estimate_spikes {FastLZeroSpikeInference} | R Documentation |
Estimate spike train, underlying calcium concentration, and changepoints based on a fluorescence trace.
estimate_spikes(dat, gam, lambda, constraint = FALSE, estimate_calcium = FALSE, EPS = 1e-04)
dat |
fluorescence data |
gam |
a scalar value for the AR(1) decay parameter |
lambda |
tuning parameter lambda |
constraint |
boolean specifying constrained or unconstrained optimization problem (see below) |
estimate_calcium |
boolean specifying whether to estimate the calcium |
EPS |
double specifying the minimum calcium value |
This algorithm solves the optimization problems
AR(1) model:
minimize_c1,...,cT 0.5 sum_t=1^T ( y_t - c_t )^2 + lambda sum_t=2^T 1_[c_t != max(gam c_t-1, EPS)]
for the global optimum, where y_t is the observed fluorescence at the tth timestep.
Constrained AR(1) model:
minimize_c1,...,cT 0.5 sum_t=1^T ( y_t - c_t )^2 + lambda sum_t=2^T 1_[c_t != max(gam c_t-1, EPS)]
subject to c_t >= max(gam c_t-1, EPS), t = 2, ..., T
We introduce the constant EPS > 0, to avoid arbitrarily small calcium concentrations that would result in numerical instabilities. In practice, this means that the estimated calcium concentration decays according to the AR(1) model for values greater than EPS and is equal to EPS thereafter.
When estimating the spikes, it is not necessary to explicitly compute the calcium concentration. Therefore, if only the spike times are required, the user can avoid this computation cost by setting the estimate_calcium boolean to false. Because estimating the calcium requires additional computation time, we suggest estimating the calcium only if it is needed.
Given the set of estimated spikes produced from the estimate_spike, the calcium concentration can be estimated with the estimate_calcium function (see examples below).
For additional information see:
1. Jewell, Hocking, Fearnhead, and Witten (2018) <arXiv:1802.07380> and
2. Jewell, Sean; Witten, Daniela. Exact spike train inference via l0 optimization. Ann. Appl. Stat. 12 (2018), no. 4, 2457–2482. doi:10.1214/18-AOAS1162. https://projecteuclid.org/euclid.aoas/1542078052
Returns a list with elements:
spikes
the set of estimated spikes
estimated_calcium
estimated calcium concentration
change_pts
the set of changepoints
cost
the cost at each time point
n_intervals
the number of intervals at each point
Estimate spikes:
estimate_spikes
estimate_calcium
Simulate:
simulate_ar1
sim <- simulate_ar1(n = 500, gam = 0.95, poisMean = 0.009, sd = 0.05, seed = 1) plot(sim) ## Fits for a single tuning parameter # AR(1) model fit <- estimate_spikes(dat = sim$fl, gam = 0.95, lambda = 1) print(fit) # compute fitted values from prev. fit fit <- estimate_calcium(fit) plot(fit) # or fit <- estimate_spikes(dat = sim$fl, gam = 0.95, lambda = 1, estimate_calcium = TRUE) plot(fit) # Constrained AR(1) model fit <- estimate_spikes(dat = sim$fl, gam = 0.95, lambda = 1, constraint = TRUE, estimate_calcium = TRUE) print(fit) plot(fit)