Neurons in the macaque lateral intraparietal (LIP) area exhibit firing rates that appear to ramp upward or downward during decision-making. These ramps are commonly assumed to reflect the gradual accumulation of evidence toward a decision threshold. However, the ramping in trial-averaged responses could instead arise from instantaneous jumps at different times on different trials. We examined single-trial responses in LIP using statistical methods for fitting and comparing latent dynamical spike-train models. We compared models with latent spike rates governed by either continuous diffusion-to-bound dynamics or discrete “stepping” dynamics. Roughly three-quarters of the choice-selective neurons we recorded were better described by the stepping model. Moreover, the inferred steps carried more information about the animal’s choice than spike counts.
Kenneth W. Latimer, Alexander C. Huk, & Jonathan W. Pillow (2015). Bayesian inference for latent stepping and ramping models of spike train data. Chapter in Advanced State Space Methods for Neural and Clinical Data, ed. Zhe Chen, Cambridge University Press.
Kenneth W. Latimer, E.J. Chichilnisky, Fred Rieke, & Jonathan W. Pillow (2014). Inferring synaptic conductances from spike trains under a biophysically inspired point process model. Advances in Neural Information Processing Systems, 27:954-962. [abstract | link | poster]
A popular approach to neural characterization describes neural responses in terms of a cascade of linear and nonlinear stages: a linear filter to describe stimulus integration, followed by a nonlinear function to convert the filter output to spike rate. However, real neurons respond to stimuli in a manner that depends on the nonlinear integration of excitatory and inhibitory synaptic inputs. Here we introduce a biophysically inspired point process model that explicitly incorporates stimulus-induced changes in synaptic conductance in a dynamical model of neuronal membrane potential. Our work makes two important contributions. First, on a theoretical level, it offers a novel interpretation of the popular generalized linear model (GLM) for neural spike trains. We show that the classic GLM is a special case of our conductance-based model in which the stimulus linearly modulates excitatory and inhibitory conductances in an equal and opposite "push-pull" fashion. Our model can therefore be viewed as a direct extension of the GLM in which we relax these constraints; the resulting model can exhibit shunting as well as hyperpolarizing inhibition, and time-varying changes in both gain and membrane time constant. Second, on a practical level, we show that our model provides a tractable model of spike responses in early sensory neurons that is both more accurate and more interpretable than the GLM. Most importantly, we show that we can accurately infer intracellular synaptic conductances from extracellularly recorded spike trains. We validate these estimates using direct intracellular measurements of excitatory and inhibitory conductances in parasol retinal ganglion cells. The stimulus-dependence of both excitatory and inhibitory conductances can be well described by a linear-nonlinear cascade, with the filter driving inhibition exhibiting opposite sign and a slight delay relative to the filter driving excitation. We show that the model fit to extracellular spike trains can predict excitatory and inhibitory conductances elicited by novel stimuli with nearly the same accuracy as a model trained directly with intracellular conductances.
Il Memming Park, Evan Archer, Kenneth W. Latimer, & Jonathan W. Pillow (2013). Universal models for binary spike patterns using centered Dirichlet processes. Advances in Neural Information Processing Systems, 26:2463-2471. [abstract | link]
Probabilistic models for binary spike patterns provide a powerful tool for understanding the statistical dependencies in large-scale neural recordings. Maximum entropy (or "maxent") models, which seek to explain dependencies in terms of low-order interactions between neurons, have enjoyed remarkable success in modeling such patterns, particularly for small groups of neurons. However, these models are computationally intractable for large populations, and low-order maxent models have been shown to be inadequate for some datasets. To overcome these limitations, we propose a family of "universal" models for binary spike patterns, where universality refers to the ability to model arbitrary distributions over all 2^m binary patterns. We construct universal models using a Dirichlet process centered on a well-behaved parametric base measure, which naturally combines the flexibility of a histogram and the parsimony of a parametric model. We derive computationally efficient inference methods using Bernoulli and cascaded logistic base measures, which scale tractably to large populations. We also establish a condition for equivalence between the cascaded logistic and the 2nd-order maxent or "Ising" model, making cascaded logistic a reasonable choice for base measure in a universal model. We illustrate the performance of these models using neural data.
