incrementalLearner
Convert linear model for binary classification to incremental learner
Description
returns a binary classification linear model for incremental learning,
IncrementalMdl
= incrementalLearner(Mdl
)IncrementalMdl
, using the traditionally trained linear model object
or linear 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.
uses additional options specified by one or more namevalue
arguments. Some options require you to train IncrementalMdl
= incrementalLearner(Mdl
,Name,Value
)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.
Examples
Convert Traditionally Trained Model to Incremental Learner
Train a linear classification model for binary learning by using fitclinear
, 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 Linear Classification Model
Fit a linear classification model to the entire data set.
TTMdl = fitclinear(feat,Y)
TTMdl = ClassificationLinear ResponseName: 'Y' ClassNames: [0 1] ScoreTransform: 'none' Beta: [60x1 double] Bias: 0.2005 Lambda: 4.1537e05 Learner: 'svm' Properties, Methods
TTMdl
is a ClassificationLinear
model object representing a traditionally trained linear classification model.
Convert Trained Model
Convert the traditionally trained linear 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: 0.2005 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 informationTTMdl
extracted from the training data.IncrementalMdl
is warm (IsWarm
is1
), which means that incremental learning functions can start tracking performance metrics.incrementalClassificationLinear
trains the model using the adaptive scaleinvariant solver, whereasfitclinear
trainedTTMdl
using the BFGS 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); [~,ilscores] = predict(IncrementalMdl,feat); compareScores = norm(ttscores(:,1)  ilscores(:,1))
compareScores = 0
The difference between the scores generated by the models is 0.
Specify SGD Solver and Standardize Predictor Data
If you train a linear classification model using the SGD or ASGD solver, incrementalLearner
preserves the solver, linear model type, and associated hyperparameter values when it converts the linear classification model.
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;
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);
Create a set of 11 logarithmically spaced regularization strengths from ${10}^{6}$ through ${10}^{0.5}$.
Lambda = logspace(6,0.5,11);
Because the variables are on different scales, use implicit expansion to standardize the predictor data.
Xtt = (Xtt  mean(Xtt))./std(Xtt);
Tune the L2 regularization parameter by applying 5fold crossvalidation. Specify the standard SGD solver.
TTCVMdl = fitclinear(Xtt,Ytt,'KFold',5,'Learner','logistic',... 'Solver','sgd','Lambda',Lambda);
TTCVMdl
is a ClassificationPartitionedLinear
model representing the five models created during crossvalidation (see TTCVMdl.Trained
). The crossvalidation procedure includes training with each specified regularization value.
Compute the crossvalidated classification error for each model and regularization.
cvloss = kfoldLoss(TTCVMdl)
cvloss = 1×11
0.0054 0.0039 0.0034 0.0033 0.0030 0.0027 0.0027 0.0031 0.0036 0.0056 0.0077
cvloss
contains the testsample classification loss for each regularization value in Lamba
.
Select the regularization value that minimizes the classification error. Train the model again using the selected regularization value.
[~,idxmin] = min(cvloss); TTMdl = fitclinear(Xtt,Ytt,'Learner','logistic','Solver','sgd',... 'Lambda',Lambda(idxmin));
TTMdl
is a ClassificationLinear
model.
Convert the traditionally trained linear classification model to a binary classification linear model for incremental learning. Specify the standard SGD solver. Prepare incremental learning functions to standardize the predictors. This action requires an initial period for estimating the predictor means and standard deviations. Specify an estimation period of 2000
observations (the default is 1000
when predictor moments are required).
IncrementalMdl = incrementalLearner(TTMdl,'Standardize',true,'EstimationPeriod',2000);
IncrementalMdl
is an incrementalClassificationLinear
model object. incrementalLearner
passes the solver and regularization strength, among other information learned from training TTMdl
, to IncrementalMdl
.
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 ${\beta}_{1}$ to see how it evolves 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*(j1) + 1); iend = min(nil,numObsPerChunk*j); idx = ibegin:iend; IncrementalMdl = fit(IncrementalMdl,Xil(idx,:),Yil(idx)); beta1(j + 1) = IncrementalMdl.Beta(1); end
IncrementalMdl
is an incrementalClassificationLinear
model object trained on all the data in the stream.
Plot ${\beta}_{1}$ to see how it evolved.
plot(beta1) ylabel('\beta_1') xline(IncrementalMdl.EstimationPeriod/numObsPerChunk,'r.') xlabel('Iteration')
Because fit
does not fit the model to the streaming data during the estimation period, ${\beta}_{1}$ is constant for the first 200 iterations (2000 observations). Then, ${\beta}_{1}$ changes abruptly during incremental fitting.
Configure Performance Metric Options
Use a trained linear classification model to initialize an incremental learner. Prepare the incremental learner by specifying a metrics warmup period, during which the updateMetricsAndFit
function only fits the model. Specify a metrics window size of 500 observations.
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 linear classification model to the first half of the data.
TTMdl = fitclinear(Xtt,Ytt);
Convert the traditionally trained linear classification model to a binary classification linear model for incremental learning. Specify the following:
A performance metrics warmup 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 that processing a chunk of 20 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 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*(j1) + 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 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(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')
The plot suggests that updateMetricsAndFit
does the following:
Fit ${\beta}_{1}$ during all incremental learning iterations.
Compute the performance metrics after the metrics warmup period only.
Compute the cumulative metrics during each iteration.
Compute the window metrics after processing 500 observations (25 iterations).
Input Arguments
Mdl
— Traditionally trained model or model template
ClassificationLinear
model object  linear model template
Traditionally trained linear model or linear model template, specified as a ClassificationLinear
model object returned by fitclinear
or a template object returned by templateLinear
, respectively.
Note
The
Lambda
property ofMdl
must be a numeric scalar. IfLambda
is a numeric vector for a traditionally trained linear model, you must select the model corresponding to one regularization strength in the regularization path by usingselectModels
.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. Usedummyvar
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.
NameValue Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Namevalue 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','scaleinvariant','MetricsWindowSize',100
specifies
the adaptive scaleinvariant solver for objective optimization, and specifies processing 100
observations before updating the window performance metrics.
Solver
— Objective function minimization technique
'scaleinvariant'
 'sgd'
 'asgd'
Objective function minimization technique, specified as the commaseparated pair
consisting of 'Solver'
and a value in this table.
Value  Description  Notes 

