Control and learning in sociotechnical systems.

<p>Control and learning in sociotechnical systems.</p

Soft regulation applications.

<p>Soft regulation applications.</p

Efficiency of soft regulation with crowd recommendation over time (distributed agents).

<p>Efficiency of soft regulation with crowd recommendation over time (distributed agents).</p

Model parameters.

<p>Model parameters.</p

Efficiency of soft regulation with crowd recommendation (large confidence levels).

<p>Efficiency of soft regulation with crowd recommendation (large confidence levels).</p

Efficient "Shotgun" Inference of Neural Connectivity from Highly Sub-sampled Activity Data

<div><p>Inferring connectivity in neuronal networks remains a key challenge in statistical neuroscience. The “common input” problem presents a major roadblock: it is difficult to reliably distinguish causal connections between pairs of observed neurons versus correlations induced by common input from unobserved neurons. Available techniques allow us to simultaneously record, with sufficient temporal resolution, only a small fraction of the network. Consequently, naive connectivity estimators that neglect these common input effects are highly biased. This work proposes a “shotgun” experimental design, in which we observe multiple sub-networks briefly, in a serial manner. Thus, while the full network cannot be observed simultaneously at any given time, we may be able to observe much larger subsets of the network over the course of the entire experiment, thus ameliorating the common input problem. Using a generalized linear model for a spiking recurrent neural network, we develop a scalable approximate expected loglikelihood-based Bayesian method to perform network inference given this type of data, in which only a small fraction of the network is observed in each time bin. We demonstrate in simulation that the shotgun experimental design can eliminate the biases induced by common input effects. Networks with thousands of neurons, in which only a small fraction of the neurons is observed in each time bin, can be quickly and accurately estimated, achieving orders of magnitude speed up over previous approaches.</p></div

Basic notation.

<p>Basic notation.</p

Parameter scans show that <i>C</i>, the correlation between true and estimated connectivity, monotonically increases with <i>T</i> in various parameter regimes.

<p>We scan over <b>(A)</b> observation probability <i>p</i>_obs, <b>(B)</b> network size <i>N</i>, <b>(C)</b> mean firing rate <i>m</i> (similar to the firing rate of the excitatory neurons—inhibitory neurons fire approximately twice as fast), and <b>(D)</b> connection sparsity parameter <i>p</i>₀ (which is proportional to actual connection sparsity <i>p</i>_conn—see Eq 37 in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004464#pcbi.1004464.s001" target="_blank">S1 Text</a>) and experiment duration <i>T</i>. Other parameters (when these are not scanned): <i>p</i>_obs = 0.2, <i>N</i> = 500.</p

Inferring input connectivity to a single neuron with many inputs and low observation ratios.

<p>The panels <b>B-D</b>,<b>F-H</b>, and <b>J-L</b> are arranged in columns as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004464#pcbi.1004464.g003" target="_blank">Fig 3</a>. In the left column <b>(A,E,I)</b> we show a sample of 1000 input weight values from the true (blue) and inferred weights (red), sorted according to the value of the true weights. In the other panels, we show all the weights. We have <i>N</i> = 10626 observed inputs, 968 of which have non-zero weights. The output neuron is always observed, while 83% of the input neurons are only partially observed with <i>p</i>_obs = 1,0.1,0.01. The rest are never observed. Other network parameters are the same as before (<i>e.g</i>., <i>T</i> = 5.5 hours), and the firing rate of the output neuron was 2.8Hz. More implementation details in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004464#pcbi.1004464.s001" target="_blank">S1 Text</a>, section B.2.</p

Expected LogLikelihood (ELL) based estimation is statistically efficient.

<p><i>Top</i><b>(A,B)</b>: The ELL-based method (blue) compares favorably to the standard MAP estimate (red) when spikes are fully observed (using the same L1 prior). <i>Bottom</i><b>(C,D)</b>: We compare the ELL based method (blue) to the Expectation Maximization (EM) approach, when only 10% of the spikes are observed. We show the results after one (cyan) and two (magenta) EM steps. The EM steps do not improve over the ELL-based method. Parameters: <i>N</i> = 50, <i>T</i> = 1.4 hours. For the Gibbs sampling we used a single sample after a burn-in period of 30 samples, as we used in our EM simulations without the ELL-based initialization (section E <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004464#pcbi.1004464.s001" target="_blank">S1 Text</a>).</p