# updateMetricsAndFit

Update performance metrics in incremental drift-aware learning model given new data and train model

## Description

returns an incremental drift-aware learning model `Mdl`

= updateMetricsAndFit(`Mdl`

,`X`

,`Y`

)`Mdl`

, which is the
input incremental drift-aware learning model `Mdl`

with the following modifications:

`updateMetricsAndFit`

measures the model performance on the incoming predictor and response data,`X`

and`Y`

respectively. When the input model is*warm*(`Mdl.IsWarm`

is`true`

),`updateMetricsAndFit`

overwrites previously computed metrics, stored in the`Metrics`

property, with the new values. Otherwise,`updateMetricsAndFit`

stores`NaN`

values in`Metrics`

instead.`updateMetricsAndFit`

fits the modified model to the incoming data by performing incremental drift-aware learning.

The input and output models have the same data type.

uses additional options specified by one or more name-value arguments. For example, you can
specify that the columns of the predictor data matrix correspond to observations, and set
observation weights.`Mdl`

= updateMetricsAndFit(`Mdl`

,`X`

,`Y`

,`Name=Value`

)

## Examples

### Compute Performance Metrics and Monitor Concept Drift

Create the random concept data and concept drift generator using the helper functions, `HelperSineGenerator`

and `HelperConceptDriftGenerator`

, respectively.

concept1 = HelperSineGenerator(ClassificationFunction=1,IrrelevantFeatures=true,TableOutput=false); concept2 = HelperSineGenerator(ClassificationFunction=3,IrrelevantFeatures=true,TableOutput=false); driftGenerator = HelperConceptDriftGenerator(concept1,concept2,15000,1000);

When `ClassificationFunction`

is 1, `HelperSineGenerator`

labels all points that satisfy *x1* < *sin(x2) *as 1, otherwise the function labels them as 0. When `ClassificationFunction`

is 3, this is reversed. That is, `HelperSineGenerato`

r labels all points that satisfy *x1* >= *sin(x2) *as 1, otherwise the function labels them as 0 [2]. The software returns the data in matrices for using in incremental learners.

`HelperConceptDriftGenerator`

establishes the concept drift. The object uses a sigmoid function `1./(1+exp(-4*(numobservations-position)./width))`

to decide the probability of choosing the first stream when generating data [3]. In this case, the position argument is 15000 and the width argument is 1000. As the number of observations exceeds the position value minus half of the width, the probability of sampling from the first stream when generating data decreases. The sigmoid function allows a smooth transition from one stream to the other. Larger width values indicate a larger transition period where both streams are approximately equally likely to be selected.

Initiate an incremental drift-aware model for classification as follows:

Create an incremental Naive Bayes classification model for binary classification.

Initiate an incremental concept drift detector that uses the Hoeffding's Bounds Drift Detection Method with moving average (HDDMA).

Using the incremental linear model and the concept drift detector, initiate an incremental drift-aware model. Specify the training period as 5000 observations.

BaseLearner = incrementalClassificationNaiveBayes(MaxNumClasses=2,Metrics="classiferror"); dd = incrementalConceptDriftDetector("hddma"); idal = incrementalDriftAwareLearner(BaseLearner,DriftDetector=dd,TrainingPeriod=5000);

Preallocate the number of variables in each chunk and number of iterations for creating a stream of data.

numObsPerChunk = 10; numIterations = 4000;

Preallocate the variables for tracking the drift status and drift time, and storing the classification error.

dstatus = zeros(numIterations,1); statusname = strings(numIterations,1); driftTimes = []; ce = array2table(zeros(numIterations,2),VariableNames=["Cumulative" "Window"]);

Simulate a data stream with incoming chunks of 10 observations each and perform incremental drift-aware learning. At each iteration:

Simulate predictor data and labels, and update

`driftGenerator`

using the helper function`hgenerate`

.Call

`updateMetricsAndFit`

to update the performance metrics and fit the incremental drift-aware model to the incoming data.Track and record the drift status and the classification error for visualization purposes.

rng(12); % For reproducibility for j = 1:numIterations % Generate data [driftGenerator,X,Y] = hgenerate(driftGenerator,numObsPerChunk); % Update performance metrics and fit idal = updateMetricsAndFit(idal,X,Y); % Record drift status and classification error statusname(j) = string(idal.DriftStatus); ce{j,:} = idal.Metrics{"ClassificationError",:}; if idal.DriftDetected dstatus(j) = 2; elseif idal.WarningDetected dstatus(j) = 1; else dstatus(j) = 0; end if idal.DriftDetected driftTimes(end+1) = j; end end

Plot the cumulative and per window classification error. Mark the warmup and training periods, and where the drift was introduced.

