A Bayesian model for identifying hierarchically organised states in neural population activity
Neural population activity in cortical circuits is not solely driven by external inputs, but is also modulated by endogenous states which vary on multiple time-scales. To understand information processing in cortical circuits, we need to understand the statistical structure of internal states and their interaction with sensory inputs. Here, we present a statistical model for extracting hierarchically organised neural population states from multi-channel recordings of neural spiking activity. Population states are modelled using a hidden Markov decision tree with state-dependent tuning parameters and a generalised linear observation model. We present a variational Bayesian inference algorithm for estimating the posterior distribution over parameters from neural population recordings. On simulated data, we show that we can identify the underlying sequence of population states and reconstruct the ground truth parameters. Using population recordings from visual cortex, we find that a model with two levels of population states outperforms both a one-state and a two-state generalised linear model. Finally, we find that modelling of state-dependence also improves the accuracy with which sensory stimuli can be decoded from the population response.
The firing properties of neurons in the mammalian brain are not constant over time. One kind of non-stationarity that has been observed is that under certain conditions, populations of neurons can switch between discrete states, across which their inputs and responsiveness can vary dramatically. In turn, there may be structure to this network state-space. Despite all this, much neurophysiological data has been analysed whilst ignoring these discrete spaces, or with hacky/ad-hoc approaches to separate out the states. This paper attempts to tackle such population datasets by integrating GLM-style modelling of stimulus-response relationships into a hierarchical discrete state-space framework. The authors construct a statistical model for neural responses under this framework, based on a hierarchical HMM (i.e., an HME), and approximate inference under it using VBEM. The authors then demonstrate its recovery of ground truth under a simulated dataset, and its application to real neural data.Quality: The statistical model and its inference appear clean and sound, and for the examples presented, it performs marginally (but significantly) better on both simulated and real data compared with less complex models (e.g. when priors are removed; or using a two-state rather than a hierarchical three state model). Having said that, while it is certainly an improvement over previously presented models within the same class (e.g. Escola et al (2011), Chen et al (2009)), the improvement in performance is pretty small. Moreover, there does not appear to be a strong argument that the *hierarchical* nature of this model actually adds anything. There is no explicit comparison with an equally powerful non-hierarchical model (e.g. 3-state HMMs with VB for the state model, to compare with the examples of 3-state HMEs). This leaves me scratching my head, since, according to the title, the hierarchical aspect of the state space is the novel component of this model. Without seeing the data, I worry a bit about whether this promise can be achieved on the real datasets in question, since the improvement of 3-state HMEs over 2-state HMMs is typically small (e.g. Fig 3C, Fig 4 caption). Of course, the authors can convince me otherwise by presenting the results, in which case I would give the paper score a bump. Otherwise, while I can appreciate the promise of this approach, the real data may not justify such a model. For instance, the "hierarchy of discrete states" may be better described by a continuous latent factor. I'm nevertheless in favour of acceptance since this work is sound and should be published, but its scope of utility may not yet have been realised. Clarity: The paper is clear and well-written. Some minor points:- line 51: "simple a global" -> "a simple global"- line 99: "as well as hierarchical relationships between trials". Not sure what this is meant to mean. The architecture of the HMDT is fixed (though its parameters are learned). What does "between trials" mean here?- line 106: abnormal sentence termination "non-geometrically".- Fig 1B: some captioning/labelling of the transition matrices is necessary -- I couldn't parse these- line 112: "ypically"- line 267: "where theta is the phase" -> should be phi- line 267: pairwise product -> outer product?- line 266-268: a little motivation for the chosen parameterisation of the stimulus would be useful (yes, it's tangential to the core of the paper, but it's a bit bewildering. These look like a filtering of the stimulus by a set of 15 direction-selective/non-selective and orientation-selective/non-selective simple cells, yes?)- line 321: demote Macaques to plain old macaques- Fig 4: not referenced in main paper- line 386: "for the characterized..."? - line 406: "both, better" omit comma- the British author and American author should wrestle it out to determine spelling conventionsOriginality: This is an improved statistical model above and beyond other recently published work. However, as mentioned above, I think a full comparison is necessary to fully evaluate this work.Significance: See comments above.