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.
123
questions
0
votes
1
answer
26
views
Shrinkage methods: does non-convex constraints ($q < 1$) also induce sparsity?
I'm reading ESLII, in particular the chapter about shrinkage methods, lasso, and ridge regression.
The optimal model parameters for a given constraint $\sum | \beta_j |^q < \alpha $ are given by ...
- 155
0
votes
0
answers
18
views
Confidence intervals for non-negative least squares
Can we use the non-parametric bootstrapping to compute the confidence intervals for the regression coefficients estimated from non-negative least squares?
I wonder whether this has the same issues ...
- 601
0
votes
0
answers
13
views
Recover Primal Linear Programming Solution from Dual with LAD Regression?
This link discusses different ways of writing a classic LAD regression with a linear program. The classic way of writing LAD regression ($y = X \beta + r$) as a linear program is
\begin{equation}
\...
3
votes
1
answer
23
views
Allow gradient descent to go beyond constraint but punish for it
Disclaimer: I considered posting this on mathSE but thought maybe this is more fitting here (no pun intended).
Status Quo
I have a list of data points $\{x_k, y_k\}$ and a set of functions $f_i(x)$ ...
- 133
1
vote
0
answers
27
views
Add constraints to linear regression which make some of the coefficients positive [duplicate]
I run a linear model which is about sales~ Investments, denote the Investments as I and ...
- 55
0
votes
1
answer
18
views
Testing for plateau with discrete timepoints
I have measured a continuous outcome at 4 timepoints (t1, t2, t3, t4), spaced evenly apart. The measurements at each time point are on different groups (i.e. the responses at t1 come from all ...
- 1
4
votes
1
answer
79
views
Linear model with constraints in R
I have the following problem: I have a simple linear model with 3 independent variables.
...
- 41
1
vote
1
answer
123
views
Fit points with a continuous, piecewise linear function with minimum number of points for each segment
I have a set of two-dimensional data points that I want to fit with a continuous piecewise linear function with one break point. However, I want each of the two segments to be supported by a minimum ...
- 13
2
votes
0
answers
28
views
Covariance matrix of beta coefficients for constrained multiple regression
I have a linear least-squares problem with constraints that two of the coefficients must be non-negative. For a typical (unconstrained) least squares estimation, I know that the variance-covariance ...
- 21
0
votes
0
answers
43
views
Why SCM weights *should* sum to 1?
When we use synthetic controls, we consider $j=2, \dots, J+1$ units across $t \in \{T_{-} \ldots T_0 \ldots T_{+}\} \in \mathbb{Z}$ pre/post event-time periods. Abadie et. al. make the point that to ...
0
votes
0
answers
36
views
How to Model Constrained Outcome in Multivariate Regression Context
I have a problem in which the ratio of two different outcomes as a function of time $\frac{Y_{1t}}{Y_{2t}}$ is unknown constant $c$. I would like to estimate regression models of the following type:
$$...
- 1
1
vote
1
answer
75
views
How do linear constraints affect the convexity of my OLS-like optimisation problem?
I would like to augment a linear regression (so a convex OLS problem) with some additional constraints on the coefficients to match the subject I'm working on.
Having $x\in \mathbb{R}^n$, the solution ...
- 11
0
votes
1
answer
52
views
Minimizing $L_2$ norm with constrained residual sum of squares (RSS)
I have some complex-valued time-series data, $y \in \mathbb{C}^n$ - a signal with additive Gaussian white noise. The goal is to find the Fourier coefficients of this signal.
Ideally, you would just do ...
- 163
0
votes
0
answers
75
views
How to get standard errors of linear regression coefficients subject to linear equality constraints
I have a regression problem with multiple sets of sum-to-one categorical features (e.g. X1=Male, X2=Female, X3=Weekday, X4=Weekend), intercept needs to be included as well as some restrictions on the ...
0
votes
0
answers
48
views
Neural network regression with a constrained dependent variable
I'm using a multi-layer perceptron model to predict the cumulative number of boardings and alightings from a bus travelling on a standard route based on previous cumulative boarding and alighting ...
1
vote
0
answers
52
views
Difference between glmnet and nnls for non-negative least squares in R
I'm trying to do some non-negative linear regressions in R, and I found in the blog here https://www.r-bloggers.com/2019/11/non-negative-least-squares/ that either the package ...
- 11
3
votes
2
answers
423
views
How to fit a constrained regression in R?
My regression:
$Y = α + β_1X_1 + β_2X_2 + β_3X_3 + β_4X_4 + β_5X_5 + β_6X_6 + β_7X_7 + β_8X_8 + β_9X_9 + β_{10}X_{10} + β_{11}X_{11} + β_{12}X_{12} + β_{13}X_{13} + β_{14}X_{14} + ε$
Constraints that ...
- 31
0
votes
1
answer
231
views
Can it be proven that non-negative least squares is a perfectly convex problem?
Can it be proven that NNLS is a perfectly convex problem?
Myre writes in section 3 of his TNT-NN manuscript:
The NNLS objective function is a convex quadratic function with
linear inequalities as ...
- 181
1
vote
1
answer
50
views
Numerical solution to the constrained ridge regression
The constrained ridge regression problem is of the form:
$\arg\min_{\|\beta\|_2\le t}\|X\beta-y\|_2$. Given a matrix $X$, a vector $y$ and the constrain parameter $t$, how do you solve it numerically?
...
- 11
0
votes
0
answers
29
views
Constraining regression coefficient to non-negative [duplicate]
I have a regression problem where I don't want the coefficients to be negative. Is setting negative coefficients of OLS to zero the same as constraining the coefficient to be non-zero and solving it ...
