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incrementalLearner

Convert kernel model for binary classification to incremental learner

Since R2022a

    Description

    IncrementalMdl = incrementalLearner(Mdl) returns a binary Gaussian kernel classification model for incremental learning, IncrementalMdl, using the traditionally trained kernel model object or kernel model template object in Mdl.

    If you specify a traditionally trained model, then its property values reflect the knowledge gained from Mdl (parameters and hyperparameters of the model). Therefore, IncrementalMdl can predict labels given new observations, and it is warm, meaning that its predictive performance is tracked.

    example

    IncrementalMdl = incrementalLearner(Mdl,Name=Value) uses additional options specified by one or more name-value arguments. Some options require you to train IncrementalMdl before its predictive performance is tracked. For example, MetricsWarmupPeriod=50,MetricsWindowSize=100 specifies a preliminary incremental training period of 50 observations before performance metrics are tracked, and specifies processing 100 observations before updating the window performance metrics.

    example

    Examples

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    Train a kernel classification model for binary learning by using fitckernel, and then convert it to an incremental learner.

    Load and Preprocess Data

    Load the human activity data set.

    load humanactivity

    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 = actid > 2;

    Train Kernel Classification Model

    Fit a kernel classification model to the entire data set.

    Mdl = fitckernel(feat,Y)
    Mdl = 
      ClassificationKernel
                  ResponseName: 'Y'
                    ClassNames: [0 1]
                       Learner: 'svm'
        NumExpansionDimensions: 2048
                   KernelScale: 1
                        Lambda: 4.1537e-05
                 BoxConstraint: 1
    
    
      Properties, Methods
    
    

    Mdl is a ClassificationKernel model object representing a traditionally trained kernel classification model.

    Convert Trained Model

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

    IncrementalMdl = incrementalLearner(Mdl,Solver="sgd",LearnRate=1)
    IncrementalMdl = 
      incrementalClassificationKernel
    
                        IsWarm: 1
                       Metrics: [1×2 table]
                    ClassNames: [0 1]
                ScoreTransform: 'none'
        NumExpansionDimensions: 2048
                   KernelScale: 1
    
    
      Properties, Methods
    
    

    IncrementalMdl is an incrementalClassificationKernel model object prepared for incremental learning.

    • The incrementalLearner function initializes the incremental learner by passing model parameters to it, along with other information Mdl extracted from the training data.

    • IncrementalMdl is warm (IsWarm is 1), which means that incremental learning functions can start tracking performance metrics.

    • incrementalClassificationKernel trains the model using the adaptive scale-invariant solver, whereas fitckernel trained Mdl using the Limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) solver.

    Predict Responses

    An incremental learner created from converting a traditionally trained model can generate predictions without further processing.

    Predict classification scores for all observations using both models.

    [~,ttscores] = predict(Mdl,feat);
    [~,ilscores] = predict(IncrementalMdl,feat);
    compareScores = norm(ttscores(:,1) - ilscores(:,1))
    compareScores = 
    0
    

    The difference between the scores generated by the models is 0.

    Use a trained kernel classification model to initialize an incremental learner. Prepare the incremental learner by specifying a metrics warm-up period and a metrics window size.

    Load the human activity data set.

    load humanactivity

    For details on the data set, enter Description at the command line.

    Responses can be one of five classes: Sitting, Standing, Walking, Running, and Dancing. Dichotomize the response by identifying whether the subject is moving (actid > 2).

    Y = actid > 2;

    Because the data set is grouped by activity, shuffle it for simplicity. Then, randomly split the data in half: the first half for training a model traditionally, and the second half for incremental learning.

    n = numel(Y);
    
    rng(1) % For reproducibility
    cvp = cvpartition(n,Holdout=0.5);
    idxtt = training(cvp);
    idxil = test(cvp);
    shuffidx = randperm(n);
    X = feat(shuffidx,:);
    Y = Y(shuffidx);
    
    % First half of data
    Xtt = X(idxtt,:);
    Ytt = Y(idxtt);
    
    % Second half of data
    Xil = X(idxil,:);
    Yil = Y(idxil);

    Fit a kernel classification model to the first half of the data.

