diff --git a/docs/build/doctrees/environment.pickle b/docs/build/doctrees/environment.pickle index 4f44043..b127453 100644 Binary files a/docs/build/doctrees/environment.pickle and b/docs/build/doctrees/environment.pickle differ diff --git a/docs/build/doctrees/pyFTS.benchmarks.doctree b/docs/build/doctrees/pyFTS.benchmarks.doctree index a2dc180..0251184 100644 Binary files a/docs/build/doctrees/pyFTS.benchmarks.doctree and b/docs/build/doctrees/pyFTS.benchmarks.doctree differ diff --git a/docs/build/doctrees/pyFTS.common.doctree b/docs/build/doctrees/pyFTS.common.doctree index 6aaf1d1..12205ff 100644 Binary files a/docs/build/doctrees/pyFTS.common.doctree and b/docs/build/doctrees/pyFTS.common.doctree differ diff --git a/docs/build/doctrees/pyFTS.probabilistic.doctree b/docs/build/doctrees/pyFTS.probabilistic.doctree index 7b1035d..a264c17 100644 Binary files a/docs/build/doctrees/pyFTS.probabilistic.doctree and b/docs/build/doctrees/pyFTS.probabilistic.doctree differ diff --git a/docs/build/html/_modules/pyFTS/benchmarks/Measures.html b/docs/build/html/_modules/pyFTS/benchmarks/Measures.html index 01187bf..d646a8a 100644 --- a/docs/build/html/_modules/pyFTS/benchmarks/Measures.html +++ b/docs/build/html/_modules/pyFTS/benchmarks/Measures.html @@ -81,7 +81,7 @@ import time import numpy as np import pandas as pd -from pyFTS.common import FuzzySet,SortedCollection +from pyFTS.common import FuzzySet, SortedCollection from pyFTS.probabilistic import ProbabilityDistribution @@ -97,10 +97,10 @@ sigma = np.var(data) n = len(data) s = 0 - for t in np.arange(0,n-k): - s += (data[t]-mu) * (data[t+k] - mu) + for t in np.arange(0, n - k): + s += (data[t] - mu) * (data[t + k] - mu) - return 1/((n-k)*sigma)*s + return 1 / ((n - k) * sigma) * s
[docs]def rmse(targets, forecasts): @@ -159,9 +159,9 @@ if isinstance(forecasts, list): forecasts = np.array(forecasts) if type == 1: - return np.mean(np.abs(forecasts - targets) / ((forecasts + targets)/2)) + return np.mean(np.abs(forecasts - targets) / ((forecasts + targets) / 2)) elif type == 2: - return np.mean(np.abs(forecasts - targets) / (abs(forecasts) + abs(targets)) )*100 + return np.mean(np.abs(forecasts - targets) / (abs(forecasts) + abs(targets))) * 100 else: return sum(np.abs(forecasts - targets)) / sum(forecasts + targets)
@@ -187,8 +187,8 @@ naive = [] y = [] - for k in np.arange(0,l-1): - y.append((forecasts[k ] - targets[k]) ** 2) + for k in np.arange(0, l - 1): + y.append((forecasts[k] - targets[k]) ** 2) naive.append((targets[k + 1] - targets[k]) ** 2) return np.sqrt(sum(y) / sum(naive)) @@ -203,11 +203,10 @@ """ res = targets - forecasts t = len(res) - us = np.sqrt(sum([u**2 for u in res])) - ys = np.sqrt(sum([y**2 for y in targets])) - fs = np.sqrt(sum([f**2 for f in forecasts])) - return us / (ys + fs) - + us = np.sqrt(sum([u ** 2 for u in res])) + ys = np.sqrt(sum([y ** 2 for y in targets])) + fs = np.sqrt(sum([f ** 2 for f in forecasts])) + return us / (ys + fs)
[docs]def BoxPierceStatistic(data, h): @@ -220,10 +219,10 @@ """ n = len(data) s = 0 - for k in np.arange(1,h+1): + for k in np.arange(1, h + 1): r = acf(data, k) - s += r**2 - return n*s
+ s += r ** 2 + return n * s
[docs]def BoxLjungStatistic(data, h): @@ -236,10 +235,10 @@ """ n = len(data) s = 0 - for k in np.arange(1,h+1): + for k in np.arange(1, h + 1): r = acf(data, k) - s += r**2 / (n -k) - return n*(n-2)*s
+ s += r ** 2 / (n - k) + return n * (n - 2) * s
[docs]def sharpness(forecasts): @@ -248,7 +247,6 @@ return np.mean(tmp)
-
[docs]def resolution(forecasts): """Resolution - Standard deviation of the intervals""" shp = sharpness(forecasts) @@ -304,9 +302,9 @@ if forecast[0] < target and target < forecast[1]: return delta elif forecast[0] > target: - return delta + 2*(forecast[0] - target)/tau + return delta + 2 * (forecast[0] - target) / tau elif forecast[1] < target: - return delta + 2*(target - forecast[1])/tau
+ return delta + 2 * (target - forecast[1]) / tau
[docs]def winkler_mean(tau, targets, forecasts): @@ -335,7 +333,7 @@ ret.append(score) except ValueError as ex: ret.append(sum([d.distribution[k] ** 2 for k in d.bins])) - return sum(ret)/len(ret)
+ return sum(ret) / len(ret)
[docs]def pmf_to_cdf(density): @@ -345,7 +343,7 @@ prev = 0 for col in density.columns: prev += density[col][row] if not np.isnan(density[col][row]) else 0 - tmp.append( prev ) + tmp.append(prev) ret.append(tmp) df = pd.DataFrame(ret, columns=density.columns) return df
@@ -354,6 +352,7 @@
[docs]def heavyside(bin, target): return 1 if bin >= target else 0
+
