Generate "transmission errors" in time series¶

These are errors that affects time index, for example: repeating values x(t) several times, dropping value x(t), or switching x(t) with x(t+1), etc.

In [1]:

import numpy as np
import matplotlib.pyplot as plt
from badgers.generators.time_series.transmission_errors import RandomTimeSwitchGenerator, RandomRepeatGenerator, RandomDropGenerator, LocalRegionsRandomDropGenerator, LocalRegionsRandomRepeatGenerator
import matplotlib.patches as patches

import numpy as np import matplotlib.pyplot as plt from badgers.generators.time_series.transmission_errors import RandomTimeSwitchGenerator, RandomRepeatGenerator, RandomDropGenerator, LocalRegionsRandomDropGenerator, LocalRegionsRandomRepeatGenerator import matplotlib.patches as patches

Setup random generator¶

In [2]:

from numpy.random import default_rng
seed = 0
rng = default_rng(seed)

from numpy.random import default_rng seed = 0 rng = default_rng(seed)

Import data (using sktime)¶

In [3]:

from sktime.datasets import load_airline

from sktime.datasets import load_airline

In [4]:

X = load_airline()
t = X.index.to_timestamp()

X = load_airline() t = X.index.to_timestamp()

In [5]:

fig, ax = plt.subplots()
ax.plot(X.values)
ax.set_title('original data')
plt.tight_layout()

fig, ax = plt.subplots() ax.plot(X.values) ax.set_title('original data') plt.tight_layout()

Generating random switches in time¶

Where x(t) and x(t+1) are switched

In [6]:

generator = RandomTimeSwitchGenerator(random_generator=rng)
Xt, y = generator.generate(X=X.copy(), y=None, n_switches=20)

generator = RandomTimeSwitchGenerator(random_generator=rng) Xt, y = generator.generate(X=X.copy(), y=None, n_switches=20)

In [7]:

fig, ax = plt.subplots()
ax.plot(X.values, alpha=0.5, ls='-', marker='.', label='original')
ax.plot(Xt.values, alpha=0.5, ls='-', marker='.', label='with random switches')
ax.set_xlabel('time units (arrows show where the switch occured)')
for i in generator.switch_indices_:
    ax.arrow(i,0,0,50, head_width=2, head_length=10)

plt.legend()
plt.tight_layout()

fig, ax = plt.subplots() ax.plot(X.values, alpha=0.5, ls='-', marker='.', label='original') ax.plot(Xt.values, alpha=0.5, ls='-', marker='.', label='with random switches') ax.set_xlabel('time units (arrows show where the switch occured)') for i in generator.switch_indices_: ax.arrow(i,0,0,50, head_width=2, head_length=10) plt.legend() plt.tight_layout()

Randomly repeating values (equivalent to delays)¶

Where x(t) is repeated several times

In [8]:

generator = RandomRepeatGenerator(random_generator=rng)
Xt, y = generator.generate(X=X.copy(), y=None, n_repeats=5, min_nb_repeats=3, max_nb_repeats=10)

generator = RandomRepeatGenerator(random_generator=rng) Xt, y = generator.generate(X=X.copy(), y=None, n_repeats=5, min_nb_repeats=3, max_nb_repeats=10)

In [9]:

fig, axes = plt.subplots(2, sharex=True, sharey=True, figsize=(6,6))
axes[0].plot(X.values, color='C0')
axes[1].plot(Xt.values, color='C1')
axes[0].set_title('Original')
axes[1].set_title('Transformed')
plt.tight_layout()

fig, axes = plt.subplots(2, sharex=True, sharey=True, figsize=(6,6)) axes[0].plot(X.values, color='C0') axes[1].plot(Xt.values, color='C1') axes[0].set_title('Original') axes[1].set_title('Transformed') plt.tight_layout()

Repeating values in certain regions of time (time intervals)¶

In [10]:

generator = LocalRegionsRandomRepeatGenerator(random_generator=rng)
Xt, y = generator.generate(X=X.copy(), y=None, n_repeats=10, min_nb_repeats=1, max_nb_repeats=4, n_regions=3, min_width_regions=5, max_width_regions=15)

generator = LocalRegionsRandomRepeatGenerator(random_generator=rng) Xt, y = generator.generate(X=X.copy(), y=None, n_repeats=10, min_nb_repeats=1, max_nb_repeats=4, n_regions=3, min_width_regions=5, max_width_regions=15)

