separately.
Args:
- samples: Floating-point tensor of samples from the distribution(s)
+ samples: Floating-point `Tensor` of samples from the distribution(s)
of interest. Entries are assumed IID across the 0th dimension.
The other dimensions must broadcast with `envelope` and `high`.
- envelope: Floating-point tensor of sizes of admissible CDF
+ envelope: Floating-point `Tensor` of sizes of admissible CDF
envelopes (i.e., the `eps` above).
- high: Floating-point tensor of upper bounds on the distributions'
- supports.
+ high: Floating-point `Tensor` of upper bounds on the distributions'
+ supports. `samples <= high`.
name: A name for this operation (optional).
Returns:
- bound: Floating-point tensor of upper bounds on the true means.
+ bound: Floating-point `Tensor` of upper bounds on the true means.
Raises:
InvalidArgumentError: If some `sample` is found to be larger than
separately.
Args:
- samples: Floating-point tensor of samples from the distribution(s)
+ samples: Floating-point `Tensor` of samples from the distribution(s)
of interest. Entries are assumed IID across the 0th dimension.
The other dimensions must broadcast with `envelope` and `low`.
- envelope: Floating-point tensor of sizes of admissible CDF
+ envelope: Floating-point `Tensor` of sizes of admissible CDF
envelopes (i.e., the `eps` above).
- low: Floating-point tensor of lower bounds on the distributions'
- supports.
+ low: Floating-point `Tensor` of lower bounds on the distributions'
+ supports. `samples >= low`.
name: A name for this operation (optional).
Returns:
- bound: Floating-point tensor of lower bounds on the true means.
+ bound: Floating-point `Tensor` of lower bounds on the true means.
Raises:
InvalidArgumentError: If some `sample` is found to be smaller than
probability above.
Args:
- n: Tensor of numbers of samples drawn.
- error_rate: Floating-point tensor of admissible rates of mistakes.
+ n: `Tensor` of numbers of samples drawn.
+ error_rate: Floating-point `Tensor` of admissible rates of mistakes.
name: A name for this operation (optional).
Returns:
- eps: Tensor of maximum distances the true CDF can be from the
+ eps: `Tensor` of maximum distances the true CDF can be from the
empirical CDF. This scales as `O(sqrt(-log(error_rate)))` and
as `O(1 / sqrt(n))`. The shape is the broadcast of `n` and
`error_rate`.
sample counts end up inflated.
Args:
- samples: A Tensor whose shape is to be protected against broadcasting.
- parameters: A list of Tensors who are parameters for the statistical test.
+ samples: A `Tensor` whose shape is to be protected against broadcasting.
+ parameters: A list of `Tensor`s who are parameters for the statistical test.
Returns:
samples: Return original `samples` with control dependencies attached
members.
Args:
- samples: Floating-point tensor of samples from the distribution(s)
+ samples: Floating-point `Tensor` of samples from the distribution(s)
of interest. Entries are assumed IID across the 0th dimension.
The other dimensions must broadcast with `low` and `high`.
- low: Floating-point tensor of lower bounds on the distributions'
+ The support is bounded: `low <= samples <= high`.
+ low: Floating-point `Tensor` of lower bounds on the distributions'
supports.
- high: Floating-point tensor of upper bounds on the distributions'
+ high: Floating-point `Tensor` of upper bounds on the distributions'
supports.
- error_rate: *Scalar* admissible total rate of mistakes.
+ error_rate: *Scalar* floating-point `Tensor` admissible total rate
+ of mistakes.
name: A name for this operation (optional).
Returns:
- low: A floating-point tensor of stochastic lower bounds on the true means.
- high: A floating-point tensor of stochastic upper bounds on the true means.
+ low: A floating-point `Tensor` of stochastic lower bounds on the
+ true means.
+ high: A floating-point `Tensor` of stochastic upper bounds on the
+ true means.
"""
with ops.name_scope(
name, "true_mean_confidence_interval_by_dkwm",
the assertion will insist on stronger evidence to fail any one member.
