md_bernoulli_cand_C1_kld: md_bernoulli_cand_C1_kld

In queelius/masked.data: Estimating Reliability of Components in Series from Masked Data with Relaxed Candidate Set Models

md_bernoulli_cand_C1_kld

Description

For each row (observation) in md, a probability ⁠Q = (q1, q2, ..., qm)⁠ is constructed such that qj is the probability that the j-th component is in the candidate set, qk = 1, where k is failed component.

Usage

md_bernoulli_cand_C1_kld(
  md,
  p,
  d,
  eps = 1e-04,
  max_iter = 100000L,
  lr = 1,
  lambda = 1,
  alpha0 = 5,
  beta0 = 0.5,
  debug = F
)

Arguments

md	component failure times for the series system
p	numeric, defines ⁠P = (p, ..., p, 1, p, ..., p)⁠.
d	numeric, the KL divergence from P = (p, p, ..., p, 1, p, ..., p) to try to obtain
eps	numeric, stopping condition.
max_iter	Integer, maximum number of iterations before giving up.
lr	numeric, learning rate.
lambda	numeric, controls how much the two constraints are weighted. Lower value specifies more enforcement of the KL-divergence constraint being closer to d. Defaults to 1.
alpha0	numeric, initial guess for alpha parameter of informative_masking_by_rank.
beta0	numeric, initial guess for beta parameter of informative_masking_by_rank.
debug	Logical, whether to output debugging information while running

Details

Q is an informed candidate model that uses informative_masking_by_rank to assign higher probabilities to components that failed earlier (which is something we typically only know in, say, a simulation study).

The probabilities Q have two constraints on them. Let ⁠P = (p, ..., p, 1, p, ..., p)⁠ be the bernoulli candidate model that satisfies conditions C1, C2, and C3. Then, the KL-divergence between P and Q is as close as possible to d while satisfying sum(P) == sum(Q).

For d = 0, Q == P. As d increases, Q becomes more informative about the components. Given the structure of informative_masking_by_rank, it may not be possible to satisfy every d specified, but we get as close as we can, which should permit useful experiments.

queelius/masked.data documentation built on Jan. 28, 2025, 4:23 a.m.