FastLZeroSpikeInference (version 2018.12.10)

estimate_spike_paths: Estimate spike train, underlying calcium concentration, and changepoints based on a fluorescence trace. Automatic tuning parameter selection within a range of values [lambda_min, lambda_max]

Description

Estimate spike train, underlying calcium concentration, and changepoints based on a fluorescence trace. Automatic tuning parameter selection within a range of values [lambda_min, lambda_max]

Usage

estimate_spike_paths(dat, gam, lambda_min = 0.01, lambda_max = 10,
  constraint = FALSE, EPS = 1e-04, max_iters = 10)

Arguments

dat

fluorescence data

gam

a scalar value for the AR(1) decay parameter

lambda_min

minimum lamba value

lambda_max

maximum lamba value

constraint

boolean specifying constrained or unconstrained optimization problem (see below)

EPS

double specifying the minimum calcium value

max_iters

maximum number of tuning parameters attempted

Value

Returns a list with elements:

path_stats a dataframe with summary statistics (number of spikes, tuning parameters, cost)

path_fits a list with estimated_spikes object for each tuning parameter

approximate_path a boolean indicating whether an early stopping criterion condition occurred

Details

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

See Also

Estimate spikes: estimate_spikes estimate_calcium

Simulate: simulate_ar1

Examples

# NOT RUN {
sim <- simulate_ar1(n = 500, gam = 0.95, poisMean = 0.009, sd = 0.05, seed = 1)
plot(sim)

## Fits for tuning parameters between [0.1, 10]
fits <- estimate_spike_paths(dat = sim$fl, gam = 0.95, lambda_min = 0.1, lambda_max = 10)
print(fits)
plot(fits)
print(fits$path_fits[[1]])
plot(fits$path_fits[[1]])

## 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)

# }