merlion.models.anomaly package

Contains all anomaly detection models. Forecaster-based anomaly detection models may be found in merlion.models.anomaly.forecast_based. Change-point detection models may be found in merlion.models.anomaly.change_point.

For anomaly detection, we define an abstract DetectorBase class which inherits from ModelBase and supports the following interface, in addition to model.save and DetectorClass.load defined for ModelBase:

model = DetectorClass(config)
- initialization with a model-specific config
- configs contain:
  - a (potentially trainable) data pre-processing transform from merlion.transform; note that model.transform is a property which refers to model.config.transform
  - a (potentially trainable) post-processing rule from merlion.post_process; note that model.post_rule is a property which refers to model.config.post_rule. In general, this post-rule will have two stages: calibration and thresholding.
  - booleans enable_calibrator and enable_threshold (both defaulting to True) indicating whether to enable calibration and thresholding in the post-rule.
  - model-specific hyperparameters
model.get_anomaly_score(time_series, time_series_prev=None)
- returns a time series of anomaly scores for each timestamp in time_series
- time_series_prev (optional): the most recent context, only used for some models. If not provided, the training data is used as the context instead.
model.get_anomaly_label(time_series, time_series_prev=None)
- returns a time series of post-processed anomaly scores for each timestamp in time_series. These scores are calibrated to correspond to z-scores if enable_calibrator is True, and they have also been filtered by a thresholding rule (model.threshold) if enable_threshold is True. threshold is specified manually in the config (though it may be modified by DetectorBase.train), .
- time_series_prev (optional): the most recent context, only used for some models. If not provided, the training data is used as the context instead.
model.train(train_data, anomaly_labels=None, train_config=None, post_rule_train_config=None)
- trains the model on the time series train_data
- anomaly_labels (optional): a time series aligned with train_data, which indicates whether each time stamp is anomalous
- train_config (optional): extra configuration describing how the model should be trained (e.g. learning rate for the LSTMDetector). Not used for all models. Class-level default provided for models which do use it.
- post_rule_train_config: extra configuration describing how to train the model’s post-rule. Class-level default is provided for all models.
- returns a time series of anomaly scores produced by the model on train_data.

`base`	Base class for anomaly detectors.
`dbl`	Dynamic Baseline anomaly detection model for time series with daily, weekly or monthly trends.
`windstats`	Window Statistics anomaly detection model for data with weekly seasonality.
`isolation_forest`	The classic isolation forest model for anomaly detection.
`random_cut_forest`	Wrapper around AWS's Random Cut Forest anomaly detection model.
`spectral_residual`	Spectral Residual algorithm for anomaly detection
`stat_threshold`	Simple static thresholding model for anomaly detection.
`zms`	Multiple z-score model (static thresholding at multiple time scales).
`autoencoder`	The autoencoder-based anomaly detector for multivariate time series
`dagmm`	Deep autoencoding Gaussian mixture model for anomaly detection (DAGMM)
`lstm_ed`	The LSTM-encoder-decoder-based anomaly detector for multivariate time series
`vae`	The VAE-based anomaly detector for multivariate time series
`deep_point_anomaly_detector`	Deep Point Anomaly Detector algorithm.

Subpackages

Submodules

merlion.models.anomaly.base module

Base class for anomaly detectors.

class merlion.models.anomaly.base.DetectorConfig(max_score=1000, threshold=None, enable_calibrator=True, enable_threshold=True, transform=None, normalize=None, **kwargs)

Bases: Config

Config object used to define an anomaly detection model.

Base class of the object used to configure an anomaly detection model.

Parameters

max_score (float) – maximum possible uncalibrated anomaly score
threshold – the rule to use for thresholding anomaly scores
enable_calibrator – whether to enable a calibrator which automatically transforms all raw anomaly scores to be z-scores (i.e. distributed as N(0, 1)).
enable_threshold – whether to enable the thresholding rule when post-processing anomaly scores
transform – Transformation to pre-process input time series.
normalize – Pre-trained normalization transformation (optional).

enable_threshold: bool = True

enable_calibrator: bool = True

calibrator: AnomScoreCalibrator = None

threshold: Threshold = None

property post_rule

Returns: The full post-processing rule. Includes calibration if enable_calibrator is True, followed by thresholding if enable_threshold is True.

classmethod from_dict(config_dict, return_unused_kwargs=False, calibrator=None, **kwargs)

Constructs a Config from a Python dictionary of parameters.

Parameters

config_dict (Dict[str, Any]) – dict that will be used to instantiate this object.
return_unused_kwargs – whether to return any unused keyword args.
dim – the dimension of the time series. handled as a special case.
kwargs – any additional parameters to set (overriding config_dict).