Args:
- samples: Floating-point tensor of samples from the distribution(s)
+ samples: Floating-point `Tensor` of samples from the distribution(s)
of interest. Entries are assumed IID across the 0th dimension.
The other dimensions must broadcast with `low` and `high`.
- low: Floating-point tensor of lower bounds on the distributions'
+ The support is bounded: `low <= samples <= high`.
+ low: Floating-point `Tensor` of lower bounds on the distributions'
supports.
- high: Floating-point tensor of upper bounds on the distributions'
+ high: Floating-point `Tensor` of upper bounds on the distributions'
supports.
- expected: Floating-point tensor of expected true means.
- false_fail_rate: *Scalar* admissible total rate of mistakes.
+ expected: Floating-point `Tensor` of expected true means.
+ false_fail_rate: *Scalar* floating-point `Tensor` admissible total
+ rate of mistakes.
name: A name for this operation (optional).
Returns:
with the same `false_pass_rate`.
Args:
- n: Tensor of numbers of samples to be drawn from the distributions
+ n: `Tensor` of numbers of samples to be drawn from the distributions
of interest.
- low: Floating-point tensor of lower bounds on the distributions'
+ low: Floating-point `Tensor` of lower bounds on the distributions'
supports.
- high: Floating-point tensor of upper bounds on the distributions'
+ high: Floating-point `Tensor` of upper bounds on the distributions'
supports.
- false_fail_rate: *Scalar* admissible total rate of false failures.
- false_pass_rate: *Scalar* admissible rate of false passes.
+ false_fail_rate: *Scalar* floating-point `Tensor` admissible total
+ rate of false failures.
+ false_pass_rate: *Scalar* floating-point `Tensor` admissible rate
+ of false passes.
name: A name for this operation (optional).
Returns:
- discr: Tensor of lower bounds on the distances between true
+ discr: `Tensor` of lower bounds on the distances between true
means detectable by a DKWM-based test.
For each batch member `i`, of `K` total, drawing `n[i]` samples from
on a scalar distribution supported on `[low, high]`.
Args:
- discrepancy: Floating-point tensor of desired upper limits on mean
+ discrepancy: Floating-point `Tensor` of desired upper limits on mean
differences that may go undetected with probability higher than
`1 - false_pass_rate`.
- low: Tensor of lower bounds on the distributions' support.
- high: Tensor of upper bounds on the distributions' support.
- false_fail_rate: *Scalar* admissible total rate of false failures.
- false_pass_rate: *Scalar* admissible rate of false passes.
+ low: `Tensor` of lower bounds on the distributions' support.
+ high: `Tensor` of upper bounds on the distributions' support.
+ false_fail_rate: *Scalar* floating-point `Tensor` admissible total
+ rate of false failures.
+ false_pass_rate: *Scalar* floating-point `Tensor` admissible rate
+ of false passes.
name: A name for this operation (optional).
Returns:
- n: Tensor of numbers of samples to be drawn from the distributions
+ n: `Tensor` of numbers of samples to be drawn from the distributions
of interest.
The `discrepancy`, `low`, and `high` tensors must have
the assertion will insist on stronger evidence to fail any one member.
Args:
- samples1: Floating-point tensor of samples from the
+ samples1: Floating-point `Tensor` of samples from the
distribution(s) A. Entries are assumed IID across the 0th
dimension. The other dimensions must broadcast with `low1`,
`high1`, `low2`, and `high2`.
- low1: Floating-point tensor of lower bounds on the supports of the
+ The support is bounded: `low1 <= samples1 <= high1`.
+ low1: Floating-point `Tensor` of lower bounds on the supports of the
distributions A.
- high1: Floating-point tensor of upper bounds on the supports of
+ high1: Floating-point `Tensor` of upper bounds on the supports of
the distributions A.
- samples2: Floating-point tensor of samples from the
+ samples2: Floating-point `Tensor` of samples from the
distribution(s) B. Entries are assumed IID across the 0th
dimension. The other dimensions must broadcast with `low1`,
`high1`, `low2`, and `high2`.
