Questions tagged [regression]
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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biexponential fits where exponents are very similar to each other but different than best monoexponential fit
I have some data which consists of an exponential process in time convolved with a gating function. I am fitting the underlying exponential using the least squares method. (I also have experimental ...
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How to model data that is repeated over time within the same group, from which outcome variable is categorical and explanatory variables are linked?
I have 1 dependent variable that is categorical. And I have 3 explanatory variables, the two continuous variables are likely interrelated and the 1 categorical variable is not interlinked.
The sample ...
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Parameter choice rules for L1 regularization?
I am solving an L1 regularized least squares of the form like:
$$ \arg \min_{\boldsymbol{x}} \frac{1}{2} {\left\| A \boldsymbol{x} - \boldsymbol{y} \right\|}_{2}^{2} + \lambda {\left\| \boldsymbol{x} \...
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Given a set of 1d-points, find the most probable periodicity that models the points (with possible omissions) as equidistant occurences
I try to detect interference fringes in a bunch of pictures. I projected on one axis, and I was able to detekt the peaks that indicate one of the fringes.
So now I'm having a list with points (e.g. $(...
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Finding a best fit line for the upper bound on an $x$ vs $y$ relationship
I am trying to do linear regression on the following conceptualized problem. I have a set of data in pairs $(x, y)$. I know that $y$ is bounded by a linear function $f(x) = mx + c$. I want to estimate ...
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SciPy ODR "Ordinary" Least Squares?
Scipy.odr has a setting for "fit types", including one for ordinary least-squares. This matches with the documentation of ODRPACK (see p. 31, Computational method).
However, the package ...
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Reverse-engineering a quadratic fit?
The square root function for an old (pre-IEEE floating point, no hidden bit) mainframe (the Soviet BESM-6 works as follows:
Making sure the argument $X$ is non-negative
Splitting $X$ into the ...
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Fitting line to a staircase function
I have a staircase/step function $n(E)$. I know the points $\{E_i\}$ at which each "step" occurs and all steps are of constant height 1. I need to fit a line $a + bE$ to this function and ...
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Parameters estimation with fewer variables than parameters
I am trying to estimate parameters, 4 of them, by fitting a system of 3 ordinary differential equations.
I am using a model published that was using 3 parameters and gave a good fit to the data, and I ...
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Preconditioning vs. regularization
I used to be more of a numerical linear algebra and computational science person, but recently, I've crossed into stats and machine learning.
For this discussion, let's focus on matrices that are not ...
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How can we solve the normal equations with limited memory?
I was asked this open ended question in an interview once:
How would you find a solution to the normal equations with limited memory?
Unlike Solving sparse least squares system with limited memory, ...
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Error curve does not oscillate in between reference points using Remez
Using the Remez algorithm, implemented using multi-precision library, in certain functions that I want to approximate, the error curve does not oscillate in between reference points, and so no roots ...
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Linearization of Remez algorithm rational case
In the rational case, we are interested to find polynomials $P(x)$ and $Q(x)$ s.t.
$f(x_k)-P(x_k)/Q(x_k)=(-1)^kE$ for $k=1,2,\ldots, N$ where $N=deg(P)+deg(Q)+2$
This can be rewritten as
$$
(1)~~~~~~(...
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Remez algorithm convergence
I have implemented the Remez algorithm in Python where all calculations were done with the Python mpmath library. I have noticed that sometimes the $|E_{max}|$ and $|E_{min}|$ do not monotonically ...
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Comparing custom linear regression solver to SciPy equivalent in Python
From a given data set, I set out to complete a task which is below
Fit the data of the previous exercise to fit Eq. (8.18) using the SciPy function ...
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Least-squares fit of explicit parabolic sheet to data points
For a given set of data points
$$\{(x_i, y_i, z_i)\}$$
there exists some
$$f_{ABC}(x,y)=Ax^2+Bxy+Cy^2$$
that minimizes
$$\sum_i(f_{ABC}(x_i,y_i)-z_i)^2$$
$A$, $B$, and $C$ can be found quickly ...
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Using linear regression to find the ideal point given a set of trajectory's data
I have a set of points in 2D obtained from a pendular movement with some noise. I want to determine where is equilibrium point ($x_0$, $y_0$) from which the rope is fixed. There are at least two ...
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Proving convexity of Frobenius norm and correlation function formulations of an optimization problem
I have been working on formulating my requirements in the form of an optimization problem in a multi-output regression setting.
Firstly, I would like to make the variables I used in the problem and ...
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Good 3D surface fits for multiscale oscillatory surfaces
I have a 3D surface in $x$, $y$, and $z$. where $z$ is a function of $x$ and $y$ and my points are on a structured grid in $x$ and $y$. My function $z$ is highly oscillatory and irregular with ...
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Efficient inversion of multidimensional non linear function
I have a function $f:x\mapsto \vec{y}$ with $x \in [0,1]$ and $\vec{y}=(y_1,...,y_n) \in \mathbb{R}^n$. $n$ is a small integer e.g. $n=8$. Each of the component functions in $y_i(x)$ "oscilate" up and ...
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Fitting a multivariate PDE (using Java)
I'm doing simulations of 2 coupled PDE's with Comsol Multiphysics. I want to fit some data (using the Application method, whose language is Java) to those simulations.
In order to answer my question ...
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Spline regularization
I am fitting some B-splines to data, but the data has a "gap" region where the spline is less constrained by the data. I want to devise a regularization scheme to help prevent the spline from ...
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Gnuplot: How can I fit a range of points (out of the entire data) to a function?
I have a set of data obtained for the I-V characteristics of an LED.
...
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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 ...
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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 $...
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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 ...
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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)...
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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 ...
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Numpy.polyfit with regularization
I am trying to use the numpy polyfit method to add regularization to my solution.
My non-regularized solution is
...
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2
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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 ...
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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 ...
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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 ...
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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,...
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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
$$\eqalign{
& \min \quad {x^T}...
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Fitting Implicit Surfaces to Oriented Point Sets
I have a question regarding quadric fit to a set of points and corresponding normals (or equivalently, tangents). Fitting quadric surfaces to point data is well explored. Some works are as follows:
...
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Data Analysis - Cooling Efficiency
I have a question as I am starting my dive into computational analysis.
I have a large set of data (~2 months) which includes the room temperature, HVAC status (heat/cool/off) and the location of ...
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Parameter identification for regression model
Consider the following regression model :
Y = AX + BU
where the size of Y is $N \times n$, A is $N \times n$, X is $n \times n$, B is $N \times n$ and U is $n \times 1$.
The matrices X,Y and U are ...
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Best way to to find fitting parameters for time series of decaying-growing oscillator type
I have discrete time series emerging from the numerical simulations.
It means that the time series can be slightly noisy.
The time series should "obey" to the following formula:
$$ \psi(t) = \sum_{i=1}...
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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 ...
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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)*(...
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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 [duplicate]
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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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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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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2
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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 ...
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666
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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 ...
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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 ...
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