[docs]def heavyside_cdf(bins, targets): ret = [] for t in targets: @@ -378,7 +377,7 @@ l = len(densities[0].bins) n = len(densities) for ct, df in enumerate(densities): - _crps += sum([(df.cummulative(bin) - (1 if bin >= targets[ct] else 0)) ** 2 for bin in df.bins]) + _crps += sum([(df.cumulative(bin) - (1 if bin >= targets[ct] else 0)) ** 2 for bin in df.bins]) return _crps / float(l * n)
@@ -393,7 +392,7 @@ :return: a list with the RMSE, SMAPE and U Statistic ''' - steps_ahead = kwargs.get('steps_ahead',1) + steps_ahead = kwargs.get('steps_ahead', 1) kwargs['type'] = 'point' indexer = kwargs.get('indexer', None) @@ -411,7 +410,7 @@ if steps_ahead == 1: forecasts = model.predict(ndata, **kwargs) - + if model.is_multivariate and model.has_seasonality: ndata = model.indexer.get_data(ndata) elif model.is_multivariate: @@ -428,12 +427,12 @@ else: steps_ahead_sampler = kwargs.get('steps_ahead_sampler', 1) nforecasts = [] - for k in np.arange(model.order, len(ndata)-steps_ahead,steps_ahead_sampler): + for k in np.arange(model.order, len(ndata) - steps_ahead, steps_ahead_sampler): sample = ndata[k - model.order: k] tmp = model.predict(sample, **kwargs) nforecasts.append(tmp[-1]) - start = model.max_lag + steps_ahead -1 + start = model.max_lag + steps_ahead - 1 ret.append(np.round(rmse(ndata[start:-1:steps_ahead_sampler], nforecasts), 2)) ret.append(np.round(mape(ndata[start:-1:steps_ahead_sampler], nforecasts), 2)) ret.append(np.round(UStatistic(ndata[start:-1:steps_ahead_sampler], nforecasts), 2)) @@ -442,7 +441,7 @@
[docs]def get_interval_statistics(data, model, **kwargs): - ''' + """ Condensate all measures for point interval forecasters :param data: test data @@ -450,7 +449,7 @@ :param kwargs: :return: a list with the sharpness, resolution, coverage, .05 pinball mean, .25 pinball mean, .75 pinball mean and .95 pinball mean. - ''' + """ steps_ahead = kwargs.get('steps_ahead', 1) kwargs['type'] = 'interval' @@ -475,7 +474,7 @@ tmp = model.predict(sample, **kwargs) forecasts.append(tmp[-1]) - start = model.max_lag + steps_ahead -1 + start = model.max_lag + steps_ahead - 1 ret.append(round(sharpness(forecasts), 2)) ret.append(round(resolution(forecasts), 2)) ret.append(round(coverage(data[model.max_lag:], forecasts), 2)) @@ -489,14 +488,14 @@
[docs]def get_distribution_statistics(data, model, **kwargs): - ''' + """ Get CRPS statistic and time for a forecasting model :param data: test data :param model: FTS model with probabilistic forecasting capability :param kwargs: :return: a list with the CRPS and execution time - ''' + """ steps_ahead = kwargs.get('steps_ahead', 1) kwargs['type'] = 'distribution' @@ -524,8 +523,6 @@ ret.append(round(_e1 - _s1, 3)) ret.append(round(brier_score(data[start:-1:skip], forecasts), 3)) return ret
- -
diff --git a/docs/build/html/_modules/pyFTS/common/FuzzySet.html b/docs/build/html/_modules/pyFTS/common/FuzzySet.html index 2ea3b36..18ab7b9 100644 --- a/docs/build/html/_modules/pyFTS/common/FuzzySet.html +++ b/docs/build/html/_modules/pyFTS/common/FuzzySet.html @@ -146,17 +146,23 @@ :param ordered_sets: a list with the fuzzy sets names ordered by their centroids. :return: A list with the best fuzzy sets that may contain x """ - max_len = len(fuzzy_sets) + max_len = len(fuzzy_sets) - 1 first = 0 last = max_len while first <= last: midpoint = (first + last) // 2 + fs = ordered_sets[midpoint] fs1 = ordered_sets[midpoint - 1] if midpoint > 0 else ordered_sets[0] fs2 = ordered_sets[midpoint + 1] if midpoint < max_len else ordered_sets[max_len] + if fuzzy_sets[fs1].centroid <= x <= fuzzy_sets[fs2].centroid: return (midpoint-1, midpoint, midpoint+1) + elif midpoint <= 1: + return [0] + elif midpoint >= max_len: + return [max_len] else: if x < fuzzy_sets[fs].centroid: last = midpoint - 1 @@ -164,6 +170,7 @@ first = midpoint + 1 +
[docs]def fuzzyfy(data, partitioner, **kwargs): """ A general method for fuzzyfication. diff --git a/docs/build/html/_modules/pyFTS/common/fts.html b/docs/build/html/_modules/pyFTS/common/fts.html index 0b2b63e..ae66fd4 100644 --- a/docs/build/html/_modules/pyFTS/common/fts.html +++ b/docs/build/html/_modules/pyFTS/common/fts.html @@ -240,7 +240,7 @@ :param data: time series data with the minimal length equal to the max_lag of the model :param kwargs: model specific parameters - :return: a list with the forecasted intervals + :return: a list with the prediction intervals """ raise NotImplementedError('This model do not perform one step ahead interval forecasts!')
