# Tagged Questions

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### linear solution of curve fitting on multiple linear functions differing by a multiplier

I recently posted this question here but I thought this could be of interest also in mathematics, given I found a partially related question here I am facing the following problem. I know nonlinear ...
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### Regression with error coming from rounding

I am looking at the following model: $c$ is a fixed vector in $\mathbb{R}_+^n$ and for any $x \in \mathbb{R}_+^n$ we obtain a value $y =[c^Tx]$, i.e. rounding $c^Tx$ to the nearest integer. I want ...
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### Deriving estimators for the parameters a and b that minimize the random error - setting up linear regression variables?

I'm reviewing old notes, and I know I solved this way back when, but can't remember how to know: Consider the simple linear regression model: $$Y_i = a + bX_i + \epsilon_i$$ where $Y_i$ is the ...
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### Convexity of LASSO

I would like to know if some variables in design matrix are correlated then LASSO is convex or not. If you give me a proof for convexity of LASSO and ADAPTIVE lasso, I will be thankful. LASSO is ...
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### Minimum required data for cosine fit

With a minimum amount of (noisy) data-points, I need to find the amplitude of a simple cosine y=A*cos(x), where x is an angle from 0:2pi. I know how to fit data to the function, and I know how to ...
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### Calculating the “likelihood of progressive fit”

I am faced with the following least squares model fitting problem: I have a process that generates time series data. This time-series data have a specific structure (i.e. i can fit a model with ...
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### Jacobian in Levenberg-Marquardt for 4-Parameter equation

I am trying to fully understand how I can use Levenberg-Marquardt to minimise a 4 parameter equation. There are lots of fancy programs to do this but the documentation about the mathematics is ...
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I know there is one to one relationship between $\lambda$ and $t$ in the following two equivalent optimization formulation. But what is exact relationship? A) $$\sum_i(y_i - \sum_k \beta_k ... 2answers 114 views ### Guess the functional form of a graph Can you guess the functional form of the following curve y is 0 at x= Infinite ; y is very small ( +ve near to zero) at x=0 Thanks and regards 1answer 468 views ### Lasso - constraint form equivalent to penalty form We know that there are two definitions to describe lasso. Regression with constraint definition:$$\min\limits_{\beta} \|y-X\beta\|^2, \sum\limits_{p}|\beta_p|\leq t, \exists t $$Regression with ... 3answers 703 views ### Exponential extrapolation Given a set of points on 2D surface (x_1,y_1),(x_2,y_2),\ldots,(x_n,y_n) and a function f(x)=k+ab^x, the task is to find values of k,a and b that minimize the following sum:$$\sum_{i=1}^n ...
I would like to fit a formula $ax^b + cx^d+ e$ to a set of points. I have two questions. If my data were perfect, how many points do I need in the worst case to get $a,b,c,d,e$ exactly? If my data ...