# updateMetrics

Update performance metrics in naive Bayes incremental learning classification model given new data

## Description

Given streaming data, `updateMetrics`

measures the performance of a configured naive Bayes classification model for incremental learning (`incrementalClassificationNaiveBayes`

object). `updateMetrics`

stores the performance metrics in the output model.

`updateMetrics`

allows for flexible incremental learning. After you call the function to update model performance metrics on an incoming chunk of data, you can perform other actions before you train the model to the data. For example, you can decide whether you need to train the model based on its performance on a chunk of data. Alternatively, you can both update model performance metrics and train the model on the data as it arrives, in one call, by using the `updateMetricsAndFit`

function.

To measure the model performance on a specified batch of data, call `loss`

instead.

returns a naive Bayes classification model for incremental learning `Mdl`

= updateMetrics(`Mdl`

,`X`

,`Y`

)`Mdl`

, which is the input naive Bayes classification model for incremental learning `Mdl`

modified to contain the model performance metrics on the incoming predictor and response data, `X`

and `Y`

respectively.

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

is `true`

), `updateMetrics`

overwrites previously computed metrics, stored in the `Metrics`

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

stores `NaN`

values in `Metrics`

instead.

## Examples

### Track Performance of Incremental Model

Train a naive Bayes classification model by using `fitcnb`

, convert it to an incremental learner, and then track its performance to streaming data.

**Load and Preprocess Data**

Load the human activity data set. Randomly shuffle the data.

load humanactivity rng(1) % For reproducibility n = numel(actid); idx = randsample(n,n); X = feat(idx,:); Y = actid(idx);

For details on the data set, enter `Description`

at the command line.

**Train Naive Bayes Classification Model**

Fit a naive Bayes classification model to a random sample of half the data.

idxtt = randsample([true false],n,true); TTMdl = fitcnb(X(idxtt,:),Y(idxtt))

TTMdl = ClassificationNaiveBayes ResponseName: 'Y' CategoricalPredictors: [] ClassNames: [1 2 3 4 5] ScoreTransform: 'none' NumObservations: 12053 DistributionNames: {1x60 cell} DistributionParameters: {5x60 cell} Properties, Methods

`TTMdl`

is a `ClassificationNaiveBayes`

model object representing a traditionally trained model.

**Convert Trained Model**

Convert the traditionally trained classification model to a naive Bayes classification model for incremental learning.

IncrementalMdl = incrementalLearner(TTMdl)

IncrementalMdl = incrementalClassificationNaiveBayes IsWarm: 1 Metrics: [1x2 table] ClassNames: [1 2 3 4 5] ScoreTransform: 'none' DistributionNames: {1x60 cell} DistributionParameters: {5x60 cell} Properties, Methods

The incremental model is warm. Therefore, `updateMetrics`

can track model performance metrics given data.

**Track Performance Metrics**

Track the model performance on the rest of the data by using the `updateMetrics`

function. Simulate a data stream by processing 50 observations at a time. At each iteration:

Call

`updateMetrics`

to update the cumulative and window minimal cost of the model given the incoming chunk of observations. Overwrite the previous incremental model to update the losses in the`Metrics`

property. Note that the function does not fit the model to the chunk of data—the chunk is "new" data for the model.Store the minimal cost and mean of the first predictor in the first class ${\mu}_{11}$.

% Preallocation idxil = ~idxtt; nil = sum(idxil); numObsPerChunk = 50; nchunk = floor(nil/numObsPerChunk); mc = array2table(zeros(nchunk,2),'VariableNames',["Cumulative" "Window"]); mu11 = [IncrementalMdl.DistributionParameters{1,1}(1); zeros(nchunk,1)]; Xil = X(idxil,:); Yil = Y(idxil); % Incremental fitting for j = 1:nchunk ibegin = min(nil,numObsPerChunk*(j-1) + 1); iend = min(nil,numObsPerChunk*j); idx = ibegin:iend; IncrementalMdl = updateMetrics(IncrementalMdl,Xil(idx,:),Yil(idx)); mc{j,:} = IncrementalMdl.Metrics{"MinimalCost",:}; mu11(j + 1) = IncrementalMdl.DistributionParameters{1,1}(1); end

`IncrementalMdl`

is an `incrementalClassificationNaiveBayes`

model object that has tracked the model performance to observations in the data stream.

