# updateMetricsAndFit

Update performance metrics in linear incremental learning model given new data and train model

## Description

Given streaming data, `updateMetricsAndFit`

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

object) or linear binary classification (`incrementalClassificationLinear`

object) by calling `updateMetrics`

on incoming data. Then `updateMetricsAndFit`

fits the model to that data by calling `fit`

. In other words, `updateMetricsAndFit`

performs *prequential evaluation* because it treats each incoming chunk of data as a test set, and tracks performance metrics measured cumulatively and over a specified window [1].

`updateMetricsAndFit`

provides a simple way to update model performance metrics and train the model on each chunk of data. Alternatively, you can perform the operations separately by calling `updateMetrics`

and then `fit`

, which allows for more flexibility (for example, you can decide whether you need to train the model based on its performance on a chunk of data).

returns an incremental learning model `Mdl`

= updateMetricsAndFit(`Mdl`

,`X`

,`Y`

)`Mdl`

, which is the input incremental 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 following this procedure:

The input and output models have the same data type.

## Examples

### Update Performance Metrics and Train Model on Data Stream

Create a default incremental linear SVM model for binary classification.

Mdl = incrementalClassificationLinear()

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 object. All its properties are read-only.

`Mdl`

must be fit to data before you can use it to perform any other operations.

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;

Fit the incremental model to the training data by using the `updateMetricsAndFit`

function. At each iteration:

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

Overwrite the previous incremental model with a new one fitted to the incoming observations.

Store ${\beta}_{1}$, the cumulative metrics, and the window metrics 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 = updateMetricsAndFit(Mdl,X(idx,:),Y(idx)); ce{j,:} = Mdl.Metrics{"ClassificationError",:}; beta1(j + 1) = Mdl.Beta(1); end

`Mdl`

is an `incrementalClassificationLinear`

model object trained on all the data in the stream. During incremental learning and after the model is warmed up, `updateMetricsAndFit`

checks the performance of the model on the incoming observations, and then fits the model to those observations.

To see how the performance metrics and ${\beta}_{1}$ evolve during training, plot them on separate tiles.

t = tiledlayout(2,1); nexttile plot(beta1) ylabel('\beta_1') xlim([0 nchunk]) nexttile h = plot(ce.Variables); xlim([0 nchunk]) ylabel('Classification Error') xline((Mdl.EstimationPeriod + Mdl.MetricsWarmupPeriod)/numObsPerChunk,'g-.') legend(h,ce.Properties.VariableNames) xlabel(t,'Iteration')

The plot suggests that `updateMetricsAndFit`

does the following:

Fit ${\beta}_{1}$ during all incremental learning iterations.

Compute the performance metrics after the metrics warm-up period only.

Compute the cumulative metrics during each iteration.

Compute the window metrics after processing 200 observations (4 iterations).

### Specify Orientation of Observations and Observation Weights

Train a linear regression model by using `fitrlinear`

, convert it to an incremental learner, track its performance, and fit it to streaming data. Carry over training options from traditional to incremental learning.

**Load and Preprocess Data**

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

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

Suppose that the data collected from Manhattan (`BOROUGH`

= `1`

) was collected using a new method that doubles its quality. Create a weight variable that attributes 2 to observations collected from Manhattan, and 1 to all other observations.

n = size(NYCHousing2015,1); NYCHousing2015.W = ones(n,1) + (NYCHousing2015.BOROUGH == 1);

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. Transpose the resulting predictor matrix.

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

**Train Linear Regression Model**

Fit a linear regression model to a random sample of half the data.

idxtt = randsample([true false],n,true); TTMdl = fitrlinear(X(:,idxtt),Y(idxtt),'ObservationsIn','columns', ... 'Weights',NYCHousing2015.W(idxtt))

TTMdl = RegressionLinear ResponseName: 'Y' ResponseTransform: 'none' Beta: [313x1 double] Bias: 0.1116 Lambda: 2.1977e-05 Learner: 'svm' Properties, Methods

`TTMdl`

is a `RegressionLinear`

model object representing a traditionally trained linear regression model.

