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      Questions tagged [linear-regression]

      The tag has no usage guidance.

      -2
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      0answers
      25 views

      how to filter measurement noise out of a set of data [migrated]

      I need to find the best way to filter white noise from a set of data $(x_0,y_0),...,(x_n,y_n)$, $n>1000$, where $x:\text{ is a time variable}$ $y:\text{ is a physical quantity}$ The noise is ...
      8
      votes
      3answers
      207 views

      Regularized linear vs. RKHS-regression

      I'm studying the difference between regularization in RKHS regression and linear regression, but I have a hard time grasping the crucial difference between the two. Given input-output pairs $(x_i,y_i)...
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      2answers
      66 views

      Unique parameterization of size MxN matrices of rank k

      Any rank k matrix $Y\in\mathbb{R}^{m\times n}$ can be written as: $$ Y = UV'$$ Where $U\in \mathbb{R}^{m\times k}, V\in \mathbb{R}^{n\times k}$. This factorization is not unique since for any ...
      4
      votes
      2answers
      192 views

      Given the joint probability distributions of $X$ and $Y$ for $Y = R\,X+C$, find the probability distributions of $R$ and $C$

      Let $R$, $C$, and $X$ be independent random variables defined on $(0,\infty)$ and $$Y=\underbrace{R\, X}_{Z}+C.$$ We are given the joint probability distribution of $X$ and $Y$, $P_{XY}(x,y)$ and ...
      3
      votes
      1answer
      75 views

      Why to multiply the penalty by $n$ in the penalized least squares and likelihood?

      In the SCAD paper by Fan and Li (2001), there exist two forms of penalized least squares as follows: $$\frac{1}{2}\left \| y-X\beta \right \|^2+\lambda \sum_{j=1}^{d}p_j (\left | \beta _j \right |),$$ ...
      2
      votes
      0answers
      37 views

      increasing inter-class distances results in decreasing linear regression error

      Let $\{\mathbf{x}_i, y_i \}$ be a set of binary-labeled samples ($\mathbf{x}_i \in \mathbb{R}^d, y_i \in \{a,b\}, a,b\in\mathbb{R}$). Let $\{ \mathbf{x}'_i, y_i \}$ be also such a set. Define $\mathbf{...
      2
      votes
      1answer
      45 views

      matrix regression under side conditions

      I want to solve the folowing problem B*M=V, where B is the unknown of size 3x3, M of size 3xN and V of size 3xN. The difficulty is, that B has to be unitary. N is in the range of 500. All matrices ...
      1
      vote
      0answers
      80 views

      A different objective function in liner regression analysis

      I'm an undergraduate student who is green in statistics. I have a problem in the chose of objective function when estimating the parameters. Let $Y = \beta^TX + \epsilon $ be the standard liner ...
      4
      votes
      1answer
      6k views

      Gauss-Newton vs Gradient Descent vs Levenberg-Marquadt for least squared method

      I need to clarify some idea I have in my mind about linear and non-linear regressions. Whatever I now about this topic comes from the book of Taylor "Introduction to error analysis": a set of ...
      1
      vote
      0answers
      57 views

      Posterior consistency of non linear model

      This is possibly a reference request. Let $G$ : $\mathbb{R}^p \to \mathbb{R}^q$ be a continuous injective/bijective function. Let $\mu$(we may also assume this to be a non degenerate Gaussian) be ...
      2
      votes
      0answers
      130 views

      Derivation of gradient of SSE in Geodesic Regression

      On page 79 (or page 5) of this this paper the gradient of the SSE of the Geodesic model is described explicitly. My question is how are these equitations derived in detail; where can I find the ...
      2
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      3answers
      1k views

      When does a Vandermonde-like matrix have full rank

      I have a matrix which is similar to Vandermonde matrix except that the entries are monomials of degree $d$ polynomial in 2 variables. Each row has the following form: $X_{i}= [1, x_{i}, y_{i}, x_{i}^...
      2
      votes
      0answers
      219 views

      Is there an efficient way to compute the “complete subset regression”?

      Background: Let $X \in \mathbb{R}^{N\times K}$ and $y \in \mathbb{R}^{N\times 1}$ be data for a regression problem. The aim is to find $\beta \in \mathbb{R}^{K\times 1}$ such that $X\beta \approx y$ ...
      1
      vote
      1answer
      132 views

      Checking the intersection of two sets

      Let $E\subset{\mathbb R}^n$ be a set of the type $I_1\times \dots \times I_n$, where $I_k$ are real intervals, and $X$ be and $n\times p$ real matrix. Suppose also that $rank(X)=p$ and $n>p$. Is ...
      -1
      votes
      1answer
      225 views

      Fitting a quadratic using regression when the y-intercept needs to be 0 [closed]

      I'm trying to fit a quadratic $a_0 + a_1x + a_2x^2$ by Polynomial Regression: $$ \begin{pmatrix} n & \Sigma x_i & \Sigma x_i\\ \Sigma x_i & \Sigma x_i^2 & \Sigma x_i^3\\ \Sigma ...

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