    Mdl = fitckernel(Xtt,Ytt);

    Convert the traditionally trained kernel classification model to a model for incremental learning. Specify the following:

    • A performance metrics warm-up period of 2000 observations

    • A metrics window size of 500 observations

    • Use of classification error and hinge loss to measure the performance of the model

    IncrementalMdl = incrementalLearner(Mdl, ...
        MetricsWarmupPeriod=2000,MetricsWindowSize=500, ...
        Metrics=["classiferror","hinge"]);

    Fit the incremental model to the second half of the data by using the updateMetricsAndFit function. At each iteration:

    • Simulate a data stream by processing 20 observations at a time.

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

    • Store the cumulative metrics, window metrics, and number of training observations to see how they evolve during incremental learning.

    % Preallocation
    nil = numel(Yil);
    numObsPerChunk = 20;
    nchunk = ceil(nil/numObsPerChunk);
    ce = array2table(zeros(nchunk,2),VariableNames=["Cumulative","Window"]);
    hinge = array2table(zeros(nchunk,2),VariableNames=["Cumulative","Window"]); 
    numtrainobs = [zeros(nchunk,1)];
    
    % 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));
        ce{j,:} = IncrementalMdl.Metrics{"ClassificationError",:};
        hinge{j,:} = IncrementalMdl.Metrics{"HingeLoss",:};
        numtrainobs(j) = IncrementalMdl.NumTrainingObservations;
    end

    IncrementalMdl is an incrementalClassificationKernel 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.

    Plot a trace plot of the number of training observations and the performance metrics on separate tiles.

    t = tiledlayout(3,1);
    nexttile
    plot(numtrainobs)
    xlim([0 nchunk])
    ylabel(["Number of","Training Observations"])
    xline(IncrementalMdl.MetricsWarmupPeriod/numObsPerChunk,"--")
    nexttile
    plot(ce.Variables)
    xlim([0 nchunk])
    ylabel("Classification Error")
    xline(IncrementalMdl.MetricsWarmupPeriod/numObsPerChunk,"--")
    legend(ce.Properties.VariableNames,Location="best")
    nexttile
    plot(hinge.Variables)
    xlim([0 nchunk])
    ylabel("Hinge Loss")
    xline(IncrementalMdl.MetricsWarmupPeriod/numObsPerChunk,"--")
    xlabel(t,"Iteration")

    Figure contains 3 axes objects. Axes object 1 with ylabel Number of Training Observations contains 2 objects of type line, constantline. Axes object 2 with ylabel Classification Error contains 3 objects of type line, constantline. These objects represent Cumulative, Window. Axes object 3 with ylabel Hinge Loss contains 3 objects of type line, constantline.

    The plot suggests that updateMetricsAndFit does the following:

    • Fit the model 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 500 observations (25 iterations).

    The default solver for incrementalClassificationKernel is the adaptive scale-invariant solver, which does not require hyperparameter tuning before you fit a model. However, if you specify either the standard stochastic gradient descent (SGD) or average SGD (ASGD) solver instead, you can also specify an estimation period, during which the incremental fitting functions tune the learning rate.

    Load the human activity data set.

    load humanactivity

    For details on the data set, enter Description at the command line.

    Responses can be one of five classes: Sitting, Standing, Walking, Running, and Dancing. Dichotomize the response by identifying whether the subject is moving (actid > 2).

    Y = actid > 2;

    Randomly split the data in half: the first half for training a model traditionally, and the second half for incremental learning.

    n = numel(Y);
    
    rng(1) % For reproducibility
    cvp = cvpartition(n,Holdout=0.5);
    idxtt = training(cvp);
    idxil = test(cvp);
    
    % First half of data 
    Xtt = feat(idxtt,:);
    Ytt = Y(idxtt);
    
    % Second half of data
    Xil = feat(idxil,:);
    Yil = Y(idxil);

    Fit a kernel classification model to the first half of the data.

    TTMdl = fitckernel(Xtt,Ytt);

    Convert the traditionally trained kernel classification model to a model for incremental learning. Specify the standard SGD solver and an estimation period of 2000 observations (the default is 1000 when a learning rate is required).

    IncrementalMdl = incrementalLearner(TTMdl,Solver="sgd",EstimationPeriod=2000);

    IncrementalMdl is an incrementalClassificationKernel model object configured for incremental learning.