- 761
2
votes
0
answers
45
views
How to get accurate estimates on Neural Networks Hessian?
I need to get not only accurate estimates on the neural network output itself but also on its second order derivatives in order to use the NN for optimization problems. With Adam optimizer I can't get ...
- 31
1
vote
0
answers
167
views
Linear Regression with constraint(s): need s.e., t-stat, and p-values of the regressors
I am performing a linear regression and what I need is (1) to constrain the sum of the regression coefficients to 1, and (2) to constrain the sum of regression coefficients to 1 AND each regression ...
0
votes
0
answers
42
views
Perform regression on a set of equations with additional constraints
I want to analyse the composition of a ternary mixture (a mixture containing of three components) by combining measurements of the mixture's density (denoted $\rho$) and its refractive index (denoted $...
- 101
0
votes
0
answers
19
views
Can regression coefficients be guaranteed to be normalized?
When solving a multivariate linear regression problem of the form $A\vec{x}=\vec{y}$ where $A$ and $\vec{y}$ are known. Is there any from of preprocessing or scaling that can be done $A$ and or $\vec{...
- 101
3
votes
3
answers
2k
views
How to test if sum of two coefficients of ols model is greater than zero using R?
The regression model is:
y = b0 +b1x1 + b2x2 + b3x3 + e
I want to test if b1 + b2 > 0.
the R package ...
- 33
2
votes
1
answer
54
views
How can this model be fit using R's lm function?
I have data that consists of a grouping variable $\tt{grp}$, a predictor $\tt{x}$, and a response $\tt{y}$. There are three groups. I want to fit to this data the model $y = \alpha_i + (\beta + \...
- 251
0
votes
1
answer
60
views
Constrained optimization of joint Bernoulli density parametrized by a neural network
I want to learn a joint distribution on $n$ Bernoulli random variables conditioned on a random variable $b\sim D$ and parametrized by a neural network, $f$:
$$p(A = (a_1, \ldots, a_n)|b) = f_{\Lambda}(...
- 151
3
votes
0
answers
36
views
Regression with coefficients having a multiplicative relationship
Assume I need to calibrate a linear model of the form shown here:
$$Y\sim\beta_0+\beta_1X_1+\beta_2X_2$$
where the $\beta$ terms are the coefficients and the $X$ terms are the independent variables. ...
- 176
1
vote
0
answers
29
views
Least-squares fit of explicit parabolic sheet to scattered data points [duplicate]
For a given set of data points
$$\{(x_i, y_i, z_i)\}$$
there exists some
$$f_{ABC}(x,y)=Ax^2+Bxy+Cy^2$$
that minimizes
$$\sum_i(f_{ABC}(x_i,y_i)-z_i)^2$$
$A$, $B$, and $C$ can be found quickly ...
- 365
6
votes
2
answers
2k
views
Monotonic splines in Python [closed]
I am trying to find a procedure to fit data monotonically in Python.
The data won’t be necessarily monotonic. I just would like to achieve a monotonic fit because of theoretical assumptions.
I ...
- 71
4
votes
1
answer
393
views
How do you apply constrains on parameters in Bayesian modeling?
In Frequentist modeling, I know how to fit and interpret models with constraints on the parameter space.
Let's say I'm fitting a $N(\mu, \sigma^2)$ distribution to my data $x_1, \dots, x_n$, and I ...
- 2,089
4
votes
0
answers
65
views
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 ...
- 231
3
votes
1
answer
69
views
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 ...
- 33
2
votes
2
answers
575
views
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 ...
- 121
0
votes
0
answers
119
views
Is there a conjugate prior for normal location family N(x|u,1) such that the mean is always positive?
The conjugate prior to normal location family is usually a normal distribution. However, I want to constrain the mean to be positive.
Is there a conjugate prior to the normal location family $x\sim N(...
- 21
3
votes
1
answer
111
views
Model/link function to deal with dependent variable in range [-1,1]?
My dependent variable, $Y$, contains values anywhere from -1 to 1 (i.e. it is bounded continuously on the range $[-1,1]$). I know that a regular OLS regression on such a variable would sometimes ...
- 642
1
vote
0
answers
106
views
Sum of residuals in constrained linear regression
Does sum of residuals == 0 hold even if we add ordinality constraints for the coefficients in a regression model?
It would be great if someone can point out to any literature (paper/presentation/...
0
votes
0
answers
172
views
Closed-form solutions for constrained multiple linear regression
Normally a multiple linear regression is unconstrained
$$y=X\beta+\epsilon$$
so that closed-form solutions in the case of data orthogonality ($X^\top X=I$) are
$$\beta=(X^\top X)^{-1} X^\top y$$
...
- 3,139
0
votes
0
answers
269
views
Restricted Weighted Linear Regression in R
I have to follwing issue. I would like to run a linear regression imposing a constraint on the weighted coefficients. Let me construct an example:
Consider the following cross-sectional regression
$...
2
votes
2
answers
1k
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 ...
- 441
0
votes
1
answer
320
views
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 ...
- 61
4
votes
2
answers
418
views
Equality-constrained least-squares when the matrix is singular
I have to solve the linear system $Ax = b$ in the least-square sense, where matrix $A$ is singular. To resolve this, I introduce $Cx = d$. However, even after this, I am not able to solve it using <...
- 151
2
votes
1
answer
2k
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 ...
- 447
1
vote
0
answers
701
views
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 ...
3
votes
0
answers
105
views
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 ...
- 181
2
votes
1
answer
1k
views
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 ...
- 551
0
votes
1
answer
575
views
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 ...
1
vote
0
answers
294
views
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.
...
- 31
0
votes
1
answer
77
views
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\...
- 113
4
votes
1
answer
612
views
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 ...
- 8,025