Returns

Config object initialized from the dict.

class merlion.models.anomaly.base.NoCalibrationDetectorConfig(enable_calibrator=False, max_score: float = 1000, threshold=None, enable_threshold=True, transform: TransformBase = None, **kwargs)

Bases: DetectorConfig

Abstract config object for an anomaly detection model that should never perform anomaly score calibration.

Base class of the object used to configure an anomaly detection model.

Parameters

enable_calibrator – False because this config assumes calibrated outputs from the model.
max_score – maximum possible uncalibrated anomaly score
threshold – the rule to use for thresholding anomaly scores
enable_threshold – whether to enable the thresholding rule when post-processing anomaly scores
transform – Transformation to pre-process input time series.

property calibrator

Returns: None

property enable_calibrator

Returns: False

class merlion.models.anomaly.base.DetectorBase(config)

Bases: ModelBase

Base class for an anomaly detection model.

Parameters: config (DetectorConfig) – model configuration

config_class: alias of DetectorConfig

property threshold

property calibrator

property post_rule

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

Trains the anomaly detector (unsupervised) and its post-rule (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.

train_post_rule(anomaly_scores, anomaly_labels=None, post_rule_train_config=None)

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_anomaly_label(time_series, time_series_prev=None)

Returns the model’s predicted sequence of anomaly scores, processed by any relevant post-rules (calibration and/or thresholding).

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, filtered by the model’s post-rule

get_figure(time_series, time_series_prev=None, *, filter_scores=True, plot_time_series_prev=False, fig=None)

Parameters

time_series (TimeSeries) – The TimeSeries we wish to plot & predict anomaly scores for.
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.
filter_scores – whether to filter the anomaly scores by the post-rule before plotting them.
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.
fig (Optional[Figure]) – a Figure we might want to add anomaly scores onto.

Return type

Figure

Returns

a Figure of the model’s anomaly score predictions.

plot_anomaly(time_series, time_series_prev=None, *, filter_scores=True, 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.

Parameters

time_series (TimeSeries) – The TimeSeries we wish to plot & predict anomaly scores for.
time_series_prev (Optional[TimeSeries]) – a TimeSeries immediately preceding time_series. Plotted as context if given.
filter_scores – whether to filter the anomaly scores by the post-rule before plotting them.
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 axes to add this plot to

Returns

matplotlib figure & axes

plot_anomaly_plotly(time_series, time_series_prev=None, *, filter_scores=True, plot_time_series_prev=False, figsize=None)

Plots the time series in plotly as a line graph, with points in the series overlaid as points color-coded to indicate their severity as anomalies.

Parameters

time_series (TimeSeries) – The TimeSeries we wish to plot & predict anomaly scores for.
time_series_prev (Optional[TimeSeries]) – a TimeSeries immediately preceding time_series. Plotted as context if given.
filter_scores – whether to filter the anomaly scores by the post-rule before plotting them.
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

class merlion.models.anomaly.base.MultipleTimeseriesDetectorMixin

Bases: MultipleTimeseriesModelMixin

Abstract mixin for anomaly detectors supporting training on multiple time series.

abstract train_multiple(multiple_train_data, anomaly_labels=None, train_config=None, post_rule_train_config=None)

Trains the anomaly detector (unsupervised) and its post-rule (supervised, if labels are given) on the input multiple time series.

Parameters

multiple_train_data (List[TimeSeries]) – a list of TimeSeries of metric values to train the model.
anomaly_labels (Optional[List[TimeSeries]]) – a list of 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

List[TimeSeries]

Returns

A list of TimeSeries of the model’s anomaly scores on the training data with each element corresponds to time series from multiple_train_data.

merlion.models.anomaly.dbl module

Dynamic Baseline anomaly detection model for time series with daily, weekly or monthly trends.

class merlion.models.anomaly.dbl.DynamicBaselineConfig(fixed_period=None, train_window=None, wind_sz='1h', trends=None, max_score=1000, threshold=None, enable_calibrator=True, enable_threshold=True, transform=None, **kwargs)

Bases: DetectorConfig

Configuration class for DynamicBaseline.

Base class of the object used to configure an anomaly detection model.

Parameters

fixed_period (Optional[Tuple[str, str]]) – (t0, tf); Train the model on all datapoints occurring between t0 and tf (inclusive).
train_window (Optional[str]) – A string representing a duration of time to serve as the scope for a rolling dynamic baseline model.
wind_sz (str) – The window size in minutes to bucket times of day. This parameter only applied if a daily trend is one of the trends used.
trends (Optional[List[str]]) – The list of trends to use. Supported trends are “daily”, “weekly” and “monthly”.
max_score – maximum possible uncalibrated anomaly score
threshold – the rule to use for thresholding anomaly scores
enable_calibrator – whether to enable a calibrator which automatically transforms all raw anomaly scores to be z-scores (i.e. distributed as N(0, 1)).
enable_threshold – whether to enable the thresholding rule when post-processing anomaly scores
transform – Transformation to pre-process input time series.

property fixed_period

property trends

determine_train_window()

to_dict(_skipped_keys=None)

Returns: dict with keyword arguments used to initialize the config class.

class merlion.models.anomaly.dbl.DynamicBaseline(config)

Bases: DetectorBase

Dynamic baseline-based anomaly detector.

