incrementalLearner - Convert binary classification support vector machine (SVM) model to incremental learner - MATLAB (original) (raw)

Convert binary classification support vector machine (SVM) model to incremental learner

Since R2020b

Syntax

Description

[IncrementalMdl](#mw%5F7debacf6-87e1-4f78-ad82-cc214d49b434%5Fsep%5Fshared-incrementalclassificationmdl) = incrementalLearner([Mdl](#mw%5F7debacf6-87e1-4f78-ad82-cc214d49b434%5Fsep%5Fshared-incrementallearner%5Fmdl)) returns a binary classification linear model for incremental learning,IncrementalMdl, using the traditionally trained linear SVM model object or SVM 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](#mw%5F7debacf6-87e1-4f78-ad82-cc214d49b434%5Fsep%5Fshared-incrementalclassificationmdl) = incrementalLearner([Mdl](#mw%5F7debacf6-87e1-4f78-ad82-cc214d49b434%5Fsep%5Fshared-incrementallearner%5Fmdl),[Name,Value](#namevaluepairarguments)) 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 an SVM model by using fitcsvm, and then convert it to an incremental learner.

Load and Preprocess Data

Load the human activity data set.

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).

Train SVM Model

Fit an SVM model to the entire data set. Discard the support vectors (Alpha) from the model so that the software uses the linear coefficients (Beta) for prediction.

TTMdl = fitcsvm(feat,Y); TTMdl = discardSupportVectors(TTMdl)

TTMdl = ClassificationSVM ResponseName: 'Y' CategoricalPredictors: [] ClassNames: [0 1] ScoreTransform: 'none' NumObservations: 24075 Beta: [60×1 double] Bias: -6.4280 KernelParameters: [1×1 struct] BoxConstraints: [24075×1 double] ConvergenceInfo: [1×1 struct] IsSupportVector: [24075×1 logical] Solver: 'SMO'

Properties, Methods

TTMdl is a ClassificationSVM model object representing a traditionally trained SVM model.

Convert Trained Model

Convert the traditionally trained SVM 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: -6.4280
       Learner: 'svm'

Properties, Methods

IncrementalMdl is an incrementalClassificationLinear model object prepared for incremental learning using SVM.

The incrementalLearner function Initializes the incremental learner by passing learned coefficients to it, along with other information TTMdl extracted from the training data.
IncrementalMdl is warm (IsWarm is 1), which means that incremental learning functions can start tracking performance metrics.
The incrementalLearner function specifies to train the model using the adaptive scale-invariant solver, whereas fitcsvm trained TTMdl using the SMO 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(TTMdl,feat); [~~,ilcores] = predict(IncrementalMdl,feat); compareScores = norm(ttscores(:,1) - ilcores(:,1))

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

The default solver is the adaptive scale-invariant solver. If you specify this solver, you do not need to tune any parameters for training. However, if you specify either the standard SGD or 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.

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).

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 an SVM model to the first half of the data. Standardize the predictor data by setting 'Standardize',true.

TTMdl = fitcsvm(Xtt,Ytt,'Standardize',true);

The Mu and Sigma properties of TTMdl contain the predictor data sample means and standard deviations, respectively.

Suppose that the distribution of the predictors is not expected to change in the future. Convert the traditionally trained SVM model to a binary classification linear 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 incrementalClassificationLinear model object. Because the predictor data of TTMdl is standardized (TTMdl.Mu and TTMdl.Sigma are nonempty), incrementalLearner prepares incremental learning functions to standardize supplied predictor data by using the previously learned moments (stored in IncrementalMdl.Mu and IncrementalMdl.Sigma).

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 β1 to see how the coefficients and rate evolve during training.