**Convert Trained Model**

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

IncrementalMdl = incrementalLearner(TTMdl)

IncrementalMdl = incrementalRegressionLinear IsWarm: 1 Metrics: [1x2 table] ResponseTransform: 'none' Beta: [313x1 double] Bias: 0.1116 Learner: 'svm' Properties, Methods

**Track Performance Metrics and Fit Model**

Perform incremental learning on the rest of the data by using the `updateMetricsAndFit`

function. At each iteration:

Simulate a data stream by processing a chunk of 500 observations.

Call

`updateMetricsAndFit`

to update the cumulative and window epsilon insensitive loss of the model given the incoming chunk of observations, and then fit the model to the data. Overwrite the previous incremental model with a new one. Specify that the observations are oriented in columns, and specify the observation weights.Store the losses and last estimated coefficient ${\beta}_{313}$.

% Preallocation idxil = ~idxtt; nil = sum(idxil); numObsPerChunk = 500; nchunk = floor(nil/numObsPerChunk); ei = array2table(zeros(nchunk,2),'VariableNames',["Cumulative" "Window"]); beta313 = [IncrementalMdl.Beta(end); zeros(nchunk,1)]; Xil = X(:,idxil); Yil = Y(idxil); Wil = NYCHousing2015.W(idxil); % Incremental fitting for j = 1:nchunk ibegin = min(nil,numObsPerChunk*(j-1) + 1); iend = min(nil,numObsPerChunk*j); idx = ibegin:iend; IncrementalMdl = updateMetricsAndFit(IncrementalMdl,Xil(:,idx),Yil(idx), ... 'ObservationsIn','columns','Weights',Wil(idx)); ei{j,:} = IncrementalMdl.Metrics{"EpsilonInsensitiveLoss",:}; beta313(j+1) = IncrementalMdl.Beta(end); end

`IncrementalMdl`

is an `incrementalRegressionLinear`

model object trained on all the data in the stream.

Plot a trace plot of the performance metrics and estimated coefficient ${\beta}_{313}$.

t = tiledlayout(2,1); nexttile h = plot(ei.Variables); xlim([0 nchunk]) ylabel('Epsilon Insensitive Loss') legend(h,ei.Properties.VariableNames) nexttile plot(beta313) ylabel('\beta_{313}') xlim([0 nchunk]) xlabel(t,'Iteration')

The cumulative loss gradually changes with each iteration (chunk of 500 observations), whereas the window loss jumps. Because the metrics window is 200 by default, `updateMetricsAndFit`

measures the performance based on the latest 200 observations in each 500 observation chunk.

${\beta}_{313}$ changes, but levels off quickly, as `fit`

processes chunks of observations.

## Input Arguments

`Mdl`

— Incremental learning model

`incrementalClassificationLinear`

model object | `incrementalRegressionLinear`

model object

Incremental learning model whose performance is measured and then the model is fit
to data, 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`

,
`updateMetricsAndFit`

does not track the performance of the model. For more
details, see Performance Metrics.

`X`

— Chunk of predictor data

floating-point matrix

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

predictor variables. The value of the `ObservationsIn`

name-value
argument 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 labels `Y`

and the number of
observations in `X`

must be equal;
`Y(`

is the label of observation
* j*)

*j*(row or column) in

`X`

.**Note**

If

`Mdl.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.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 responses (or labels)

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

Chunk of responses (or labels) with which to measure the model performance and then fit the model to, 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*)

*j*(row or column) in

`X`

.For classification problems:

`updateMetricsAndFit`

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`

,`updateMetricsAndFit`

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 contains at least one missing (

`NaN`

) value,`updateMetricsAndFit`

ignores the observation. Consequently,`updateMetricsAndFit`

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

.The chunk size

*n*and the stochastic gradient descent (SGD) hyperparameter mini-batch size (`Mdl.BatchSize`

) can be different values, and*n*does not have to be an exact multiple of the mini-batch size. If*n*<`Mdl.BatchSize`

,`updateMetricsAndFit`

uses the*n*available observations when it applies SGD. If*n*>`Mdl.BatchSize`

, the function updates the model with a mini-batch of the specified size multiple times, and then uses the rest of the observations for the last mini-batch. The number of observations for the last mini-batch can be smaller than`Mdl.BatchSize`

.