@@ -250,7 +250,7 @@ :param data: time series data with the minimal length equal to the max_lag of the model :param kwargs: model specific parameters - :return: a list with the forecasted Probability Distributions + :return: a list with probabilistic.ProbabilityDistribution objects representing the forecasted Probability Distributions """ raise NotImplementedError('This model do not perform one step ahead distribution forecasts!') diff --git a/docs/build/html/_modules/pyFTS/models/chen.html b/docs/build/html/_modules/pyFTS/models/chen.html index 485d328..4623c94 100644 --- a/docs/build/html/_modules/pyFTS/models/chen.html +++ b/docs/build/html/_modules/pyFTS/models/chen.html @@ -124,7 +124,7 @@
[docs] def train(self, data, **kwargs): - tmpdata = FuzzySet.fuzzyfy_series(data, self.sets, method='maximum') + tmpdata = FuzzySet.fuzzyfy(data, partitioner=self.partitioner, method='maximum', mode='sets') flrs = FLR.generate_non_recurrent_flrs(tmpdata) self.generate_flrg(flrs)
diff --git a/docs/build/html/_modules/pyFTS/models/ismailefendi.html b/docs/build/html/_modules/pyFTS/models/ismailefendi.html index 2b85b82..007804a 100644 --- a/docs/build/html/_modules/pyFTS/models/ismailefendi.html +++ b/docs/build/html/_modules/pyFTS/models/ismailefendi.html @@ -136,7 +136,7 @@
[docs] def train(self, ndata, **kwargs): - tmpdata = FuzzySet.fuzzyfy_series(ndata, self.sets, method='maximum') + tmpdata = FuzzySet.fuzzyfy(ndata, partitioner=self.partitioner, method='maximum', mode='sets') flrs = FLR.generate_recurrent_flrs(tmpdata) self.generate_flrg(flrs)
diff --git a/docs/build/html/_modules/pyFTS/models/sadaei.html b/docs/build/html/_modules/pyFTS/models/sadaei.html index 80da7d0..de65e0a 100644 --- a/docs/build/html/_modules/pyFTS/models/sadaei.html +++ b/docs/build/html/_modules/pyFTS/models/sadaei.html @@ -140,7 +140,7 @@ self.flrgs[flr.LHS].append_rhs(flr.RHS)
[docs] def train(self, data, **kwargs): - tmpdata = FuzzySet.fuzzyfy_series(data, self.sets, method='maximum') + tmpdata = FuzzySet.fuzzyfy(data, partitioner=self.partitioner, method='maximum', mode='sets') flrs = FLR.generate_recurrent_flrs(tmpdata) self.generate_flrg(flrs, self.c)
diff --git a/docs/build/html/_modules/pyFTS/models/song.html b/docs/build/html/_modules/pyFTS/models/song.html index 91b1d9d..084cc08 100644 --- a/docs/build/html/_modules/pyFTS/models/song.html +++ b/docs/build/html/_modules/pyFTS/models/song.html @@ -124,7 +124,7 @@
[docs] def train(self, data, **kwargs): - tmpdata = FuzzySet.fuzzyfy_series(data, self.sets, method='maximum') + tmpdata = FuzzySet.fuzzyfy(data, partitioner=self.partitioner, method='maximum', mode='sets') flrs = FLR.generate_non_recurrent_flrs(tmpdata) self.operation_matrix(flrs)
diff --git a/docs/build/html/_modules/pyFTS/models/yu.html b/docs/build/html/_modules/pyFTS/models/yu.html index 7fea056..bd54588 100644 --- a/docs/build/html/_modules/pyFTS/models/yu.html +++ b/docs/build/html/_modules/pyFTS/models/yu.html @@ -132,7 +132,7 @@ self.flrgs[flr.LHS].append_rhs(flr.RHS)
[docs] def train(self, ndata, **kwargs): - tmpdata = FuzzySet.fuzzyfy_series(ndata, self.sets, method='maximum') + tmpdata = FuzzySet.fuzzyfy(ndata, partitioner=self.partitioner, method='maximum', mode='sets') flrs = FLR.generate_recurrent_flrs(tmpdata) self.generate_FLRG(flrs)
diff --git a/docs/build/html/_modules/pyFTS/probabilistic/ProbabilityDistribution.html b/docs/build/html/_modules/pyFTS/probabilistic/ProbabilityDistribution.html index dd830e1..cbe2d27 100644 --- a/docs/build/html/_modules/pyFTS/probabilistic/ProbabilityDistribution.html +++ b/docs/build/html/_modules/pyFTS/probabilistic/ProbabilityDistribution.html @@ -135,10 +135,21 @@ self.name = kwargs.get("name", "")
[docs] def set(self, value, density): + """ + Assert a probability 'density' for a certain value 'value', such that P(value) = density + + :param value: A value in the universe of discourse from the distribution + :param density: The probability density to assign to the value + """ k = self.bin_index.find_ge(value) self.distribution[k] = density
[docs] def append(self, values): + """ + Increment the frequency count for the values + + :param values: A list of values to account the frequency + """ if self.type == "histogram": for k in values: v = self.bin_index.find_ge(k) @@ -152,6 +163,11 @@ self.distribution[self.bins[v]] = d
[docs] def append_interval(self, intervals): + """ + Increment the frequency count for all values inside an interval + + :param intervals: A list of intervals do increment the frequency + """ if self.type == "histogram": for interval in intervals: for k in self.bin_index.inside(interval[0], interval[1]): @@ -159,6 +175,12 @@ self.count += 1
