Questions tagged [fitting]

Questions on the use of Mathematica to construct models for approximating empirical data.

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Nonlinear least squares on a GPU with Mathematica 9

Update: A Mathematica wrapper for (https://github.com/zitmen/cuLM) should allow for us to directly implement the Levenberg-Marquardt algorithm in CUDA for nonlinear least squares fitting. In a ...
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15 votes
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334 views

New issue or new setting(s) of Goodness-of-Fit Tests in 11.3@student edition

Bug introduced in 11.3 or earlier and persisting through 11.3.0 or later Just before upgrading to 11.3.0 on last Friday, i was having p-value results from 11.2.0. Not worrying about upgrade may ...
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14 votes
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947 views

Implementation of Partial Least Squares (PLS)?

I'm looking for a PLS implementation for Wolfram Mathematica. I just can't seem to find any implementation for it - do you know one? In general, I'm a bit confused that there exist only so few third-...
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7 votes
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301 views

Multivariate Adaptive Regression Splines (MARS) - Mathematica implementation?

Does anybody have or know of a Mathematica implementation of the Multivariate Adaptive Regression Splines (MARS) algorithm?
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7 votes
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Is there a way to produce a FittedModel object as the solution to a regularized regression?

I can get the Ridge or Tikhonov regression solution to Y = \[Beta].X easily enough as ...
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6 votes
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530 views

How to fit B-splines to unstructured grids (triangulated surfaces)?

As a continuation of trying to calculate curvature tensors on triangulated surfaces (here), I am interested in trying other methods. One approach is to use NURBS. To be more precise I would like to be ...
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6 votes
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559 views

Custom Methods for NMinimize/NonLinearModelFit

Is there a way to write custom methods for NonLinearModelFit or NMinimize? To give background, I currently have a batch of code ...
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6 votes
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392 views

Problems extending NelderMeadMinimize into 2D

Update The eventual route I followed was to adapt a version of the NM-simplex written in C and link to it with MathLink. Once I've tested this out fully I'll post it here. I've been playing around ...
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5 votes
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CirclePoints and CircleThrough

$Version 12.2.0 for Microsoft Windows (64-bit) (December 12, 2020) For points (located on a unit circle), ...
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5 votes
1 answer
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Is MeanPredictionBands synonymous with a confidence interval in Mathematica?

I am a little confused by Mathematica's use of the term prediction interval in NonlinearModelFit. We are given two kinds of prediction bands as an option: ...
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5 votes
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317 views

Histogram (automatic binning)

There are different methods for choosing widths of bins for a histogram, like Freedman-Diaconis rule. In Mathematica, without choosing a specific method, with the command ...
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5 votes
0 answers
91 views

Improving speed performance of 'Fit' with BSplines?

Context In the context of this (vaguely controversial) question, I am stumbling into a performance issue with Fit. Let me illustrate on fitting a set of ...
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5 votes
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What does the PerformanceGoal option of FindMinimum do?

FindFit and FindMinimum both have a PerformanceGoal option. It is not documented. What does ...
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5 votes
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170 views

What are the most reliable test of goodness of fit in Mathematica

I realise this is possibly a VERY open ended question, and potentially has answers dotted around e.g. here . What are the most robust methods of testing the result of ...
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5 votes
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709 views

Estimate process parameters of geometric Brownian motion with a two-state Markov chain

I have the following sequence. Consider a model that follows a geometric Brownian motion whose drift switches between two different regimes representing the up trend and down trend. The regime ...
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390 views

Softmax Regression Classification Algorithm

I'm following the Stanford Machine Learning course while simultaneously developing my Mathematica abilities. I'm having issues with my Softmax Classifier implementation (for ref, have a look at these ...
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5 votes
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156 views

Fitting data with unique variable per measurement

Imagine we are in the following situation, we have a nonlinear system of functions $f$ with coördinates $x_i$, and unknown parameters $\delta_i$'s and $t$. Let this system be defined as, \begin{...
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Third syntax version of LogitModelFit: unexpected result of "BestFit"

