysis approaches. A range of strategies have been proposed in modalities such as electro-encephalography but gaining a fundamental insight into latent sources of trial-to-trial variability in neural recordings is still a major challenge. In this paper, we present a proof-of-concept study to the analysis of trial-to-trial variability dynamics founded on non-autonomous dynamical systems. At this initial stage, we evaluate the capacity of a simple statistic based on the behaviour of trajectories in classification settings, the trajectory coherence, in order to identify trial-to-trial dynamics. First, we derive the conditions leading to observable changes in datasets generated by a compact dynamical system (the Duffing equation). This canonical system plays the role of a ubiquitous model of non-stationary supervised classification problems. Second, we estimate the coherence of class-trajectories in empirically reconstructed space of system states. We show how this analysis can discern variations attributable to non-autonomous deterministic processes from stochastic fluctuations. The analyses are benchmarked using simulated and two different real datasets which have been shown to exhibit attractor dynamics. As an illustrative example, we focused on the analysis of the rat's frontal cortex ensemble dynamics during a decision-making task. Results suggest that, in line with recent hypotheses, rather than internal noise, it is the deterministic trend which most likely underlies the observed trial-to-trial variability. Thus, the empirical tool developed within this study potentially allows us to infer the source of variability in in-vivo neural recordings
Bayesian Inference on Matrix Manifolds for Linear Dimensionality Reduction
We reframe linear dimensionality reduction as a problem of Bayesian inference
on matrix manifolds. This natural paradigm extends the Bayesian framework to
dimensionality reduction tasks in higher dimensions with simpler models at
greater speeds. Here an orthogonal basis is treated as a single point on a
manifold and is associated with a linear subspace on which observations vary
maximally. Throughout this paper, we employ the Grassmann and Stiefel manifolds
for various dimensionality reduction problems, explore the connection between
the two manifolds, and use Hybrid Monte Carlo for posterior sampling on the
Grassmannian for the first time. We delineate in which situations either
manifold should be considered. Further, matrix manifold models are used to
yield scientific insight in the context of cognitive neuroscience, and we
conclude that our methods are suitable for basic inference as well as accurate
prediction.Comment: All datasets and computer programs are publicly available at
http://www.ics.uci.edu/~babaks/Site/Codes.htm
Provably scale-covariant networks from oriented quasi quadrature measures in cascade
This article presents a continuous model for hierarchical networks based on a
combination of mathematically derived models of receptive fields and
biologically inspired computations. Based on a functional model of complex
cells in terms of an oriented quasi quadrature combination of first- and
second-order directional Gaussian derivatives, we couple such primitive
computations in cascade over combinatorial expansions over image orientations.
Scale-space properties of the computational primitives are analysed and it is
shown that the resulting representation allows for provable scale and rotation
covariance. A prototype application to texture analysis is developed and it is
demonstrated that a simplified mean-reduced representation of the resulting
QuasiQuadNet leads to promising experimental results on three texture datasets.Comment: 12 pages, 3 figures, 1 tabl
Stimulus-invariant processing and spectrotemporal reverse correlation in primary auditory cortex
The spectrotemporal receptive field (STRF) provides a versatile and
integrated, spectral and temporal, functional characterization of single cells
in primary auditory cortex (AI). In this paper, we explore the origin of, and
relationship between, different ways of measuring and analyzing an STRF. We
demonstrate that STRFs measured using a spectrotemporally diverse array of
broadband stimuli -- such as dynamic ripples, spectrotemporally white noise,
and temporally orthogonal ripple combinations (TORCs) -- are very similar,
confirming earlier findings that the STRF is a robust linear descriptor of the
cell. We also present a new deterministic analysis framework that employs the
Fourier series to describe the spectrotemporal modulations contained in the
stimuli and responses. Additional insights into the STRF measurements,
including the nature and interpretation of measurement errors, is presented
using the Fourier transform, coupled to singular-value decomposition (SVD), and
variability analyses including bootstrap. The results promote the utility of
the STRF as a core functional descriptor of neurons in AI.Comment: 42 pages, 8 Figures; to appear in Journal of Computational
Neuroscienc
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