h = plot(ce.Variables); xlim([0 numIterations]) ylim([0 0.22]) ylabel("Classification Error") xlabel("Iteration") xline(idal.MetricsWarmupPeriod/numObsPerChunk,"g-.","Warmup Period",LineWidth=1.5) xline(idal.MetricsWarmupPeriod/numObsPerChunk+driftTimes,"g-.","Warmup Period",LineWidth=1.5) xline(idal.TrainingPeriod/numObsPerChunk,"b-.","Training Period",LabelVerticalAlignment="middle",LineWidth=1.5) xline(driftTimes,"m--","Drift",LabelVerticalAlignment="middle",LineWidth=1.5) legend(h,ce.Properties.VariableNames) legend(h,Location="best")

The `updateMetricsAndFit`

function first evaluates the performance of the model by calling `updateMetrics`

on incoming data, and then fits the model to data by calling `fit`

:

The `updateMetrics`

function evaluates the performance of the model as it processes incoming observations. The function writes specified metrics, measured cumulatively and within a specified window of processed observations, to the `Metrics`

model property.

The `fit`

function fits the model by updating the base learner and monitoring for drift given an incoming batch of data. When you call `fit`

, the software performs the following procedure:

Trains the model up to

`NumTrainingObservations`

observations.After training, the software starts tracking the model loss to see if any concept drift has occurred and updates drift status accordingly.

When the drift status is

`Warning`

, the software trains a temporary model to replace the`BaseLearner`

in preparation for an imminent drift.When the drift status is

`Drift`

, temporary model replaces the`BaseLearner`

.When the drift status is

`Stable`

, the software discards the temporary model.

For more information, see the **Algorithms** section.

Plot the drift status versus the iteration number.

gscatter(1:numIterations,dstatus,statusname,"gmr","o",5,"on","Iteration","Drift Status","filled")

## Input Arguments

`Mdl`

— Incremental drift-aware learning model

`incrementalDriftAwareLearner`

model object

Incremental drift-aware learning model fit to streaming data, specified as an `incrementalDriftAwareLearner`

model object. You can create
`Mdl`

using the `incrementalDriftAwareLearner`

function. For more details, see the object reference page.

`X`

— Chunk of predictor data

floating-point matrix

Chunk of predictor data to which the model is fit, specified as a floating-point matrix of *n* observations and `Mdl.BaseLearner.NumPredictors`

predictor variables.

When `Mdl.BaseLearner`

accepts the `ObservationsIn`

name-value argument, the value of `ObservationsIn`

determines the orientation of the variables and observations. The default `ObservationsIn`

value is `"rows"`

, which indicates that observations in the predictor data are oriented along the rows of `X`

.

The length of the observation responses (or labels) `Y`

and the number of observations in `X`

must be equal; `Y(`

is the response (or label) of observation * j*)

*j*(row or column) in

`X`

.**Note**

If

`Mdl.BaseLearner.NumPredictors`

= 0,`updateMetricsAndFit`

infers the number of predictors from`X`

, and sets the corresponding property of the output model. Otherwise, if the number of predictor variables in the streaming data changes from`Mdl.BaseLearner.NumPredictors`

,`updateMetricsAndFit`

issues an error.`updateMetricsAndFit`

supports only floating-point input predictor data. If your input data includes categorical data, you must prepare an encoded version of the categorical data. Use`dummyvar`

to convert each categorical variable to a numeric matrix of dummy variables. Then, concatenate all dummy variable matrices and any other numeric predictors. For more details, see Dummy Variables.

**Data Types: **`single`

| `double`

`Y`

— Chunk of observed responses (or labels)

floating-point vector | categorical array | character array | string array | logical vector | cell array of character vectors

Chunk of responses (or labels) to which the model is fit, specified as one of the following:

Floating-point vector of

*n*elements for regression models, where*n*is the number of rows in`X`

.Categorical, character, or string array, logical vector, or cell array of character vectors for classification models. If

`Y`

is a character array, it must have one class label per row. Otherwise,`Y`

must be a vector with*n*elements.

The length of `Y`

and the number of observations in
`X`

must be equal;
`Y(`

is the response (or label) of
observation * j*)

*j*(row or column) in

`X`

.For classification problems:

When

`Mdl.BaseLearner.ClassNames`

is nonempty, the following conditions apply:If

`Y`

contains a label that is not a member of`Mdl.BaseLearner.ClassNames`

,`updateMetricsAndFit`

issues an error.The data type of

`Y`

and`Mdl.BaseLearner.ClassNames`

must be the same.

When

`Mdl.BaseLearner.ClassNames`

is empty,`updateMetricsAndFit`

infers`Mdl.BaseLearner.ClassNames`

from data.

