Questions tagged [regression]

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16 votes
3 answers

How to model nonlinear regression?

As part of my research in statistics, I recently stumbled upon this paper1 which provides an operational perspective into linear models. In simple linear regression, quadratic programming can be used ...
TheSimpliFire's user avatar
  • 5,341
7 votes
3 answers

Training ML models to be used as objectives in optimization problems

Suppose that we have data (in my case, from a chemical process) which includes input data $X$ (characteristic of the material to be processed) and decision data $Y$ (decisions taken by operators to ...
Borelian's user avatar
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7 votes
1 answer

Ridge Regression lagrange duality

In every machine learning book we see that it is roughly mentioned that the ridge regression: $$p_1^* = \min\limits_{\beta} \ \left( \mathrm{RSS} + \lambda\sum_{j=1}^p \beta_j^2 \right)$$ is ...
independentvariable's user avatar
4 votes
0 answers

Fast solvers for LASSO-type non-convex optimization problems

Given $y \in \mathbb{R}^{n \times 1}, X \in \mathbb{R}^{n \times p}$, $p > n$, assume a LASSO-type optimization problem in the form of $$ \hat\beta=\underset{\beta}{\operatorname{argmin}}\frac{1}{2}...
runr's user avatar
  • 141
3 votes
1 answer

Translate standard weighted least square regression to quadratic programming

Sorry if this is really easy for you gurus. I'm trying to derive the reformulation of a weighted least square regression to a quadratic programming form. I understand there is a closed form solution ...
inf's user avatar
  • 129
2 votes
1 answer

How to show that minimizing the epsilon-insensitive loss is equivalent to a quadratic program with inequality constraints?

This question is about an optimization problem that arises in support vector regression (SVR). Suppose you have $N$ pairs $(\vec{x}_n, y_n)$ as data and would like to find a vector of weights $\vec w \...
ForceBru's user avatar
  • 123
2 votes
1 answer

Lagrange for quadratic programming with linear constraint

First of all, thanks for the help in previous post. The problem I'm facing is some legacy codes used Lagrange multipliers to solve a weighted regression problem. New requirements changed and I'm ...
inf's user avatar
  • 129
2 votes
1 answer

Loglog transformation of optimization problem, how can the solution be equal to the nontransformed counterpart?

Consider the following two functions: $$y_t = e^{lt} \cdot e^{st} \cdot \prod_{p=0}^{n} x_{tp}^{b_{tp}}\tag1$$ Where $e^{lt}$ captures the trend, $e^{st}$ captures the seasonality and $x_{tp}$ is our ...
richardhansson's user avatar
2 votes
0 answers

Tanaka's Fuzzy House Price Problem

I would like to understand and solve Tanaka's fuzzy house price problem (Table III). Unfortunately I couldn't able to build the problem structure and restrictions here (according to (19)). Anyone have ...
maninthemirror's user avatar
0 votes
3 answers

Operational research and Linear regression

I have a pretty large data set with several independent variables and one variable that I would like to explain the behavior (dependent variable). What I want to do is find the linear coefficient and ...
ooo's user avatar
  • 119
0 votes
1 answer

non-linear regression analysis using a floor function over the independent variable?

I have created a data set to understand better an equation and apply it to predict behavior. The equation is y = 10/(1+k*⌊((x/t)^s)⌋). To create the data set and see if it is working properly, I did ...
Juan Pablo Molano Gallardo's user avatar