merlion.models.anomaly.forecast_based package

Contains all forecaster-based anomaly detectors. These models support all functionality of both anomaly detectors (merlion.models.anomaly) and forecasters (merlion.models.forecast).

Forecasting-based anomaly detectors are instances of an abstract ForecastingDetectorBase class. Many forecasting models support anomaly detection variants, where the anomaly score is based on the difference between the predicted and true time series value, and optionally the model’s uncertainty in its own prediction.

`base`	Base class for anomaly detectors based on forecasting models.
`arima`	Classic ARIMA (AutoRegressive Integrated Moving Average) forecasting model, adapted for anomaly detection.
`sarima`	Seasonal ARIMA (SARIMA) forecasting model, adapted for anomaly detection.
`ets`	ETS (error, trend, seasonal) forecasting model, adapted for anomaly detection.
`prophet`	Adaptation of Facebook's Prophet forecasting model to anomaly detection.
`lstm`	Adaptation of a LSTM neural net forecaster, to the task of anomaly detection.
`mses`	MSES (Multi-Scale Exponential Smoother) forecasting model adapted for anomaly detection.

Submodules

merlion.models.anomaly.forecast_based.base module

Base class for anomaly detectors based on forecasting models.

class merlion.models.anomaly.forecast_based.base.ForecastingDetectorBase(config)

Bases: ForecasterBase, DetectorBase, ABC

Base class for a forecast-based anomaly detector.

Parameters: config (ForecasterConfig) – model configuration

forecast_to_anom_score(time_series, forecast, stderr)

Compare a model’s forecast to a ground truth time series, in order to compute anomaly scores. By default, we compute a z-score if model uncertainty (stderr) is given, or the residuals if there is no model uncertainty.

Parameters

time_series (TimeSeries) – the ground truth time series.
forecast (TimeSeries) – the model’s forecasted values for the time series
stderr (Optional[TimeSeries]) – the standard errors of the model’s forecast

Return type

TimeSeries

Returns

Anomaly scores based on the difference between the ground truth values of the time series, and the model’s forecast.

train(train_data, anomaly_labels=None, train_config=None, post_rule_train_config=None)

Trains the underlying forecaster (unsupervised) on the training data. Converts the forecast into anomaly scores, and and then trains the post-rule for filtering anomaly scores (supervised, if labels are given) on the input time series.

Parameters

train_data (TimeSeries) – a TimeSeries of metric values to train the model.
anomaly_labels (Optional[TimeSeries]) – a TimeSeries indicating which timestamps are anomalous. Optional.
train_config – Additional training configs, if needed. Only required for some models.
post_rule_train_config – The config to use for training the model’s post-rule. The model’s default post-rule train config is used if none is supplied here.

Return type

TimeSeries

Returns

A TimeSeries of the model’s anomaly scores on the training data.

get_anomaly_score(time_series, time_series_prev=None)

Returns the model’s predicted sequence of anomaly scores.

Parameters

time_series (TimeSeries) – the TimeSeries we wish to predict anomaly scores for.
time_series_prev (Optional[TimeSeries]) – a TimeSeries immediately preceding time_series. If given, we use it to initialize the time series anomaly detection model. Otherwise, we assume that time_series immediately follows the training data.

Return type

TimeSeries

Returns

a univariate TimeSeries of anomaly scores

get_figure(*, time_series=None, time_stamps=None, time_series_prev=None, plot_anomaly=True, filter_scores=True, plot_forecast=False, plot_forecast_uncertainty=False, plot_time_series_prev=False)

Parameters

time_series (Optional[TimeSeries]) – the time series over whose timestamps we wish to make a forecast. Exactly one of time_series or time_stamps should be provided.
time_stamps (Optional[List[int]]) – a list of timestamps we wish to forecast for. Exactly one of time_series or time_stamps should be provided.
time_series_prev (Optional[TimeSeries]) – a TimeSeries immediately preceding time_stamps. If given, we use it to initialize the time series model. Otherwise, we assume that time_stamps immediately follows the training data.
plot_anomaly – Whether to plot the model’s predicted anomaly scores.
filter_scores – whether to filter the anomaly scores by the post-rule before plotting them.
plot_forecast – Whether to plot the model’s forecasted values.
plot_forecast_uncertainty – whether to plot uncertainty estimates (the inter-quartile range) for forecast values. Not supported for all models.
plot_time_series_prev – whether to plot time_series_prev (and the model’s fit for it). Only used if time_series_prev is given.

