lassoPlot

Trace plot of lasso fit

Syntax

lassoPlot(B)

lassoPlot(B,FitInfo)

lassoPlot(B,FitInfo,Name=Value)

[ax,figh] = lassoPlot(___)

Description

lassoPlot(B) creates a trace plot of the values in B against the L¹ norm of B.

lassoPlot(B,FitInfo) creates a plot with type depending on the data type of FitInfo and the value, if any, of the PlotType name-value argument.

lassoPlot(B,FitInfo,Name=Value) creates a plot with additional options specified by one or more name-value arguments.

[ax,figh] = lassoPlot(___), for any previous input syntax, returns the axes ax and the figure window figh that contain the plot of the lasso fit.

Examples

Lasso Plot with Default Plot Type

Load the sample data.

load acetylene

Prepare the design matrix for lasso fit with interactions. The x2fx function returns the quadratic model in the order of a constant term, linear terms and interaction terms: constant term, x1, x2, x3, x1.*x2, x1.*x3, and x2.*x3.

X = [x1 x2 x3];
D = x2fx(X,"interaction");
D(:,1) = []; % No constant term

Fit a regularized model of the data using the lasso function.

B = lasso(D,y);

Plot the lasso fits with labeled coefficients by using the PredictorNames name-value argument. Each line represents a trace of the values in B for a single predictor variable: x1, x2, x3, x1.*x2, x1.*x3, and x2.*x3.

lassoPlot(B,PredictorNames=["x1" "x2" "x3" "x1.*x2" "x1.*x3" "x2.*x3"]);
legend(Location="NorthWest")

Lasso Plot with Lambda Plot Type

Load the sample data.

load acetylene

Prepare the data for lasso fit with interactions.

X = [x1 x2 x3];
D = x2fx(X,"interaction");
D(:,1) = []; % No constant term

Fit a regularized model of the data using the lasso function.

[B,FitInfo] = lasso(D,y);

Plot the fits with the Lambda plot type and logarithmic scaling.

lassoPlot(B,FitInfo,PlotType="Lambda",XScale="log");

Lasso Plot with Cross-Validated Fits

Visually examine the cross-validated error of various levels of regularization.

Load the sample data.

load acetylene

Create a design matrix with interactions and no constant term.

X = [x1 x2 x3];
D = x2fx(X,"interaction");
D(:,1) = []; % No constant term

Construct the lasso fit using 10-fold cross-validation. Include the FitInfo output so you can plot the result.

rng default % For reproducibility 
[B,FitInfo] = lasso(D,y,CV=10);

Plot the cross-validated fits. The green circle and dotted line locate the Lambda with minimum cross-validation error. The blue circle and dotted line locate the point with minimum cross-validation error plus one standard error.

lassoPlot(B,FitInfo,PlotType="CV");
legend("show")

Input Arguments

B — Coefficients of sequence of regression fits

numeric matrix

Coefficients of a sequence of regression fits, specified as a numeric matrix of size p-by-L, where p is the number of predictors and L is the number of regularization coefficients Lambda. You can calculate B using the lasso or lassoglm function.

FitInfo — Fit information of models

structure | numeric vector

Fit information of the generalized linear models, specified as a structure or a numeric vector.

• When FitInfo is a structure, such as returned from the lasso or lassoglm function, the lassoPlot function creates a plot based on the PlotType name-value argument.

• When FitInfo is a vector, the lassoPlot function forms the x-axis of the plot from the values in FitInfo. The length of FitInfo must equal the number of columns of B.

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: lassoPlot(B,XScale="log") uses a logarithmic scaled x-axis.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: lassoPlot(B,"XScale","log") uses a logarithmic scaled x-axis.

Parent — Parent axes

Axes object

Parent axes in which to draw the plot, specified as an Axes object. If you do not specify Parent, then lassoPlot creates the plot using the current axes. For more information on creating an Axes object, see axes.

PlotType — Plot type

"L1" (default) | "Lambda" | "CV"

Plot type, specified as "L1", "Lambda", or "CV". The PlotType argument applies when you specify the FitInfo argument.

PlotType	Plot
"L1"	lassoPlot creates the x-axis from the L1 norm of the coefficients in B. The x-axis at the top of the plot contains the degrees of freedom (df), meaning the number of nonzero coefficients of B.
"Lambda"	lassoPlot creates the x-axis from the Lambda field of FitInfo. The x-axis at the top of the plot contains the degrees of freedom (df), meaning the number of nonzero coefficients of B. When you choose this value, FitInfo must be a structure.
"CV"	For each Lambda, lassoPlot plots an estimate of the mean squared prediction error on new data for the model fitted by lasso with that value of Lambda. lassoPlot plots error bars for the estimates. When you choose this value, FitInfo must be a cross-validated structure.

If you include a cross-validated FitInfo structure, lassoPlot also indicates two specific Lambda values with green and blue dashed lines.

• A green, dashed line indicates the value of Lambda with a minimum cross-validated mean squared error (MSE).

• A blue, dashed line indicates the greatest Lambda that is within one standard error of the minimum MSE. This Lambda value makes the sparsest model with relatively low MSE.

To display the label for each plot in the legend of the figure, type legend("show") in the Command Window.

PredictorNames — Predictor names

{"B1","B2",...} (default) | string scalar | character vector

Predictor names, specified as a string array or cell array of character vectors. The predictor names label each coefficient of B. If the length of the PredictorNames argument is less than the number of rows of B, the remaining labels are padded with default values.

If you do not specify this argument, but you specify the FitInfo argument as a structure and the PredictorNames field of the structure is not empty ({}), then the lassoPlot function uses those predictor names instead of default values.

To display the legend with the predictor name as the label for each plot, type legend("show") in the Command Window.

XScale — Scale of values along x-axis

"linear" | "log"

Scale of values along the x-axis, specified as one of these values.

• "linear" — Linear x-axis. This is the default value when the PlotType argument is "L1" or "Lambda".

• "log" — Logarithmic scaled x-axis. This is the default value when the PlotType argument is "CV".

Data Types: string | char

Output Arguments

ax — Axes of plot

Axes object

Axes of the plot, returned as an Axes object. For more information, see Axes Appearance.

figh — Figure window of plot

Figure object

Figure window of the plot, returned as a Figure object. For more information, see Special Object Identifiers.

Version History

Introduced in R2011b