Tagged Questions

Regression analysis is the process of measuring and establishing a relationship between a dependent variable and one or more independent variables.

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Curve fitting for oscillating data

This is my first question. I have the following data that I'd like to express as a function: Any suggestions how to modify the function shown below so as to get a closer fit?
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Nonlinear Least Square Regression - Black-Box or LMA Type Methods

In Nonlinear Least Square Regression, is providing errors from all calculated points to the solver like LMA provide any advantage (in terms of speed and number of iterations) over minimizing the sum ...
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Calculus of Variations with unknown cost function but some data

I have a problem that I've framed out in a particular way, but I don't know if I'm re-inventing the wheel here. Is there an existing literature base in this problem? Does it have a corresponding term ...
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Fitting a rectangle to a point set

I have an ordered list of (2d-)points that are forming a (not axis aligned) rectangle and I'd like to recover that rectangle. Approximations like a minimal enclosing rectangle can't be used so that I'...
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For finding the track of an object through space(3d) over time, what is the correct slope equation to use in the algorithm?

I am working on a program that tracks a flying object through space and predicts the future position of said object. I was given some equations to use, but some of them do not look right, mainly the ...
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Clever ways to update LU factorization for ridge regression

Ridge regression can be posed as minimizing the following objective function (over $x$): $$\frac{1}{2} \lVert Ax - b \lVert_2^2 ~+ \frac{\lambda}{2} \lVert x \lVert_2^2$$ Which has a closed form ...
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R - Best practice to deal with redundancy and suppression in multivariate regression analysis?

I have to run a OLS on census and secondary DV. I am pretty new to R and I wonder what is the best and simplest way to deal with redundancy and suppression.
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Finding rate of convergence by curve fitting in Matlab

I have some data: number of nodes $N$ and error in energy norm corresponing to it. I have seen in some references that the rate of convergence is reported by $$\| u-u_h\| _E=CN^{\alpha}$$ How can ...
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Using differential evolution to identify multiple local minima

I have quite a complicated minimisation problem over around 10 to 20 variables. Using differential evolution I can reliably find a global minima and with repeat fitting I return parameter values that ...
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Oscillating convergence in my Resilient BackPropagation (RPROP) implementation

I have implemented in matlab a neural network that uses rprop's algorithm to update its weights. Strangely the error on the training set does not converge to a local minimum, but oscillates. Here is ...
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Problems Implementing the Remez Algorithm

So first off: *** This code is not being used in production software. It is a personal project of mine, trying to understand approximation theory and advanced curve fitting. In other words, I'm ...
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linear solution of curve fitting on multiple linear functions differing by a multiplier

I am facing the following problem. I know nonlinear least squares can provide a solution but I am wondering if a linear way to solve this data fitting problem may exists. This is my input dataset: I'...
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Surface fitting

I do not need a complete answer but just some advice. I have a sparse matrix of points in a volume. I know a surface passing by these points exists and this surface is mostly flat and relatively ...
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Polynomial Fitting with Least Squares using Numpy and Scipy

I am trying to fit data to a polynomial using Python - Numpy. The points, with lines sketched above them are as in the picture. I am trying to fit those points to a polynomial of 4. or 5. degree. ...
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what went wrong with my logistic regression implementation in c++?

I have implemented a simple logistic regression function with IRLS algorithm using the armadillo linear algebra libray ...
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Partitioning Data for Multiple Regression Lines

We're all familiar with traditional least-squares method for constructing a straight line through a set of data points. The question is: suppose I show you a scatter plot which clearly is suggestive ...
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Differential equation - Model Fitting

My question is a quite simple one about statistics. I need to know the following thing. I have a differential equation from my model which I can solve. Now I can compare this solution with the ...
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Parameter Fitting: Need measure of data 'support' for a parameter solution

I am estimating parameters on a dataset that would, for the most part, result in a weakly constrained solution. The dataset however also contains a few more data points that make the solution well-...
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Fitting one set of points to another by a rigid motion

I'm not really sure how to explain this problem clearly, so please bear with me. I have a basis of 3 orthonormal unit vectors and a position, a standard 4x4 transform matrix in computer graphics. ...
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How to obtain the minimum set of variables required in a model to produce accurate estimation?

I have a system which I assume is linear. I have a matrix $A$ of which each row is a coefficient of a unknown variables in vector $x$. I have vector $B$ which contains the result of each $Ax$. ...
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Averaging scattered data

I have multiple sets of measured data that can easily be visualized using a scatter plot (red and black points in the figure). If my measurements were perfect, the red and black points should lie on a ...
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parameters estimation

I have to estimate a parameter (K), but I don't know how I can do it. I think by a regression model (minimum least square?), but I'm not sure. The system is: ...
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Determining optimal number of clusters and Davies–Bouldin Index?

I'm trying to evaluate what is the right number of cluster needed for clusterize some data. I know that this is possible using Davies–Bouldin Index (DBI). To using DBI you have to compute it for any ...
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How to compute the optimal ridge regression model

I found R function ridge.cv very useful. I would like to implement the equivalent function in MATLAB. As a starting point, I used MATLAB function ...
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When fitting a Gaussian-like function, how does the amount of baseline datapoints affect the fit?

I am fitting a curve to some instrument data. The data is a pulse with a particular functional form, which starts from and returns to a constant (with noise) baseline level before and after the pulse. ...
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Matching Similar Items from a Set

I'm trying to match items. Given a set of $n$ items I can rank on a scale from 0 to 100 of how similar they are to one another. For instance, if item $n_1$ is milk and item $n_2$ is also milk, then ...
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Reporting curve-fit results in a scientific paper

(I hope this question fits this site; if not, accept my apologies). I ran a certain simulation, and got a time series y(t), t = 0, 1, ... 20. After trying some functions, I found that: ...
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Recover curves from noisy collection of points

Background: I'm trying to make a system that tracks a number of bubbles in a video I'm implementing the bubble detection in the single image case using the Circular Hough Transform. Due to occlusion,...
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What methods are suggested to solve problems of the form $\min || {A} x - y ||_k$, subject to $x^T P x \leq c$, and/or $x^T Q x = d$?
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What are all of the different methods for parameterizing an amino acid (or other small molecule)?

What are all of the different ways to derive the partial charges, van der Waals interactions, bond lengths, etc. of an amino acid (in other words, all of the parameters that could be used in a ...
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Polynomial Regression using Semidefinite Programming

I'm trying to design the frequency response function for a low-pass filter. I need the function to be polynomial and to fulfill the following constraints: the coefficients must sum to 1, the function ...