- low2: Floating-point tensor of lower bounds on the supports of the
+ The support is bounded: `low2 <= samples2 <= high2`.
+ low2: Floating-point `Tensor` of lower bounds on the supports of the
distributions B.
- high2: Floating-point tensor of upper bounds on the supports of
+ high2: Floating-point `Tensor` of upper bounds on the supports of
the distributions B.
- false_fail_rate: *Scalar* admissible total rate of mistakes.
+ false_fail_rate: *Scalar* floating-point `Tensor` admissible total
+ rate of mistakes.
name: A name for this operation (optional).
Returns:
with the same `false_pass_rate`.
Args:
- n1: Tensor of numbers of samples to be drawn from the distributions A.
- low1: Floating-point tensor of lower bounds on the supports of the
+ n1: `Tensor` of numbers of samples to be drawn from the distributions A.
+ low1: Floating-point `Tensor` of lower bounds on the supports of the
distributions A.
- high1: Floating-point tensor of upper bounds on the supports of
+ high1: Floating-point `Tensor` of upper bounds on the supports of
the distributions A.
- n2: Tensor of numbers of samples to be drawn from the distributions B.
- low2: Floating-point tensor of lower bounds on the supports of the
+ n2: `Tensor` of numbers of samples to be drawn from the distributions B.
+ low2: Floating-point `Tensor` of lower bounds on the supports of the
distributions B.
- high2: Floating-point tensor of upper bounds on the supports of
+ high2: Floating-point `Tensor` of upper bounds on the supports of
the distributions B.
- false_fail_rate: *Scalar* admissible total rate of false failures.
- false_pass_rate: *Scalar* admissible rate of false passes.
+ false_fail_rate: *Scalar* floating-point `Tensor` admissible total
+ rate of false failures.
+ false_pass_rate: *Scalar* floating-point `Tensor` admissible rate
+ of false passes.
name: A name for this operation (optional).
Returns:
- discr: Tensor of lower bounds on the distances between true means
+ discr: `Tensor` of lower bounds on the distances between true means
detectable by a two-sample DKWM-based test.
For each batch member `i`, of `K` total, drawing `n1[i]` samples
(https://en.wikipedia.org/wiki/CDF-based_nonparametric_confidence_interval).
Args:
- discrepancy: Floating-point tensor of desired upper limits on mean
+ discrepancy: Floating-point `Tensor` of desired upper limits on mean
differences that may go undetected with probability higher than
`1 - false_pass_rate`.
- low1: Floating-point tensor of lower bounds on the supports of the
+ low1: Floating-point `Tensor` of lower bounds on the supports of the
distributions A.
- high1: Floating-point tensor of upper bounds on the supports of
+ high1: Floating-point `Tensor` of upper bounds on the supports of
the distributions A.
- low2: Floating-point tensor of lower bounds on the supports of the
+ low2: Floating-point `Tensor` of lower bounds on the supports of the
distributions B.
- high2: Floating-point tensor of upper bounds on the supports of
+ high2: Floating-point `Tensor` of upper bounds on the supports of
the distributions B.
- false_fail_rate: *Scalar* admissible total rate of false failures.
- false_pass_rate: *Scalar* admissible rate of false passes.
+ false_fail_rate: *Scalar* floating-point `Tensor` admissible total
+ rate of false failures.
+ false_pass_rate: *Scalar* floating-point `Tensor` admissible rate
+ of false passes.
name: A name for this operation (optional).
Returns:
- n1: Tensor of numbers of samples to be drawn from the distributions A.
- n2: Tensor of numbers of samples to be drawn from the distributions B.
+ n1: `Tensor` of numbers of samples to be drawn from the distributions A.
+ n2: `Tensor` of numbers of samples to be drawn from the distributions B.
For each batch member `i`, of `K` total, drawing `n1[i]` samples
from scalar distribution A supported on `[low1[i], high1[i]]` and `n2[i]`