Return type

Figure

Returns

a Figure of the model’s anomaly score predictions and/or forecast.

plot_anomaly(time_series, time_series_prev=None, *, filter_scores=True, plot_forecast=False, plot_forecast_uncertainty=False, plot_time_series_prev=False, figsize=(1000, 600), ax=None)

Plots the time series in matplotlib as a line graph, with points in the series overlaid as points color-coded to indicate their severity as anomalies. Optionally allows you to overlay the model’s forecast & the model’s uncertainty in its forecast (if applicable).

Parameters

time_series (TimeSeries) – The time series we wish to plot, with color-coding to indicate anomalies.
time_series_prev (Optional[TimeSeries]) – A time series immediately preceding time_series, which is used to initialize the time series model. Otherwise, we assume time_series immediately follows the training data.
filter_scores – whether to filter the anomaly scores by the post-rule before plotting them.
plot_forecast – Whether to plot the model’s forecast, in addition to the anomaly scores.
plot_forecast_uncertainty – Whether to plot the model’s uncertainty in its own forecast, in addition to the forecast and anomaly scores. Only used if plot_forecast is True.
plot_time_series_prev – whether to plot time_series_prev (and the model’s fit for it). Only used if time_series_prev is given.
figsize – figure size in pixels
ax – matplotlib axis to add this plot to

Returns

matplotlib figure & axes

plot_anomaly_plotly(time_series, time_series_prev=None, *, filter_scores=True, plot_forecast=False, plot_forecast_uncertainty=False, plot_time_series_prev=False, figsize=(1000, 600))

Plots the time series in matplotlib as a line graph, with points in the series overlaid as points color-coded to indicate their severity as anomalies. Optionally allows you to overlay the model’s forecast & the model’s uncertainty in its forecast (if applicable).

Parameters

time_series (TimeSeries) – The time series we wish to plot, with color-coding to indicate anomalies.
time_series_prev (Optional[TimeSeries]) – A time series immediately preceding time_series, which is used to initialize the time series model. Otherwise, we assume time_series immediately follows the training data.
filter_scores – whether to filter the anomaly scores by the post-rule before plotting them.
plot_forecast – Whether to plot the model’s forecast, in addition to the anomaly scores.
plot_forecast_uncertainty – Whether to plot the model’s uncertainty in its own forecast, in addition to the forecast and anomaly scores. Only used if plot_forecast is True.
plot_time_series_prev – whether to plot time_series_prev (and the model’s fit for it). Only used if time_series_prev is given.
figsize – figure size in pixels

Returns

plotly figure

plot_forecast(*, time_series=None, time_stamps=None, time_series_prev=None, plot_forecast_uncertainty=False, plot_time_series_prev=False, figsize=(1000, 600), ax=None)

Plots the forecast for the time series in matplotlib, optionally also plotting the uncertainty of the forecast, as well as the past values (both true and predicted) of the time series.

Parameters

time_series (Optional[TimeSeries]) – the time series over whose timestamps we wish to make a forecast. Exactly one of time_series or time_stamps should be provided.
time_stamps (Optional[List[int]]) – a list of timestamps we wish to forecast for. Exactly one of time_series or time_stamps should be provided.
time_series_prev (Optional[TimeSeries]) – a TimeSeries immediately preceding time_stamps. If given, we use it to initialize the time series model. Otherwise, we assume that time_stamps immediately follows the training data.
plot_forecast_uncertainty – whether to plot uncertainty estimates (the inter-quartile range) for forecast values. Not supported for all models.
plot_time_series_prev – whether to plot time_series_prev (and the model’s fit for it). Only used if time_series_prev is given.
figsize – figure size in pixels
ax – matplotlib axis to add this plot to

Returns

(fig, ax): matplotlib figure & axes the figure was plotted on

plot_forecast_plotly(*, time_series=None, time_stamps=None, time_series_prev=None, plot_forecast_uncertainty=False, plot_time_series_prev=False, figsize=(1000, 600))

Plots the forecast for the time series in plotly, optionally also plotting the uncertainty of the forecast, as well as the past values (both true and predicted) of the time series.

