The equivalence of information-theoretic and likelihood-based methods for neural dimensionality reduction

Stimulus dimensionality-reduction methods in neuroscience seek to identify a low-dimensional space of stimulus features that affect a neuron's probability of spiking. One popular method, known as maximally informative dimensions (MID), uses an information-theoretic quantity known as "single-spike information" to identify this space. Here we examine MID from a model-based perspective. We show that MID is a maximum-likelihood estimator for the parameters of a linear-nonlinear-Poisson (LNP) model, and that the empirical single-spike information corresponds to the normalized log-likelihood under a Poisson model. This equivalence implies that MID does not necessarily find maximally informative stimulus dimensions when spiking is not well described as Poisson. We provide several examples to illustrate this shortcoming, and derive a lower bound on the information lost when spiking is Bernoulli in discrete time bins. To overcome this limitation, we introduce model-based dimensionality reduction methods for neurons with non-Poisson firing statistics, and show that they can be framed equivalently in likelihood-based or information-theoretic terms. Finally, we show how to overcome practical limitations on the number of stimulus dimensions that MID can estimate by constraining the form of the non-parametric nonlinearity in an LNP model. We illustrate these methods with simulations and data from primate visual cortex

Gravitational wave surrogates through automated machine learning

We analyze a prospect for predicting gravitational waveforms from compact binaries based on automated machine learning (AutoML) from around a hundred different possible regression models, without having to resort to tedious and manual case-by-case analyses and fine-tuning. The particular study of this article is within the context of the gravitational waves emitted by the collision of two spinless black holes in initial quasi-circular orbit. We find, for example, that approaches such as Gaussian process regression with radial bases as kernels, an approach which is generalizable to multiple dimensions with low computational evaluation cost, do provide a sufficiently accurate solution. The results here presented suggest that AutoML might provide a framework for regression in the field of surrogates for gravitational waveforms. Our study is within the context of surrogates of numerical relativity simulations based on reduced basis and the empirical interpolation method, where we find that for the particular case analyzed AutoML can produce surrogates which are essentially indistinguishable from the NR simulations themselves.Fil: Barsotti, Damián. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Cerino, Franco. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; ArgentinaFil: Tiglio, Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Villanueva, Uziel Aarón. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentin

Models of Neuronal Stimulus-Response Functions: Elaboration, Estimation, and Evaluation

Rich, dynamic, and dense sensory stimuli are encoded within the nervous system by the time-varying activity of many individual neurons. A fundamental approach to understanding the nature of the encoded representation is to characterize the function that relates the moment-by-moment firing of a neuron to the recent history of a complex sensory input. This review provides a unifying and critical survey of the techniques that have been brought to bear on this effort thus far—ranging from the classical linear receptive field model to modern approaches incorporating normalization and other nonlinearities. We address separately the structure of the models; the criteria and algorithms used to identify the model parameters; and the role of regularizing terms or “priors.” In each case we consider benefits or drawbacks of various proposals, providing examples for when these methods work and when they may fail. Emphasis is placed on key concepts rather than mathematical details, so as to make the discussion accessible to readers from outside the field. Finally, we review ways in which the agreement between an assumed model and the neuron's response may be quantified. Re-implemented and unified code for many of the methods are made freely available

Evidence for sparse synergies in grasping actions

Converging evidence shows that hand-actions are controlled at the level of synergies and not single muscles. One intriguing aspect of synergy-based action-representation is that it may be intrinsically sparse and the same synergies can be shared across several distinct types of hand-actions. Here, adopting a normative angle, we consider three hypotheses for hand-action optimal-control: sparse-combination hypothesis (SC) – sparsity in the mapping between synergies and actions - i.e., actions implemented using a sparse combination of synergies; sparse-elements hypothesis (SE) – sparsity in synergy representation – i.e., the mapping between degrees-of-freedom (DoF) and synergies is sparse; double-sparsity hypothesis (DS) – a novel view combining both SC and SE – i.e., both the mapping between DoF and synergies and between synergies and actions are sparse, each action implementing a sparse combination of synergies (as in SC), each using a limited set of DoFs (as in SE). We evaluate these hypotheses using hand kinematic data from six human subjects performing nine different types of reach-to-grasp actions. Our results support DS, suggesting that the best action representation is based on a relatively large set of synergies, each involving a reduced number of degrees-of-freedom, and that distinct sets of synergies may be involved in distinct tasks

Nonlinear decoding of a complex movie from the mammalian retina

Retina is a paradigmatic system for studying sensory encoding: the transformation of light into spiking activity of ganglion cells. The inverse problem, where stimulus is reconstructed from spikes, has received less attention, especially for complex stimuli that should be reconstructed “pixel-by-pixel”. We recorded around a hundred neurons from a dense patch in a rat retina and decoded movies of multiple small randomly-moving discs. We constructed nonlinear (kernelized and neural network) decoders that improved significantly over linear results. An important contribution to this was the ability of nonlinear decoders to reliably separate between neural responses driven by locally fluctuating light signals, and responses at locally constant light driven by spontaneous-like activity. This improvement crucially depended on the precise, non-Poisson temporal structure of individual spike trains, which originated in the spike-history dependence of neural responses. We propose a general principle by which downstream circuitry could discriminate between spontaneous and stimulus-driven activity based solely on higher-order statistical structure in the incoming spike trains