Plot a trace plot of the performance metrics and ${\mu}_{11}$.

t = tiledlayout(2,1); nexttile h = plot(mc.Variables); xlim([0 nchunk]) ylabel('Minimal Cost') legend(h,mc.Properties.VariableNames) nexttile plot(mu11) ylabel('\mu_{11}') xlim([0 nchunk]) xlabel(t,'Iteration')

The cumulative loss is stable, whereas the window loss jumps throughout the training.

${\mu}_{11}$ does not change because `updateMetrics`

does not fit the model to the data.

### Configure Incremental Model to Track Performance Metrics and Specify Weights

Create a naive Bayes classification model for incremental learning by calling `incrementalClassificationNaiveBayes`

and specifying a maximum of 5 expected classes in the data. Specify tracking misclassification error rate in addition to minimal cost.

Mdl = incrementalClassificationNaiveBayes('MaxNumClasses',5,'Metrics',"classiferror");

`Mdl`

is an `incrementalClassificationNaiveBayes`

model. All its properties are read-only.

Determine whether the model is warm by querying the model property.

isWarm = Mdl.IsWarm

`isWarm = `*logical*
0

`Mdl.IsWarm`

is `0`

; therefore, `Mdl`

is not warm.

Determine the number of observations incremental fitting functions, such as `fit`

, must process before measuring the performance of the model by displaying the size of the metrics warm-up period.

numObsBeforeMetrics = Mdl.MetricsWarmupPeriod

numObsBeforeMetrics = 1000

Load the human activity data set. Randomly shuffle the data.

load humanactivity n = numel(actid); rng(1) % For reproducibility idx = randsample(n,n); X = feat(idx,:); Y = actid(idx);

For details on the data set, enter `Description`

at the command line.

Suppose that the data from a stationary subject (`Y`

<= 2) has double the quality of the data from a moving subject. Create a weight variable that assigns a weight of 2 to observations from a stationary subject and 1 to a moving subject.

W = ones(n,1) + (Y <= 2);

Implement incremental learning by performing the following actions at each iteration:

Simulate a data stream by processing a chunk of 50 observations.

Measure model performance metrics on the incoming chunk using

`updateMetrics`

. Specify the corresponding observation weights and overwrite the input model.Fit the model to the incoming chunk. Specify the corresponding observation weights and overwrite the input model.

Store ${\mu}_{11}$ and the misclassification error rate to see how they evolve during incremental learning.

% Preallocation numObsPerChunk = 50; nchunk = floor(n/numObsPerChunk); ce = array2table(zeros(nchunk,2),'VariableNames',["Cumulative" "Window"]); mu11 = zeros(nchunk,1); % Incremental learning for j = 1:nchunk ibegin = min(n,numObsPerChunk*(j-1) + 1); iend = min(n,numObsPerChunk*j); idx = ibegin:iend; Mdl = updateMetrics(Mdl,X(idx,:),Y(idx),'Weights',W(idx)); ce{j,:} = Mdl.Metrics{"ClassificationError",:}; Mdl = fit(Mdl,X(idx,:),Y(idx),'Weights',W(idx)); mu11(j) = Mdl.DistributionParameters{1,1}(1); end

Now, `Mdl`

is an `incrementalClassificationNaiveBayes`

model object trained on all the data in the stream.

To see how the parameters evolve during incremental learning, plot them on separate tiles.

t = tiledlayout(2,1); nexttile plot(mu11) ylabel('\mu_{11}') xlabel('Iteration') axis tight nexttile plot(ce.Variables) ylabel('ClassificationError') xline(numObsBeforeMetrics/numObsPerChunk,'r-.') xlim([0 nchunk]) legend(ce.Properties.VariableNames) xlabel(t,'Iteration')

mdlIsWarm = numObsBeforeMetrics/numObsPerChunk

mdlIsWarm = 20

The plot suggests that `fit`

always fits the model to the data, and `updateMetrics`

does not track the classification error until after the metrics warm-up period (20 chunks).

### Perform Conditional Training

Incrementally train a naive Bayes classification model only when its performance degrades.

Load the human activity data set. Randomly shuffle the data.

load humanactivity n = numel(actid); rng(1) % For reproducibility idx = randsample(n,n); X = feat(idx,:); Y = actid(idx);

For details on the data set, enter `Description`

at the command line.

