API reference

BootstrapAsymptotics

State evolution and simulation for bootstrap-related methods applied to linear and logistic regression.

Exports

• BayesOpt
• ERM
• FullResampling
• LabelResampling
• Logistic
• Overlaps
• PairBootstrap
• ResidualBootstrap
• Ridge
• Subsampling
• bias_state_evolution
• bias_variance_empirical
• bias_variance_true
• fit
• gamp
• sample_all
• sample_data
• sample_labels
• sample_weights
• state_evolution
• state_evolution_BayesOpt
• variance_state_evolution

struct BayesOpt <: BootstrapAsymptotics.Algorithm

Bayes optimal estimation algorithm.

struct ERM <: BootstrapAsymptotics.Algorithm

Empirical Risk Minimization algorithm.

struct FullResampling <: BootstrapAsymptotics.Algorithm

Full resampling algorithm.

struct LabelResampling <: BootstrapAsymptotics.Algorithm

Label resampling algorithm.

struct Logistic <: BootstrapAsymptotics.Problem

Logistic regression problem with ridge penalty.

Fields

• α::Float64: ratio of population over dimension n/d

• λ::Float64: regularization strength

• ρ::Float64: teacher weight

struct Overlaps{hat, T1<:(AbstractVector), T2<:(AbstractMatrix), T3<:(AbstractMatrix)}

Overlap or hat overlap storage for state evolution between two algorithms.

Fields

• m::AbstractVector

• Q::AbstractMatrix

• V::AbstractMatrix

struct PairBootstrap <: BootstrapAsymptotics.Algorithm

Standard (pair) bootstrap algorithm.

Fields

• p_max::Int64: maximum weight for state evolution

struct ResidualBootstrap <: BootstrapAsymptotics.Algorithm

Residual bootstrap algorithm, aka ERM + label resampling.

struct Ridge <: BootstrapAsymptotics.Problem

Least squares regression problem with ridge penalty.

Fields

• α::Float64: ratio of population over dimension n/d

• Δ::Float64: Gaussian noise variance

• λ::Float64: regularization strength

• ρ::Float64: teacher weight

struct Subsampling <: BootstrapAsymptotics.Algorithm

Subsampling algorithm.

Fields

• r::Float64: subsampling fraction

bias_state_evolution(
    problem,
    algo;
    check_convergence,
    kwargs...
)

bias_variance_empirical(rng, problem, algo; n, K)

bias_variance_empirical(rng, problem, algo; n, K)

bias_variance_empirical(rng, problem, algo; n, K)

bias_variance_empirical(rng, problem, algo; n, K)

bias_variance_true(rng, problem; n, K, conditional)

gamp(problem, X, y; max_iter, rtol)

Run generalized approximate message passing on logistic regression to recover the Bayes optimal estimator.

sample_all(rng, problem, n)

Sample X, w and y all at once for a given problem with population size n.

sample_data(rng, problem, n)

Sample the data matrix X for a given problem with population size n.

sample_labels(rng, , X, w)

Sample the labels vector y for a given problem from the features X and weights w.

sample_weights(rng, problem, n)

Sample the weights vector w for a given problem with population size n (from which the dimension is deduced).

state_evolution(
    problem,
    algo1,
    algo2;
    rtol,
    max_iteration,
    show_progress
)

Peform state evolution on a problem for the couple (algorithm1, algorithm2), by creating and then iteratively updating overlaps and hat overlaps.

Keyword arguments

• rtol: relative tolerance used at every step of the procedure, especially to check overlap convergence
• max_iteration: maximum number of overlap updates
• show_progress: whether to display a progress bar

state_evolution_BayesOpt(problem; rtol, max_iteration)

Special case of state evolution for the Bayes optimal estimator.

variance_state_evolution(
    problem,
    algo;
    check_convergence,
    kwargs...
)

variance_state_evolution(
    problem,
    algo;
    check_convergence,
    kwargs...
)

fit([rng], problem, algorithm, X, y, [w_star])

Fit an algorithm to data X, y generated by problem, with randomness source rng.