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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scipy exp model fitting: prevent coefficients blowup

I'm trying to fit a few X-Y points that look like exponential. I used the following scipy code: ...
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Finding equation of surface from known data

I have the raw data of $X$, $Y$, $Z$, where $X$ and $Y$ are inputs and $Z$ is the output. Plotting the surface gives the red curve: The surface seems to be a simple function involving trigonometric ...
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Equivalency of lasso problems

In the literature, I've seen the lasso problem phrased as the minimization of: $$\frac12x^tAx-x^tb+\lambda||x||_1$$ or of: $$\frac12||Ax-b||_2^2+\lambda'||x||_1=\frac12x^tA^tAx-x^tA^tb+b^tb+\lambda'||...
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3 votes
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How can I draw a regression line in log scale?

The supplied code draws some data points and the corresponding regression line. The regression line goes through or is near most of the data points on a linear scale. . However, on a log scale, the ...
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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 ...
QMStatMech's user avatar
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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 ...
Elly's user avatar
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2 votes
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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} \...
yourds's user avatar
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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. $(...
Quantumwhisp's user avatar
2 votes
1 answer
127 views

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 ...
Bernd's user avatar
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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 ...
Leo B.'s user avatar
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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 ...
adch99's user avatar
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4 votes
1 answer
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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 ...
Rem's user avatar
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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 ...
anonuser01's user avatar
1 vote
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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, ...
user5965026's user avatar
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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 ...
Daniel's user avatar
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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)~~~~~~(...
Daniel's user avatar
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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 ...
Daniel's user avatar
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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 ...
Kishan Bhatt's user avatar
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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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2 votes
1 answer
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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 ...
arantxa's user avatar
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2 votes
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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 ...
venkat's user avatar
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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 ...
Patrick Dietrich's user avatar
1 vote
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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 ...
J.A's user avatar
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1 vote
1 answer
457 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 ...
vibe's user avatar
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2 votes
1 answer
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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. ...
ntk47's user avatar
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-1 votes
1 answer
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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 $...
jitter's user avatar
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2 votes
2 answers
699 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 ...
ntk47's user avatar
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1 vote
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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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2 votes
2 answers
100 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 ...
Colin's user avatar
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1 answer
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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 ...
intergalactic_baba_yaga's user avatar
0 votes
2 answers
66 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 ...
thedude's user avatar
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1 answer
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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 ...
KabaT's user avatar
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2 answers
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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 ...
Dan Anderson's user avatar
1 vote
0 answers
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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,...
neo4k's user avatar
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1 vote
1 answer
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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}...
user40780's user avatar
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15 votes
3 answers
1k 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: ...
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1 vote
1 answer
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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 ...
Caoder's user avatar
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1 vote
1 answer
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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 ...
user41037's user avatar
1 vote
0 answers
49 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}...
Dmitry Kabanov's user avatar
7 votes
1 answer
215 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 ...
spektr's user avatar
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1 vote
1 answer
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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)*(...
user20730's user avatar
4 votes
0 answers
81 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 ...
Sycorax's user avatar
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2 votes
1 answer
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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'...
FooBar's user avatar
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0 votes
1 answer
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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 ...
cluemein's user avatar
  • 103
3 votes
1 answer
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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 ...
digbyterrell's user avatar
1 vote
2 answers
3k 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 ...
Rosa's user avatar
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1 vote
0 answers
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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 ...
Teo Teo's user avatar
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