Detects anomalies by comparing data to historical data that has occurred in the same window of time, as defined by any combination of time of day, day of week, or day of month.

A DBL model can have a fixed period or a dynamic rolling period. A fixed period model trains its baselines exclusively on datapoints occurring in the fixed period, while a rolling period model trains continually on the most recent datapoints within its train-window.

Parameters: config (DynamicBaselineConfig) – model configuration

config_class: alias of DynamicBaselineConfig

property require_even_sampling: bool

Whether the model assumes that training data is sampled at a fixed frequency

Return type: bool

property require_univariate: bool

Whether the model only works with univariate time series.

Return type: bool

property train_window

property fixed_period

property has_fixed_period

property data: UnivariateTimeSeries

Return type: UnivariateTimeSeries

get_relevant(data): Returns the subset of the data that should be used for training or updating.

get_baseline(time_stamps)

Returns the dynamic baselines corresponding to the time stamps :type time_stamps: List[float] :param time_stamps: a list of timestamps

Return type: Tuple[UnivariateTimeSeries, UnivariateTimeSeries]

update(new_data)

get_baseline_figure(time_series, time_series_prev=None, *, filter_scores=True, plot_time_series_prev=False, fig=None, jitter_time_stamps=True)

Return type: Figure

class merlion.models.anomaly.dbl.Trend(value)

Bases: Enum

Enumeration of the supported trends.

daily = 1

weekly = 2

monthly = 3

class merlion.models.anomaly.dbl.Segment(key)

Bases: object

Class representing a segment. The class maintains a mean (baseline) along with a variance so that a z-score can be computed.

add(x)

drop(x)

score(x)

class merlion.models.anomaly.dbl.Segmenter(trends, wind_sz)

Bases: object

Class for managing the segments that belong to a DynamicBaseline model.

Parameters

trends (List[Trend]) – A list of trend types to create segments based on.
wind_sz (str) – The window size in minutes to bucket times of day. Only used if a daily trend is one of the trends used.

day_delta = Timedelta('1 days 00:00:00')

hour_delta = Timedelta('0 days 01:00:00')

min_delta = Timedelta('0 days 00:01:00')

zero_delta = Timedelta('0 days 00:00:00')

reset()

property wind_delta

property trends

property trend

window_key(t)

weekday_key(t)

day_key(t)

segment_key(timestamp)

add(t, x)

drop(t, x)

score(t, x)

get_baseline(t)

Return type: Tuple[float, float]

merlion.models.anomaly.windstats module

Window Statistics anomaly detection model for data with weekly seasonality.

class merlion.models.anomaly.windstats.WindStatsConfig(wind_sz=30, max_day=4, max_score: float = 1000, threshold=None, enable_calibrator=True, enable_threshold=True, transform: TransformBase = None, **kwargs)

Bases: DetectorConfig

Config class for WindStats.

Base class of the object used to configure an anomaly detection model.

Parameters

wind_sz – the window size in minutes, default is 30 minute window
max_day – maximum number of week days stored in memory (only mean and std of each window are stored). Here, the days are first bucketed by weekday and then by window id.
max_score – maximum possible uncalibrated anomaly score
threshold – the rule to use for thresholding anomaly scores
enable_calibrator – whether to enable a calibrator which automatically transforms all raw anomaly scores to be z-scores (i.e. distributed as N(0, 1)).
enable_threshold – whether to enable the thresholding rule when post-processing anomaly scores
transform – Transformation to pre-process input time series.

class merlion.models.anomaly.windstats.WindStats(config=None)

Bases: DetectorBase

Sliding Window Statistics based Anomaly Detector. This detector assumes the time series comes with a weekly seasonality. It divides the week into buckets of the specified size (in minutes). For a given (t, v) it computes an anomaly score by comparing the current value v against the historical values (mean and standard deviation) for that window of time. Note that if multiple matches (specified by the parameter max_day) can be found in history with the same weekday and same time window, then the minimum of the scores is returned.

config.wind_sz: the window size in minutes, default is 30 minute window config.max_days: maximum number of week days stored in memory (only mean and std of each window are stored) here the days are first bucketized by weekday and then bucketized by window id.

config_class: alias of WindStatsConfig

property require_even_sampling: bool

Whether the model assumes that training data is sampled at a fixed frequency

Return type: bool

property require_univariate: bool

Whether the model only works with univariate time series.

