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Update performance metrics in linear model for incremental learning given new data

Given streaming data, `updateMetrics`

measures the performance of a configured incremental learning model for linear regression (`incrementalRegressionLinear`

object) or linear binary classification (`incrementalClassificationLinear`

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 an incremental learning model `Mdl`

= updateMetrics(`Mdl`

,`X`

,`Y`

)`Mdl`

, which is the input incremental learning model `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.

The input and output models have the same data type.

Train a linear model for binary classification by using `fitclinear`

, 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.

Responses can be one of five classes: Sitting, Standing, Walking, Running, or Dancing. Dichotomize the response by identifying whether the subject is moving (`actid`

> 2).

Y = Y > 2;

**Train Linear Model for Binary Classification**

Fit a linear model for binary classification to a random sample of half the data.

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

TTMdl = ClassificationLinear ResponseName: 'Y' ClassNames: [0 1] ScoreTransform: 'none' Beta: [60x1 double] Bias: -0.3965 Lambda: 8.2967e-05 Learner: 'svm' Properties, Methods

`TTMdl`

is a `ClassificationLinear`

model object representing a traditionally trained linear model for binary classification.

**Convert Trained Model**

Convert the traditionally trained classification model to a binary classification linear model for incremental learning.

IncrementalMdl = incrementalLearner(TTMdl)

IncrementalMdl = incrementalClassificationLinear IsWarm: 1 Metrics: [1x2 table] ClassNames: [0 1] ScoreTransform: 'none' Beta: [60x1 double] Bias: -0.3965 Learner: 'svm' Properties, Methods

IncrementalMdl.IsWarm

`ans = `*logical*
1

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 classification error 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 classification error and first coefficient ${\beta}_{1}$.

% Preallocation idxil = ~idxtt; nil = sum(idxil); numObsPerChunk = 50; nchunk = floor(nil/numObsPerChunk); ce = array2table(zeros(nchunk,2),'VariableNames',["Cumulative" "Window"]); beta1 = [IncrementalMdl.Beta(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)); ce{j,:} = IncrementalMdl.Metrics{"ClassificationError",:}; beta1(j + 1) = IncrementalMdl.Beta(1); end

`IncrementalMdl`

is an `incrementalClassificationLinear`

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

Plot a trace plot of the performance metrics and estimated coefficient ${\beta}_{1}$.

figure; subplot(2,1,1) h = plot(ce.Variables); xlim([0 nchunk]); ylabel('Classification Error') legend(h,ce.Properties.VariableNames) subplot(2,1,2) plot(beta1) ylabel('\beta_1') xlim([0 nchunk]); xlabel('Iteration')

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

${\beta}_{1}$ does not change because `updateMetrics`

does not fit the model to the data.

Create a incremental linear SVM model for binary classification. Specify an estimation period of 5,000 observations and the SGD solver.

Mdl = incrementalClassificationLinear('EstimationPeriod',5000,'Solver','sgd')

Mdl = incrementalClassificationLinear IsWarm: 0 Metrics: [1x2 table] ClassNames: [1x0 double] ScoreTransform: 'none' Beta: [0x1 double] Bias: 0 Learner: 'svm' Properties, Methods

`Mdl`

is an `incrementalClassificationLinear`

model. All its properties are read-only.

Determine whether the model is warm and the size of the metrics warm-up period by querying model properties.

isWarm = Mdl.IsWarm

`isWarm = `*logical*
0

mwp = Mdl.MetricsWarmupPeriod

mwp = 1000

`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.

numObsBeforeMetrics = Mdl.MetricsWarmupPeriod + Mdl.EstimationPeriod

numObsBeforeMetrics = 6000

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.

Responses can be one of five classes: Sitting, Standing, Walking, Running, or Dancing. Dichotomize the response by identifying whether the subject is moving (`actid`

> 2).

Y = Y > 2;

Perform incremental learning. At each iteration, perform the following actions:

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

Measure model performance metrics on the incoming chunk using

`updateMetrics`

. Overwrite the input model.Fit the model to the incoming chunk. Overwrite the input model.

Store ${\beta}_{1}$ 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"]); beta1 = zeros(nchunk,1); % Incremental fitting 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)); ce{j,:} = Mdl.Metrics{"ClassificationError",:}; Mdl = fit(Mdl,X(idx,:),Y(idx)); beta1(j) = Mdl.Beta(1); end

`IncrementalMdl`

is an `incrementalClassificationLinear`

model object trained on all the data in the stream.

To see how the parameters evolved during incremental learning, plot them on separate subplots.

figure; subplot(2,1,1) plot(beta1) ylabel('\beta_1') xline(Mdl.EstimationPeriod/numObsPerChunk,'r-.'); xlabel('Iteration') axis tight subplot(2,1,2) plot(ce.Variables); ylabel('ClassificationError') xline(Mdl.EstimationPeriod/numObsPerChunk,'r-.'); xline(numObsBeforeMetrics/numObsPerChunk,'g-.'); xlabel('Iteration') xlim([0 nchunk]); legend(ce.Properties.VariableNames)

mdlIsWarm = numObsBeforeMetrics/numObsPerChunk

mdlIsWarm = 120

The plot suggests that `fit`

does not fit the model to the data or update the parameters until after the estimation period. Also, `updateMetrics`

does not track the classification error until after the estimation and metrics warm-up periods (120 chunks).