Configure a naive Bayes classification model for incremental learning so that the maximum number of expected classes is 5, the tracked performance metric includes the misclassification error rate, and the metrics window size is 1000. Fit the configured model to the first 1000 observations.

Mdl = incrementalClassificationNaiveBayes('MaxNumClasses',5,'MetricsWindowSize',1000, ... 'Metrics','classiferror'); initobs = 1000; Mdl = fit(Mdl,X(1:initobs,:),Y(1:initobs));

`Mdl`

is an `incrementalClassificationNaiveBayes`

model object.

Perform incremental learning, with conditional fitting, by following this procedure for each iteration:

Simulate a data stream by processing a chunk of 100 observations at a time.

Update the model performance on the incoming chunk of data.

Fit the model to the chunk of data only when the misclassification error rate is greater than 0.05.

When tracking performance and fitting, overwrite the previous incremental model.

Store the misclassification error rate and the mean of the first predictor in the second class ${\mu}_{21}$ to see how they evolve during training.

Track when

`fit`

trains the model.

% Preallocation numObsPerChunk = 100; nchunk = floor((n - initobs)/numObsPerChunk); mu21 = zeros(nchunk,1); ce = array2table(nan(nchunk,2),'VariableNames',["Cumulative" "Window"]); trained = false(nchunk,1); % Incremental fitting for j = 1:nchunk ibegin = min(n,numObsPerChunk*(j-1) + 1 + initobs); iend = min(n,numObsPerChunk*j + initobs); idx = ibegin:iend; Mdl = updateMetrics(Mdl,X(idx,:),Y(idx)); ce{j,:} = Mdl.Metrics{"ClassificationError",:}; if ce{j,2} > 0.05 Mdl = fit(Mdl,X(idx,:),Y(idx)); trained(j) = true; end mu21(j) = Mdl.DistributionParameters{2,1}(1); end

`Mdl`

is an `incrementalClassificationNaiveBayes`

model object trained on all the data in the stream.

To see how the model performance and ${\mu}_{21}$ evolve during training, plot them on separate tiles.

t = tiledlayout(2,1); nexttile plot(mu21) hold on plot(find(trained),mu21(trained),'r.') xlim([0 nchunk]) ylabel('\mu_{21}') legend('\mu_{21}','Training occurs','Location','best') hold off nexttile plot(ce.Variables) xlim([0 nchunk]) ylabel('Misclassification Error Rate') legend(ce.Properties.VariableNames,'Location','best') xlabel(t,'Iteration')

The trace plot of ${\mu}_{21}$ shows periods of constant values, during which the loss within the previous observation window is at most 0.05.

## Input Arguments

`Mdl`

— Naive Bayes classification model for incremental learning

`incrementalClassificationNaiveBayes`

model object

Naive Bayes classification model for incremental learning to measure the performance
of, specified as an `incrementalClassificationNaiveBayes`

model object. You can create
`Mdl`

directly or by converting a supported, traditionally trained
machine learning model using the `incrementalLearner`

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

If `Mdl.IsWarm`

is `false`

,
`updateMetrics`

does not track the performance of the model. Before
`updateMetrics`

can track performance metrics, you must perform all
the following actions:

Fit the input model

`Mdl`

to all expected classes (see the`MaxNumClasses`

and`ClassNames`

arguments of`incrementalClassificationNaiveBayes`

).Fit the input model

`Mdl`

to`Mdl.MetricsWarmupPeriod`

observations by passing`Mdl`

and the data to`fit`

. For more details, see Performance Metrics.

`X`

— Chunk of predictor data

floating-point matrix

Chunk of predictor data to measure the model performance, specified as an
*n*-by-`Mdl.NumPredictors`

floating-point
matrix.

The length of the observation labels `Y`

and the number of
observations in `X`

must be equal;
`Y(`

is the label of observation
* j*)

*j*(row) in

`X`

.**Note**

If `Mdl.NumPredictors`

= 0, `updateMetrics`

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.NumPredictors`

,
`updateMetrics`

issues an error.

**Data Types: **`single`

| `double`

`Y`

— Chunk of labels

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

Chunk of labels with which to measure the model performance, specified as a categorical, character, or string array; logical or floating-point vector; or cell array of character vectors.