The third listed syntax version of LogitModelFit allows one to specify input in a simple way: Only a design matrix (with a row of values of the explanatory input ...
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5 votes
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546 views

Module in numerical model for NonlinearModelFit is slow and leaks memory

I am trying to make a NonlinearModelFit where the model is the result of a numerical calculation. My code works, but it is very slow and also seems to have a memory ...
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5 votes
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930 views

Analytical model fitting

I have a special type of model fitting problem that I am trying to solve in Mathematica. Any insight how to attack it using available tools of Mathematica will be great to hear. We have a variable $$ ...
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4 votes
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121 views

How can I get the standard error of parameters from FindFit?

I used FindFit with Norm function as written below. ...
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4 votes
0 answers
140 views

Fit Markov Chain

Assume a simple Markov Chain with the transition matrix ...
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  • 387
4 votes
0 answers
87 views

How to get statistics of FindFit with changed norm-function?

I changed the norm-function of FindFit according to this answer, because apparently it is not supported for NonlinearModelFit ...
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4 votes
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85 views

Optimization`FindFit`ObjectiveFunction and PenaltyFunction

Consider the following toy example: model = a Cos[w t]; data = Table[{t, Cos[2.1 t]}, {t, 0, 10, .25}] + RandomReal[.1, 41]; as both an unconstrained problem: <...
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4 votes
0 answers
392 views

Goodness of Fit of Copula Distribution

I am trying to find out goodness of fit of copula distribution, but Mathematica 10 gives me the same answer for each copula type. e.g ...
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4 votes
0 answers
212 views

Memory problem in Mathematica 10

I'm having a problem with memory. I'm doing nonliner fits of several data lists to a system of differential equations. When I evaluate the "Do" cycle the memory grows with the iteration step up to my ...
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  • 971
3 votes
0 answers
86 views

Finding multiple minimizers

Is it possible to find all (or as many as possible) minimizers of a given function? For example, minimizing the function $\cos(\pi(p-q))+\cos(\pi(q+p))$ for $-3\leq p,q\leq 3 $ can be done using ...
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3 votes
0 answers
204 views

Errors Using FindFit and FindRoot

I'm trying to fit the following equation to data: where and x and y are the dimensionless variables x=V/Vr and y=Ir/(2*I0). n=1 and I'm trying to find Vr and R. The blue is an example of the curve ...
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3 votes
0 answers
114 views

Can FindFit be used with units?

I am trying to use the units capabilities of Mathematica throughout a course that I am teaching, but am finding that it isn't uniformly implemented across many functions. In particular, I would love ...
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3 votes
0 answers
5k views

Failed to converge to the requested accuracy or precision within 100 iterations for NonlinearModelFit

So I have a lot of data, from the following type: ...
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3 votes
0 answers
308 views

How to extract the conditional variance from a fitted GARCH model?

In R's garchFit (fGarch) I can simply call "@h.t" or "@sigma.t" to get the conditional variance or standard deviation for a fitted GARCH model. Is there a convenient way achieve this with Mathematica'...
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  • 119
3 votes
0 answers
345 views

Power law fitting package that optimizes fitting parameters based off of the KolmogorovSmirnov MC method

I'm exploring power law fitting and would like to get to a point of making a power law package like what was discussed in this post, where OP references the R poweRlaw package. As per the comments/...
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  • 465
3 votes
0 answers
68 views

Meaning/Format of RAW Image Data

I took photographs and I want to fit the (overall intensity or red intensity) of the photographs to a function of (x,y). I have some questions about how RAW data is structured. What is the difference ...
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3 votes
0 answers
138 views

Estimating VARX(p,q) models in Mathematica

I would like to estimate the parameters of a vector autogressive process VARX(p,q) with n endogenous variables y and m exogenous variables x: $$ y_t = v + B_1 y_{t-1} + ... + B_p y_{t-p} + \theta_0 ...
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3 votes
0 answers
295 views

Least squares approximation

I have data points which is mydata = {{0, 0}, {1, 1}, {2, 0}}; From this data, I need to do the least squares approximation by using Bernstein polynomials to produce a set of Bezier points. Before ...
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3 votes
0 answers
158 views

PearsonChiSquareTest for count/frequency data?