Return type: bool

merlion.models.anomaly.isolation_forest module

The classic isolation forest model for anomaly detection.

class merlion.models.anomaly.isolation_forest.IsolationForestConfig(max_n_samples=None, n_estimators=100, max_score=1000, threshold=None, enable_calibrator=True, enable_threshold=True, transform=None, **kwargs)

Bases: DetectorConfig

Configuration class for IsolationForest.

Base class of the object used to configure an anomaly detection model.

Parameters

max_n_samples (Optional[int]) – Maximum number of samples to allow the isolation forest to train on. Specify None to use all samples in the training data.
n_estimators (int) – number of trees in the isolation forest.
max_score – maximum possible uncalibrated anomaly score
threshold – the rule to use for thresholding anomaly scores
enable_calibrator – whether to enable a calibrator which automatically transforms all raw anomaly scores to be z-scores (i.e. distributed as N(0, 1)).
enable_threshold – whether to enable the thresholding rule when post-processing anomaly scores
transform – Transformation to pre-process input time series.

class merlion.models.anomaly.isolation_forest.IsolationForest(config)

Bases: DetectorBase

The classic isolation forest algorithm, proposed in Liu et al. 2008

Parameters: config (IsolationForestConfig) – model configuration

config_class: alias of IsolationForestConfig

property require_even_sampling: bool

Whether the model assumes that training data is sampled at a fixed frequency

Return type: bool

property require_univariate: bool

Whether the model only works with univariate time series.

Return type: bool

merlion.models.anomaly.random_cut_forest module

Wrapper around AWS’s Random Cut Forest anomaly detection model.

class merlion.models.anomaly.random_cut_forest.JVMSingleton

Bases: object

classmethod gateway()

class merlion.models.anomaly.random_cut_forest.RandomCutForestConfig(n_estimators=100, parallel=False, seed=None, max_n_samples=512, thread_pool_size=1, online_updates=False, max_score=1000, threshold=None, enable_calibrator=True, enable_threshold=True, transform=None, **kwargs)

Bases: DetectorConfig

Configuration class for RandomCutForest. Refer to https://github.com/aws/random-cut-forest-by-aws/tree/main/Java for further documentation and defaults of the Java class.

Base class of the object used to configure an anomaly detection model.

Parameters

n_estimators (int) – The number of trees in this forest.
parallel (bool) – If true, then the forest will create an internal thread pool. Forest updates and traversals will be submitted to this thread pool, and individual trees will be updated or traversed in parallel. For larger shingle sizes, dimensions, and number of trees, parallelization may improve throughput. We recommend users benchmark against their target use case.
seed (Optional[int]) – the random seed
max_n_samples (int) – The number of samples retained by by stream samplers in this forest.
thread_pool_size (int) – The number of threads to use in the internal thread pool.
online_updates (bool) – Whether to update the model while running using it to evaluate new data.
max_score – maximum possible uncalibrated anomaly score
threshold – the rule to use for thresholding anomaly scores
enable_calibrator – whether to enable a calibrator which automatically transforms all raw anomaly scores to be z-scores (i.e. distributed as N(0, 1)).
enable_threshold – whether to enable the thresholding rule when post-processing anomaly scores
transform – Transformation to pre-process input time series.

property java_params

class merlion.models.anomaly.random_cut_forest.RandomCutForest(config)

Bases: DetectorBase

The random cut forest is a refinement of the classic isolation forest algorithm. It was proposed in Guha et al. 2016.

Parameters: config (RandomCutForestConfig) – model configuration

config_class: alias of RandomCutForestConfig

property require_even_sampling: bool

Whether the model assumes that training data is sampled at a fixed frequency

Return type: bool

property require_univariate: bool

Whether the model only works with univariate time series.

Return type: bool

property online_updates: bool

Return type: bool

merlion.models.anomaly.spectral_residual module

Spectral Residual algorithm for anomaly detection

class merlion.models.anomaly.spectral_residual.SpectralResidualConfig(local_wind_sz=21, q=3, estimated_points=5, predicting_points=5, target_seq_index=None, max_score: float = 1000, threshold=None, enable_calibrator=True, enable_threshold=True, transform: TransformBase = None, **kwargs)

Bases: DetectorConfig

Config class for SpectralResidual anomaly detector.

Base class of the object used to configure an anomaly detection model.

Parameters

local_wind_sz – Number of previous saliency points to consider when computing the anomaly score
q – Window size of local frequency average computations
estimated_points – Number of padding points to add to the timeseries for saliency map calculations.
predicting_points – Number of points to consider when computing gradient for padding points
target_seq_index – Index of the univariate whose anomalies we want to detect.
max_score – maximum possible uncalibrated anomaly score
threshold – the rule to use for thresholding anomaly scores
enable_calibrator – whether to enable a calibrator which automatically transforms all raw anomaly scores to be z-scores (i.e. distributed as N(0, 1)).
enable_threshold – whether to enable the thresholding rule when post-processing anomaly scores
transform – Transformation to pre-process input time series.

