--- /dev/null
+# Copyright (c) 2019 Cisco and/or its affiliates.
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at:
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+"""Module holding BitCountingStats class."""
+
+import math
+
+from .AvgStdevStats import AvgStdevStats
+
+
+class BitCountingStats(AvgStdevStats):
+ """Class for statistics which include information content of a group.
+
+ The information content is based on an assumption that the data
+ consists of independent random values from a normal distribution.
+
+ Instances are only statistics, the data itself is stored elsewhere.
+
+ The coding needs to know the previous average, and a maximal value
+ so both values are required as inputs.
+
+ This is a subclass of AvgStdevStats, even though all methods are overriden.
+ Only for_runs method calls the parent implementation, without using super().
+ """
+
+ def __init__(
+ self, size=0, avg=None, stdev=0.0, max_value=None, prev_avg=None):
+ """Construct the stats object by computing from the values needed.
+
+ The values are not sanitized, faulty callers can cause math errors.
+
+ The None values are allowed for stats for zero size data,
+ but such stats can report arbitrary avg and max_value.
+ Stats for nonzero size data cannot contain None,
+ else ValueError is raised.
+
+ The max_value needs to be numeric for nonzero size,
+ but its relations to avg and prev_avg are not examined.
+
+ The bit count is not real, as that would depend on numeric precision
+ (number of significant bits in values).
+ The difference is assumed to be constant per value,
+ which is consistent with Gauss distribution
+ (but not with floating point mechanic).
+ The hope is the difference will have
+ no real impact on the classification procedure.
+
+ :param size: Number of values participating in this group.
+ :param avg: Population average of the participating sample values.
+ :param stdev: Population standard deviation of the sample values.
+ :param max_value: Maximal expected value.
+ TODO: This might be more optimal,
+ but max-invariant algorithm will be nicer.
+ :param prev_avg: Population average of the previous group.
+ If None, no previous average is taken into account.
+ If not None, the given previous average is used to discourage
+ consecutive groups with similar averages
+ (opposite triangle distribution is assumed).
+ :type avg: float
+ :type size: int
+ :type stdev: float
+ :type max_value: Union[float, NoneType]
+ :type prev_avg: Union[float, NoneType]
+ """
+ self.avg = avg
+ self.size = size
+ self.stdev = stdev
+ self.max_value = max_value
+ self.prev_avg = prev_avg
+ # Zero size should in principle have non-zero bits (coding zero size),
+ # but zero allows users to add empty groups without affecting bits.
+ self.bits = 0.0
+ if self.size < 1:
+ return
+ if avg is None:
+ raise ValueError(f"Avg is None: {self!r}")
+ if max_value is None or max_value <= 0.0:
+ raise ValueError(f"Invalid max value: {self!r}")
+ # Length of the sequence must be also counted in bits,
+ # otherwise the message would not be decodable.
+ # Model: probability of k samples is 1/k - 1/(k+1) == 1/k/(k+1)
+ # This is compatible with zero size leading to zero bits.
+ self.bits += math.log(size * (size + 1), 2)
+ if prev_avg is None:
+ # Avg is considered to be uniformly distributed
+ # from zero to max_value.
+ self.bits += math.log(max_value + 1.0, 2)
+ else:
+ # Opposite triangle distribution with minimum.
+ self.bits += math.log(
+ max_value * (max_value + 1) / (abs(avg - prev_avg) + 1), 2)
+ if self.size < 2:
+ return
+ # Stdev is considered to be uniformly distributed
+ # from zero to max_value. That is quite a bad expectation,
+ # but resilient to negative samples etc.
+ self.bits += math.log(max_value + 1.0, 2)
+ # Now we know the samples lie on sphere in size-1 dimensions.
+ # So it is (size-2)-sphere, with radius^2 == stdev^2 * size.
+ # https://en.wikipedia.org/wiki/N-sphere
+ sphere_area_ln = math.log(2) + math.log(math.pi) * ((size - 1) / 2.0)
+ sphere_area_ln -= math.lgamma((size - 1) / 2.0)
+ sphere_area_ln += math.log(stdev + 1.0) * (size - 2)
+ sphere_area_ln += math.log(size) * ((size - 2) / 2.0)
+ self.bits += sphere_area_ln / math.log(2)
+
+ def __str__(self):
+ """Return string with human readable description of the group.
+
+ :returns: Readable description.
+ :rtype: str
+ """
+ return (
+ f"size={self.size} avg={self.avg} stdev={self.stdev}"
+ f" bits={self.bits}"
+ )
+
+ def __repr__(self):
+ """Return string executable as Python constructor call.
+
+ :returns: Executable constructor call.
+ :rtype: str
+ """
+ return (
+ f"BitCountingStats(size={self.size!r},avg={self.avg!r}"
+ f",stdev={self.stdev!r},max_value={self.max_value!r}"
+ f",prev_avg={self.prev_avg!r})"
+ )
+
+ @classmethod
+ def for_runs(cls, runs, max_value=None, prev_avg=None):
+ """Return new stats instance describing the sequence of runs.
+
+ If you want to append data to existing stats object,
+ you can simply use the stats object as the first run.
+
+ Instead of a verb, "for" is used to start this method name,
+ to signify the result contains less information than the input data.
+
+ The two optional values can come from outside of the runs provided.
+
+ The max_value cannot be None for non-zero size data.
+ The implementation does not check if no datapoint exceeds max_value.
+
+ TODO: Document the behavior for zero size result.
+
+ :param runs: Sequence of data to describe by the new metadata.
+ :param max_value: Maximal expected value.
+ :param prev_avg: Population average of the previous group, if any.
+ :type runs: Iterable[Union[float, AvgStdevStats]]
+ :type max_value: Union[float, NoneType]
+ :type prev_avg: Union[float, NoneType]
+ :returns: The new stats instance.
+ :rtype: cls
+ """
+ asd = AvgStdevStats.for_runs(runs)
+ ret_obj = cls(size=asd.size, avg=asd.avg, stdev=asd.stdev,
+ max_value=max_value, prev_avg=prev_avg)
+ return ret_obj
Code Review / csit.git / blobdiff