    Fit the incremental model to the second half of the data by using the fit function. At each iteration:

    • Simulate a data stream by processing 10 observations at a time.

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

    • Store the initial learning rate and number of training observations to see how they evolve during training.

    % Preallocation
    nil = numel(Yil);
    numObsPerChunk = 10;
    nchunk = floor(nil/numObsPerChunk);
    learnrate = [zeros(nchunk,1)];
    numtrainobs = [zeros(nchunk,1)];
    
    % Incremental fitting
    for j = 1:nchunk
        ibegin = min(nil,numObsPerChunk*(j-1) + 1);
        iend   = min(nil,numObsPerChunk*j);
        idx = ibegin:iend;
        IncrementalMdl = fit(IncrementalMdl,Xil(idx,:),Yil(idx));
        learnrate(j) = IncrementalMdl.SolverOptions.LearnRate;
        numtrainobs(j) = IncrementalMdl.NumTrainingObservations;
    end

    IncrementalMdl is an incrementalClassificationKernel model object trained on all the data in the stream.

    Plot a trace plot of the number of training observations and the initial learning rate on separate tiles.

    t = tiledlayout(2,1);
    nexttile
    plot(numtrainobs)
    xlim([0 nchunk])
    xline(IncrementalMdl.EstimationPeriod/numObsPerChunk,"-.");
    ylabel("Number of Training Observations")
    nexttile
    plot(learnrate)
    xlim([0 nchunk])
    ylabel("Initial Learning Rate")
    xline(IncrementalMdl.EstimationPeriod/numObsPerChunk,"-.");
    xlabel(t,"Iteration")

    Figure contains 2 axes objects. Axes object 1 with ylabel Number of Training Observations contains 2 objects of type line, constantline. Axes object 2 with ylabel Initial Learning Rate contains 2 objects of type line, constantline.

    The plot suggests that the fit function does not fit the model to the streaming data during the estimation period. The initial learning rate jumps from 0.7 to its autotuned value after the estimation period. During training, the software uses a learning rate that gradually decays from the initial value specified in the LearnRateSchedule property of IncrementalMdl.

    Input Arguments

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    Traditionally trained Gaussian kernel model or kernel model template, specified as a ClassificationKernel model object returned by fitckernel or a template object returned by templateKernel, respectively.

    If Mdl is a kernel model template object, incrementalLearner determines whether to standardize the predictor variables based on the Standardize property of the model template object. For more information, see Standardize Data

    Note

    Incremental learning functions support only numeric input predictor data. If Mdl was trained on categorical data, you must prepare an encoded version of the categorical data to use incremental learning functions. 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, in the same way that the training function encodes categorical data. For more details, see Dummy Variables.

    Name-Value Arguments

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    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: Solver="sgd",MetricsWindowSize=100 specifies the stochastic gradient descent solver for objective optimization, and specifies processing 100 observations before updating the window performance metrics.

    General Options

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    Objective function minimization technique, specified as a value in this table.

    ValueDescriptionNotes
    "scale-invariant"

    Adaptive scale-invariant solver for incremental learning [1]

    • This algorithm is parameter free and can adapt to differences in predictor scales. Try this algorithm before using SGD or ASGD.

    • To shuffle an incoming chunk of data before the fit function fits the model, set Shuffle to true.

    "sgd"Stochastic gradient descent (SGD) [2][3]

    • To train effectively with SGD, standardize the data and specify adequate values for hyperparameters using options listed in SGD and ASGD Solver Options.

    • The fit function always shuffles an incoming chunk of data before fitting the model.

    "asgd"Average stochastic gradient descent (ASGD) [4]

    • To train effectively with ASGD, standardize the data and specify adequate values for hyperparameters using options listed in SGD and ASGD Solver Options.

    • The fit function always shuffles an incoming chunk of data before fitting the model.

    Example: Solver="sgd"

    Data Types: char | string

    Number of observations processed by the incremental model to estimate hyperparameters before training or tracking performance metrics, specified as a nonnegative integer.

    Note

    • If Mdl is prepared for incremental learning (all hyperparameters required for training are specified), incrementalLearner forces EstimationPeriod to 0.

