loss
Description
loss
returns the regression or classification loss of
a configured incremental learning model for kernel regression (incrementalRegressionKernel
object) or binary kernel classification (incrementalClassificationKernel
object).
To measure model performance on a data stream and store the results in the output model,
call updateMetrics
or
updateMetricsAndFit
.
Examples
Measure Model Performance During Incremental Learning
The performance of an incremental model on streaming data is measured in three ways:
Cumulative metrics measure the performance since the start of incremental learning.
Window metrics measure the performance on a specified window of observations. The metrics are updated every time the model processes the specified window.
The
loss
function measures the performance on a specified batch of data only.
Load the human activity data set. Randomly shuffle the data.
load humanactivity n = numel(actid); rng(1) % For reproducibility idx = randsample(n,n); X = feat(idx,:); Y = actid(idx);
For details on the data set, enter Description
at the command line.
Responses can be one of five classes: Sitting, Standing, Walking, Running, or Dancing. Dichotomize the response by identifying whether the subject is moving (actid
> 2).
Y = Y > 2;
Create an incremental kernel model for binary classification. Specify a metrics window size of 1000 observations. Configure the model for loss
by fitting it to the first 10 observations.
p = size(X,2); Mdl = incrementalClassificationKernel(MetricsWindowSize=1000); initobs = 10; Mdl = fit(Mdl,X(1:initobs,:),Y(1:initobs));
Mdl
is an incrementalClassificationKernel
model. All its properties are read-only.
Simulate a data stream, and perform the following actions on each incoming chunk of 50 observations:
Call
updateMetrics
to measure the cumulative performance and the performance within a window of observations. Overwrite the previous incremental model with a new one to track performance metrics.Call
loss
to measure the model performance on the incoming chunk.Call
fit
to fit the model to the incoming chunk. Overwrite the previous incremental model with a new one fitted to the incoming observations.Store all performance metrics to see how they evolve during incremental learning.
% Preallocation numObsPerChunk = 50; nchunk = floor((n - initobs)/numObsPerChunk); ce = array2table(zeros(nchunk,3),VariableNames=["Cumulative","Window","Loss"]); % Incremental learning for j = 1:nchunk ibegin = min(n,numObsPerChunk*(j-1) + 1 + initobs); iend = min(n,numObsPerChunk*j + initobs); idx = ibegin:iend; Mdl = updateMetrics(Mdl,X(idx,:),Y(idx)); ce{j,["Cumulative","Window"]} = Mdl.Metrics{"ClassificationError",:}; ce{j,"Loss"} = loss(Mdl,X(idx,:),Y(idx)); Mdl = fit(Mdl,X(idx,:),Y(idx)); end
Mdl
is an incrementalClassificationKernel
model object trained on all the data in the stream. During incremental learning and after the model is warmed up, updateMetrics
checks the performance of the model on the incoming observations, and the fit
function fits the model to those observations. loss
is agnostic of the metrics warm-up period, so it measures the classification error for all iterations.
To see how the performance metrics evolve during training, plot them.
plot(ce.Variables) xlim([0 nchunk]) ylabel("Classification Error") xline(Mdl.MetricsWarmupPeriod/numObsPerChunk,"--") legend(ce.Properties.VariableNames) xlabel("Iteration")
The yellow line represents the classification error on each incoming chunk of data. After the metrics warm-up period, Mdl
tracks the cumulative and window metrics. The cumulative and batch losses converge as the fit
function fits the incremental model to the incoming data.
Compute Custom Loss on Incoming Chunks of Data
Fit an incremental learning model for regression to streaming data, and compute the mean absolute deviation (MAD) on the incoming data batches.
Load the robot arm data set. Obtain the sample size n
and the number of predictor variables p
.
load robotarm
n = numel(ytrain);
p = size(Xtrain,2);
For details on the data set, enter Description
at the command line.
Create an incremental kernel model for regression. Configure the model as follows:
Specify a metrics warm-up period of 1000 observations.
Specify a metrics window size of 500 observations.
Track the mean absolute deviation (MAD) to measure the performance of the model. Create an anonymous function that measures the absolute error of each new observation. Create a structure array containing the name
MeanAbsoluteError
and its corresponding function.Configure the model to predict responses by fitting it to the first 10 observations.
maefcn = @(z,zfit,w)(abs(z - zfit));
maemetric = struct(MeanAbsoluteError=maefcn);
Mdl = incrementalRegressionKernel(MetricsWarmupPeriod=1000,MetricsWindowSize=500, ...
Metrics=maemetric);
initobs = 10;
Mdl = fit(Mdl,Xtrain(1:initobs,:),ytrain(1:initobs));
Mdl
is an incrementalRegressionKernel
model object configured for incremental learning.
Perform incremental learning. At each iteration:
Simulate a data stream by processing a chunk of 50 observations.
