arXiv subjects

Laurence Aitchison

Publications and source records attributed to Laurence Aitchison.

75 records · Page 5Linked to original sources

arXiv2016

Zipf's law arises naturally in structured, high-dimensional data

Zipf's law, which states that the probability of an observation is inversely proportional to its rank, has been observed in many domains. While there are models that explain Zipf's law in each of them, those explanations are typically domain specific. Recently, methods from statistical physics were used to show that a fairly broad class of models does provide a general explanation of Zipf's law. This explanation rests on the observation that real world data is often generated from underlying causes, known as latent variables. Those latent variables mix together multiple models that do not obey Zipf's law, giving a model that does. Here we extend that work both theoretically and empirically. Theoretically, we provide a far simpler and more intuitive explanation of Zipf's law, which at the same time considerably extends the class of models to which this explanation can apply. Furthermore, we also give methods for verifying whether this explanation applies to a particular dataset. Empirically, these advances allowed us extend this explanation to important classes of data, including word frequencies (the first domain in which Zipf's law was discovered), data with variable sequence length, and multi-neuron spiking activity.

q-bio.NC↗

arXiv2015

Synaptic sampling: A connection between PSP variability and uncertainty explains neurophysiological observations

When an action potential is transmitted to a postsynaptic neuron, a small change in the postsynaptic neuron's membrane potential occurs. These small changes, known as a postsynaptic potentials (PSPs), are highly variable, and current models assume that this variability is corrupting noise. In contrast, we show that this variability could have an important computational role: representing a synapse's uncertainty about the optimal synaptic weight (i.e. the best possible setting for the synaptic weight). We show that this link between uncertainty and variability, that we call synaptic sampling, leads to more accurate estimates of the uncertainty in task relevant quantities, leading to more effective decision making. Synaptic sampling makes four predictions, all of which have some experimental support. First the more variable a synapse is, the more it should change during LTP protocols. Second, variability should increase as the presynpatic firing rate falls. Third, PSP variance should be proportional to PSP mean. Fourth, variability should increase with distance from the cell soma. We provide support for the first two predictions by reanalysing existing datasets, and we find preexisting data in support of the last two predictions.

q-bio.NC↗

arXiv2014

Fast sampling for Bayesian inference in neural circuits

Time is at a premium for recurrent network dynamics, and particularly so when they are stochastic and correlated: the quality of inference from such dynamics fundamentally depends on how fast the neural circuit generates new samples from its stationary distribution. Indeed, behavioral decisions can occur on fast time scales (~100 ms), but it is unclear what neural circuit dynamics afford sampling at such high rates. We analyzed a stochastic form of rate-based linear neuronal network dynamics with synaptic weight matrix $W$, and the dependence on $W$ of the covariance of the stationary distribution of joint firing rates. This covariance $Σ$ can be actively used to represent posterior uncertainty via sampling under a linear-Gaussian latent variable model. The key insight is that the mapping between $W$ and $Σ$ is degenerate: there are infinitely many $W$'s that lead to sampling from the same $Σ$ but differ greatly in the speed at which they sample. We were able to explicitly separate these extra degrees of freedom in a parametric form and thus study their effects on sampling speed. We show that previous proposals for probabilistic sampling in neural circuits correspond to using a symmetric $W$ which violates Dale's law and results in critically slow sampling, even for moderate stationary correlations. In contrast, optimizing network dynamics for speed consistently yielded asymmetric $W$'s and dynamics characterized by fast transients, such that samples of network activity became fully decorrelated over ~10 ms. Importantly, networks with separate excitatory/inhibitory populations proved to be particularly efficient samplers, and were in the balanced regime. Thus, plausible neural circuit dynamics can perform fast sampling for efficient decoding and inference.

q-bio.NC↗