    • If Mdl is not prepared for incremental learning, incrementalLearner sets EstimationPeriod to 1000.

    For more details, see Estimation Period.

    Example: EstimationPeriod=100

    Data Types: single | double

    SGD and ASGD Solver Options

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    Mini-batch size, specified as a positive integer. At each learning cycle during training, incrementalLearner uses BatchSize observations to compute the subgradient.

    The number of observations in the last mini-batch (last learning cycle in each function call of fit or updateMetricsAndFit) can be smaller than BatchSize. For example, if you supply 25 observations to fit or updateMetricsAndFit, the function uses 10 observations for the first two learning cycles and 5 observations for the last learning cycle.

    Example: BatchSize=5

    Data Types: single | double

    Ridge (L2) regularization term strength, specified as a nonnegative scalar.

    Example: Lambda=0.01

    Data Types: single | double

    Initial learning rate, specified as "auto" or a positive scalar.

    The learning rate controls the optimization step size by scaling the objective subgradient. LearnRate specifies an initial value for the learning rate, and LearnRateSchedule determines the learning rate for subsequent learning cycles.

    When you specify "auto":

    • The initial learning rate is 0.7.

    • If EstimationPeriod > 0, fit and updateMetricsAndFit change the rate to 1/sqrt(1+max(sum(X.^2,2))) at the end of EstimationPeriod.

    Example: LearnRate=0.001

    Data Types: single | double | char | string

    Learning rate schedule, specified as a value in this table, where LearnRate specifies the initial learning rate ɣ0.

    ValueDescription
    "constant"The learning rate is ɣ0 for all learning cycles.
    "decaying"

    The learning rate at learning cycle t is

    γt=γ0(1+λγ0t)c.

    • λ is the value of Lambda.

    • If Solver is "sgd", then c = 1.

    • If Solver is "asgd", then c = 0.75 [4].

    Example: LearnRateSchedule="constant"

    Data Types: char | string

    Adaptive Scale-Invariant Solver Options

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    Flag for shuffling the observations at each iteration, specified as logical 1 (true) or 0 (false).

    ValueDescription
    logical 1 (true)The software shuffles the observations in an incoming chunk of data before the fit function fits the model. This action reduces bias induced by the sampling scheme.
    logical 0 (false)The software processes the data in the order received.

    Example: Shuffle=false

    Data Types: logical

    Performance Metrics Options

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    Model performance metrics to track during incremental learning with the updateMetrics or updateMetricsAndFit function, specified as a built-in loss function name, string vector of names, function handle (@metricName), structure array of function handles, or cell vector of names, function handles, or structure arrays.

    The following table lists the built-in loss function names. You can specify more than one by using a string vector.

    NameDescription
    "binodeviance"Binomial deviance
    "classiferror"Classification error
    "exponential"Exponential loss
    "hinge"Hinge loss
    "logit"Logistic loss
    "quadratic"Quadratic loss

    For more details on the built-in loss functions, see loss.

    Example: Metrics=["classiferror","hinge"]

    To specify a custom function that returns a performance metric, use function handle notation. The function must have this form:

    metric = customMetric(C,S)

    • The output argument metric is an n-by-1 numeric vector, where each element is the loss of the corresponding observation in the data processed by the incremental learning functions during a learning cycle.

    • You specify the function name (customMetric).

    • C is an n-by-2 logical matrix with rows indicating the class to which the corresponding observation belongs. The column order corresponds to the class order in the model for incremental learning. Create C by setting C(p,q) = 1, if observation p is in class q, for each observation in the specified data. Set the other element in row p to 0.

    • S is an n-by-2 numeric matrix of predicted classification scores. S is similar to the score output of predict, where rows correspond to observations in the data and the column order corresponds to the class order in the model for incremental learning. S(p,q) is the classification score of observation p being classified in class q.

    To specify multiple custom metrics and assign a custom name to each, use a structure array. To specify a combination of built-in and custom metrics, use a cell vector.

    Example: Metrics=struct(Metric1=@customMetric1,Metric2=@customMetric2)

    Example: Metrics={@customMetric1,@customMetric2,"logit",struct(Metric3=@customMetric3)}

    updateMetrics and updateMetricsAndFit store specified metrics in a table in the property IncrementalMdl.Metrics. The data type of Metrics determines the row names of the table.

