Questions tagged [regression]
Regression analysis is the process of measuring and establishing a relationship between a dependent variable and one or more independent variables.
0
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1answer
16 views
Minimize squared error of linear function
Let $M$ be a $m \times n$ matrix, $x$ a $n$-vector, $y$ a $m$-vector, and $\|\cdot\|_2$ represent the $L_2$ norm (i.e., Euclidean norm). Given $M,y$, the goal is to find $x$ that minimizes the ...
1
vote
1answer
55 views
Correct weighting in least squares fitting
I am trying to fit some data points $d_i$ to a non-linear model function $m_i$, which depends on a number of fit parameters $f_k$ (I want to determine these) and also on some known, constant values $...
2
votes
2answers
94 views
What equation should I fit this set of data points to?
I have done an experiment Estimation of silver nitrate by potentiometric titration with standard KCl solution.
A plot of $\dfrac{\Delta E}{\Delta V}$ versus Volume of KCl solution gives the ...
1
vote
0answers
33 views
fitting exponential versus exponential w/ power
I have two models which I would like to investigate for my data. One form is:
\begin{equation}
\label{one}
f(r) = A e^{-B r}
\end{equation}
and the second is:
\begin{equation}
\label{two}
g(r)...
2
votes
2answers
40 views
Fitting 2D mapping data from multiple measurements
Given a set of points in a plane, and series of measurements of the distances between those points, how would I go about generating a best-fit model of the position of the points?
For example, given ...
0
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1answer
650 views
Numpy.polyfit with regularization
I am trying to use the numpy polyfit method to add regularization to my solution.
My non-regularized solution is
...
0
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2answers
51 views
Finding parameters numerically
I suspect that a function $f(x,y)$ is of the form $f(x,y)=a(bx+c)^{dy+e}$. I have access to several values of $f(x,y)$. How do I proceed numerically to find the parameters $\{a,b,c,d,e\}$?
By ...
0
votes
1answer
29 views
Propagation of error in fitting two sets of data to each other
I have two sets of experimental data: $\phi(t)$ and $I(t)$. In theory they are related to each other as: $\phi(t) = nI(t) $. By fitting these curves together I can find the value of $n$ (which is a ...
0
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2answers
59 views
will this methodology end up giving me a nonsense regression equation.
I'm wondering if this is a valid methodology to find the best regression equation for a given data set.
User provides a rang of estimated value for some set of variables. Th algorithm uses the ...
1
vote
0answers
47 views
Update model parameter with new data, discarding old data
I have this dataset, and I am using y = (a * x^n) / (b + x^n) Hill function as the model, where a is the limit of the Hill curve,...
1
vote
1answer
257 views
Compressed sensing: $\ell_0$ “norm” vs $\ell_1$ norm
Suppose we have a very efficient way to perform $\ell_0$ "norm" compressed vs $\ell_1$ norm compressed sensing. Specifically, $\ell_0$ "norm" compressed sensing is
$$\eqalign{
& \min \quad {x^T}...
12
votes
3answers
393 views
Fitting Implicit Surfaces to Oriented Point Sets
I have a question regarding quadric fit to a set of points and corresponding normals (or equivalently, tangents). Fitting quadric surfaces to point data is well explored. Some works are as follows:
...
1
vote
1answer
237 views
Data Analysis - Cooling Efficiency
I have a question as I am starting my dive into computational analysis.
I have a large set of data (~2 months) which includes the room temperature, HVAC status (heat/cool/off) and the location of ...
1
vote
1answer
30 views
Parameter identification for regression model
Consider the following regression model :
Y = AX + BU
where the size of Y is $N \times n$, A is $N \times n$, X is $n \times n$, B is $N \times n$ and U is $n \times 1$.
The matrices X,Y and U are ...
1
vote
0answers
42 views
Best way to to find fitting parameters for time series of decaying-growing oscillator type
I have discrete time series emerging from the numerical simulations.
It means that the time series can be slightly noisy.
The time series should "obey" to the following formula:
$$ \psi(t) = \sum_{i=1}...
8
votes
1answer
201 views
Methods to Estimate Optimal Distance Measure for Multidimensional Data Set
My problem at hand pertains to choosing a distance measure for use in locally weighted regression. In my particular problem, I have a data set that is upwards of 10 dimensions, where the variables ...
1
vote
1answer
456 views
Curve fitting for oscillating data
This is my first question. I have the following data that I'd like to approximate as a parametric function:
\begin{align}
y = a + (bx_1 + cx_2 + dx_3 + ex_1x_2 + fx_1x_3 + gx_2x_3 + hx_1x_2x_3 + i)*(...
4
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0answers
75 views
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 ...
3
votes
1answer
957 views
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'...
0
votes
1answer
75 views
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 ...