The length of the observation labels `Y`

and the number of observations in
`X`

must be equal; `Y(`

is the label of observation * j*)

*j*(row) in

`X`

.`updateMetrics`

issues an error when one or both of these conditions are met:

`Y`

contains a new label and the maximum number of classes has already been reached (see the`MaxNumClasses`

and`ClassNames`

arguments of`incrementalClassificationNaiveBayes`

).The

`ClassNames`

property of the input model`Mdl`

is nonempty, and the data types of`Y`

and`Mdl.ClassNames`

are different.

**Data Types: **`char`

| `string`

| `cell`

| `categorical`

| `logical`

| `single`

| `double`

`Weights`

— Chunk of observation weights

floating-point vector of positive values

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

weighs the observations in `X`

with the corresponding values in `Weights`

. The size of
`Weights`

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

.

By default, `Weights`

is `ones(`

.* n*,1)

For more details, including normalization schemes, see Observation Weights.

**Data Types: **`double`

| `single`

**Note**

If an observation (predictor or label) or weight contains at
least one missing (`NaN`

) value, `updateMetrics`

ignores the
observation. Consequently, `updateMetrics`

uses fewer than *n*
observations to compute the model performance, where *n* is the number of
observations in `X`

.

## Output Arguments

`Mdl`

— Updated naive Bayes classification model for incremental learning

`incrementalClassificationNaiveBayes`

model object

Updated naive Bayes classification model for incremental learning, returned as an incremental learning model object of the same data type as the input model `Mdl`

, an `incrementalClassificationNaiveBayes`

object.

If the model is not warm, `updateMetrics`

does
not compute performance metrics. As a result, the `Metrics`

property of
`Mdl`

remains completely composed of `NaN`

values. If the
model is warm, `updateMetrics`

computes the cumulative and window performance
metrics on the new data `X`

and `Y`

, and overwrites the
corresponding elements of `Mdl.Metrics`

. All other properties of the input
model `Mdl`

carry over to the output model `Mdl`

. For more details, see
Performance Metrics.

## Tips

Unlike traditional training, incremental learning might not have a separate test (holdout) set. Therefore, to treat each incoming chunk of data as a test set, pass the incremental model and each incoming chunk to

`updateMetrics`

before training the model on the same data using`fit`

.

## Algorithms

### Performance Metrics

`updateMetrics`

tracks only model performance metrics, specified by the row labels of the table in`Mdl.Metrics`

, from new data only when the incremental model is*warm*(`IsWarm`

property is`true`

).If you create an incremental model by using

`incrementalLearner`

and`MetricsWarmupPeriod`

is 0 (default for`incrementalLearner`

), the model is warm at creation.Otherwise, an incremental model becomes warm after the

`fit`

function performs both of these actions:Fit the incremental model to

`Mdl.MetricsWarmupPeriod`

observations, which is the*metrics warm-up period*.Fit the incremental model to all expected classes (see the

`MaxNumClasses`

and`ClassNames`

arguments of`incrementalClassificationNaiveBayes`

).

`Mdl.Metrics`

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`

updates the metrics at the following frequencies:`Cumulative`

— The function computes cumulative metrics since the start of model performance tracking. The function updates metrics every time you call it and bases the calculation on the entire supplied data set.`Window`

— The function computes metrics based on all observations within a window determined by the`Mdl.MetricsWindowSize`

property.`Mdl.MetricsWindowSize`

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

metrics. For example, if`Mdl.MetricsWindowSize`

is 20, the function computes 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 a buffer of length

`Mdl.MetricsWindowSize`

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

When the buffer is full, overwrite

`Mdl.Metrics.Window`

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

observations enter the buffer, and the earliest observations are removed from the buffer. For example, suppose`Mdl.MetricsWindowSize`

is 20, the metrics buffer has 10 values from a previously processed batch, and 15 values are incoming. To compose the length 20 window, the function uses 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.

### Observation Weights

For each conditional predictor distribution, `updateMetrics`

computes the weighted average and standard deviation.

If the prior class probability distribution is known (in other words, the prior distribution is not empirical), `updateMetrics`

normalizes observation weights to sum to the prior class probabilities in the respective classes. This action implies that the default observation weights are the respective prior class probabilities.

If the prior class probability distribution is empirical, the software normalizes the specified observation weights to sum to 1 each time you call `updateMetrics`

.

## Version History

**Introduced in R2021a**

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