Benjamin Scholl, Kenneth W. Latimer, & Nicholas J. Priebe (2012). A retinal source of spatial contrast gain control. J. Neurosci, 32(29):9824-9830. [abstract | link]
Sensory cortex is able to encode a broad range of stimulus features despite a great variation in signal strength. In cat primary visual cortex (V1), for example, neurons are able to extract stimulus features like orientation or spatial configuration over a wide range of stimulus contrasts. The contrast-invariant spatial tuning found in V1 neuron responses has been modeled as a gain control mechanism, but at which stage of the visual pathway it emerges has remained unclear. Here we describe our findings that contrast-invariant spatial tuning occurs not only in the responses of lateral geniculate nucleus (LGN) relay cells but also in their afferent retinal input. Our evidence suggests that a similar contrast-invariant mechanism is found throughout the stages of the early visual pathway, and that the contrast-invariant spatial selectivity is evident in both retinal ganglion cell and LGN cell responses.
Kenneth W. Latimer, Jacob L. Yates, Alexander C. Huk, & Jonathan W. Pillow (2015, COSYNE). Deciphering the neural representation of perceptual decisions with latent variable models. [abstract]
Neural activity in the lateral intraparietal area (LIP) of macaque cortex has been hypothesized to represent an accumulation of evidence for decision-making. In particular, the ramp-like firing rates observed in LIP neurons have been interpreted as a neural correlate of the diffusion-to-bound model, which captures many of the aspects of decision-making behavior. An alternative hypothesis is that the spike rates of LIP neurons follow a discrete stepping process, in which the spike rate jumps stochastically between decision states on each trial. Attempts to differentiate between these hypotheses have relied on analyses of trial-averaged responses, which cannot reveal the dynamics of spike rates on individual trials. Here we address this problem within a Bayesian model comparison framework using latent dynamical models of LIP spike trains. We define explicit statistical models of spike responses in which the spike rate is governed by either a continuous diffusion-to-bound process or a discrete stepping process. We use Markov Chain Monte Carlo (MCMC) methods to fit these models to spike trains recorded from LIP neurons. These methods provide access to the full posterior distribution over parameters under each model, and allow us to infer bound-hitting or step times on each trial. In contrast to previous results, we find that the stepping model provides a better description than the diffusion-to-bound model for 31 out of 40 cells in a population of choice-selective LIP neurons. This indicates that a majority of neurons are better explained as stepping than as ramping during decision formation. Additionally, we extend our approach to model decision-related dynamics in multi-cell recordings, where traditional analyses have limited power to reveal shared representations of decision.
Kenneth W. Latimer, E.J. Chichilnisky, Fred Rieke, & Jonathan W. Pillow (2014, COSYNE). Inferring synaptic conductances from spike trains with a point process encoding model. [abstract]
Sensory neurons respond to stimuli in a manner that depends on the integration of excitatory and inhibitory synaptic inputs. However, statistical models for spike responses tend to describe stimulus integration with a linear filter and relegate all nonlinear processing steps to a single post-integration nonlinearity. Here we introduce a novel point process model, an extension of the well-known generalized linear model (GLM), that allows us to characterize the tuning of a neuron’s excitatory and inhibitory synaptic inputs from its extracellularly recorded spike responses to a visual stimulus. We validate our method using direct intracellular measurements of excitatory and inhibitory conductances in parasol retinal ganglion cells in primate retina. Our work makes two novel theoretical contributions: first, we show that the standard generalized linear encoding model is mathematically equivalent to a conductance-based model in which the stimulus linearly modulates excitatory and inhibitory conductances in an equal and opposite “push-pull” fashion; second, we relax these assumptions to obtain a more flexible, biophysically realistic model in which conductances have distinct tuning and nonlinear stimulus dependence. The resulting conductance-based model can produce shunting as well as hyperpolarizing inhibition, and can exhibit changes in gain and membrane time constant due to changes in total conductance. We apply our method to neural responses to a full-field temporal noise stimulus. We find that the stimulus-dependence of both excitatory and inhibitory conductances can be well described by a linear-nonlinear cascade, with the filter driving inhibition exhibiting opposite sign and a slight delay relative to the filter driving excitation. We show that the model fit to extracellular spike trains can predict excitatory and inhibitory conductances with nearly the same accuracy as a model fit directly to intracellularly measured conductances.