**Data Types: **`single`

| `double`

| `categorical`

| `char`

| `string`

| `logical`

| `cell`

### Name-Value Arguments

Specify optional pairs of arguments as
`Name1=Value1,...,NameN=ValueN`

, where `Name`

is
the argument name and `Value`

is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.

**Example: **`ObservationsIn="columns",Weights=W`

specifies that the columns
of the predictor matrix correspond to observations, and the vector `W`

contains observation weights to apply during incremental learning.

`ObservationsIn`

— Orientation of data in `X`

`"rows"`

(default) | `"columns"`

Predictor data observation dimension, specified as `"columns"`

or
`"rows"`

.

`updateMetricsAndFit`

supports `ObservationsIn`

only if
`Mdl.BaseLearner`

supports the `ObservationsIn`

name-value argument.

**Example: **`ObservationsIn="columns"`

**Data Types: **`char`

| `string`

`Weights`

— Chunk of observation weights

floating-point vector of positive values

Chunk of observation weights, specified as a floating-point vector of positive values. `updateMetricsAndFit`

weighs the observations in `X`

with the corresponding values in `Weights`

. The size of `Weights`

must equal *n*, which is the number of observations in `X`

.

By default, `Weights`

is `ones(`

.* n*,1)

**Example: **`Weights=w`

**Data Types: **`double`

| `single`

## Output Arguments

`Mdl`

— Updated incremental drift-aware learning model

`incrementalDriftAwareLearner`

model object

Updated incremental drift-aware learning model, returned as an incremental learning
model object of the same data type as the input model `Mdl`

,
`incrementalDriftAwareLearner`

.

## Algorithms

### Incremental Drift-Aware Learning

*Incremental learning*, or *online
learning*, is a branch of machine learning concerned with processing incoming
data from a data stream, possibly given little to no knowledge of the distribution of the
predictor variables, aspects of the prediction or objective function (including tuning
parameter values), or whether the observations are labeled. Incremental learning differs
from traditional machine learning, where enough labeled data is available to fit to a model,
perform cross-validation to tune hyperparameters, and infer the predictor distribution. For
more details, see Incremental Learning Overview.

Unlike other incremental learning functionality offered by Statistics and Machine Learning Toolbox™, `updateMetricsAndFit`

model object combines incremental learning and
concept drift detection.

After creating an `incrementalDriftAwareLearner`

object, use `updateMetrics`

to update model performance metrics and `fit`

to fit the
base model to incoming chunk of data, check for potential drift in the model performance
(concept drift), and update or reset the incremental drift-aware learner, if necessary. You
can also use `updateMetricsAndFit`

. The `fit`

function
implements the Reactive Drift Detection Method (RDDM) [1] as follows:

After

`Mdl.BaseLearner.EstimationPeriod`

(if necessary) and`MetricsWarmupPeriod`

, the function trains the incremental drift-aware model up to`NumTrainingObservations`

observations until it reaches`TrainingPeriod`

. (If the`TrainingPeriod`

value is smaller than the`Mdl.BaseLearner.MetricsWarmupPeriod`

value, then`incrementalDriftAwareLearner`

sets the`TrainingPeriod`

value as`Mdl.BaseLearner.MetricsWarmupPeriod`

.)When

`NumTrainingObservations > TrainingPeriod`

, the software starts tracking the model loss. The software computes the per observation loss using the`perObservationLoss`

function. While computing the per observation loss, the software uses the`"classiferror"`

loss metric for classification models and`"squarederror"`

for regression models. The function then appends the loss values computed using the last chunk of data to the existing buffer loss values.Next, the software checks to see if any concept drift occurred by using the

`detectdrift`

function and updates`DriftStatus`

accordingly.

Based on the drift status, `fit`

performs the following procedure:

The software first increases the consecutive`DriftStatus`

is`'Warning'`

–`'Warning'`

status count by 1.If the consecutive

`'Warning'`

status count is less than the`WarningCountLimit`

value and the`PreviousDriftStatus`

value is`Stable`

, then the software trains a temporary incremental learner (if one does not exist) and sets it (or the existing one) to`BaseLearner`

.Then the software resets the temporary incremental learner using the learner's

`reset`

function.If the consecutive

`'Warning'`

status count is less than the`WarningCountLimit`

value and the`PreviousDriftStatus`

value is`'Warning'`

, then the software trains the existing temporary incremental model using the latest chunk of data.If the consecutive

`'Warning'`

status count is more than the`WarningCountLimit`

value, then the software sets the`DriftStatus`

value to`'Drift'`

.