The Saliency Map is computed as follows:

\[\begin{split}R(f) &= \log(A(\mathscr{F}(\textbf{x}))) - \left(\frac{1}{q}\right)_{1 \times q} * (A(\mathscr{F}(\textbf{x})) \\ S_m &= \mathscr{F}^{-1} (R(f))\end{split}\]

where \(*\) is the convolution operator, and \(\mathscr{F}\) is the Fourier Transform. The anomaly scores then are computed as:

\[S(x) = \frac{S(x) - \overline{S(\textbf{x})}}{\overline{S(\textbf{x})}}\]

where \(\textbf{x}\) are the last local_wind_sz points in the timeseries.

The estimated_points and predicting_points parameters are used to pad the end of the timeseries with reasonable values. This is done so that the later points in the timeseries are in the middle of averaging windows rather than in the end.

class merlion.models.anomaly.spectral_residual.SpectralResidual(config=None)

Bases: DetectorBase

Spectral Residual Algorithm for Anomaly Detection.

Spectral Residual Anomaly Detection algorithm based on the algorithm described by Ren et al. (2019). After taking the frequency spectrum, compute the log deviation from the mean. Use inverse fourier transform to obtain the saliency map. Anomaly scores for a point in the time series are obtained by comparing the saliency score of the point to the average of the previous points.

Parameters: config (Optional[SpectralResidualConfig]) – model configuration

config_class: alias of SpectralResidualConfig

property require_even_sampling: bool

Whether the model assumes that training data is sampled at a fixed frequency

Return type: bool

property require_univariate: bool

Whether the model only works with univariate time series.

Return type: bool

property target_seq_index: int

Return type: int

merlion.models.anomaly.stat_threshold module

Simple static thresholding model for anomaly detection.

class merlion.models.anomaly.stat_threshold.StatThresholdConfig(max_score=1000, threshold=None, enable_calibrator=True, enable_threshold=True, transform=None, normalize=None, **kwargs)

Bases: DetectorConfig, NormalizingConfig

Config class for StatThreshold.

Base class of the object used to configure an anomaly detection model.

Parameters

max_score (float) – maximum possible uncalibrated anomaly score
threshold – the rule to use for thresholding anomaly scores
enable_calibrator – whether to enable a calibrator which automatically transforms all raw anomaly scores to be z-scores (i.e. distributed as N(0, 1)).
enable_threshold – whether to enable the thresholding rule when post-processing anomaly scores
transform – Transformation to pre-process input time series.
normalize – Pre-trained normalization transformation (optional).

class merlion.models.anomaly.stat_threshold.StatThreshold(config)

Bases: DetectorBase

Anomaly detection based on a static threshold.

Parameters: config (DetectorConfig) – model configuration

config_class: alias of StatThresholdConfig

property require_even_sampling: bool

Whether the model assumes that training data is sampled at a fixed frequency

Return type: bool

property require_univariate: bool

Whether the model only works with univariate time series.

Return type: bool

merlion.models.anomaly.zms module

Multiple z-score model (static thresholding at multiple time scales).

class merlion.models.anomaly.zms.ZMSConfig(base=2, n_lags=None, lag_inflation=1.0, max_score=1000, threshold=None, enable_calibrator=True, enable_threshold=True, transform=None, normalize=None, **kwargs)

Bases: DetectorConfig, NormalizingConfig

Configuration class for ZMS anomaly detection model. The transform of this config is actually a pre-processing step, followed by the desired number of lag transforms, and a final mean/variance normalization step. This full transform may be accessed as ZMSConfig.full_transform. Note that the normalization is inherited from NormalizingConfig.

Base class of the object used to configure an anomaly detection model.

Parameters

base (int) – The base to use for computing exponentially distant lags.
n_lags (Optional[int]) – The number of lags to be used. If None, n_lags will be chosen later as the maximum number of lags possible for the initial training set.
lag_inflation (float) – See math below for the precise mathematical role of the lag inflation. Consider the lag inflation a measure of distrust toward higher lags, If lag_inflation > 1, the higher the lag inflation, the less likely the model is to select a higher lag’s z-score as the anomaly score.
max_score – maximum possible uncalibrated anomaly score
threshold – the rule to use for thresholding anomaly scores
enable_calibrator – whether to enable a calibrator which automatically transforms all raw anomaly scores to be z-scores (i.e. distributed as N(0, 1)).
enable_threshold – whether to enable the thresholding rule when post-processing anomaly scores
transform – Transformation to pre-process input time series.
normalize – Pre-trained normalization transformation (optional).