Il Memming Park, Evan Archer, Kenneth W. Latimer, & Jonathan W. Pillow (2014, COSYNE). Scalable nonparametric models for binary spike patterns. [abstract]
Probabilistic models for binary spike patterns provide a powerful tool for understanding statistical dependencies in large-scale neural recordings. Maximum entropy (or "maxent") models, which seek to explain dependencies in terms of low-order interactions between neurons, have enjoyed remarkable success in modeling such patterns, particularly for small groups of neurons. However, these models are not computationally tractable for large populations, and low-order maxent models have been shown to be inadequate for some datasets. To overcome these limitations, we propose a family of "universal" models for binary spike patterns, where universality refers to the model’s ability to describe arbitrary distributions over all 2^m binary patterns. Universal binary models consist of a well-behaved parametric base distribution; they combine the flexibility of a histogram with the parsimony of a parametric model. Universal models automatically trade off between parametric and nonparametric behavior, depending on the amount of data. We derive computationally efficient inference methods using the cascaded logistic base distribution (Park et al. 2013, Pachitariu et al. 2013), which permits tractable scaling to large populations. The cascaded logistic model assumes the dependencies among neurons take a simple cascaded form, equivalent to a series of logistic regressions, with each neuron depending only upon those that came before. We prove a condition for the equivalence between the cascaded logistic and the 2nd-order maxent (or "Ising") model, making cascade-logistic a reasonable choice for base distribution in a universal model. Specifically, any Ising model with pentadiagonal interactions is also a cascaded logistic model. We evaluate the performance of these models with neural data, and will compare to the "Reliable Interaction Model", a recently proposed framework for building flexible models of binary spike patterns within the maximum entropy formalism (Ganmor et al. 2011).
Kenneth W. Latimer, Jacob L. Yates, Miriam L. R. Meister, Alexander C. Huk, & Jonathan W. Pillow (2012, Society for Neuroscience Annual Meeting). Analyzing perceptual decision-making in area LIP with hidden Markov models. [abstract]
Neurons in macaque lateral intraparietal area (LIP) show activity coupled to both visual signals and motor output. This bridge between perception and action is thought to play an important role in perceptual decision-making processes (Shadlen & Newsome, 2001). The activity of LIP neurons, recorded during a motion direction discrimination task, show an average spike rate that ramps up or down in relation to the strength of the visual motion stimulus. This apparent spike-rate ramping has been postulated as evidence of integration of information and the formation of a decision of motion direction in LIP. Previous studies have proposed several specific descriptions of how the activity of LIP cells occurs during the course of a perceptual discrimination trial (Gold & Shadlen, 2007). However, statistical inference methods for fitting comparing models of LIP responses have not been applied to single-trial, spike-train data. Instead, model comparison has been performed on data averaged over many trials. Averaging activity over hundreds of trials could obscure how neural representations evolve during single trials. As a result, there is a lack of appropriate, well-defined statistical tools for comparing observed spike-train data to hypotheses of LIP’s involvement in decision-making. We formulated two simple models of LIP spiking responses during a decision-making task as hidden Markov models: a drift-diffusion model and a discrete-switch decision model. Using this formulation, we fit the models directly to a set of spike trains instead of data averaged over many trials. Model parameters were fit using maximum likelihood and Markov chain Monte Carlo methods. The model fits allowed us to apply a variety of model comparison metrics including Bayes factors and Bayesian information criterion. We analyzed simulated data to assess how our method can discriminate between models given a realistic amount of data. This established an estimate of what can be inferred about hypotheses of encoding in LIPfrom single-unit recordings. We then applied our techniques to actual recordings. We contrasted our findings with the trial-averaged statistical methods used in previous studies. Our methods establish that models of single-trial LIP responses can be defined and tested rigorously within a Bayesian inference framework.