The software performs the following steps.`DriftStatus`

is`'Drift'`

–Sets the consecutive

`'Warning'`

status count to 0.Resets

`DriftDetector`

using the`reset`

function.Empties the buffer loss values and appends the loss values for the latest chunk of data to buffer loss values.

If the temporary incremental model is not empty, then the software sets the current

`BaseLearner`

value to the temporary incremental model and empties the temporary incremental model.If the temporary incremental model is empty, then the software resets the

`BaseLearner`

value by using the learner's`reset`

function.

The software first increases the consecutive`DriftStatus`

is`'Stable'`

–`'Stable'`

status count by 1.If the consecutive

`'Stable'`

status count is less than the`StableCountLimit`

and the`PreviousDriftStatus`

value is`'Warning'`

, then the software sets the number of warnings to zero and empties the temporary model.If the consecutive

`'Stable'`

status count is more than the`StableCountLimit`

value, then the software resets the`DriftDetector`

using the`reset`

function. Then the software tests all of the saved loss values in the buffer for concept drift by using the`detectdrift`

function.

Once `DriftStatus`

is set to `'Drift'`

, and the
`BaseLearner`

and `DriftDetector`

are reset, the
software waits until `Mdl.BaseLearner.EstimationPeriod`

+
`Mdl.BaseLearner.MetricsWarmupPeriod`

before it starts computing the
performance metrics.

### Performance Metrics

The

`updateMetrics`

and`updateMetricsAndFit`

functions track model performance metrics (`Metrics`

) from new data when the incremental model is*warm*(`Mdl.BaseLearner.IsWarm`

property). An incremental model becomes warm after`fit`

or`updateMetricsAndFit`

fits the incremental model to`MetricsWarmupPeriod`

observations, which is the*metrics warm-up period*.If

`Mdl.BaseLearner.EstimationPeriod`

> 0, the functions estimate hyperparameters before fitting the model to data. Therefore, the functions must process an additional`EstimationPeriod`

observations before the model starts the metrics warm-up period.The

`Metrics`

property of the incremental model stores two forms of each performance metric as variables (columns) of a table,`Cumulative`

and`Window`

, with individual metrics in rows. When the incremental model is warm,`updateMetrics`

and`updateMetricsAndFit`

update the metrics at the following frequencies:`Cumulative`

— The functions compute cumulative metrics since the start of model performance tracking. The functions update metrics every time you call the functions, and base the calculation on the entire supplied data set until a model reset.`Window`

— The functions compute metrics based on all observations within a window determined by the`MetricsWindowSize`

name-value argument.`MetricsWindowSize`

also determines the frequency at which the software updates`Window`

metrics. For example, if`MetricsWindowSize`

is 20, the functions compute metrics based on the last 20 observations in the supplied data (`X((end – 20 + 1):end,:)`

and`Y((end – 20 + 1):end)`

).Incremental functions that track performance metrics within a window use the following process:

Store

`MetricsWindowSize`

amount of values for each specified metric, and store the same amount of observation weights.Populate elements of the metrics values with the model performance based on batches of incoming observations, and store the corresponding observation weights.

When the window of observations is filled, overwrite

`Mdl.Metrics.Window`

with the weighted average performance in the metrics window. If the window is overfilled when the function processes a batch of observations, the latest incoming`MetricsWindowSize`

observations are stored, and the earliest observations are removed from the window. For example, suppose`MetricsWindowSize`

is 20, there are 10 stored values from a previously processed batch, and 15 values are incoming. To compose the length 20 window, the functions use the measurements from the 15 incoming observations and the latest 5 measurements from the previous batch.

The software omits an observation with a

`NaN`

score when computing the`Cumulative`

and`Window`

performance metric values.

## References

[1] Barros, Roberto S.M. , et al.
"RDDM: Reactive drift detection method." *Expert Systems with
Applications*. vol. 90, Dec. 2017, pp. 344-55. https://doi.org/10.1016/j.eswa.2017.08.023

[2] Bifet, Albert, et al. "New
Ensemble Methods for Evolving Data Streams." *Proceedings of the 15th ACM SIGKDD
International Conference on Knowledge Discovery and Data Mining*. ACM Press,
2009, p. 139. https://doi.org/10.1145/1557019.1557041.

[3] Gama, João, et al. "Learning with
drift detection". *Advances in Artificial Intelligence – SBIA 2004*, edited
by Ana L. C. Bazzan and Sofiane Labidi, vol. 3171, Springer Berlin Heidelberg, 2004, pp. 286–95.
https://doi.org/10.1007/978-3-540-28645-5_29.

## Version History

**Introduced in R2022b**

## See Also

`predict`

| `perObservationLoss`

| `fit`

| `incrementalDriftAwareLearner`

| `updateMetrics`

| `loss`

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