Parameters

time_series (Optional[TimeSeries]) – the time series over whose timestamps we wish to make a forecast. Exactly one of time_series or time_stamps should be provided.
time_stamps (Optional[List[int]]) – a list of timestamps we wish to forecast for. Exactly one of time_series or time_stamps should be provided.
time_series_prev (Optional[TimeSeries]) – a TimeSeries immediately preceding time_stamps. If given, we use it to initialize the time series model. Otherwise, we assume that time_stamps immediately follows the training data.
plot_forecast_uncertainty – whether to plot uncertainty estimates (the inter-quartile range) for forecast values. Not supported for all models.
plot_time_series_prev – whether to plot time_series_prev (and the model’s fit for it). Only used if time_series_prev is given.
figsize – figure size in pixels

merlion.models.anomaly.forecast_based.arima module

Classic ARIMA (AutoRegressive Integrated Moving Average) forecasting model, adapted for anomaly detection.

class merlion.models.anomaly.forecast_based.arima.ArimaDetectorConfig(max_forecast_steps=None, target_seq_index=None, order=(4, 1, 2), **kwargs)

Bases: ArimaConfig, DetectorConfig

Configuration class for Arima. Just a Sarima model with seasonal order (0, 0, 0, 0).

Parameters

max_forecast_steps – Number of steps we would like to forecast for.
target_seq_index – The index of the univariate (amongst all univariates in a general multivariate time series) whose value we would like to forecast.
order – Order is (p, d, q) for an ARIMA(p, d, q) process. d must be an integer indicating the integration order of the process, while p and q must be integers indicating the AR and MA orders (so that all lags up to those orders are included).
seasonal_order – Seasonal order is (P, D, Q, S) for seasonal ARIMA process, where s is the length of the seasonality cycle (e.g. s=24 for 24 hours on hourly granularity). P, D, Q are as for ARIMA.

class merlion.models.anomaly.forecast_based.arima.ArimaDetector(config)

Bases: ForecastingDetectorBase, Arima

config_class: alias of ArimaDetectorConfig

merlion.models.anomaly.forecast_based.sarima module

Seasonal ARIMA (SARIMA) forecasting model, adapted for anomaly detection.

class merlion.models.anomaly.forecast_based.sarima.SarimaDetectorConfig(max_forecast_steps=None, target_seq_index=None, order=(4, 1, 2), seasonal_order=(2, 0, 1, 24), **kwargs)

Bases: SarimaConfig, DetectorConfig

Config class for Sarima (Seasonal AutoRegressive Integrated Moving Average).

Parameters

max_forecast_steps – Number of steps we would like to forecast for.
target_seq_index – The index of the univariate (amongst all univariates in a general multivariate time series) whose value we would like to forecast.
order – Order is (p, d, q) for an ARIMA(p, d, q) process. d must be an integer indicating the integration order of the process, while p and q must be integers indicating the AR and MA orders (so that all lags up to those orders are included).
seasonal_order – Seasonal order is (P, D, Q, S) for seasonal ARIMA process, where s is the length of the seasonality cycle (e.g. s=24 for 24 hours on hourly granularity). P, D, Q are as for ARIMA.

class merlion.models.anomaly.forecast_based.sarima.SarimaDetector(config)

Bases: ForecastingDetectorBase, Sarima

config_class: alias of SarimaDetectorConfig

merlion.models.anomaly.forecast_based.ets module

ETS (error, trend, seasonal) forecasting model, adapted for anomaly detection.

class merlion.models.anomaly.forecast_based.ets.ETSDetectorConfig(max_forecast_steps=None, target_seq_index=None, error='add', trend='add', damped_trend=True, seasonal='add', seasonal_periods='auto', **kwargs)

Bases: ETSConfig, NoCalibrationDetectorConfig

Configuration class for ETS model. ETS model is an underlying state space model consisting of an error term (E), a trend component (T), a seasonal component (S), and a level component. Each component is flexible with different traits with additive (‘add’) or multiplicative (‘mul’) formulation. Refer to https://otexts.com/fpp2/taxonomy.html for more information about ETS model.

