1,720,998 research outputs found
Identifiability of a Binomial Synapse
Get PDFSynapses are highly stochastic transmission units. A classical model describing this stochastic transmission is called the binomial model, and its underlying parameters can be estimated from postsynaptic responses to evoked stimuli. The accuracy of parameter estimates obtained via such a model-based approach depends on the identifiability of the model. A model is said to be structurally identifiable if its parameters can be uniquely inferred from the distribution of its outputs. However, this theoretical property does not necessarily imply practical identifiability. For instance, if the number of observations is low or if the recording noise is high, the model's parameters can only be loosely estimated. Structural identifiability, which is an intrinsic property of a model, has been widely characterized; but practical identifiability, which is a property of both the model and the experimental protocol, is usually only qualitatively assessed. Here, we propose a formal definition for the practical identifiability domain of a statistical model. For a given experimental protocol, this domain corresponds to the set of parameters for which the model is correctly identified as the ground truth compared to a simpler alternative model. Considering a model selection problem instead of a parameter inference problem allows to derive a non-arbitrary criterion for practical identifiability. We apply our definition to the study of neurotransmitter release at a chemical synapse. Our contribution to the analysis of synaptic stochasticity is three-fold: firstly, we propose a quantitative criterion for the practical identifiability of a statistical model, and compute the identifiability domains of different variants of the binomial release model (uni or multi-quantal, with or without short-term plasticity); secondly, we extend the Bayesian Information Criterion (BIC), a classically used tool for model selection, to models with correlated data (which is the case for most models of chemical synapses); finally, we show that our approach allows to perform data free model selection, i.e., to verify if a model used to fit data was indeed identifiable even without access to the data, but having only access to the fitted parameters
Asymptotically exact unweighted particle filter for manifold-valued hidden states and point process observations
Get PDFISSN:2475-145
Online Maximum Likelihood Estimation of the Parameters of Partially Observed Diffusion Processes
Get PDFWe revisit the problem of estimating the parameters of a partially observed diffusion process, consisting of a hidden state process and an observed process, with a continuous time parameter. The estimation is to be done online, i.e. the parameter estimate should be updated recursively based on the observation filtration. Here, we use an old but under-exploited representation of the incomplete-data log-likelihood function in terms of the filter of the hidden state from the observations. By performing a stochastic gradient ascent, we obtain a fully recursive algorithm for the time evolution of the parameter estimate. We prove the convergence of the algorithm under suitable conditions regarding the ergodicity of the process consisting of state, filter, and tangent filter. Additionally, our parameter estimation is shown numerically to have the potential of improving suboptimal filters, and can be applied even when the system is not identifiable due to parameter redundancies. Online parameter estimation is a challenging problem that is ubiquitous in fields such as robotics, neuroscience, or finance in order to design adaptive filters and optimal controllers for unknown or changing systems
Interactions between short-term and long-term plasticity: shooting for a moving target
Get PDFFar from being static transmission units, synapses are highly dynamical elements that change over multiple time scales depending on the history of the neural activity of both the pre- and postsynaptic neuron. Moreover, synaptic changes on different time scales interact: long-term plasticity (LTP) can modify the properties of short-term plasticity (STP) in the same synapse. Most existing theories of synaptic plasticity focus on only one of these time scales (either STP or LTP or late-LTP) and the theoretical principles underlying their interactions are thus largely unknown. Here we develop a normative model of synaptic plasticity that combines both STP and LTP and predicts specific patterns for their interactions. Recently, it has been proposed that STP arranges for the local postsynaptic membrane potential at a synapse to behave as an optimal estimator of the presynaptic membrane potential based on the incoming spikes. Here we generalize this approach by considering an optimal estimator of a non-linear function of the membrane potential and the long-term synaptic efficacy -- which itself may be subject to change on a slower time scale. We find that an increase in the long-term synaptic efficacy necessitates changes in the dynamics of STP. More precisely, for a realistic non-linear function to be estimated, our model predicts that after the induction of LTP, causing long-term synaptic efficacy to increase, a depressing synapse should become even more depressing. That is, in a protocol using trains of presynaptic stimuli, as the initial EPSP becomes stronger due to LTP, subsequent EPSPs should become weakened and this weakening should be more pronounced with LTP. This form of redistribution of synaptic efficacies agrees well with electrophysiological data on synapses connecting layer 5 pyramidal neurons
Matching Recall and Storage in Sequence Learning with Spiking Neural Networks
Get PDFStoring and recalling spiking sequences is a general problem the brain needs to solve. It is, however, unclear what type of biologically plausible learning rule is suited to learn a wide class of spatiotemporal activity patterns in a robust way. Here we consider a recurrent network of stochastic spiking neurons composed of both visible and hidden neurons. We derive a generic learning rule that is matched to the neural dynamics by minimizing an upper bound on the Kullback–Leibler divergence from the target distribution to the model distribution. The derived learning rule is consistent with spike-timing dependent plasticity in that a presynaptic spike preceding a postsynaptic spike elicits potentiation while otherwise depression emerges. Furthermore, the learning rule for synapses that target visible neurons can be matched to the recently proposed voltage-triplet rule. The learning rule for synapses that target hidden neurons is modulated by a global factor, which shares properties with astrocytes and gives rise to testable predictions
- …