[docs] def density(self, values): + """ + Return the probability densities for the input values + + :param values: List of values to return the densities + :return: List of probability densities for the input values + """ ret = [] scalar = False @@ -183,6 +205,12 @@ return ret
[docs] def differential_offset(self, value): + """ + Auxiliary function for probability distributions of differentiated data + + :param value: + :return: + """ nbins = [] dist = {} @@ -201,6 +229,11 @@ self.qtl = None
[docs] def expected_value(self): + """ + Return the expected value of the distribution, as E[X] = ∑ x * P(x) + + :return: The expected value of the distribution + """ return np.nansum([v * self.distribution[v] for v in self.bins])
[docs] def build_cdf_qtl(self): @@ -221,7 +254,13 @@ self.quantile_index = SortedCollection.SortedCollection(iterable=_keys)
-
[docs] def cummulative(self, values): +
[docs] def cumulative(self, values): + """ + Return the cumulative probability densities for the input values + + :param values: A list of input values + :return: The cumulative probability densities for the input values + """ if self.cdf is None: self.build_cdf_qtl() @@ -235,6 +274,12 @@ return self.cdf[values]
[docs] def quantile(self, values): + """ + Return the quantile values for the input values + + :param values: input values + :return: The list of the quantile values for the input values + """ if self.qtl is None: self.build_cdf_qtl() @@ -250,21 +295,43 @@ return ret
[docs] def entropy(self): + """ + Return the entropy of the probability distribution, H[X] = + + :return:the entropy of the probability distribution + """ h = -sum([self.distribution[k] * np.log(self.distribution[k]) if self.distribution[k] > 0 else 0 for k in self.bins]) return h
[docs] def crossentropy(self,q): + """ + Cross entropy between the actual probability distribution and the informed one. + + :param q: a probabilistic.ProbabilityDistribution object + :return: Cross entropy between this probability distribution and the given distribution + """ h = -sum([self.distribution[k] * np.log(q.distribution[k]) if self.distribution[k] > 0 else 0 for k in self.bins]) return h
[docs] def kullbackleiblerdivergence(self,q): + """ + Kullback-Leibler divergence between the actual probability distribution and the informed one. + + :param q: a probabilistic.ProbabilityDistribution object + :return: Kullback-Leibler divergence + """ h = sum([self.distribution[k] * np.log(self.distribution[k]/q.distribution[k]) if self.distribution[k] > 0 else 0 for k in self.bins]) return h
[docs] def empiricalloglikelihood(self): + """ + Empirical Log Likelihood of the probability distribution + + :return: + """ _s = 0 for k in self.bins: if self.distribution[k] > 0: @@ -272,6 +339,12 @@ return _s
[docs] def pseudologlikelihood(self, data): + """ + Pseudo log likelihood of the probability distribution with respect to data + + :param data: + :return: + """ densities = self.density(data) @@ -282,6 +355,12 @@ return _s
[docs] def averageloglikelihood(self, data): + """ + Average log likelihood of the probability distribution with respect to data + + :param data: + :return: + """ densities = self.density(data) diff --git a/docs/build/html/_modules/pyFTS/probabilistic/kde.html b/docs/build/html/_modules/pyFTS/probabilistic/kde.html index 370fe66..1b2dc6b 100644 --- a/docs/build/html/_modules/pyFTS/probabilistic/kde.html +++ b/docs/build/html/_modules/pyFTS/probabilistic/kde.html @@ -92,6 +92,12 @@ self.transf = Transformations.Scale(min=0,max=1)
[docs] def kernel_function(self, u): + """ + Apply the kernel + + :param u: + :return: + """ if self.kernel == "epanechnikov": tmp = (3/4)*(1.0 - u**2) return tmp if tmp > 0 else 0 diff --git a/docs/build/html/genindex.html b/docs/build/html/genindex.html index d3e38f4..cf59e77 100644 --- a/docs/build/html/genindex.html +++ b/docs/build/html/genindex.html @@ -362,7 +362,7 @@
  • crps() (in module pyFTS.benchmarks.Measures)
    • -
  • cummulative() (pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution method) +
  • cumulative() (pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution method)
  • current_milli_time() (in module pyFTS.common.Util)
    • diff --git a/docs/build/html/objects.inv b/docs/build/html/objects.inv index d5cb636..0bbabca 100644 Binary files a/docs/build/html/objects.inv and b/docs/build/html/objects.inv differ diff --git a/docs/build/html/pyFTS.benchmarks.html b/docs/build/html/pyFTS.benchmarks.html index fb3a96d..2666697 100644 --- a/docs/build/html/pyFTS.benchmarks.html +++ b/docs/build/html/pyFTS.benchmarks.html @@ -1430,7 +1430,7 @@ Value: the measure value