1
vote
1answer
352 views
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 ...
1
vote
2answers
1k views
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 ...
1
vote
0answers
149 views
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 ...
4
votes
1answer
216 views
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 ...
1
vote
2answers
309 views
Polynomial approximation
Is there any universal method to fill this matrix for any $n$ value:
$\textbf{A} = \left[ \matrix{n & \sum x_i & \sum x_i^2 & \cdots & \sum x_i^n \cr
\sum x_i & \sum ...
0
votes
1answer
482 views
Power series regression linear fit in VBA excel
I wrote a program that calculates the best fit in VBA excel for the following model
$$
y_k=c_1x_k+c_0+c_{-1}(x_k)^{-1}
$$
solving for the best fit parameters $c_1$, $c_0$, and $c_{-1}$. However I ...
1
vote
1answer
178 views
Constrained linear least squares matrix equation
It has been a while since I have done linear least squares, so forgive the simple question, but here goes:
I am attempting to find the best fit coefficients, $\{c_i\}$, of a linear combination of ...
0
votes
1answer
2k views
How do I correctly multiply vectors and matrices in Python and MATLAB?
I have been trying for 2-3 days now to get L2 regularized logistric regression to work in Matlab (CVX) and Python(CVXPY) but no success. I am fairly new to convex optimization so I am quite frustrated....
0
votes
1answer
95 views
Can Box-Cox transformation be applied for data of this form?
I have data of the form:
X Y
3.53 0
4.93 50
5.53 60
6.21 70
7.37 80
9.98 90
16.56 100
And I want to find out $n$ so that this can be ...
4
votes
0answers
567 views
Neural network performs worse when using more input variables
This question is based more on the theory of neural networks than my particular implementation. Therefore I will leave out my code unless requested.
I'm working on a project in C# which can create ...
1
vote
1answer
109 views
What are good parametrizations of rational functions for response surface models?
For fitting a response surface model to a physical process, I have 3-4 relevant "signals", like a feature density, a signal based on a feature width, or a signal based on a distance to the next ...
1
vote
0answers
2k views
Piecewise linear approximation of an experimental data curve. Knots position constrained
I need to fit a curve, obtained from experimental data, with a piecewise linear model (4 knots and therefore 3 lines).
I tried using the MATLAB function
...
2
votes
1answer
119 views
fitting a non-linear curve
I have an equation:
$\ddot{x}+(\delta+\epsilon\cos{t})x=0$ known as the Mathieu equation.The $\delta-\epsilon$ parameter space of this equation looks something like
The red lines in this diagram ...
7
votes
4answers
2k views
Seeking a free symbolic regression software
Now that Formulize / Eureqa started charging $2500 a year for using it and having crippled the trial version, does anyone know of any replacements that can do similar things like find an equation ...
1
vote
0answers
55 views
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'...
6
votes
4answers
3k views
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 ...
3
votes
0answers
908 views
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. ...
1
vote
1answer
140 views
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
...
1
vote
1answer
72 views
Least Angle when $\textbf{A}^T\textbf{A}$ is singular
I'm teaching myself this regression stuff, so forgive me if this is a basic question. I can't seem to find a discussion of my particular problem.
So I'm least-squares-ing this overdetermined system $\...
3
votes
0answers
72 views
Why not use this simpler variant of Stepwise Regression?
In stepwise regression, you step predictor by predictor, each time selecting the one with the greatest correlation with the measurement, subtracting greedily to leave a residual with no correlation to ...
4
votes
2answers
6k views
Tikhonov regularization in the non-negative least square - NNLS (python:scipy)
I am working on a project that I need to add a regularization into the NNLS algorithm. Is there a way to add the Tikhonov regularization into the NNLS implementation of scipy [1]?
[2] talks about it, ...
4
votes
2answers
295 views
Can the Levenberg-Marquardt algorithm be used for minimization and not fitting
Can the Levenberg-Marquardt algorithm be used for minimization and not fitting?
Usually we input the derivative of the function we want to fit in the minimizer. Now if I assume I have an objective ...
2
votes
1answer
700 views
Some questions about MINPACK usage and messages
I am trying to use the nonlinear fitting routines of MINPACK for fitting a rather complicated equation of state to a set of experimental data. A subset of the data is fitted fairly well to a ...
3
votes
1answer
188 views
How to detect specific behavior in time series?
I was not quite sure what the right SE for this was, so I posted this also here on DSP. Please tell me which one to remove :)
Problem statement
I have a few hundred unrelated time series, say $P_i(t)...
3
votes
0answers
58 views
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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0answers
74 views
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 ...
3
votes
2answers
66 views
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-...
7
votes
1answer
5k views
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.
...
3
votes
1answer
56 views
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 $Ax$.
...
3
votes
3answers
1k views
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 ...