Call
updateMetrics
to compute cumulative and window metrics on the incoming chunk of data. Overwrite the previous incremental model with a new one fitted to overwrite the previous metrics.Call
loss
to compute the MAD on the incoming chunk of data. Whereas the cumulative and window metrics require that custom losses return the loss for each observation,loss
requires the loss on the entire chunk. Compute the mean of the absolute deviation.Call
fit
to fit the incremental model to the incoming chunk of data.Store the cumulative, window, and chunk metrics to see how they evolve during incremental learning.
% Preallocation numObsPerChunk = 50; nchunk = floor((n - initobs)/numObsPerChunk); mae = array2table(zeros(nchunk,3),VariableNames=["Cumulative","Window","Chunk"]); % Incremental fitting for j = 1:nchunk ibegin = min(n,numObsPerChunk*(j-1) + 1 + initobs); iend = min(n,numObsPerChunk*j + initobs); idx = ibegin:iend; Mdl = updateMetrics(Mdl,Xtrain(idx,:),ytrain(idx)); mae{j,1:2} = Mdl.Metrics{"MeanAbsoluteError",:}; mae{j,3} = loss(Mdl,Xtrain(idx,:),ytrain(idx),LossFun=@(x,y,w)mean(maefcn(x,y,w))); Mdl = fit(Mdl,Xtrain(idx,:),ytrain(idx)); end
Mdl
is an incrementalRegressionKernel
model object trained on all the data in the stream. During incremental learning and after the model is warmed up, updateMetrics
checks the performance of the model on the incoming observations, and the fit
function fits the model to those observations.
Plot the performance metrics to see how they evolved during incremental learning.
plot(mae.Variables) ylabel("Mean Absolute Deviation") xlabel("Iteration") xlim([0 nchunk]) xline(Mdl.EstimationPeriod/numObsPerChunk,"-.") xline((Mdl.EstimationPeriod + Mdl.MetricsWarmupPeriod)/numObsPerChunk,"--") legend(mae.Properties.VariableNames)
The plot suggests the following:
updateMetrics
computes the performance metrics after the metrics warm-up period only.updateMetrics
computes the cumulative metrics during each iteration.updateMetrics
computes the window metrics after processing 500 observations (10 iterations).Because
Mdl
was configured to predict observations from the beginning of incremental learning,loss
can compute the MAD on each incoming chunk of data.
Input Arguments
Mdl
— Incremental learning model
incrementalClassificationKernel
model object | incrementalRegressionKernel
model object
Incremental learning model, specified as an incrementalClassificationKernel
or incrementalRegressionKernel
model object. You can create Mdl
directly or by converting a supported, traditionally trained machine learning model using the incrementalLearner
function. For more details, see the corresponding reference page.
You must configure Mdl
to predict labels for a batch of observations.
If
Mdl
is a converted, traditionally trained model, you can predict labels without any modifications.Otherwise, you must fit
Mdl
to data usingfit
orupdateMetricsAndFit
.
X
— Batch of predictor data
floating-point matrix
Batch of predictor data, specified as a floating-point matrix of
n observations and Mdl.NumPredictors
predictor
variables.
The length of the observation labels Y
and the number of
observations in X
must be equal;
Y(
is the label of observation
j (row) in j
)X
.
Note
loss
supports only floating-point
input predictor data. If your input data includes categorical data, you must prepare an encoded
version of the categorical data. Use dummyvar
to convert each categorical variable
to a numeric matrix of dummy variables. Then, concatenate all dummy variable matrices and any
other numeric predictors. For more details, see Dummy Variables.
Data Types: single
| double
Y
— Batch of responses (labels)
categorical array | character array | string array | logical vector | floating-point vector | cell array of character vectors
Batch of responses (labels), specified as a categorical, character, or string array, a logical or floating-point vector, or a cell array of character vectors for classification problems; or a floating-point vector for regression problems.
The length of the observation labels Y
and the number of
observations in X
must be equal;
Y(
is the label of observation
j (row) in j
)X
.
For classification problems:
loss
supports binary classification only.If
Y
contains a label that is not a member ofMdl.ClassNames
,loss
issues an error.The data type of
Y
andMdl.ClassNames
must be the same.
Data Types: char
| string
| cell
| categorical
| logical
| single
| double
Name-Value Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.
Example: LossFun="epsiloninsensitive",Weights=W
returns the epsilon
insensitive loss and specifies the observation weights as the vector
W
.
LossFun
— Loss function
string vector | function handle | cell vector | structure array
Loss function, specified as a built-in loss function name or function handle.
Classification problems: The following table lists the available loss functions when
Mdl
is anincrementalClassificationKernel
model. Specify one using its corresponding character vector or string scalar.Name Description "binodeviance"
Binomial deviance "classiferror"
(default)Misclassification rate in decimal "exponential"
Exponential loss "hinge"
Hinge loss "logit"
Logistic loss "quadratic"
Quadratic loss For more details, see Classification Loss.