% Preallocation nil = numel(Yil); numObsPerChunk = 10; nchunk = floor(nil/numObsPerChunk); learnrate = [IncrementalMdl.LearnRate; zeros(nchunk,1)]; beta1 = [IncrementalMdl.Beta(1); 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)); beta1(j + 1) = IncrementalMdl.Beta(1); learnrate(j + 1) = IncrementalMdl.LearnRate; end

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

To see how the initial learning rate and β1 evolve during training, plot them on separate tiles.

t = tiledlayout(2,1); nexttile plot(beta1) ylabel('\beta_1') xline(IncrementalMdl.EstimationPeriod/numObsPerChunk,'r-.') nexttile plot(learnrate) ylabel('Initial Learning Rate') xline(IncrementalMdl.EstimationPeriod/numObsPerChunk,'r-.') xlabel(t,'Iteration')

$Figure contains 2 axes objects. Axes object 1 with ylabel \beta_1 contains 2 objects of type line, constantline. Axes object 2 with ylabel Initial Learning Rate contains 2 objects of type line, constantline.$

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.

Because fit does not fit the model to the streaming data during the estimation period, β1 is constant for the first 200 iterations (2000 observations). Then, β1 changes during incremental fitting.

Use a trained SVM model to initialize an incremental learner. Prepare the incremental learner by specifying a metrics warm-up period, during which the updateMetricsAndFit function only fits the model. Specify a metrics window size of 500 observations.

Load the human activity data set.

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).

Because the data set is grouped by activity, shuffle it to reduce bias. 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 an SVM model to the first half of the data.

TTMdl = fitcsvm(Xtt,Ytt);

Convert the traditionally trained SVM model to a binary classification linear 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(TTMdl,'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 β1, the cumulative metrics, and the window metrics 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"]); beta1 = [IncrementalMdl.Beta(1); 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",:}; beta1(j + 1) = IncrementalMdl.Beta(1); end

IncrementalMdl 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 β1 evolve during training, plot them on separate tiles.

t = tiledlayout(3,1); nexttile plot(beta1) ylabel('\beta_1') xlim([0 nchunk]); xline(IncrementalMdl.MetricsWarmupPeriod/numObsPerChunk,'r-.'); nexttile h = plot(ce.Variables); xlim([0 nchunk]); ylabel('Classification Error') xline(IncrementalMdl.MetricsWarmupPeriod/numObsPerChunk,'r-.'); legend(h,ce.Properties.VariableNames,'Location','northwest') nexttile h = plot(hinge.Variables); xlim([0 nchunk]); ylabel('Hinge Loss') xline(IncrementalMdl.MetricsWarmupPeriod/numObsPerChunk,'r-.'); legend(h,hinge.Properties.VariableNames,'Location','northwest') xlabel(t,'Iteration')

$Figure contains 3 axes objects. Axes object 1 with ylabel \beta_1 contains 2 objects of type line, constantline. Axes object 2 with ylabel Classification Error contains 3 objects of type line, constantline. These objects represent Cumulative, Window. Axes object 3 with ylabel Hinge Loss contains 3 objects of type line, constantline. These objects represent Cumulative, Window.$

The plot suggests that updateMetricsAndFit does the following:

Fit β1 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).

Input Arguments

Name-Value Arguments

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Specify optional pairs of arguments asName1=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: 'Solver','scale-invariant','MetricsWindowSize',100 specifies the adaptive scale-invariant solver for objective optimization, and specifies processing 100 observations before updating the window performance metrics.

General Options

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Data Types: char | string

Data Types: single | double

SGD and ASGD Solver Options

Adaptive Scale-Invariant Solver Options

Performance Metrics Options

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

Data Types: single | double

Output Arguments

More About

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Incremental learning, or online learning, is a branch of machine learning concerned with processing incoming data from a data stream, possibly given little to no knowledge of the distribution of the predictor variables, aspects of the prediction or objective function (including tuning parameter values), or whether the observations are labeled. Incremental learning differs from traditional machine learning, where enough labeled data is available to fit to a model, perform cross-validation to tune hyperparameters, and infer the predictor distribution.

Given incoming observations, an incremental learning model processes data in any of the following ways, but usually in this order:

Predict labels.
Measure the predictive performance.
Check for structural breaks or drift in the model.
Fit the model to the incoming observations.

For more details, see Incremental Learning Overview.

The adaptive scale-invariant solver for incremental learning, introduced in [1], is a gradient-descent-based objective solver for training linear predictive models. The solver is hyperparameter free, insensitive to differences in predictor variable scales, and does not require prior knowledge of the distribution of the predictor variables. These characteristics make it well suited to incremental learning.