\[\begin{split}\begin{align*} \text{Let } \space z_k(x_t) \text{ be the z-score of the } & k\text{-lag at } t, \space \Delta_k(x_t) \text{ and } p \text{ be the lag inflation} \\ & \\ \text{the anomaly score } z(x_t) & = z_{k^*}(x_t) \\ \text{where } k^* & = \text{argmax}_k \space | z_k(x_t) | / k^p \end{align*}\end{split}\]

property full_transform: Returns the full transform, including the pre-processing step, lags, and final mean/variance normalization.

to_dict(_skipped_keys=None)

Returns: dict with keyword arguments used to initialize the config class.

property n_lags

class merlion.models.anomaly.zms.ZMS(config)

Bases: DetectorBase

Multiple Z-Score based Anomaly Detector.

ZMS is designed to detect spikes, dips, sharp trend changes (up or down) relative to historical data. Anomaly scores capture not only magnitude but also direction. This lets one distinguish between positive (spike) negative (dip) anomalies for example.

The algorithm builds models of normalcy at multiple exponentially-growing time scales. The zeroth order model is just a model of the values seen recently. The kth order model is similar except that it models not values, but rather their k-lags, defined as x(t)-x(t-k), for k in 1, 2, 4, 8, 16, etc. The algorithm assigns the maximum absolute z-score of all the models of normalcy as the overall anomaly score.

\[\begin{split}\begin{align*} \text{Let } \space z_k(x_t) \text{ be the z-score of the } & k\text{-lag at } t, \space \Delta_k(x_t) \text{ and } p \text{ be the lag inflation} \\ & \\ \text{the anomaly score } z(x_t) & = z_{k^*}(x_t) \\ \text{where } k^* & = \text{argmax}_k \space | z_k(x_t) | / k^p \end{align*}\end{split}\]

Parameters: config (DetectorConfig) – model configuration

config_class: alias of ZMSConfig

property require_even_sampling: bool

Whether the model assumes that training data is sampled at a fixed frequency

Return type: bool

property require_univariate: bool

Whether the model only works with univariate time series.

Return type: bool

property n_lags

property lag_scales: List[int]

Return type: List[int]

property lag_inflation

property adjust_z_scores: bool

Return type: bool

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

Trains the anomaly detector (unsupervised) and its post-rule (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.

merlion.models.anomaly.autoencoder module

The autoencoder-based anomaly detector for multivariate time series

class merlion.models.anomaly.autoencoder.AutoEncoderConfig(hidden_size=5, layer_sizes=(25, 10, 5), sequence_len=1, lr=0.001, batch_size=512, num_epochs=50, **kwargs)

Bases: DetectorConfig, NormalizingConfig

Configuration class for AutoEncoder. The normalization is inherited from NormalizingConfig. The input data will be standardized automatically.

Base class of the object used to configure an anomaly detection model.

Parameters

hidden_size (int) – The latent size
layer_sizes (Sequence[int]) – The hidden layer sizes for the MLP encoder and decoder, e.g., (25, 10, 5) for encoder and (5, 10, 25) for decoder
sequence_len (int) – The input series length, e.g., input = [x(t-sequence_len+1)…,x(t-1),x(t)]
lr (float) – The learning rate during training
batch_size (int) – The batch size during training
num_epochs (int) – The number of training epochs
max_score – maximum possible uncalibrated anomaly score
threshold – the rule to use for thresholding anomaly scores
enable_calibrator – whether to enable a calibrator which automatically transforms all raw anomaly scores to be z-scores (i.e. distributed as N(0, 1)).
enable_threshold – whether to enable the thresholding rule when post-processing anomaly scores
transform – Transformation to pre-process input time series.
normalize – Pre-trained normalization transformation (optional).

class merlion.models.anomaly.autoencoder.AutoEncoder(config)

Bases: DetectorBase

The autoencoder-based multivariate time series anomaly detector. This detector utilizes an autoencoder to infer the correlations between different time series and estimate the joint distribution of the variables for anomaly detection.

paper: Pierre Baldi. Autoencoders, Unsupervised Learning, and Deep Architectures. 2012.

Parameters: config (AutoEncoderConfig) – model configuration

config_class: alias of AutoEncoderConfig

property require_even_sampling: bool

Whether the model assumes that training data is sampled at a fixed frequency

Return type: bool

property require_univariate: bool

Whether the model only works with univariate time series.

Return type: bool

merlion.models.anomaly.vae module

The VAE-based anomaly detector for multivariate time series

class merlion.models.anomaly.vae.VAEConfig(encoder_hidden_sizes=(25, 10, 5), decoder_hidden_sizes=(5, 10, 25), latent_size=5, sequence_len=1, kld_weight=1.0, dropout_rate=0.0, num_eval_samples=10, lr=0.001, batch_size=1024, num_epochs=10, **kwargs)

Bases: DetectorConfig, NormalizingConfig

Configuration class for VAE. The normalization is inherited from NormalizingConfig. The input data will be standardized automatically.

