# Questions tagged [constrained-regression]

constrained regression is (linear or nonlinear) regression models with further constraints on the coefficients. That could be non-negativity constraints, constraints on the norm of the coefficient vector or otherwise.

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### Linear regression of higher order polynomial with slope constraint

I am trying to constrain the coefficients on a higher order polynomial (let's say an order 6) for the curve to be decreasing. I have found this link, where the fitting of a 3rd order polynomial is ...
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### Inequality Constrained Least Squares: Computation of the Confidence Interval of the mean response

Suppose I wish to find perform inequality constraint least squares on the model $$y=X\beta +\epsilon$$ subject to a set of constraints $$T\beta>c \space \space.$$ Is there a way to compute the ...
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### How to fit several linear models with linear intercept-slope constrain?

I have a data where several groups exist: $i = 1, 2, 3...n$ ($n$ about 600 groups in total). For group $i$ theory predicts a linear relation $y = a_i + b_i * x$ with $a_i$ and $b_i$ intercept and ...
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### Relation between regularization and Lagrange multipliers

This is sort of a follow-up to What is the connection between regularization and the method of lagrange multipliers ? that I thought deserved a new question. Consider an optimization problem of the ...
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### Constrained parameters update during hidden Markov model forward-backward algorithm

I want to train a Gaussian hidden Markov model. I currently use the Python package hmmlearn. I looked thouroghly at the code to see how parameters are updated after each training iteration, but I ...
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### Adding limits to regression coefficients

For my problem, I have data that contains daily observations of the total time and the volumes of task A completed, task B completed, C, D.. and I am looking to estimate the time it takes to solve ...
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163 views

### Predict a vector of values with constraints? [duplicate]

I am aware of a variety of methods for simultaneously predicting multiple outcomes known sometimes as multivariate regression/analysis. However, my situation is a little more special. I am trying to ...
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### How can you constrain values to be positive when fitting a model?

I'm currently fitting a model using maximum likelihood estimation on biological data (electroencephalography). Basically, I'm fitting normal distributions to several subsets of data (experimental ...
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### least square with equality constraint and singular matrix

I have the following problem to solve: Ax = b where A is singular. To resolve this I introduce a condition Cx = d Even after this, I am not able to solve it using scipy.optimize.minimize as it ...
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### Multilevel modeling, constraint for positive values

I'm currently trying to fit a shifted inverse gaussian to reaction time data (always postive). My paramterization of the model includes 3 parameters, alpha, gamma and tau, which must always be ...
512 views

### Is it possible to apply a monotonicity constraint on a Gaussian process regression fit?

Below is a code using scikit-learn where I simply apply Gaussian process regression (GPR) on a set of observed data to produce an expected fit. I know physically that this curve should be ...
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### R - Linear Regression with parameters constraint - contr.sum contrast

I am facing a problem with running a simple OLS regression with two categorical independent variable. I would like to impose that the sum of the coefficients referred to one variable (x in the ...
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### How to run linear regression with constraints in R? [duplicate]

If I have the following data n<-1000 x1<-rnorm(n,1,1) x2<-rnorm(n,2,2) x3<-rnorm(n,3,3) e<-rnorm(n) y<-3+0.5*x1+0.2*x2+0.3*x3+e I want to fit a ...
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### method for predicting a curve

I have data on several curves. the data is of the form: curve_id x y and there are many x/y pairs for each curve and x is limited to some known range. overall, the curves look quite similar in ...
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### polynomial regression in R: how to add hard constraints (go through specified points)? [duplicate]

I'd like to perform polynomial regression on my data (which lies in [0,10]), but I need to ensure that the endpoints of the range are fixed, i.e. that the curve goes through (0,0) and (10,10). So the ...
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### nlme ignoring certain control arguments to nlminb

Issue: Do constrained optimization of parameters in nlme::nlme I'm trying to fit a non-linear mixed effects model using nlme::nlme, which can use 2 optimization schemes: stats::nlminb or stats::nlm. ...
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### Confidence limits for constrained penalized log likelihood model

I am estimating parameter $\beta$ as: \begin{align} \hat \beta &= \mathop{\mathrm{arg\,max}}_\beta \;\; l(\beta;X,y) - \frac{\lambda}{2}\left(\tilde y-g(\beta,\tilde X)\right)^\prime C^\prime C\...
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### Is constrained (nonnegative) least squares a form a regularisation?

Is nonnegative least squares already a form of regularisation? By adding a constraint that $\beta \geq 0$ (the coefficients), does it make sense to add another regularisation term as in LASSO or ridge ...
736 views

### Calculating the p-values in a constrained (non-negative) least squares

I have been using Matlab to perform unconstrained least squares (ordinary least squares) and it automatically outputs the coefficients, test statistic and the p-values. My question is, upon ...
590 views

### Constrained Linear Regression with coefficients related by inequality

I have a (slightly simplified) model of the following form: $Y=c_1X_1 + c_2X_2 + \epsilon$ subject to the constraint $0\leq c_1\leq c_2$. The distribution of $\epsilon$ is actually not important to ...
262 views

### RDA and CCA output- unconstrained inertia 0.00 rank 0

I get an ouput for RDA and for CCA that says that my unconstrained inertia is 0, rank 0. I thought that would be a good thing in the meaning that all the variance in the data is explained by my (...