Incrementally train a linear regression model only when its performance degrades.

Load and shuffle the 2015 NYC housing data set. For more details on the data, see NYC Open Data.

load NYCHousing2015 rng(1) % For reproducibility n = size(NYCHousing2015,1); shuffidx = randsample(n,n); NYCHousing2015 = NYCHousing2015(shuffidx,:);

Extract the response variable `SALEPRICE`

from the table. For numerical stability, scale `SALEPRICE`

by `1e6`

.

Y = NYCHousing2015.SALEPRICE/1e6; NYCHousing2015.SALEPRICE = [];

Create dummy variable matrices from the categorical predictors.

catvars = ["BOROUGH" "BUILDINGCLASSCATEGORY" "NEIGHBORHOOD"]; dumvarstbl = varfun(@(x)dummyvar(categorical(x)),NYCHousing2015,... 'InputVariables',catvars); dumvarmat = table2array(dumvarstbl); NYCHousing2015(:,catvars) = [];

Treat all other numeric variables in the table as linear predictors of sales price. Concatenate the matrix of dummy variables to the rest of the predictor data, and transpose the data to speed up computations.

idxnum = varfun(@isnumeric,NYCHousing2015,'OutputFormat','uniform'); X = [dumvarmat NYCHousing2015{:,idxnum}]';

Configure a linear regression model for incremental learning so that it does not have an estimation or metrics warm-up period. Specify a metrics window size of 1000 observations. Fit the configured model to the first 100 observations, and specify that the observations are oriented along the columns of the data.

Mdl = incrementalRegressionLinear('EstimationPeriod',0,'MetricsWarmupPeriod',0,... 'MetricsWindowSize',1000); numObsPerChunk = 100; Mdl = fit(Mdl,X(:,1:numObsPerChunk),Y(1:numObsPerChunk),'ObservationsIn','columns');

`Mdl`

is an `incrementalRegressionLinear`

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.

Update the model performance by computing the epsilon insensitive loss, within a 200 observation window. Specify that the observations are oriented along the columns of the data.

Fit the model to the chunk of data only when the loss more than doubles from the minimum loss experienced. Specify that the observations are oriented along the columns of the data.

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

Store the epsilon insensitive loss and ${\beta}_{313}$ to see the how the loss and coefficient evolve during training.

Track when

`fit`

trains the model.

% Preallocation n = numel(Y) - numObsPerChunk; nchunk = floor(n/numObsPerChunk); beta313 = zeros(nchunk,1); ei = array2table(nan(nchunk,2),'VariableNames',["Cumulative" "Window"]); trained = false(nchunk,1); % Incremental fitting for j = 2:nchunk ibegin = min(n,numObsPerChunk*(j-1) + 1); iend = min(n,numObsPerChunk*j); idx = ibegin:iend; Mdl = updateMetrics(Mdl,X(:,idx),Y(idx),'ObservationsIn','columns'); ei{j,:} = Mdl.Metrics{"EpsilonInsensitiveLoss",:}; minei = min(ei{:,2}); pdiffloss = (ei{j,2} - minei)/minei*100; if pdiffloss > 100 Mdl = fit(Mdl,X(:,idx),Y(idx),'ObservationsIn','columns'); trained(j) = true; end beta313(j) = Mdl.Beta(end); end

`Mdl`

is an `incrementalRegressionLinear`

model object trained on all the data in the stream.

To see how the model performance and ${\beta}_{313}$ evolved during training, plot them on separate subplots.

subplot(2,1,1) plot(beta313) hold on plot(find(trained),beta313(trained),'r.') ylabel('\beta_{313}') xline(Mdl.EstimationPeriod/numObsPerChunk,'r-.'); legend('\beta_{313}','Training occurs','Location','southeast') hold off subplot(2,1,2) plot(ei.Variables) ylabel('Epsilon Insensitive Loss') xline(Mdl.EstimationPeriod/numObsPerChunk,'r-.'); xlabel('Iteration') legend(ei.Properties.VariableNames)

The trace plot of ${\beta}_{313}$ shows periods of constant values, during which the loss did not double from the minimum experienced.

`Mdl`

— Incremental learning model whose performance is measured`incrementalClassificationLinear`

model object | `incrementalRegressionLinear`

model objectIncremental learning model whose performance is measured, specified as an `incrementalClassificationLinear`

or `incrementalRegressionLinear`

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. You must fit `Mdl`

to `Mdl.EstimationPeriod + Mdl.MetricsWarmupPeriod`

observations by passing `Mdl`

and the data to `fit`

before `updateMetrics`

can track performance metrics. For more details, see Algorithms.

`X`

— Chunk of predictor datafloating-point matrix

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

predictor variables. The value of the `'ObservationsIn'`

name-value pair argument determines the orientation of the variables and observations.