Base class of the object used to configure an anomaly detection model.

Parameters

encoder_hidden_sizes (Sequence[int]) – The hidden layer sizes of the MLP encoder
decoder_hidden_sizes (Sequence[int]) – The hidden layer sizes of the MLP decoder
latent_size (int) – The latent size
sequence_len (int) – The input series length, e.g., input = [x(t-sequence_len+1)…,x(t-1),x(t)]
kld_weight (float) – The regularization weight for the KL divergence term
dropout_rate (float) – The dropout rate for the encoder and decoder
num_eval_samples (int) – The number of sampled latent variables during prediction
lr (float) – The learning rate during training
batch_size (int) – The batch size during training
num_epochs (int) – The number of training epochs
max_score – maximum possible uncalibrated anomaly score
threshold – the rule to use for thresholding anomaly scores
enable_calibrator – whether to enable a calibrator which automatically transforms all raw anomaly scores to be z-scores (i.e. distributed as N(0, 1)).
enable_threshold – whether to enable the thresholding rule when post-processing anomaly scores
transform – Transformation to pre-process input time series.
normalize – Pre-trained normalization transformation (optional).

class merlion.models.anomaly.vae.VAE(config)

Bases: DetectorBase

The VAE-based multivariate time series anomaly detector. This detector utilizes a variational autoencoder to infer the correlations between different time series and estimate the distribution of the reconstruction errors for anomaly detection.

paper: Diederik P Kingma and Max Welling. Auto-Encoding Variational Bayes. 2013.

Parameters: config (VAEConfig) – model configuration

config_class: alias of VAEConfig

property require_even_sampling: bool

Whether the model assumes that training data is sampled at a fixed frequency

Return type: bool

property require_univariate: bool

Whether the model only works with univariate time series.

Return type: bool

merlion.models.anomaly.dagmm module

Deep autoencoding Gaussian mixture model for anomaly detection (DAGMM)

class merlion.models.anomaly.dagmm.DAGMMConfig(gmm_k=3, hidden_size=5, sequence_len=1, lambda_energy=0.1, lambda_cov_diag=0.005, lr=0.001, batch_size=256, num_epochs=10, **kwargs)

Bases: DetectorConfig, NormalizingConfig

Configuration class for DAGMM. The normalization is inherited from NormalizingConfig. The input data will be standardized automatically.

Base class of the object used to configure an anomaly detection model.

Parameters

gmm_k (int) – The number of Gaussian distributions
hidden_size (int) – The hidden size of the autoencoder module in DAGMM
sequence_len (int) – The input series length, e.g., input = [x(t-sequence_len+1)…,x(t-1),x(t)]
lambda_energy (float) – The regularization weight for the energy term
lambda_cov_diag (float) – The regularization weight for the covariance diagonal entries
lr (float) – The learning rate during training
batch_size (int) – The batch size during training
num_epochs (int) – The number of training epochs
max_score – maximum possible uncalibrated anomaly score
threshold – the rule to use for thresholding anomaly scores
enable_calibrator – whether to enable a calibrator which automatically transforms all raw anomaly scores to be z-scores (i.e. distributed as N(0, 1)).
enable_threshold – whether to enable the thresholding rule when post-processing anomaly scores
transform – Transformation to pre-process input time series.
normalize – Pre-trained normalization transformation (optional).

class merlion.models.anomaly.dagmm.DAGMM(config)

Bases: DetectorBase, MultipleTimeseriesDetectorMixin

Deep autoencoding Gaussian mixture model for anomaly detection (DAGMM). DAGMM combines an autoencoder with a Gaussian mixture model to model the distribution of the reconstruction errors. DAGMM jointly optimizes the parameters of the deep autoencoder and the mixture model simultaneously in an end-to-end fashion.

paper: Bo Zong, Qi Song, Martin Renqiang Min, Wei Cheng, Cristian Lumezanu, Daeki Cho and Haifeng Chen. Deep Autoencoding Gaussian Mixture Model for Unsupervised Anomaly Detection. 2018..

config_class: alias of DAGMMConfig

property require_even_sampling: bool

Whether the model assumes that training data is sampled at a fixed frequency

Return type: bool

property require_univariate: bool

Whether the model only works with univariate time series.

Return type: bool

train_multiple(multiple_train_data, anomaly_labels=None, train_config=None, post_rule_train_config=None)

Trains the anomaly detector (unsupervised) and its post-rule (supervised, if labels are given) on the input multiple time series.