'scaleinvariant'  Adaptive scaleinvariant solver for incremental learning [1] 

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

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

The default Solver
value depends on the input model object
Mdl
:
If
Mdl
uses ridge regularization and the SGD or ASGD solver,IncrementalMdl
uses the same solver.(If
Mdl
is a traditionally trained model, you can view theSolver
value inMdl.ModelParameters.Solver
. IfMdl
is a model template, you can view theSolver
value by displaying the object in the Command Window or the Variables editor.)Otherwise, the default
Solver
value is'scaleinvariant'
.
Example: 'Solver','sgd'
Data Types: char
 string
EstimationPeriod
— Number of observations processed to estimate hyperparameters
nonnegative integer
Number of observations processed by the incremental model to estimate hyperparameters before training or tracking performance metrics, specified as the commaseparated pair consisting of 'EstimationPeriod'
and a nonnegative integer.
Note
If
Mdl
is prepared for incremental learning (all hyperparameters required for training are specified),incrementalLearner
forcesEstimationPeriod
to0
.If
Mdl
is not prepared for incremental learning,incrementalLearner
setsEstimationPeriod
to1000
.
For more details, see Estimation Period.
Example: 'EstimationPeriod',100
Data Types: single
 double
Standardize
— Flag to standardize predictor data
false
(default)  true
Flag to standardize the predictor data, specified as the commaseparated pair consisting of 'Standardize'
and a value in this table.
Value  Description 

true  The software standardizes the predictor data. For more details, see Standardize Data. 
false  The software does not standardize the predictor data. 
Example: 'Standardize',true
Data Types: logical
BatchSize
— Minibatch size
positive integer
Minibatch size, specified as the commaseparated pair consisting of
'BatchSize'
and a positive integer. At each learning cycle during
training, incrementalLearner
uses BatchSize
observations to
compute the subgradient.
The number of observations for the last minibatch (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 uses 5 observations for the last
learning cycle.
The default BatchSize
value depends on the input model object
Mdl
:
If
Mdl
uses ridge regularization and the SGD or ASGD solver, you cannot setBatchSize
. Instead,incrementalLearner
setsBatchSize
toMdl.ModelParameters.BatchSize
of the traditionally trained model, or to theBatchSize
property of the model template.Otherwise, the default
BatchSize
value is10
.
Example: 'BatchSize',1
Data Types: single
 double
Lambda
— Ridge (L2) regularization term strength
nonnegative scalar
Ridge (L2) regularization term strength, specified as a nonnegative scalar.
The default Lambda
value depends on the input model object
Mdl
:
If
Mdl
uses ridge regularization and the SGD or ASGD solver, you cannot setLambda
. Instead,incrementalLearner
setsLambda
to theLambda
property ofMdl
.Otherwise, the default
Lambda
value is1e5
.
Note
incrementalLearner
does not support lasso regularization. If the
Regularization
property of Mdl
is
'lasso (L1)'
, incrementalLearner
uses ridge
regularization instead, and sets the Solver
namevalue argument
to 'scaleinvariant'
by default.
Example: 'Lambda',0.01
Data Types: single
 double
LearnRate
— Initial learning rate
'auto'
 positive scalar
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
andupdateMetricsAndFit
change the rate to1/sqrt(1+max(sum(X.^2,obsDim)))
at the end ofEstimationPeriod
. TheobsDim
value is1
if the observations compose the columns of the predictor data; otherwise, the value is2
.
The default LearnRate
value depends on the input model object
Mdl
:
If
Mdl
uses ridge regularization and the SGD or ASGD solver, you cannot setLearnRate
. Instead,incrementalLearner
setsLearnRate
toMdl.ModelParameters.LearnRate
of the traditionally trained model, or to theLearnRate
property of the model template.Otherwise, the default
LearnRate
value is'auto'
.
Example: 'LearnRate',0.001
Data Types: single
 double
 char
 string
LearnRateSchedule
— Learning rate schedule
'decaying'
(default)  'constant'
Learning rate schedule, specified as the commaseparated pair consisting of 'LearnRateSchedule'
and a value in this table, where LearnRate
specifies the initial learning rate ɣ_{0}.
Value  Description 