### 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.

*
Before R2021a, use commas to separate each name and value, and enclose*
`Name`

*in quotes.*

**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`

— 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 weights

floating-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. `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)

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

**Data Types: **`double`

| `single`

## Output Arguments

`Mdl`

— Updated incremental learning model

`incrementalClassificationLinear`

model object | `incrementalRegressionLinear`

model object

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

, either `incrementalClassificationLinear`

or `incrementalRegressionLinear`

.

When you call `updateMetricsAndFit`

, the following conditions apply:

If the model is not warm,

`updateMetricsAndFit`

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

property of`Mdl`

remains completely composed of`NaN`

values. For more details, see Performance Metrics.If

`Mdl.EstimationPeriod`

> 0,`updateMetricsAndFit`

estimates hyperparameters using the first`Mdl.EstimationPeriod`

observations passed to it; the function does not train the input model using that data. However, if an incoming chunk of*n*observations is greater than or equal to the number of observations remaining in the estimation period*m*,`updateMetricsAndFit`

estimates hyperparameters using the first*n*–*m*observations, and fits the input model to the remaining*m*observations. Consequently, the software updates the`Beta`

and`Bias`

properties, hyperparameter properties, and recordkeeping properties such as`NumTrainingObservations`

.

For classification problems, if the `ClassNames`

property of the input model `Mdl`

is an empty array, `updateMetricsAndFit`

sets the `ClassNames`

property of the output model `Mdl`

to `unique(Y)`

.

## Algorithms

### Performance Metrics

`updateMetricsAndFit`

tracks 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 an incremental fitting, like`updateMetricsAndFit`

, fits the incremental model to`Mdl.MetricsWarmupPeriod`

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

`Mdl.EstimationPeriod`

> 0,`updateMetricsAndFit`

estimates 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,`updateMetricsAndFit`

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 the function 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 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.

The software omits an observation with a

`NaN`

prediction (score for classification and response for regression) when computing the`Cumulative`

and`Window`

performance metric values.

### Observation Weights

For classification problems, if the prior class probability distribution is known (in other words, the prior distribution is not empirical), `updateMetricsAndFit`

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 `updateMetricsAndFit`

.

## References

[1] Bifet, Albert, Ricard Gavaldá, Geoffrey Holmes, and Bernhard Pfahringer. *Machine Learning for Data Streams with Practical Example in MOA*. Cambridge, MA: The MIT Press, 2007.

## Extended Capabilities

### C/C++ Code Generation

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

Usage notes and limitations:

Use

`saveLearnerForCoder`

,`loadLearnerForCoder`

, and`codegen`

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

function. Save a trained model by using`saveLearnerForCoder`

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

and calls the`updateMetricsAndFit`

function. Then use`codegen`

to generate code for the entry-point function.To generate single-precision C/C++ code for

`updateMetricsAndFit`

, specify the name-value argument`"DataType","single"`

when you call the`loadLearnerForCoder`

function.This table contains notes about the arguments of

`updateMetricsAndFit`

. 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`updateMetricsAndFit`

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, the fitted coefficients computed in MATLAB and 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.

## Version History

**Introduced in R2020b**

## See Also

### Objects

### Functions

### Topics

- Incremental Learning Overview
- Configure Incremental Learning Model
- Implement Incremental Learning for Classification Using Succinct Workflow
- Initialize Incremental Learning Model from Logistic Regression Model Trained in Classification Learner
- Initialize Incremental Learning Model from SVM Regression Model Trained in Regression Learner

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