MATLAB: Give constant parameters to fitnlm

fitnlmStatistics and Machine Learning Toolbox

I want to use fitnlm (rather than fminsearch and a cost function) because it has the built in statistics. I need to run the fit of the model with different costant parameters but I am not able to tell the function to pick a parameter from the workspace (the function return an error if I give three arguments like @(parameterToOptimise,xData,constantParameter).

My example is:

fit function

and the values to fit are y and I have a constraint on the area under the curve that is A (depending on the fit problem).

I would like to write

@(α,x,Area)[(α+1)*Area/(

–

] (luckly

and

are constant, so I can write the numerical values), but I am not able to give a constant parameter to the function

Best Answer

fitnlm() makes a best fit of your model to your data. I don't believe it takes into account some criteria like the area under the fitted curve is in some range.

I'm attaching a demo to fit a power law with fitnlm(). Change the model to be what you need. If you need more help, attach your data in a .mat file.

Related Solutions

MATLAB: Parameter estimation nlinfit vs. fitnlm

There is no real difference. Both nlinfit and fitnlm are Statistics Toolbox functions for nonlinear regression, and so use the same fundamental functions. The fitnlm function is a shell around nlinfit and its friends. The advantage to fitnlm is that it’s slightly easier to use, and delivers a few more statistics. The important results — parameter confidence intervals and confidence intervals on the fitted equation — are easy to get with either, but actually slightly easier with nlinfit, nlparci and nlpredci.

Experiment with both, and see which is most appropriate to your application.

Don’t neglect lsqcurvefit if you have access to it (Optimization Toolbox). It can do two things that the Statistics Toolbox functions cannot: (1) accept bounds on the parameters, and (2) fit matrix dependent variables. It doesn’t have access to all the statistics the Statistics Toolbox functions do, but it definitely has its uses.

MATLAB: How to use fitnlm

Try this:

% Fits a Gaussian to the USA daily deaths for CoVid-19, which includes data for only the left portion of the Gaussian, not the full Gaussian.
%--------------------------------------------------------------------------------------------------------------------------------------------------------




% CLEAN UP - INITIALIZATION STEPS
clc;    % Clear the command window.
fprintf('Beginning to run %s.m.\n', mfilename);
close all;  % Close all figures (except those of imtool.)
clearvars;  % Erase all existing variables.
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 20;
%--------------------------------------------------------------------------------------------------------------------------------------------------------
% TRAINING DATA PREPARATION
% Read in data from workbook.
data = readmatrix('Fitnlm_Gaussian_CoVid19.xlsx');
% Get rid of nans
validRows = ~isnan(data(:, 2));
% Get rid of zero counts
validRows = validRows & (data(:, 2) > 0);
data = data(validRows, :)
X = data(:, 1);
Y = data(:, 2);
hFig = figure;
plot(X, Y, 'b.-', 'LineWidth', 2, 'MarkerSize', 30);
grid on;
xlabel('Date', 'FontSize', fontSize);
ylabel('Daily Deaths', 'FontSize', fontSize);
title('CoVid-19 Daily Deaths', 'FontSize', fontSize);
% Make x axis be dates.
datetick('x', 'mmm dd, yyyy', 'keepticks');
ax = gca;
ax.XTickLabelRotation = -45;
% Convert X and Y into a table, which is the form fitnlm() likes the input data to be in.
tbl = table(X(:), Y(:));
%--------------------------------------------------------------------------------------------------------------------------------------------------------
% MODEL DEFINITION
% Define the model as Y = a + b * exp(-(x - c)^2 / d)
% Create an anonymous function for it.
% Note how this "x" of ModelFunction is related to big X and big Y.
% x((:, 1) is actually X and x(:, 2) is actually Y - the first and second columns of the table.
ModelFunction = @(b, x) b(1) + b(2) * exp(-(x(:, 1) - b(3)).^2/b(4));  
%--------------------------------------------------------------------------------------------------------------------------------------------------------
% MODEL CREATION : ESTIMATION OF PARAMETERS
% Guess starting model values to start with.  Just make your best guess.  
% These are just starting points for the coefficients and will be adjusted during the fit to produce the real coefficients.
beta0 = [0, max(X), mean(X), var(X)]; % A guess at what the coefficients will be.
% Now the next line is where the actual model computation is done.
mdl = fitnlm(tbl, ModelFunction, beta0);
% Now the model creation is done and the coefficients have been determined.
% YAY!!!!
% Extract the coefficient values from the the model object.
% The actual coefficients are in the "Estimate" column of the "Coefficients" table that's part of the mode.
coefficients = mdl.Coefficients{:, 'Estimate'}
%--------------------------------------------------------------------------------------------------------------------------------------------------------
% MODEL PLOTTING : PLOTTING FITTED/ESTIMATED VALUES OVER THE WHOLE RANGE OF X.
% Let's do a fit, but let's get more points on the fit, beyond just the widely spaced training points,
% so that we'll get a much smoother curve.
xFitted = linspace(min(X), max(X), 1920); % Let's use 1920 points, which will fit across an HDTV screen about one sample per pixel.
% Create smoothed/regressed data using the model:
yFitted = ModelFunction(coefficients, xFitted(:));
% yFitted = coefficients(1) + coefficients(2) * exp(-(xFitted - coefficients(3)).^2 / coefficients(4));
% Now we know that since it's a Gaussian there should not be any negative values.  So clip to 0
yFitted = max(0, yFitted);
% Now we're done and we can plot the smooth model as a red line going through the noisy blue markers.
hold on;
plot(xFitted, yFitted, 'r-', 'LineWidth', 2);
grid on;
title('CoVid-19 Daily Deaths in the USA -- Exponential Regression with fitnlm()', 'FontSize', fontSize);
% Put a line at the peak.
darkGreen = [0, 0.5, 0];
xline(coefficients(3), 'Color', darkGreen, 'LineWidth', 3);
% Put up text for the green line.
str = sprintf(' Peak at %s', datestr(coefficients(3)));
text(coefficients(3), 100, str, 'Color', darkGreen, 'FontSize', 14, 'FontWeight', 'bold');
legendHandle = legend('Actual Y', 'Fitted Y', 'Location', 'northwest');
legendHandle.FontSize = 25;
hFig.WindowState = 'maximized';
fprintf('Done running %s.m.\n', mfilename);

Best Answer

Related Solutions

MATLAB: Parameter estimation nlinfit vs. fitnlm

MATLAB: How to use fitnlm

Related Question