The length of the observation labels `Y`

and the number of observations in `X`

must be equal; `Y(`

is the label of observation * j*)

`X`

.**Note**

If

`Mdl.NumPredictors`

= 0,`updateMetrics`

infers the number of predictors from`X`

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

,`updateMetrics`

issues an error.`updateMetrics`

supports only floating-point input predictor data. If the input model`Mdl`

represents a converted, traditionally trained model fit to categorical data, use`dummyvar`

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

**Data Types: **`single`

| `double`

`Y`

— Chunk of labelscategorical 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 for classification problems; or a floating-point vector for regression problems.

The length of the observation labels `Y`

and the number of observations in `X`

must be equal; `Y(`

is the label of observation * j*)

`X`

.For classification problems:

`updateMetrics`

supports binary classification only.When the

`ClassNames`

property of the input model`Mdl`

is nonempty, the following conditions apply:If

`Y`

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

,`updateMetrics`

issues an error.The data type of

`Y`

and`Mdl.ClassNames`

must be the same.

**Data Types: **`char`

| `string`

| `cell`

| `categorical`

| `logical`

| `single`

| `double`

**Note**

If an observation (predictor or label) or weight `Weight`

contains at least one missing (`NaN`

) value, `updateMetrics`

ignores the observation. Consequently, `updateMetrics`

uses fewer than *n* observations to compute the model performance.

Specify optional
comma-separated pairs of `Name,Value`

arguments. `Name`

is
the argument name and `Value`

is the corresponding value.
`Name`

must appear inside quotes. You can specify several name and value
pair arguments in any order as
`Name1,Value1,...,NameN,ValueN`

.

`'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'`

— Predictor data observation dimension`'rows'`

(default) | `'columns'`

Predictor data observation dimension, specified as the comma-separated pair consisting of `'ObservationsIn'`

and `'columns'`

or `'rows'`

.

**Data Types: **`char`

| `string`

`'Weights'`

— Chunk of observation weightsfloating-point vector of positive values

Chunk of observation weights, specified as the comma-separated pair consisting of `'Weights'`

and 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*, which is 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`

`Mdl`

— Updated incremental learning model`incrementalClassificationLinear`

model object | `incrementalRegressionLinear`

model objectUpdated incremental learning model, returned as an incremental learning model object of the same data type as the input model `Mdl`

, either `incrementalClassificationLinear`

or `incrementalRegressionLinear`

.

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 Algorithms.

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`

.

`updateMetrics`

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

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

property is`true`

). An incremental model is warm after the`fit`

function fits the incremental model to`Mdl.MetricsWarmupPeriod`

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

`Mdl.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`

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:

For each specified metric, store a buffer of length

`Mdl.MetricsWindowSize`

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

When the buffer is filled, overwrite

`Mdl.Metrics.Window`

with the weighted average performance in the metrics window. If the buffer is overfilled 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.

For classification problems, 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 observation weights are the respective prior class probabilities by default.

For regression problems or if the prior class probability distribution is empirical, the software normalizes the specified observation weights to sum to 1 each time you call `updateMetrics`

.

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

Use

`saveLearnerForCoder`

,`loadLearnerForCoder`

, and`codegen`

(MATLAB Coder) to generate code for the`updateMetrics`

function. Save a trained model by using`saveLearnerForCoder`

. Define an entry-point function that loads the saved model by using`loadLearnerForCoder`

and calls the`updateMetrics`

function. Then use`codegen`

to generate code for the entry-point function.To generate single-precision C/C++ code for updateMetrics, specify the name-value argument

`'DataType','single'`

when you call the`loadLearnerForCoder`

function.This table contains notes about the arguments of

`updateMetrics`

. Arguments not included in this table are fully supported.Argument Notes and Limitations `Mdl`

For usage notes and limitations of the model object, see

`incrementalClassificationLinear`

or`incrementalRegressionLinear`

.`X`

Batch-to-batch, the number of observations can be a variable size, but must equal the number of observations in

`Y`

.The number of predictor variables must equal to

`Mdl.NumPredictors`

.`X`

must be`single`

or`double`

.

`Y`

Batch-to-batch, the number of observations can be a variable size, but must equal the number of observations in

`X`

.For classification problems, all labels in

`Y`

must be represented in`Mdl.ClassNames`

.`Y`

and`Mdl.ClassNames`

must have the same data type.

The following restrictions apply:

If you configure

`Mdl`

to shuffle data (`Mdl.Shuffle`

is`true`

, or`Mdl.Solver`

is`'sgd'`

or`'asgd'`

), the`updateMetrics`

function randomly shuffles each incoming batch of observations before it fits the model to the batch. The order of the shuffled observations might not match the order generated by MATLAB^{®}. Therefore, if you fit`Mdl`

before updating the performance metrics, the metrics computed in MATLAB and those computed by the generated code might not be equal.Use a homogeneous data type for all floating-point input arguments and object properties, specifically, either

`single`

or`double`

.

For more information, see Introduction to Code Generation.

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