Questions tagged [fitting]
Questions on the use of Mathematica to construct models for approximating empirical data.
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questions with no upvoted or accepted answers
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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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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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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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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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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
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530
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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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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
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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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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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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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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 ...
user79703
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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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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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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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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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5
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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 ...
5
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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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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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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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How can I get the standard error of parameters from FindFit?
I used FindFit with Norm function as written below.
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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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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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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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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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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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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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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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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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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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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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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
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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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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
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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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3
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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
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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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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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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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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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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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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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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 $\...
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Finding percentage of points within tilted ellipse?
I am trying to find the number of data points that I have that are within a tilted ellipse that I have generated to represent the 68% confidence region. I generated some data using:
...
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How to fit my data with following equation?
I have set of data of electronic specific heat ($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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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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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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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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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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