Parameters

multiple_train_data (List[TimeSeries]) – a list of TimeSeries of metric values to train the model.
anomaly_labels (Optional[List[TimeSeries]]) – a list of TimeSeries indicating which timestamps are anomalous. Optional.
train_config –
Additional training config dict with keys:
- ”n_epochs”: int indicating how many times the model must be
  
  trained on the timeseries in multiple_train_data. Defaults to 1.
- ”shuffle”: bool indicating if the multiple_train_data collection
  
  should be shuffled before every epoch. Defaults to True if “n_epochs” > 1.
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

List[TimeSeries]

Returns

A list of TimeSeries of the model’s anomaly scores on the training data with each element corresponds to time series from multiple_train_data.

merlion.models.anomaly.lstm_ed module

The LSTM-encoder-decoder-based anomaly detector for multivariate time series

class merlion.models.anomaly.lstm_ed.LSTMEDConfig(hidden_size=5, sequence_len=20, n_layers=(1, 1), dropout=(0, 0), lr=0.001, batch_size=256, num_epochs=10, **kwargs)

Bases: DetectorConfig, NormalizingConfig

Configuration class for LSTM-encoder-decoder. The normalization is inherited from NormalizingConfig. The input data will be standardized automatically.

Base class of the object used to configure an anomaly detection model.

Parameters

hidden_size (int) – The hidden state size of the LSTM modules
sequence_len (int) – The input series length, e.g., input = [x(t-sequence_len+1)…,x(t-1),x(t)]
n_layers (Sequence[int]) – The number of layers for the LSTM encoder and decoder. n_layer has two values, i.e., n_layer[0] is the number of encoder layers and n_layer[1] is the number of decoder layers.
dropout (Sequence[int]) – The dropout rate for the LSTM encoder and decoder. dropout has two values, i.e., dropout[0] is the dropout rate for the encoder and dropout[1] is the dropout rate for the decoder.
lr (float) – The learning rate during training
batch_size (int) – The batch size during training
num_epochs (int) – The number of training epochs
max_score – maximum possible uncalibrated anomaly score
threshold – the rule to use for thresholding anomaly scores
enable_calibrator – whether to enable a calibrator which automatically transforms all raw anomaly scores to be z-scores (i.e. distributed as N(0, 1)).
enable_threshold – whether to enable the thresholding rule when post-processing anomaly scores
transform – Transformation to pre-process input time series.
normalize – Pre-trained normalization transformation (optional).

class merlion.models.anomaly.lstm_ed.LSTMED(config)

Bases: DetectorBase

The LSTM-encoder-decoder-based multivariate time series anomaly detector. The time series representation is modeled by an encoder-decoder network where both encoder and decoder are LSTMs. The distribution of the reconstruction error is estimated for anomaly detection.

Parameters: config (LSTMEDConfig) – model configuration

config_class: alias of LSTMEDConfig

property require_even_sampling: bool

Whether the model assumes that training data is sampled at a fixed frequency

Return type: bool

property require_univariate: bool

Whether the model only works with univariate time series.

Return type: bool

merlion.models.anomaly.deep_point_anomaly_detector module

Deep Point Anomaly Detector algorithm.

class merlion.models.anomaly.deep_point_anomaly_detector.DeepPointAnomalyDetectorConfig(max_score=1000, threshold=None, enable_calibrator=True, enable_threshold=True, transform=None, normalize=None, **kwargs)

Bases: DetectorConfig

Config object used to define an anomaly detection model.

Base class of the object used to configure an anomaly detection model.

Parameters

max_score (float) – maximum possible uncalibrated anomaly score
threshold – the rule to use for thresholding anomaly scores
enable_calibrator – whether to enable a calibrator which automatically transforms all raw anomaly scores to be z-scores (i.e. distributed as N(0, 1)).
enable_threshold – whether to enable the thresholding rule when post-processing anomaly scores
transform – Transformation to pre-process input time series.
normalize – Pre-trained normalization transformation (optional).

class merlion.models.anomaly.deep_point_anomaly_detector.DeepPointAnomalyDetector(config)

Bases: DetectorBase

Given a time series tuple (time, signal), this algorithm trains an MLP with each element in time and corresponding signal as input-taget pair. Once the MLP is trained for a few itertions, the loss values at each time is regarded as the anomaly score for the corresponding signal. The intuition is that DNNs learn global patterns before overfitting local details. Therefore any point anomalies in the signal will have high MLP loss. These intuitions can be found in: Arpit, Devansh, et al. “A closer look at memorization in deep networks.” ICML 2017 Rahaman, Nasim, et al. “On the spectral bias of neural networks.” ICML 2019

Parameters: config (DeepPointAnomalyDetectorConfig) – model configuration

config_class: alias of DeepPointAnomalyDetectorConfig

property require_even_sampling: bool

Whether the model assumes that training data is sampled at a fixed frequency

Return type: bool

property require_univariate: bool

Whether the model only works with univariate time series.

Return type: bool