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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Find necessary operators for symbolic regression
I wrote a symbolic regression tool in Python. It is possible to give unary and binary operators. If nothing is specified, I want to determine potential operators. So, I want to know if there is an ...
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Logistic Regression: Gradient Descent and Accelerated Version Thereof not acting as intended
Consider the regularized logistic regression problem:
$$\min_{\theta \in \mathbb{R}^n}\sum_{i=1}^m \ln \left(1+e^{-y_i\theta^T x_i}\right)+\frac{\lambda}{2}\big\lVert\theta\big\rVert^2_2.$$
Here, $y_i ...
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Gradient Descent vs Accelerated Gradient Descent
I have this Exercise in my Numerical Optimization class and here it is:
In this exercise, you will consider the ridge regression problem:
$$\min_{x \in \mathbb{R}^n}\frac{1}{2}\|Ax-y\|^2_2+\frac{\...
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Fitting a spherical surface given points with known distances from the (unknown) surface
There are numerous techniques to fit a sphere (with unknown centre and radius) through points in $R^3$, such that the fitted sphere passes through the points as closely as possible (in the least-...
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Linear least squares with selective parameter fitting
Suppose I have a linear model depending on 2 sets of parameters $a,b$
$$
z(t) = \sum_i a_i \Phi_i(t) + \sum_j b_j \Psi_j(t)
$$
Now suppose my data vector $z$ can be naturally divided into 2 sets: $x,y$...
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scipy exp model fitting: prevent coefficients blowup
I'm trying to fit a few X-Y points that look like exponential.
I used the following scipy code:
...
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Finding equation of surface from known data
I have the raw data of $X$, $Y$, $Z$, where $X$ and $Y$ are inputs and $Z$ is the output. Plotting the surface gives the red curve:
The surface seems to be a simple function involving trigonometric ...
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Equivalency of lasso problems
In the literature, I've seen the lasso problem phrased as the minimization of: $$\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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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 ...
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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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