    -Returns:

    a list with the forecasted Probability Distributions

    +Returns:

    a list with probabilistic.ProbabilityDistribution objects representing the forecasted Probability Distributions

    @@ -1451,7 +1451,7 @@ Value: the measure value

    -Returns:

    a list with the forecasted intervals

    +Returns:

    a list with the prediction intervals

    @@ -1505,7 +1505,7 @@ Value: the measure value

    -Returns:

    a list with the forecasted Probability Distributions

    +Returns:

    a list with probabilistic.ProbabilityDistribution objects representing the forecasted Probability Distributions

    @@ -1655,7 +1655,7 @@ Value: the measure value

    -Returns:

    a list with the forecasted Probability Distributions

    +Returns:

    a list with probabilistic.ProbabilityDistribution objects representing the forecasted Probability Distributions

    @@ -1676,7 +1676,7 @@ Value: the measure value

    -Returns:

    a list with the forecasted intervals

    +Returns:

    a list with the prediction intervals

    diff --git a/docs/build/html/pyFTS.common.html b/docs/build/html/pyFTS.common.html index 479e27f..613ee7e 100644 --- a/docs/build/html/pyFTS.common.html +++ b/docs/build/html/pyFTS.common.html @@ -1648,7 +1648,7 @@ when the LHS pattern is identified on time t.

    -Returns:

    a list with the forecasted Probability Distributions

    +Returns:

    a list with probabilistic.ProbabilityDistribution objects representing the forecasted Probability Distributions

    @@ -1669,7 +1669,7 @@ when the LHS pattern is identified on time t.

    -Returns:

    a list with the forecasted intervals

    +Returns:

    a list with the prediction intervals

    diff --git a/docs/build/html/pyFTS.probabilistic.html b/docs/build/html/pyFTS.probabilistic.html index a240e8c..9954767 100644 --- a/docs/build/html/pyFTS.probabilistic.html +++ b/docs/build/html/pyFTS.probabilistic.html @@ -118,17 +118,46 @@ If type is KDE the PDF is continuous

    append(values)[source]
    -
    +

    Increment the frequency count for the values

    + +++ + + + +
    Parameters:values – A list of values to account the frequency
    +
    append_interval(intervals)[source]
    -
    +

    Increment the frequency count for all values inside an interval

    + +++ + + + +
    Parameters:intervals – A list of intervals do increment the frequency
    +
    averageloglikelihood(data)[source]
    -
    +

    Average log likelihood of the probability distribution with respect to data

    + +++ + + + + + +
    Parameters:data –
    Returns:
    +
    @@ -144,42 +173,117 @@ If type is KDE the PDF is continuous

    crossentropy(q)[source]
    -
    +

    Cross entropy between the actual probability distribution and the informed one.

    + +++ + + + + + +
    Parameters:q – a probabilistic.ProbabilityDistribution object
    Returns:Cross entropy between this probability distribution and the given distribution
    +
    -
    -cummulative(values)[source]
    -
    +
    +cumulative(values)[source]
    +

    Return the cumulative probability densities for the input values

    + +++ + + + + + +
    Parameters:values – A list of input values
    Returns:The cumulative probability densities for the input values
    +
    density(values)[source]
    -
    +

    Return the probability densities for the input values

    + +++ + + + + + +
    Parameters:values – List of values to return the densities
    Returns:List of probability densities for the input values
    +
    differential_offset(value)[source]
    -
    +

    Auxiliary function for probability distributions of differentiated data

    + +++ + + + + + +
    Parameters:value –
    Returns:
    +
    empiricalloglikelihood()[source]
    -
    +

    Empirical Log Likelihood of the probability distribution

    + +++ + + + +
    Returns:
    +
    entropy()[source]
    -
    +

    Return the entropy of the probability distribution, H[X] =

    +

    :return:the entropy of the probability distribution

    +
    expected_value()[source]
    -
    +

    Return the expected value of the distribution, as E[X] = ∑ x * P(x)

    + +++ + + + +
    Returns:The expected value of the distribution
    +
    kullbackleiblerdivergence(q)[source]
    -
    +

    Kullback-Leibler divergence between the actual probability distribution and the informed one.