Parameters

max_forecast_steps – Number of steps we would like to forecast for.
target_seq_index – The index of the univariate (amongst all univariates in a general multivariate time series) whose value we would like to forecast.
error – The error term. “add” or “mul”.
trend – The trend component. “add”, “mul” or None.
damped_trend – Whether or not an included trend component is damped.
seasonal – The seasonal component. “add”, “mul” or None.
seasonal_periods – The length of the seasonality cycle. ‘auto’ indicates automatically select the seasonality cycle. If no seasonality exists, change seasonal to None.

class merlion.models.anomaly.forecast_based.ets.ETSDetector(config)

Bases: ForecastingDetectorBase, ETS

Parameters: config (ETSConfig) – model configuration

config_class: alias of ETSDetectorConfig

merlion.models.anomaly.forecast_based.prophet module

Adaptation of Facebook’s Prophet forecasting model to anomaly detection.

class merlion.models.anomaly.forecast_based.prophet.ProphetDetectorConfig(max_forecast_steps=None, target_seq_index=None, yearly_seasonality='auto', weekly_seasonality='auto', daily_seasonality='auto', add_seasonality='auto', seasonality_mode='additive', holidays=None, uncertainty_samples=100, **kwargs)

Bases: ProphetConfig, DetectorConfig

Configuration class for Facebook’s Prophet model, as described by Taylor & Letham, 2017.

Parameters

max_forecast_steps (Optional[int]) – Max # of steps we would like to forecast for.
target_seq_index (Optional[int]) – The index of the univariate (amongst all univariates in a general multivariate time series) whose value we would like to forecast.
yearly_seasonality (Union[bool, int]) – If bool, whether to enable yearly seasonality. By default, it is activated if there are >= 2 years of history, but deactivated otherwise. If int, this is the number of Fourier series components used to model the seasonality (default = 10).
weekly_seasonality (Union[bool, int]) – If bool, whether to enable weekly seasonality. By default, it is activated if there are >= 2 weeks of history, but deactivated otherwise. If int, this is the number of Fourier series components used to model the seasonality (default = 3).
daily_seasonality (Union[bool, int]) – If bool, whether to enable daily seasonality. By default, it is activated if there are >= 2 days of history, but deactivated otherwise. If int, this is the number of Fourier series components used to model the seasonality (default = 4).
add_seasonality – ‘auto’ indicates automatically adding extra seasonality by detection methods (default = None).
seasonality_mode – ‘additive’ (default) or ‘multiplicative’.
holidays – pd.DataFrame with columns holiday (string) and ds (date type) and optionally columns lower_window and upper_window which specify a range of days around the date to be included as holidays. lower_window=-2 will include 2 days prior to the date as holidays. Also optionally can have a column prior_scale specifying the prior scale for that holiday.
uncertainty_samples (int) – The number of posterior samples to draw in order to calibrate the anomaly scores.

class merlion.models.anomaly.forecast_based.prophet.ProphetDetector(config)

Bases: ForecastingDetectorBase, Prophet

Parameters: config (ProphetConfig) – model configuration

config_class: alias of ProphetDetectorConfig

merlion.models.anomaly.forecast_based.lstm module

Adaptation of a LSTM neural net forecaster, to the task of anomaly detection.

class merlion.models.anomaly.forecast_based.lstm.LSTMDetectorConfig(max_forecast_steps, target_seq_index=None, nhid=1024, model_strides=(1,), **kwargs)

Bases: LSTMConfig, DetectorConfig

Configuration class for LSTM.