    Metrics Value Data TypeDescription of Metrics Property Row NameExample
    String or character vectorName of corresponding built-in metricRow name for "classiferror" is "ClassificationError"
    Structure arrayField nameRow name for struct(Metric1=@customMetric1) is "Metric1"
    Function handle to function stored in a program fileName of functionRow name for @customMetric is "customMetric"
    Anonymous functionCustomMetric_j, where j is metric j in MetricsRow name for @(C,S)customMetric(C,S)... is CustomMetric_1

    For more details on performance metrics options, see Performance Metrics.

    Data Types: char | string | struct | cell | function_handle

    Number of observations the incremental model must be fit to before it tracks performance metrics in its Metrics property, specified as a nonnegative integer. The incremental model is warm after incremental fitting functions fit (EstimationPeriod + MetricsWarmupPeriod) observations to the incremental model.

    For more details on performance metrics options, see Performance Metrics.

    Example: MetricsWarmupPeriod=50

    Data Types: single | double

    Number of observations to use to compute window performance metrics, specified as a positive integer.

    For more details on performance metrics options, see Performance Metrics.

    Example: MetricsWindowSize=250

    Data Types: single | double

    Output Arguments

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    Binary Gaussian kernel classification model for incremental learning, returned as an incrementalClassificationKernel model object. IncrementalMdl is also configured to generate predictions given new data (see predict).

    The incrementalLearner function initializes IncrementalMdl for incremental learning using the model information in Mdl. The following table shows the Mdl properties that incrementalLearner passes to corresponding properties of IncrementalMdl. The function also passes other model information required to initialize IncrementalMdl, such as learned model coefficients, regularization term strength, and the random number stream.

    Input Object Mdl TypePropertyDescription
    ClassificationKernel model object or kernel model template objectKernelScaleKernel scale parameter, a positive scalar
    LearnerLinear classification model type, a character vector
    NumExpansionDimensionsNumber of dimensions of expanded space, a positive integer
    ClassificationKernel model objectClassNamesClass labels for binary classification, a two-element list
    MuPredictor variable means, a numeric vector
    NumPredictorsNumber of predictors, a positive integer
    PriorPrior class label distribution, a numeric vector
    ScoreTransformScore transformation function, a function name or function handle
    SigmaPredictor variable standard deviations, a numeric vector

    Note that incrementalLearner does not use the Cost property of the traditionally trained model in Mdl because incrementalClassificationKernel does not support this property.

    More About

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    Algorithms

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    References

    [1] Kempka, Michał, Wojciech Kotłowski, and Manfred K. Warmuth. "Adaptive Scale-Invariant Online Algorithms for Learning Linear Models." Preprint, submitted February 10, 2019. https://arxiv.org/abs/1902.07528.

    [2] Langford, J., L. Li, and T. Zhang. “Sparse Online Learning Via Truncated Gradient.” J. Mach. Learn. Res., Vol. 10, 2009, pp. 777–801.

    [3] Shalev-Shwartz, S., Y. Singer, and N. Srebro. “Pegasos: Primal Estimated Sub-Gradient Solver for SVM.” Proceedings of the 24th International Conference on Machine Learning, ICML ’07, 2007, pp. 807–814.

    [4] Xu, Wei. “Towards Optimal One Pass Large Scale Learning with Averaged Stochastic Gradient Descent.” CoRR, abs/1107.2490, 2011.

    [5] Rahimi, A., and B. Recht. “Random Features for Large-Scale Kernel Machines.” Advances in Neural Information Processing Systems. Vol. 20, 2008, pp. 1177–1184.

    [6] Le, Q., T. Sarlós, and A. Smola. “Fastfood — Approximating Kernel Expansions in Loglinear Time.” Proceedings of the 30th International Conference on Machine Learning. Vol. 28, No. 3, 2013, pp. 244–252.

    [7] Huang, P. S., H. Avron, T. N. Sainath, V. Sindhwani, and B. Ramabhadran. “Kernel methods match Deep Neural Networks on TIMIT.” 2014 IEEE International Conference on Acoustics, Speech and Signal Processing. 2014, pp. 205–209.

    Version History

    Introduced in R2022a