Logistic regression learners return posterior probabilities as classification scores, but SVM learners do not (see
predict
).To specify a custom loss function, use function handle notation. The function must have this form:
lossval = lossfcn(C,S,W)
The output argument
lossval
is an n-by-1 floating-point vector, wherelossval(
is the classification loss of observationj
)
.j
You specify the function name (
).lossfcn
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 theClassNames
property. 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 n-by-2 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 theClassNames
property.S(
is the classification score of observationp
,q
)
being classified in classp
.q
W
is an n-by-1 numeric vector of observation weights.
Regression problems: The following table lists the available loss functions when
Mdl
is anincrementalRegressionKernel
model. Specify one using its corresponding character vector or string scalar.Name Description Learner Supporting Metric "epsiloninsensitive"
Epsilon insensitive loss 'svm'
"mse"
(default)Weighted mean squared error 'svm'
and'leastsquares'
For more details, see Regression Loss.
To specify a custom loss function, use function handle notation. The function must have this form:
lossval = lossfcn(Y,YFit,W)
The output argument
lossval
is a floating-point scalar.You specify the function name (
).lossfcn
Y
is a length n numeric vector of observed responses.YFit
is a length n numeric vector of corresponding predicted responses.W
is an n-by-1 numeric vector of observation weights.
Example: LossFun="mse"
Example: LossFun=@
lossfcn
Data Types: char
| string
| function_handle
Weights
— Batch of observation weights
floating-point vector of positive values
Batch of observation weights, specified as a floating-point vector of positive values. loss
weighs the observations in the input data with the corresponding values in Weights
. The size of Weights
must equal n, which is the number of observations in the input data.
By default, Weights
is ones(
.n
,1)
For more details, see Observation Weights.
Example: Weights=W
specifies the observation weights as the vector
W
.
Data Types: double
| single
Output Arguments
More About
Classification Loss
Classification loss functions measure the predictive inaccuracy of classification models. When you compare the same type of loss among many models, a lower loss indicates a better predictive model.
Consider the following scenario.
L is the weighted average classification loss.
n is the sample size.
yj is the observed class label. The software codes it as –1 or 1, indicating the negative or positive class (or the first or second class in the
ClassNames
property), respectively.f(Xj) is the positive-class classification score for observation (row) j of the predictor data X.
mj = yjf(Xj) is the classification score for classifying observation j into the class corresponding to yj. Positive values of mj indicate correct classification and do not contribute much to the average loss. Negative values of mj indicate incorrect classification and contribute significantly to the average loss.
The weight for observation j is wj.
Given this scenario, the following table describes the supported loss functions that you
can specify by using the LossFun
name-value argument.
Loss Function | Value of LossFun | Equation |
---|---|---|
Binomial deviance | "binodeviance" | |
Exponential loss | "exponential" | |
Misclassification rate in decimal | "classiferror" | where is the class label corresponding to the class with the maximal score, and I{·} is the indicator function. |
Hinge loss | "hinge" | |
Logit loss | "logit" | |
Quadratic loss | "quadratic" |
The loss
function does not omit an observation with a
NaN
score when computing the weighted average loss. Therefore,
loss
can return NaN
when the predictor
data X
contains missing values, and the name-value argument
LossFun
is not specified as "classiferror"
. In
most cases, if the data set does not contain missing predictors, the
loss
function does not return NaN
.
This figure compares the loss functions over the score m for one observation. Some functions are normalized to pass through the point (0,1).
Regression Loss
Regression loss functions measure the predictive inaccuracy of regression models. When you compare the same type of loss among many models, a lower loss indicates a better predictive model.
Consider the following scenario.
L is the weighted average classification loss.
n is the sample size.
yj is the observed response of observation j.
f(Xj) is the predicted value of observation j of the predictor data X.
The weight for observation j is wj.
Given this scenario, the following table describes the supported loss functions that you can specify by using the LossFun
name-value argument.
Loss Function | Value of LossFun | Equation |
---|---|---|
Epsilon insensitive loss | "epsiloninsensitive" | |
Mean squared error | "mse" |
The loss
function does not omit an observation with a
NaN
prediction when computing the weighted average loss. Therefore,
loss
can return NaN
when the predictor
data X
contains missing values. In most cases, if the data set does not
contain missing predictors, the loss
function does not return
NaN
.
Algorithms
Observation Weights
For classification problems, if the prior class probability distribution is known (in other words, the prior distribution is not empirical), loss
normalizes observation weights to sum to the prior class probabilities in the respective classes. This action implies that observation weights are the respective prior class probabilities by default.
For regression problems or if the prior class probability distribution is empirical, the software normalizes the specified observation weights to sum to 1 each time you call loss
.
Version History
Introduced in R2022a
See Also
Objects
Functions
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