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updateMetrics

Update incremental learning model performance metrics on new data

Description

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 it 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. In contrast, you can additionally, and subsequently, train the model on the data as it arrives, in one call, by using updateMetricsAndFit instead.

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

example

Mdl = updateMetrics(Mdl,X,Y) returns an incremental learning model Mdl, which is the input incremental learning model Mdl modified to contain the model performance 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 are the same data type.

example

Mdl = updateMetrics(Mdl,X,Y,Name,Value) uses additional options specified by one or more name-value pair arguments. For example, you can specify observation weights or that the columns of the predictor data matrix correspond to observations.

Examples

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Train a linear model for binary classification by using fitclinear, convert it to an incremental learner, and then track its performance to streaming chunks of data.

Load and Preprocess Data

Load the human activity data set. Randomly shuffle the data. Orient the observations of the predictor data in columns.

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, display Description.

Responses can be one of five classes. 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: [60×1 double]
              Bias: -0.2998
            Lambda: 8.2967e-05
           Learner: 'svm'


  Properties, Methods

TTMdl is a ClassificationLinear model object representing a traditionally trained linear model for binary classification model.

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: [1×2 table]
        ClassNames: [0 1]
    ScoreTransform: 'none'
              Beta: [60×1 double]
              Bias: -0.2998
           Learner: 'svm'


  Properties, Methods

IncrementalMdl.IsWarm
ans = logical
   1

The incremental model is warm. Therefore, updateMetrics can track model performance metrics given data.

Separately Track Performance Metrics and Fit Model

Use updateMetrics to track the model performance on the rest of the data. Simulate a data stream by processing 50 observations at a time. At each iteration:

  1. 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.

  2. Store the classification error and first coefficient β1.

% 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 plots of the performance metrics and estimated coefficient β1.

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.

β1 does not change because updateMetrics does not fit the model to the data.

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

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

            IsWarm: 0
           Metrics: [1×2 table]
        ClassNames: [1×0 double]
    ScoreTransform: 'none'
              Beta: [0×1 double]
              Bias: 0
           Learner: 'svm'


  Properties, Methods

isWarm = Mdl.IsWarm
isWarm = logical
   0

mwp = Mdl.MetricsWarmupPeriod
mwp = 1000
numObsBeforeMetrics = Mdl.MetricsWarmupPeriod + Mdl.EstimationPeriod
numObsBeforeMetrics = 6000

Mdl is an incrementalClassificationLinear model. All its properties are read-only.

Mdl.IsWarm is 0, therefore, Mdl is not warm. This characteristic means that you must pass the model to fit and train the model on 6000 observations, in this case, before updateMetrics can track metrics.

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, display Description.

Responses can be one of five classes. Dichotomize the response by identifying whether the subject is moving (actid > 2).

Y = Y > 2;

Use fit to fit the incremental model to the training data, in chunks of 50 observations at a time, to simulate a data stream. At each iteration:

  • Process 50 observations.

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

  • Store β1, the number of training observations, and the prior probability of whether the subject moved (Y = true) to monitor their evolution during incremental training.

% 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 that has experienced 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 nor update the parameters until after the estimation period, and 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, and the metrics window size is 1000. Fit the configured model to the first 100 observations, 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 at a time.

  • 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 β313 to see the evolution of the loss and coefficient.

  • 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 that has experienced all the data in the stream.

To see how the model performance and β313 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 β313 shows periods of constant values, during which the loss did not double from the minimum experienced.

Input Arguments

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Incremental learning model whose performance is measured, specified as a incrementalClassificationLinear or incrementalRegressionLinear model object, created directly or by converting a supported traditionally trained machine learning model using incrementalLearner. For more details, see the reference page corresponding to the learning problem.

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.

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(j) is the label of observation (row or column) j in 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

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, and 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(j) is the label of observation j (row or column) in 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.

Name-Value Pair Arguments

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.

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.

Predictor data observation dimension, specified as the comma-separated pair consisting of 'ObservationsIn' and 'columns' or 'rows'.

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

Output Arguments

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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.

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. Otherwise, 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 Mdl. For more details, see Algorithms.

For classification problems, if the ClassNames property of the input model Mdl is an empty array, updateMetrics sets the ClassNames property of the output model Mdl to unique(Y).

Tips

  • Unlike traditional training, a separate test (hold out) set might not exist for incremental learning. 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

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Performance Metrics

  • 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 fit fit 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, and, 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 oriented along rows. When the incremental model is warm, updateMetrics 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.

    • Window — The functions compute metrics based on all observations within a window determined by the Mdl.MetricsWindowSize name-value pair argument. Mdl.MetricsWindowSize also determines the frequency at which the software updates Window metrics. For example, if Mdl.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 using the following process:

      1. For each specified metric, store a buffer of length Mdl.MetricsWindowSize and a buffer of observation weights.

      2. 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.

      3. 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 functions use the measurements from the 15 incoming observations and the latest 5 measurements from the previous batch.

Observation Weights

For classification problems, if the prior class probability distribution is known (Mdl.Prior is not composed of NaN values), 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 unknown, the software normalizes the specified observation weights to sum to 1 each time you call updateMetrics.

Introduced in R2020b