PWFTS new m-step-ahead probabilistic forecasting method
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Petrônio Cândido
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9fb79ea080
@ -77,6 +77,8 @@ class SeasonalEnsembleFTS(ensemble.EnsembleFTS):
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smooth = kwargs.get("smooth", "KDE")
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alpha = kwargs.get("alpha", None)
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uod = self.get_UoD()
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for k in data.index:
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tmp = self.get_models_forecasts(data.ix[k])
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@ -88,9 +90,8 @@ class SeasonalEnsembleFTS(ensemble.EnsembleFTS):
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name = str(self.indexer.get_index(data.ix[k]))
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dist = ProbabilityDistribution.ProbabilityDistribution(smooth,
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uod=[self.original_min, self.original_max],
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data=tmp, name=name, **kwargs)
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dist = ProbabilityDistribution.ProbabilityDistribution(smooth, uod=uod, data=tmp,
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name=name, **kwargs)
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ret.append(dist)
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@ -17,7 +17,7 @@ class ProbabilityDistribution(object):
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self.type = type
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if self.type == "KDE":
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self.kde = kde.KernelSmoothing(kwargs.get("h", 10), kwargs.get("method", "epanechnikov"))
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self.kde = kde.KernelSmoothing(kwargs.get("h", 0.5), kwargs.get("kernel", "epanechnikov"))
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self.nbins = kwargs.get("num_bins", 100)
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@ -8,39 +8,38 @@ Kernel Density Estimation
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class KernelSmoothing(object):
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"""Kernel Density Estimation"""
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def __init__(self,h, method="epanechnikov"):
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def __init__(self,h, kernel="epanechnikov"):
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self.h = h
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self.method = method
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self.kernel = kernel
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self.transf = Transformations.Scale(min=0,max=1)
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def kernel(self, u):
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if self.method == "epanechnikov":
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def kernel_function(self, u):
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if self.kernel == "epanechnikov":
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tmp = (3/4)*(1.0 - u**2)
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return tmp if tmp > 0 else 0
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elif self.method == "gaussian":
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elif self.kernel == "gaussian":
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return (1.0/np.sqrt(2*np.pi))*np.exp(-0.5*u**2)
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elif self.method == "uniform":
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elif self.kernel == "uniform":
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return 0.5
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elif self.method == "triangular":
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elif self.kernel == "triangular":
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tmp = 1.0 - np.abs(u)
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return tmp if tmp > 0 else 0
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elif self.method == "logistic":
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elif self.kernel == "logistic":
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return 1.0/(np.exp(u)+2+np.exp(-u))
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elif self.method == "cosine":
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elif self.kernel == "cosine":
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return (np.pi/4.0)*np.cos((np.pi/2.0)*u)
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elif self.method == "sigmoid":
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elif self.kernel == "sigmoid":
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return (2.0/np.pi)*(1.0/(np.exp(u)+np.exp(-u)))
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elif self.method == "tophat":
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elif self.kernel == "tophat":
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return 1 if np.abs(u) < 0.5 else 0
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elif self.method == "exponential":
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elif self.kernel == "exponential":
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return 0.5 * np.exp(-np.abs(u))
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def probability(self, x, data):
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l = len(data)
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ndata = self.transf.apply(data)
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nx = self.transf.apply(x)
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p = sum([self.kernel((nx - k)/self.h) for k in ndata]) / l*self.h
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p = sum([self.kernel_function((nx - k)/self.h) for k in ndata]) / l*self.h
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return p
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163
pyFTS/pwfts.py
163
pyFTS/pwfts.py
@ -566,23 +566,27 @@ class ProbabilisticWeightedFTS(ifts.IntervalFTS):
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ret = []
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resolution = kwargs.get('resolution',100)
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method = kwargs.get('method', 2)
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smooth = "KDE" if method != 4 else "none"
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nbins = kwargs.get("num_bins", 100)
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method = kwargs.get('method',2)
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uod = self.get_UoD()
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_bins = np.linspace(uod[0], uod[1], nbins).tolist()
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intervals = self.forecastAheadInterval(data, steps)
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if method != 4:
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intervals = self.forecastAheadInterval(data, steps)
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else:
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l = len(data)
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for k in np.arange(l - self.order, l):
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dist = ProbabilityDistribution.ProbabilityDistribution(smooth, uod=uod, bins=_bins, **kwargs)
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dist.set(data[k], 1.0)
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ret.append(dist)
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grid = self.getGridClean(resolution)
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for k in np.arange(self.order, steps + self.order):
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index = SortedCollection.SortedCollection(iterable=grid.keys())
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data = []