    + +++ + + + + + +
    Parameters:q – a probabilistic.ProbabilityDistribution object
    Returns:Kullback-Leibler divergence
    +
    @@ -195,17 +299,52 @@ If type is KDE the PDF is continuous

    pseudologlikelihood(data)[source]
    -
    +

    Pseudo log likelihood of the probability distribution with respect to data

    + +++ + + + + + +
    Parameters:data –
    Returns:
    +
    quantile(values)[source]
    -
    +

    Return the quantile values for the input values

    + +++ + + + + + +
    Parameters:values – input values
    Returns:The list of the quantile values for the input values
    +
    set(value, density)[source]
    -
    +

    Assert a probability ‘density’ for a certain value ‘value’, such that P(value) = density

    + +++ + + + +
    Parameters:
      +
    • value – A value in the universe of discourse from the distribution
      • +
    • density – The probability density to assign to the value
      • +
    +
    +
    @@ -246,7 +385,18 @@ If type is KDE the PDF is continuous

    kernel_function(u)[source]
    -
    +

    Apply the kernel

    + +++ + + + + + +
    Parameters:u –
    Returns:
    +
    diff --git a/docs/build/html/searchindex.js b/docs/build/html/searchindex.js index 1e04a06..aeb5a16 100644 --- a/docs/build/html/searchindex.js +++ b/docs/build/html/searchindex.js @@ -1 +1 @@ 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\ No newline at end of file diff --git a/pyFTS/benchmarks/Measures.py b/pyFTS/benchmarks/Measures.py index 2cae1a6..ca156fe 100644 --- a/pyFTS/benchmarks/Measures.py +++ b/pyFTS/benchmarks/Measures.py @@ -7,7 +7,7 @@ pyFTS module for common benchmark metrics import time import numpy as np import pandas as pd -from pyFTS.common import FuzzySet,SortedCollection +from pyFTS.common import FuzzySet, SortedCollection from pyFTS.probabilistic import ProbabilityDistribution @@ -23,10 +23,10 @@ def acf(data, k): sigma = np.var(data) n = len(data) s = 0 - for t in np.arange(0,n-k): - s += (data[t]-mu) * (data[t+k] - mu) + for t in np.arange(0, n - k): + s += (data[t] - mu) * (data[t + k] - mu) - return 1/((n-k)*sigma)*s + return 1 / ((n - k) * sigma) * s def rmse(targets, forecasts): @@ -85,9 +85,9 @@ def smape(targets, forecasts, type=2): if isinstance(forecasts, list): forecasts = np.array(forecasts) if type == 1: - return np.mean(np.abs(forecasts - targets) / ((forecasts + targets)/2)) + return np.mean(np.abs(forecasts - targets) / ((forecasts + targets) / 2)) elif type == 2: - return np.mean(np.abs(forecasts - targets) / (abs(forecasts) + abs(targets)) )*100 + return np.mean(np.abs(forecasts - targets) / (abs(forecasts) + abs(targets))) * 100 else: return sum(np.abs(forecasts - targets)) / sum(forecasts + targets) @@ -113,8 +113,8 @@ def UStatistic(targets, forecasts): naive = [] y = [] - for k in np.arange(0,l-1): - y.append((forecasts[k ] - targets[k]) ** 2) + for k in np.arange(0, l - 1): + y.append((forecasts[k] - targets[k]) ** 2) naive.append((targets[k + 1] - targets[k]) ** 2) return np.sqrt(sum(y) / sum(naive)) @@ -129,11 +129,10 @@ def TheilsInequality(targets, forecasts): """ res = targets - forecasts t = len(res) - us = np.sqrt(sum([u**2 for u in res])) - ys = np.sqrt(sum([y**2 for y in targets])) - fs = np.sqrt(sum([f**2 for f in forecasts])) - return us / (ys + fs) - + us = np.sqrt(sum([u ** 2 for u in res])) + ys = np.sqrt(sum([y ** 2 for y in targets])) + fs = np.sqrt(sum([f ** 2 for f in forecasts])) + return us / (ys + fs) def BoxPierceStatistic(data, h): @@ -146,10 +145,10 @@ def BoxPierceStatistic(data, h): """ n = len(data) s = 0 - for k in np.arange(1,h+1): + for k in np.arange(1, h + 1): r = acf(data, k) - s += r**2 - return n*s + s += r ** 2 + return n * s def BoxLjungStatistic(data, h): @@ -162,10 +161,10 @@ def BoxLjungStatistic(data, h): """ n = len(data) s = 0 - for k in np.arange(1,h+1): + for k in np.arange(1, h + 1): r = acf(data, k) - s += r**2 / (n -k) - return n*(n-2)*s + s += r ** 2 / (n - k) + return n * (n - 2) * s def sharpness(forecasts): @@ -174,7 +173,6 @@ def sharpness(forecasts): return np.mean(tmp) - def resolution(forecasts): """Resolution - Standard deviation of the intervals""" shp = sharpness(forecasts) @@ -230,9 +228,9 @@ def winkler_score(tau, target, forecast): if forecast[0] < target and target < forecast[1]: return delta elif forecast[0] > target: - return delta + 2*(forecast[0] - target)/tau + return delta + 2 * (forecast[0] - target) / tau elif forecast[1] < target: - return delta + 2*(target - forecast[1])/tau + return delta + 2 * (target - forecast[1]) / tau def winkler_mean(tau, targets, forecasts): @@ -261,7 +259,7 @@ def brier_score(targets, densities): ret.append(score) except ValueError as ex: ret.append(sum([d.distribution[k] ** 2 for k in d.bins])) - return sum(ret)/len(ret) + return sum(ret) / len(ret) def pmf_to_cdf(density): @@ -271,7 +269,7 @@ def pmf_to_cdf(density): prev = 0 for col in density.columns: prev += density[col][row] if not