In [11]:

fig, axes = plt.subplots(3, sharex=True, sharey=False, figsize=(6,8))
axes[0].plot(X.values, color='C0')
axes[1].plot(generator.repeats_probabilities_, color='C2')
axes[2].plot(Xt.values, color='C1')
axes[0].set_title('Original (arrows show where points were repeated)')
axes[1].set_title('Repeat probability')
axes[2].set_title('Transformed')

for i, l in generator.repeats_:
    axes[0].arrow(i,0,0,50, head_width=2, head_length=10)

plt.tight_layout()

fig, axes = plt.subplots(3, sharex=True, sharey=False, figsize=(6,8)) axes[0].plot(X.values, color='C0') axes[1].plot(generator.repeats_probabilities_, color='C2') axes[2].plot(Xt.values, color='C1') axes[0].set_title('Original (arrows show where points were repeated)') axes[1].set_title('Repeat probability') axes[2].set_title('Transformed') for i, l in generator.repeats_: axes[0].arrow(i,0,0,50, head_width=2, head_length=10) plt.tight_layout()

Randomly dropping values¶

This is different from missingness as in missingness the time index in not affected

In [12]:

generator = RandomDropGenerator(random_generator=rng)
Xt, y = generator.generate(X=X.copy(), y=None, n_drops=10)

generator = RandomDropGenerator(random_generator=rng) Xt, y = generator.generate(X=X.copy(), y=None, n_drops=10)

In [13]:

fig, axes = plt.subplots(2, sharex=True, sharey=True, figsize=(6,6))
axes[0].plot(X.values, color='C0')
axes[1].plot(Xt.values, color='C1')
axes[0].set_title('Original (arrows show where points were dropped)')
axes[1].set_title('Transformed')

for i in generator.drops_indices_:
    axes[0].arrow(i,0,0,50, head_width=2, head_length=10)

plt.tight_layout()

fig, axes = plt.subplots(2, sharex=True, sharey=True, figsize=(6,6)) axes[0].plot(X.values, color='C0') axes[1].plot(Xt.values, color='C1') axes[0].set_title('Original (arrows show where points were dropped)') axes[1].set_title('Transformed') for i in generator.drops_indices_: axes[0].arrow(i,0,0,50, head_width=2, head_length=10) plt.tight_layout()

Dropping values in certain regions of time (certain time intervals)¶

In [14]:

generator = LocalRegionsRandomDropGenerator(random_generator=rng)
Xt, y = generator.generate(X=X.copy(), y=None, n_drops=10, n_regions=3, min_width_regions=5, max_width_regions=15)

generator = LocalRegionsRandomDropGenerator(random_generator=rng) Xt, y = generator.generate(X=X.copy(), y=None, n_drops=10, n_regions=3, min_width_regions=5, max_width_regions=15)

In [15]:

fig, axes = plt.subplots(3, sharex=True, sharey=False, figsize=(6,8))
axes[0].plot(X.values, color='C0')
axes[1].plot(generator.drops_probabilities_, color='C2')
axes[2].plot(Xt.values, color='C1')
axes[0].set_title('Original (arrows show where points were dropped)')
axes[1].set_title('Drop probability')
axes[2].set_title('Transformed')

for i in generator.drops_indices_:
    axes[0].arrow(i,0,0,50, head_width=2, head_length=10)

plt.tight_layout()

fig, axes = plt.subplots(3, sharex=True, sharey=False, figsize=(6,8)) axes[0].plot(X.values, color='C0') axes[1].plot(generator.drops_probabilities_, color='C2') axes[2].plot(Xt.values, color='C1') axes[0].set_title('Original (arrows show where points were dropped)') axes[1].set_title('Drop probability') axes[2].set_title('Transformed') for i in generator.drops_indices_: axes[0].arrow(i,0,0,50, head_width=2, head_length=10) plt.tight_layout()

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