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if method == 1:
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grids = []
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for k in np.arange(0, steps):
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grids.append(self.getGridClean(resolution))
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for k in np.arange(self.order, steps + self.order):
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if method == 1:
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lags = {}
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@ -612,139 +616,74 @@ class ProbabilisticWeightedFTS(ifts.IntervalFTS):
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self.buildTreeWithoutOrder(root, lags, 0)
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# Trace the possible paths
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for p in root.paths():
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path = list(reversed(list(filter(None.__ne__, p))))
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qtle = self.forecastInterval(path)
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qtle = np.ravel(self.forecastInterval(path))
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grids[k - self.order] = self.gridCount(grids[k - self.order], resolution, index, np.ravel(qtle))
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data.extend(np.linspace(qtle[0],qtle[1],100).tolist())
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for k in np.arange(0, steps):
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tmp = np.array([grids[k][q] for q in sorted(grids[k])])
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ret.append(tmp / sum(tmp))
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elif method == 2:
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ret = []
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for k in np.arange(self.order, steps + self.order):
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grid = self.getGridClean(resolution)
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grid = self.gridCount(grid, resolution, index, intervals[k])
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elif method == 2:
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for qt in np.arange(0, 50, 1):
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# print(qt)
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qtle_lower = self.forecastInterval(
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[intervals[x][0] + qt * ((intervals[x][1] - intervals[x][0]) / 100) for x in
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np.arange(k - self.order, k)])
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grid = self.gridCount(grid, resolution, index, np.ravel(qtle_lower))
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qtle_lower = np.ravel(qtle_lower)
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data.extend(np.linspace(qtle_lower[0], qtle_lower[1], 100).tolist())
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qtle_upper = self.forecastInterval(
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[intervals[x][1] - qt * ((intervals[x][1] - intervals[x][0]) / 100) for x in
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np.arange(k - self.order, k)])
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grid = self.gridCount(grid, resolution, index, np.ravel(qtle_upper))
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qtle_upper = np.ravel(qtle_upper)
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data.extend(np.linspace(qtle_upper[0], qtle_upper[1], 100).tolist())
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qtle_mid = self.forecastInterval(
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[intervals[x][0] + (intervals[x][1] - intervals[x][0]) / 2 for x in np.arange(k - self.order, k)])
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grid = self.gridCount(grid, resolution, index, np.ravel(qtle_mid))
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qtle_mid = np.ravel(qtle_mid)
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data.extend(np.linspace(qtle_mid[0], qtle_mid[1], 100).tolist())
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tmp = np.array([grid[k] for k in sorted(grid) if not np.isnan(grid[k])])
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try:
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ret.append(tmp / sum(tmp))
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except Exception as ex:
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ret.append(0)
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elif method == 3:
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i = intervals[k]
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else:
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ret = []
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data = np.linspace(i[0],i[1],100).tolist()
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for k in np.arange(self.order, steps + self.order):
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grid = self.getGridClean(resolution)
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grid = self.gridCount(grid, resolution, index, intervals[k])
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tmp = np.array([grid[k] for k in sorted(grid)])
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ret.append(tmp / sum(tmp))
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grid = self.getGridClean(resolution)
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df = pd.DataFrame(ret, columns=sorted(grid))
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return df
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def density(self, x, num_bins=100):
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affected_flrgs = []
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affected_flrgs_memberships = []
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mv = FuzzySet.fuzzyInstance(x, self.sets)
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tmp = np.argwhere(mv)
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idx = np.ravel(tmp)
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if idx.size == 0: # the element is out of the bounds of the Universe of Discourse
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if x <= self.sets[0].lower:
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idx = [0]
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elif x >= self.sets[-1].upper:
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idx = [len(self.sets) - 1]
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else:
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raise Exception(x)
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dist = ProbabilityDistribution.ProbabilityDistribution(smooth, bins=_bins,
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uod=uod, **kwargs)
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lags = {}
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for kk in idx:
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flrg = ProbabilisticWeightedFLRG(self.order)
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flrg.appendLHS(self.sets[kk])
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affected_flrgs.append(flrg)
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affected_flrgs_memberships.append(mv[kk])
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cc = 0
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total_prob = 0.0
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for dd in ret[k - self.order: k]:
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vals = [float(v) for v in dd.bins if round(dd.density(v),4) > 0]
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lags[cc] = sorted(vals)
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cc += 1
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for count, flrg in enumerate(affected_flrgs):
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_flrg = self.flrgs[flrg.strLHS()]