np.isnan(density[col][row]) else 0 - tmp.append( prev ) + tmp.append(prev) ret.append(tmp) df = pd.DataFrame(ret, columns=density.columns) return df @@ -280,6 +278,7 @@ def pmf_to_cdf(density): def heavyside(bin, target): return 1 if bin >= target else 0 + def heavyside_cdf(bins, targets): ret = [] for t in targets: @@ -304,7 +303,7 @@ def crps(targets, densities): l = len(densities[0].bins) n = len(densities) for ct, df in enumerate(densities): - _crps += sum([(df.cummulative(bin) - (1 if bin >= targets[ct] else 0)) ** 2 for bin in df.bins]) + _crps += sum([(df.cumulative(bin) - (1 if bin >= targets[ct] else 0)) ** 2 for bin in df.bins]) return _crps / float(l * n) @@ -319,7 +318,7 @@ def get_point_statistics(data, model, **kwargs): :return: a list with the RMSE, SMAPE and U Statistic ''' - steps_ahead = kwargs.get('steps_ahead',1) + steps_ahead = kwargs.get('steps_ahead', 1) kwargs['type'] = 'point' indexer = kwargs.get('indexer', None) @@ -337,7 +336,7 @@ def get_point_statistics(data, model, **kwargs): if steps_ahead == 1: forecasts = model.predict(ndata, **kwargs) - + if model.is_multivariate and model.has_seasonality: ndata = model.indexer.get_data(ndata) elif model.is_multivariate: @@ -354,12 +353,12 @@ def get_point_statistics(data, model, **kwargs): else: steps_ahead_sampler = kwargs.get('steps_ahead_sampler', 1) nforecasts = [] - for k in np.arange(model.order, len(ndata)-steps_ahead,steps_ahead_sampler): + for k in np.arange(model.order, len(ndata) - steps_ahead, steps_ahead_sampler): sample = ndata[k - model.order: k] tmp = model.predict(sample, **kwargs) nforecasts.append(tmp[-1]) - start = model.max_lag + steps_ahead -1 + start = model.max_lag + steps_ahead - 1 ret.append(np.round(rmse(ndata[start:-1:steps_ahead_sampler], nforecasts), 2)) ret.append(np.round(mape(ndata[start:-1:steps_ahead_sampler], nforecasts), 2)) ret.append(np.round(UStatistic(ndata[start:-1:steps_ahead_sampler], nforecasts), 2)) @@ -368,7 +367,7 @@ def get_point_statistics(data, model, **kwargs): def get_interval_statistics(data, model, **kwargs): - ''' + """ Condensate all measures for point interval forecasters :param data: test data @@ -376,7 +375,7 @@ def get_interval_statistics(data, model, **kwargs): :param kwargs: :return: a list with the sharpness, resolution, coverage, .05 pinball mean, .25 pinball mean, .75 pinball mean and .95 pinball mean. - ''' + """ steps_ahead = kwargs.get('steps_ahead', 1) kwargs['type'] = 'interval' @@ -401,7 +400,7 @@ def get_interval_statistics(data, model, **kwargs): tmp = model.predict(sample, **kwargs) forecasts.append(tmp[-1]) - start = model.max_lag + steps_ahead -1 + start = model.max_lag + steps_ahead - 1 ret.append(round(sharpness(forecasts), 2)) ret.append(round(resolution(forecasts), 2)) ret.append(round(coverage(data[model.max_lag:], forecasts), 2)) @@ -415,14 +414,14 @@ def get_interval_statistics(data, model, **kwargs): def get_distribution_statistics(data, model, **kwargs): - ''' + """ Get CRPS statistic and time for a forecasting model :param data: test data :param model: FTS model with probabilistic forecasting capability :param kwargs: :return: a list with the CRPS and execution time - ''' + """ steps_ahead = kwargs.get('steps_ahead', 1) kwargs['type'] = 'distribution' @@ -450,5 +449,3 @@ def get_distribution_statistics(data, model, **kwargs): ret.append(round(_e1 - _s1, 3)) ret.append(round(brier_score(data[start:-1:skip], forecasts), 3)) return ret - - diff --git a/pyFTS/common/Membership.py b/pyFTS/common/Membership.py index 7a2355b..3561253 100644 --- a/pyFTS/common/Membership.py +++ b/pyFTS/common/Membership.py @@ -87,4 +87,4 @@ def singleton(x, parameters): :param parameters: a list with one real value :returns """ - return x == parameters[0] \ No newline at end of file + return x == parameters[0] diff --git a/pyFTS/common/fts.py b/pyFTS/common/fts.py index dd6f732..3783857 100644 --- a/pyFTS/common/fts.py +++ b/pyFTS/common/fts.py @@ -166,7 +166,7 @@ class FTS(object): :param data: time series data with the minimal length equal to the max_lag of the model :param kwargs: model specific parameters - :return: a list with the forecasted intervals + :return: a list with the prediction intervals """ raise NotImplementedError('This model do not perform one step ahead interval forecasts!') @@ -176,7 +176,7 @@ class FTS(object): :param data: time series data with the minimal length equal to the max_lag of the model :param kwargs: model specific parameters - :return: a list with the forecasted Probability Distributions + :return: a list with probabilistic.ProbabilityDistribution objects representing the forecasted Probability Distributions """ raise NotImplementedError('This model do not perform one step ahead distribution forecasts!') diff --git a/pyFTS/probabilistic/ProbabilityDistribution.py b/pyFTS/probabilistic/ProbabilityDistribution.py index 5613975..ac8b76c 100644 --- a/pyFTS/probabilistic/ProbabilityDistribution.py +++ b/pyFTS/probabilistic/ProbabilityDistribution.py @@ -61,10 +61,21 @@ class ProbabilityDistribution(object): self.name = kwargs.get("name", "") def set(self, value, density): + """ + Assert a probability 'density' for a certain value 'value', such that P(value) = density + + :param value: A value in the universe of discourse from the distribution + :param density: The probability density to assign to the value + """ k = self.bin_index.find_ge(value) self.distribution[k] = density def append(self, values): + """ + Increment the frequency count for the values + + :param values: A list of values to account the frequency + """ if self.type == "histogram": for k in values: v = self.bin_index.find_ge(k) @@ -78,6 +89,11 @@ class ProbabilityDistribution(object): self.distribution[self.bins[v]] = d def append_interval(self, intervals): + """ + Increment the frequency count for all values inside an interval + + :param intervals: A list of intervals do increment the frequency + """ if self.type == "histogram": for interval in intervals: for k in self.bin_index.inside(interval[0], interval[1]): @@ -85,6 +101,12 @@ class ProbabilityDistribution(object): self.count += 1 def density(self, values): + """ + Return the probability densities for the input values + + :param values: List of values to return the densities + :return: List of probability densities for the input values + """ ret = [] scalar = False @@ -109,6 +131,12 @@ class ProbabilityDistribution(object): return ret def differential_offset(self, value): + """ + Auxiliary function for probability distributions of differentiated data + + :param value: + :return: + """ nbins = [] dist = {} @@ -127,6 +155,11 @@ class ProbabilityDistribution(object): self.qtl = None def expected_value(self): + """ + Return the expected value of the distribution, as E[X] = ∑ x * P(x) + + :return: The expected value of the distribution + """ return np.nansum([v * self.distribution[v] for v in self.bins]) def build_cdf_qtl(self): @@ -147,7 +180,13 @@ class ProbabilityDistribution(object): self.quantile_index = SortedCollection.SortedCollection(iterable=_keys) - def cummulative(self, values): + def cumulative(self, values): + """ + Return the cumulative probability densities for the input values + + :param values: A list of input values + :return: The cumulative probability densities for the input values + """ if self.cdf is None: self.build_cdf_qtl() @@ -161,6 +200,12 @@ class ProbabilityDistribution(object): return self.cdf[values] def quantile(self, values): + """ + Return the quantile values for the input values + + :param values: input values + :return: The list of the quantile values for the input values + """ if self.qtl is None: self.build_cdf_qtl() @@ -176,21 +221,43 @@ class ProbabilityDistribution(object): return ret def entropy(self): + """ + Return the entropy of the probability distribution, H[X] = + + :return:the entropy of the probability distribution + """ h = -sum([self.distribution[k] * np.log(self.distribution[k]) if self.distribution[k] > 0 else 0 for k in self.bins]) return h def crossentropy(self,q): + """ + Cross entropy between the actual probability distribution and the informed one. + + :param q: a probabilistic.ProbabilityDistribution object + :return: Cross entropy between this probability distribution and the given distribution + """ h = -sum([self.distribution[k] * np.log(q.distribution[k]) if self.distribution[k] > 0 else 0 for k in self.bins]) return h def kullbackleiblerdivergence(self,q): + """ + Kullback-Leibler divergence between the actual probability distribution and the informed one. + + :param q: a probabilistic.ProbabilityDistribution object + :return: Kullback-Leibler divergence + """ h = sum([self.distribution[k] * np.log(self.distribution[k]/q.distribution[k]) if self.distribution[k] > 0 else 0 for k in self.bins]) return h def empiricalloglikelihood(self): + """ + Empirical Log Likelihood of the probability distribution + + :return: + """ _s = 0 for k in self.bins: if self.distribution[k] > 0: @@ -198,6 +265,12 @@ class ProbabilityDistribution(object): return _s def pseudologlikelihood(self, data): + """ + Pseudo log likelihood of the probability distribution with respect to data + + :param data: + :return: + """ densities = self.density(data) @@ -208,6 +281,12 @@ class ProbabilityDistribution(object): return _s def averageloglikelihood(self, data): + """ + Average log likelihood of the probability distribution with respect to data + + :param data: + :return: + """ densities = self.density(data) diff --git a/pyFTS/probabilistic/kde.py b/pyFTS/probabilistic/kde.py index 9eb95b5..b5c668f 100644 --- a/pyFTS/probabilistic/kde.py +++ b/pyFTS/probabilistic/kde.py @@ -18,6 +18,12 @@ class KernelSmoothing(object): self.transf = Transformations.Scale(min=0,max=1) def kernel_function(self, u): + """ + Apply the kernel + + :param u: + :return: + """ if self.kernel == "epanechnikov": tmp = (3/4)*(1.0 - u**2) return tmp if tmp > 0 else 0