Parameters

max_forecast_steps (int) – Max # of steps we would like to forecast for.
target_seq_index (Optional[int]) – The index of the univariate (amongst all univariates in a general multivariate time series) whose value we would like to forecast.
nhid – hidden dimension of LSTM
model_strides – tuple indicating the stride(s) at which we would like to subsample the input data before giving it to the model.

class merlion.models.anomaly.forecast_based.lstm.LSTMDetector(config)

Bases: ForecastingDetectorBase, LSTM

Parameters: config (LSTMConfig) – model configuration

config_class: alias of LSTMDetectorConfig

merlion.models.anomaly.forecast_based.mses module

MSES (Multi-Scale Exponential Smoother) forecasting model adapted for anomaly detection.

class merlion.models.anomaly.forecast_based.mses.MSESDetectorConfig(online_updates=True, **kwargs)

Bases: MSESConfig, DetectorConfig

Configuration class for an MSES forecasting model.

Letting w be the recency weight, B the maximum backstep, x_t the last seen data point, and l_s,t the series of losses for scale s.

\[\begin{split}\begin{align*} \hat{x}_{t+h} & = \sum_{b=0}^B p_{b} \cdot (x_{t-b} + v_{b+h,t} + a_{b+h,t}) \\ \space \\ \text{where} \space\space & v_{b+h,t} = \text{EMA}_w(\Delta_{b+h} x_t) \\ & a_{b+h,t} = \text{EMA}_w(\Delta_{b+h}^2 x_t) \\ \text{and} \space\space & p_b = \sigma(z)_b \space\space \\ \text{if} & \space\space z_b = (b+h)^\phi \cdot \text{EMA}_w(l_{b+h,t}) \cdot \text{RWSE}_w(l_{b+h,t})\\ \end{align*}\end{split}\]

Parameters

max_forecast_steps – Max number of steps to forecast ahead.
target_seq_index – The index of the univariate (amongst all univariates in a general multivariate time series) whose value we would like to forecast.
max_backstep – Max backstep to use in forecasting. If we train with x(0),…,x(t), Then, the b-th model MSES uses will forecast x(t+h) by anchoring at x(t-b) and predicting xhat(t+h) = x(t-b) + delta_hat(b+h).
recency_weight – The recency weight parameter to use when estimating delta_hat.
accel_weight – The weight to scale the acceleration by when computing delta_hat. Specifically, delta_hat(b+h) = velocity(b+h) + accel_weight * acceleration(b+h).
optimize_acc – If True, the acceleration correction will only be used at scales ranging from 1,…(max_backstep+max_forecast_steps)/2.
eta – The parameter used to control the rate at which recency_weight gets tuned when online updates are made to the model and losses can be computed.
rho – The parameter that determines what fraction of the overall error is due to velcity error, while the rest is due to the complement. The error at any scale will be determined as rho * velocity_error + (1-rho) * loss_error.
phi – The parameter used to exponentially inflate the magnitude of loss error at different scales. Loss error for scale s will be increased by a factor of phi ** s.
inflation – The inflation exponent to use when computing the distribution p(b|h) over the models when forecasting at horizon h according to standard errors of the estimated velocities over the models; inflation=1 is equivalent to using the softmax function.

class merlion.models.anomaly.forecast_based.mses.MSESDetector(config)

Bases: ForecastingDetectorBase, MSES

Parameters: config (MSESConfig) – model configuration

config_class: alias of MSESDetectorConfig

property online_updates

train(train_data, anomaly_labels=None, train_config=None, post_rule_train_config=None)

Trains the forecaster on the input time series.

Parameters

train_data (TimeSeries) – a TimeSeries of metric values to train the model.
train_config – Additional training configs, if needed. Only required for some models.

Return type

TimeSeries

Returns

the model’s prediction on train_data, in the same format as if you called ForecasterBase.forecast on the time stamps of train_data

get_anomaly_score(time_series, time_series_prev=None)

Returns the model’s predicted sequence of anomaly scores.

Parameters

time_series (TimeSeries) – the TimeSeries we wish to predict anomaly scores for.
time_series_prev (Optional[TimeSeries]) – a TimeSeries immediately preceding time_series. If given, we use it to initialize the time series anomaly detection model. Otherwise, we assume that time_series immediately follows the training data.

Return type

TimeSeries

Returns

a univariate TimeSeries of anomaly scores