I read with interest a previous question on the PearsonChiSquareTest from a few years ago, and one answer was very helpful: Performing a chi-square goodness of fit ...
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  • 43
3 votes
0 answers
167 views

Writing a function to set up and solve the least squares problem

I have setup the explicit line equation for a given set of points using least-squares approximation and the knots computed below. I have tried extending the same code for use with an arbitrary degree, ...
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3 votes
0 answers
288 views

The CorrelationMatrix is equal to corrcoef of Matlab?

How can I generate a matrix which is equivalent to the results of the "correlation coefficients" command (corrcoef) in Matlab? When I make a LinearModelFit, I can get a CorrelationMatrix, but is this ...
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  • 609
3 votes
0 answers
901 views

NonLinearModelFit with Two Dimensional List of Weights

I'm currently trying to fit Planck's law (B[λ, T]) to measurements, thereby determining Planck's constant. I have a list of triplets containing wavelength, ...
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3 votes
0 answers
1k views

Is it possible to marginalize one or several parameters obtained from fitting procedure?

Statistical model analysis package has a few fitting functions. Their arguments are data points, fitting model and parameters in the fit. The result is a set of best values for parameters, which ...
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3 votes
0 answers
274 views

Mathematica Complains about Non Symmetric Covariance matrix, when it's not the case

I was doing some fitting with Mathematica7 using NonlinearModelFit. It's quite long the program to do the fit and that's why I am not displaying here ... It goes ok, and I can get the fit parameters ...
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  • 701
2 votes
0 answers
123 views

How to perform feature selection for machine learning applications?

Feature selection is fairly easy in e.g. Python's scikit-learn which sports a module and tutorials or MATLAB. Mathematica even touts that it uses feature selection ...
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  • 493
2 votes
0 answers
71 views

ProbitModelFit is causing kernel crashes in Mathematica 12.0

Mathematica 12.0 I am running ProbitModelFit on a small data set (~130 rows). Intermittently, the function causes a kernel crash. I am curious if anyone else is ...
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2 votes
0 answers
96 views

Matrix regularization, how to pick $\lambda$

Since v12 FindFit[] now supports regularisation, such as Tikhonov regularization. Do there exist statistics to help guide the choice of the hyper-parameter $\...
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  • 3,842
2 votes
0 answers
92 views

Finding percentage of points within tilted ellipse?

I am trying to find the number of data points that I have that are within a tilted ellipse that I have generated to represent the 68% confidence region. I generated some data using: ...
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  • 379
2 votes
0 answers
236 views

How to fit my data with following equation?

I have set of data of electronic specific heat ($C_{el}/\gamma_n T$) vs temperature ($T/T_c$). My fit equation is this $$\frac{C_{el}}{\gamma_n T}=-\frac{6}{\pi ^2}\alpha \frac{\mathrm{d} }{\mathrm{...
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2 votes
0 answers
78 views

Strange result in LinearModelFit ANOVATable

For one of the models I'm building, the p-value in the ANOVA table obtained from the "ANOVATable" properties of a LinearModelFit ...
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  • 29
2 votes
0 answers
89 views

What does the following error message mean, in the context of NonlinearModelFit?

I am deliberately not including data or a model for this question, as I want a more general answer so that I may be able to trouble shoot this myself in the future. When performing a fit, usually a ...
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  • 2,291
2 votes
0 answers
131 views

How can you set the fit tolerance in `NonlinearModelFit`?

In NonlinearModelFit how can you set the tolerances of where the fitting terminates. I know you can set MaxIterations but how ...
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  • 2,291
2 votes
0 answers
99 views

What is optimized for each available FitRegularization setting?

Fit and FindFit now have a FitRegularization option, but the documentation is brief. What is optimized/minimized when each available setting is used?
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