The standard SGD and ASGD solvers are sensitive to differing scales among the predictor variables, resulting in models that can perform poorly. To achieve better accuracy using SGD and ASGD, you can standardize the predictor data, and tune the regularization and learning rate parameters. For traditional machine learning, enough data is available to enable hyperparameter tuning by cross-validation and predictor standardization. However, for incremental learning, enough data might not be available (for example, observations might be available only one at a time) and the distribution of the predictors might be unknown. These characteristics make parameter tuning and predictor standardization difficult or impossible to do during incremental learning.

The incremental fitting functions for classification fit and updateMetricsAndFit use the more aggressive ScInOL2 version of the algorithm.

Algorithms

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During the estimation period, the incremental fitting functions fit and updateMetricsAndFit use the first incoming EstimationPeriod observations to estimate (tune) hyperparameters required for incremental training. Estimation occurs only when EstimationPeriod is positive. This table describes the hyperparameters and when they are estimated, or tuned.

Hyperparameter	Model Property	Usage	Conditions
Predictor means and standard deviations	Mu and Sigma	Standardize predictor data	The hyperparameters are estimated when both of these conditions apply: Incremental fitting functions are configured to standardize predictor data (see Standardize Data).Mdl.Mu and Mdl.Sigma are empty arrays [].
Learning rate	LearnRate	Adjust the solver step size	The hyperparameter is estimated when both of these conditions apply: You change the solver of Mdl to SGD or ASGD (seeSolver).You do not specify the 'LearnRate' name-value argument as a positive scalar.

During the estimation period, fit does not fit the model, and updateMetricsAndFit does not fit the model or update the performance metrics. At the end of the estimation period, the functions update the properties that store the hyperparameters.

If incremental learning functions are configured to standardize predictor variables, they do so using the means and standard deviations stored in the Mu and Sigma properties of the incremental learning model IncrementalMdl.

If you standardize the predictor data when you train the input modelMdl by using fitcsvm, the following conditions apply:
- incrementalLearner passes the means inMdl.Mu and standard deviations inMdl.Sigma to the corresponding incremental learning model properties.
- Incremental learning functions always standardize the predictor data.
When you set Standardize=true by using theStandardize name-value argument of templateSVM, and the Mdl.Mu andMdl.Sigma properties are empty, the following conditions apply:
- If the estimation period is positive (see theEstimationPeriod property ofIncrementalMdl), incremental fitting functions estimate the means and standard deviations using the estimation period observations.
- If the estimation period is 0, incrementalLearner forces the estimation period to 1000. Consequently, incremental fitting functions estimate new predictor variable means and standard deviations during the forced estimation period.
When incremental fitting functions estimate predictor means and standard deviations, the functions compute weighted means and weighted standard deviations using the estimation period observations. Specifically, the functions standardize predictor j (xj) using
- xj is predictor_j_, and xjk is observation k of predictor j in the estimation period.
- μj∗=1∑kwk∗∑kwk∗xjk.
- (σj∗)2=1∑kwk∗∑kwk∗(xjk−μj∗)2.
- wj∗=wj∑∀j∈Class kwjpk,
  * p k is the prior probability of class k (Prior property of the incremental model).
  * wj is observation weight_j_.
The updateMetrics and updateMetricsAndFit functions are incremental learning functions that track model performance metrics ('Metrics') from new data when the incremental model is warm (IsWarm property). An incremental model becomes warm after fit or updateMetricsAndFit fit the incremental model to 'MetricsWarmupPeriod' observations, which is the metrics warm-up period.
If '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 and updateMetricsAndFit 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 'MetricsWindowSize' name-value pair argument. 'MetricsWindowSize' also determines the frequency at which the software updates Window metrics. For example, if 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 use the following process:
  1. Store a buffer of length MetricsWindowSize for each specified metric, and store 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 observation weights in the weights buffer.
  3. When the buffer is filled, overwrite IncrementalMdl.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 MetricsWindowSize observations enter the buffer, and the earliest observations are removed from the buffer. For example, suppose 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.
The software omits an observation with a NaN score when computing the Cumulative and Window performance metric values.

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.

Version History

Introduced in R2020b