# Tagged Questions

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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### 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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### PenaltyFunction Option in NMinimize

I am curious if anybody has some experience in using the built-in Option "PenaltyFunction" in any of the numerical optimization functions like NMinimize. According to the documentation the user ...
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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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### 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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### 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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### 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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### 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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### FindFit with a sophisticated function (2), with corrected question and code

I am trying to find a fit to the distribution function (empiricial data) in terms of a function which is itself an integral of a product of two simplier functions. In particular, I observe T(x) (this ...
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### Evaluation of likelihood very slow

I am trying to implement a simple statistical model for the first time in Mathematica. My model is made my one random variable which is the sum of background and signal. Background is an exponential ...
266 views

### Solution to heat equation with Neumann boundary conditions and lateral heat loss

I am conducting an experiment on heat conduction in a copper rod. To do so I am using a thin copper rod with several temperature probes, then I am going to compare the data with a solution to the heat ...
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### How does LinearModelFit handle cases where the design matrix rank is lower than the model terms?

So, I understand what this error means: ...
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### Fit a custom process to a data: inhomogeneous 2-state Markov chain

I would like to fit a custom process - a time inhomogeneous 2-state Markov chain, to data. The time inhomogeneity is a result of the transition probabilities varying sinusoidally through time with a ...
166 views

### How to control precision of parameters in NonlinearModelFit?

I am using NonlinearModelFit for fitting a dataset to some complex numerical model function that depends on a few parameters. The final required precision of these parameters is very low, like 3 ...
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### How do I add custom deviation when using LinearModelFit?

I have a set of data in the form a list S1={{x,y},{x,y}} etc. I also have a function that calculates a corrected standard deviation in the y direction for ...
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### Error associated with parameters in Minimize (or NMinimize) in discrete fitting

my problem goes as follows: I need to a discrete fit of a discrete function. Say I have the following made up data points, which are generated by the parabola ...
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### Updating procedural fitting algorithm to more efficient style?

For some time now, I have used this procedural programming approach to fit data in my research that is too cumbersome for the built in Mathematica functions. (Although this simple example works fine ...
184 views

### Comparing two ways of fitting systems of ODEs to data

I'd like to ask you if you see any difference between the two following ways of estimating parameters. Given my system of ordinary differential equations that I want to use to find the values of all ...
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### Cross-validation of a FittedModel

Although I would know how to perform cross-validation tests after fitting a model using a function like NonLinearModelFit, I wonder if there is a way to do this providing the right parameters to the ...
319 views

### Developing easy code to apply Delta Method to generate prediction bands for custom distributions

I think that this is an interesting issue for all those who when to not only adjust one prediction function, but also to obtain the prediction bands to asses the graphical or tabular error I'm trying ...
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### A more efficient way of fitting a non-linear model that returns an entire list?

I have a function that takes two parameters, del and nu, and returns a list npoints long ...
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### LeastSquares with some parameters missing

I want to do a partial least squares (PLS) regression using LeastSquares on my data. The input parameters are temperature, humidity and pressure for a given date. ...