Questions tagged [regression]
Regression analysis is the process of measuring and establishing a relationship between a dependent variable and one or more independent variables.
82
questions
8
votes
3answers
1k views
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 ...
1
vote
3answers
121 views
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 ...
3
votes
1answer
102 views
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 ...
0
votes
0answers
11 views
Optimal Time Series Weight for Quantile Estimation
Given a time series, $x_1$, $x_2$, ..., $x_t$, .... I want to solve for
$$\mathrm{min}_{w_1, w_2, ..., w_m}\rho(x_t-\mathrm{Quantile}(q; x_{t-1}, x_{t-2}, ..., x_{t-m}; w_{t-1}, w_{t-2}, ..., w_{t-m}))...
3
votes
1answer
191 views
Preconditioning vs. regularization
I used to be more of a numerical linear algebra and computational science person, but recently, I've crossed into stats and machine learning.
For this discussion, let's focus on matrices that are not ...
1
vote
3answers
160 views
How can we solve the normal equations with limited memory?
I was asked this open ended question in an interview once:
How would you find a solution to the normal equations with limited memory?
Unlike Solving sparse least squares system with limited memory, ...
1
vote
0answers
70 views
Error curve does not oscillate in between reference points using Remez
Using the Remez algorithm, implemented using multi-precision library, in certain functions that I want to approximate, the error curve does not oscillate in between reference points, and so no roots ...
2
votes
1answer
74 views
Linearization of Remez algorithm rational case
In the rational case, we are interested to find polynomials $P(x)$ and $Q(x)$ s.t.
$f(x_k)-P(x_k)/Q(x_k)=(-1)^kE$ for $k=1,2,\ldots, N$ where $N=deg(P)+deg(Q)+2$
This can be rewritten as
$$
(1)~~~~~~(...
2
votes
0answers
113 views
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 ...
0
votes
0answers
35 views
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 ...
3
votes
0answers
55 views
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 ...
2
votes
1answer
60 views
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 ...
2
votes
0answers
127 views
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 ...
2
votes
0answers
44 views
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 ...
0
votes
0answers
70 views
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 ...
1
vote
0answers
36 views
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 ...
1
vote
1answer
127 views
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 ...
1
vote
1answer
4k views
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.
...
-1
votes
1answer
38 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
70 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
508 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
35 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
59 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
votes
1answer
2k 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
votes
2answers
63 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
31 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
votes
2answers
62 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
52 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
310 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
$$\eqalign{
& \min \quad {x^T}...
15
votes
3answers
973 views
Fitting Implicit Surfaces to Oriented Point Sets
I have a question regarding quadric fit to a set of points and corresponding normals (or equivalently, tangents). Fitting quadric surfaces to point data is well explored. Some works are as follows:
...
1
vote
1answer
242 views
Data Analysis - Cooling Efficiency
I have a question as I am starting my dive into computational analysis.
I have a large set of data (~2 months) which includes the room temperature, HVAC status (heat/cool/off) and the location of ...
1
vote
1answer
35 views
Parameter identification for regression model
Consider the following regression model :
Y = AX + BU
where the size of Y is $N \times n$, A is $N \times n$, X is $n \times n$, B is $N \times n$ and U is $n \times 1$.
The matrices X,Y and U are ...
1
vote
0answers
47 views
Best way to to find fitting parameters for time series of decaying-growing oscillator type
I have discrete time series emerging from the numerical simulations.
It means that the time series can be slightly noisy.
The time series should "obey" to the following formula:
$$ \psi(t) = \sum_{i=1}...
7
votes
1answer
209 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
1k 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
votes
0answers
79 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 ...
2
votes
1answer
2k 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
76 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 ...
3
votes
1answer
777 views
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 ...
1
vote
2answers
2k 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
205 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 ...
7
votes
1answer
649 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
330 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
596 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
650 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
143 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
1k 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
127 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
...