'constant'  The learning rate is ɣ_{0} for all learning cycles. 
'decaying'  The learning rate at learning cycle t is $${\gamma}_{t}=\frac{{\gamma}_{0}}{{\left(1+\lambda {\gamma}_{0}t\right)}^{c}}.$$

If Mdl
uses ridge regularization and the SGD or ASGD solver,
you cannot set LearnRateSchedule
. Instead,
incrementalLearner
sets LearnRateSchedule
to
'decaying'
.
Example: 'LearnRateSchedule','constant'
Data Types: char
 string
Shuffle
— Flag for shuffling observations in batch
true
(default)  false
Flag for shuffling the observations in the batch at each iteration, specified as the commaseparated pair consisting of 'Shuffle'
and a value in this table.
Value  Description 

true  The software shuffles an incoming chunk of data before the
fit function fits the model. This action
reduces bias induced by the sampling scheme. 
false  The software processes the data in the order received. 
Example: 'Shuffle',false
Data Types: logical
Metrics
— Model performance metrics to track during incremental learning
"classiferror"
(default)  string vector  function handle  cell vector  structure array  "binodeviance"
 "exponential"
 "hinge"
 "logit"
 "quadratic"
Model performance metrics to track during incremental learning with the updateMetrics
or updateMetricsAndFit
function, specified as a builtin 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 builtin loss function names. You can specify more than one by using a string vector.
Name  Description 

"binodeviance"  Binomial deviance 
"classiferror"  Classification error 
"exponential"  Exponential loss 
"hinge"  Hinge loss 
"logit"  Logistic loss 
"quadratic"  Quadratic loss 
For more details on the builtin 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 nby1 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 nby2 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. CreateC
by settingC(
=p
,q
)1
, if observation
is in classp
, for each observation in the specified data. Set the other element in rowq
top
0
.S
is an nby2 numeric matrix of predicted classification scores.S
is similar to thescore
output ofpredict
, where rows correspond to observations in the data, and the column order corresponds to the class order in the model for incremental learning.S(
is the classification score of observationp
,q
)
being classified in classp
.q
To specify multiple custom metrics and assign a custom name to each, use a structure array. To specify a combination of builtin 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 Type  Description of Metrics Property Row Name  Example 

String or character vector  Name of corresponding builtin metric  Row name for "classiferror" is "ClassificationError" 
Structure array  Field name  Row name for struct('Metric1',@customMetric1) is "Metric1" 
Function handle to function stored in a program file  Name of function  Row name for @customMetric is "customMetric" 
Anonymous function  CustomMetric_ , where is metric in Metrics  Row 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
MetricsWarmupPeriod
— Number of observations fit before tracking performance metrics
0
(default)  nonnegative integer
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
MetricsWindowSize
— Number of observations to use to compute window performance metrics
200
(default)  positive integer
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',100
Data Types: single
 double
Output Arguments
IncrementalMdl
— Binary classification linear model for incremental learning
incrementalClassificationLinear
model object
Binary classification linear model for incremental learning, returned as an incrementalClassificationLinear
model object. IncrementalMdl
is also configured to generate predictions given new data (see predict
).
To initialize IncrementalMdl
for incremental learning,
incrementalLearner
passes the values of the Mdl
properties in this
table to corresponding properties of IncrementalMdl
.
Input Object Mdl Type  Property  Description 