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pk = _flrg.frequency_count / self.global_frequency_count
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priori = pk * (affected_flrgs_memberships[count]) # / _flrg.partition_function(uod=self.get_UoD(), nbins=num_bins))
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#print(flrg.strLHS() + ": PK=" + str(pk) + " Priori=" + str(priori))
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#posteriori = self.get_conditional_probability(k, flrg) * priori
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total_prob += priori
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root = tree.FLRGTreeNode(None)
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return total_prob
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self.buildTreeWithoutOrder(root, lags, 0)
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def AprioriPDF(self, **kwargs):
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nbins = kwargs.get('num_bins', 100)
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pdf = ProbabilityDistribution.ProbabilityDistribution(uod=[self.original_min, self.original_max], num_bins=nbins)
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t = 0.0
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# Trace the possible paths
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for p in root.paths():
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path = list(reversed(list(filter(None.__ne__, p))))
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for k in pdf.bins:
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#print("BIN: " + str(k) )
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affected_flrgs = []
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affected_flrgs_memberships = []
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pk = np.prod([ret[k - self.order + o].density(path[o])
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for o in np.arange(0,self.order)])
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mv = FuzzySet.fuzzyInstance(k, self.sets)
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tmp = np.argwhere(mv)
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idx = np.ravel(tmp)
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d = self.forecastDistribution(path)[0]
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if idx.size == 0: # the element is out of the bounds of the Universe of Discourse
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if k <= self.sets[0].lower:
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idx = [0]
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elif k >= self.sets[-1].upper:
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idx = [len(self.sets) - 1]
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else:
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raise Exception(k)
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for bin in _bins:
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dist.set(bin, dist.density(bin) + pk * d.density(bin))
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for kk in idx:
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flrg = ProbabilisticWeightedFLRG(self.order)
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flrg.appendLHS(self.sets[kk])
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affected_flrgs.append(flrg)
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affected_flrgs_memberships.append(mv[kk])
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if method != 4:
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dist = ProbabilityDistribution.ProbabilityDistribution(smooth, bins=_bins, data=data,
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uod=uod, **kwargs)
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total_prob = 0.0
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ret.append(dist)
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for count, flrg in enumerate(affected_flrgs):
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_flrg = self.flrgs[flrg.strLHS()]
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pk = _flrg.frequency_count / self.global_frequency_count
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priori = pk * (affected_flrgs_memberships[count] / _flrg.partition_function(uod=self.get_UoD()))
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#print(flrg.strLHS() + ": PK=" + str(pk) + " Priori=" + str(priori))
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posteriori = self.get_conditional_probability(k, flrg) * priori
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total_prob += posteriori
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return ret
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t += total_prob
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pdf.set(k, total_prob)
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print(t)
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return pdf
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def __str__(self):
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tmp = self.name + ":\n"
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@ -22,8 +22,15 @@ from numpy import random
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os.chdir("/home/petronio/dados/Dropbox/Doutorado/Codigos/")
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'''
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enrollments = pd.read_csv("DataSets/Enrollments.csv", sep=";")
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enrollments = np.array(enrollments["Enrollments"])
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'''
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taiexpd = pd.read_csv("DataSets/TAIEX.csv", sep=",")
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data = np.array(taiexpd["avg"][:5000])
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del(taiexpd)
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import importlib
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import pandas as pd
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@ -37,20 +44,20 @@ from pyFTS.benchmarks import benchmarks as bchmk
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#uod = [10162, 21271]
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enrollments_fs1 = Grid.GridPartitioner(enrollments, 6)
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fs1 = Grid.GridPartitioner(data[:3000], 30)
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#for s in enrollments_fs1.sets:
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# print(s) #.partition_function(uod, 100))
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pfts1_enrollments = pwfts.ProbabilisticWeightedFTS("1", partitioner=enrollments_fs1)
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pfts1_enrollments.train(enrollments, None, 1)
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pfts1_enrollments.shortname = "1st Order"
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pfts1 = pwfts.ProbabilisticWeightedFTS("1", partitioner=fs1)
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pfts1.train(data, None, 1)
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pfts1.shortname = "1st Order"
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#print(pfts1_enrollments)
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tmp = pfts1_enrollments.forecastDistribution([15000])
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#print(tmp[0])
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tmp = pfts1.forecastAheadDistribution(data[3000:3020],20, method=3, h=0.45, kernel="gaussian")
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print(tmp[0])
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print(tmp[0].quantile([0.05, 0.95]))
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#print(tmp[0].quantile([0.05, 0.95]))
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#pfts1_enrollments.AprioriPDF
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#norm = pfts1_enrollments.global_frequency_count
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