ClassificationLinear model object or
linear model template object  Beta  Linear model coefficients, a numeric vector 
Bias  Model intercept, a numeric scalar  
Learner  Linear classification model type, a character vector  
ModelParameters.FitBias of a model object or
FitBias of a template object  Linear model intercept inclusion flag, a logical scalar  
ClassificationLinear model object  ClassNames  Class labels for binary classification, a twoelement list 
NumPredictors  Number of predictors, a positive integer  
Prior  Prior class label distribution, a numeric vector  
ScoreTransform  Score transformation function, a function name or function handle 
If Mdl
uses ridge regularization and the SGD or ASGD solver,
incrementalLearner
also passes the properties in this
table.
Input Object Mdl Type  Property  Description 

ClassificationLinear model object or linear
model template object  Lambda  Ridge (L2) regularization term strength, a nonnegative scalar 
ModelParameters.LearnRate of a model object or
LearnRate of a template object  Learning rate, a positive scalar  
ModelParameters.BatchSize of a model object or
BatchSize of a template object  Minibatch size, a positive integer  
ModelParameters.Solver of a model object or
Solver of a template object  Objective function minimization technique, a character vector 
Note that incrementalLearner
does not use the
Cost
property of the traditionally trained model in
Mdl
because incrementalClassificationLinear
does
not support this property.
More About
Incremental Learning
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 crossvalidation 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.
Adaptive ScaleInvariant Solver for Incremental Learning
The adaptive scaleinvariant solver for incremental learning, introduced in [1], is a gradientdescentbased 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 crossvalidation 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
Estimation Period
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 
 Standardize predictor data  The hyperparameters are estimated when you set

Learning rate  LearnRate  Adjust solver step size  The hyperparameter is estimated when both of these conditions apply:

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.
Standardize Data
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
.
When you set
'Standardize',true
, andIncrementalMdl.Mu
andIncrementalMdl.Sigma
are empty, the following conditions apply:If the estimation period is positive (see the
EstimationPeriod
property ofIncrementalMdl
), incremental fitting functions estimate means and standard deviations using the estimation period observations.If the estimation period is 0,
incrementalLearner
forces the estimation period to1000
. 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 (x_{j}) using
$${x}_{j}^{\ast}=\frac{{x}_{j}{\mu}_{j}^{\ast}}{{\sigma}_{j}^{\ast}}.$$
where
x_{j} is predictor j, and x_{jk} is observation k of predictor j in the estimation period.
$${\mu}_{j}^{\ast}=\frac{1}{{\displaystyle \sum _{k}{w}_{k}^{\ast}}}{\displaystyle \sum _{k}{w}_{k}^{\ast}{x}_{jk}}.$$
$${\left({\sigma}_{j}^{\ast}\right)}^{2}=\frac{1}{{\displaystyle \sum _{k}{w}_{k}^{\ast}}}{\displaystyle \sum _{k}{w}_{k}^{\ast}{\left({x}_{jk}{\mu}_{j}^{\ast}\right)}^{2}}.$$
$${w}_{j}^{\ast}=\frac{{w}_{j}}{{\displaystyle \sum _{\forall j\in \text{Class}k}{w}_{j}}}{p}_{k},$$ where
p_{k} is the prior probability of class k (
Prior
property of the incremental model).w_{j} is observation weight j.
Performance Metrics
The
updateMetrics
andupdateMetricsAndFit
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 afterfit
orupdateMetricsAndFit
fit the incremental model to'MetricsWarmupPeriod'
observations, which is the metrics warmup period.If
'EstimationPeriod'
> 0, the functions estimate hyperparameters before fitting the model to data. Therefore, the functions must process an additionalEstimationPeriod
observations before the model starts the metrics warmup period.The
Metrics
property of the incremental model stores two forms of each performance metric as variables (columns) of a table,Cumulative
andWindow
, with individual metrics in rows. When the incremental model is warm,updateMetrics
andupdateMetricsAndFit
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'
namevalue pair argument.'MetricsWindowSize'
also determines the frequency at which the software updatesWindow
metrics. For example, ifMetricsWindowSize
is 20, the functions compute metrics based on the last 20 observations in the supplied data (X((end – 20 + 1):end,:)
andY((end – 20 + 1):end)
).Incremental functions that track performance metrics within a window use the following process:
Store a buffer of length
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
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 incomingMetricsWindowSize
observations enter the buffer, and the earliest observations are removed from the buffer. For example, supposeMetricsWindowSize
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 theCumulative
andWindow
performance metric values.
References
[1] Kempka, Michał, Wojciech Kotłowski, and Manfred K. Warmuth. "Adaptive ScaleInvariant 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] ShalevShwartz, S., Y. Singer, and N. Srebro. “Pegasos: Primal Estimated SubGradient 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
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