Questions tagged [constraint]
The constraint tag has no usage guidance.
115
questions
1
vote
0answers
13 views
How would you run a SUR with nonlinear constraints?
Chiappari et al (2012) estimate two Seemingly Unrelated Regressions like this:
$$
y_1 = a_1 + b_{11}x_1 + b_{12}x_2
$$
$$
y_2 = a_2 + b_{21}x_1 + b_{22}x_2
$$
Next, they want to test the hypothesis ...
1
vote
1answer
27 views
Sampling the inside of a curve [closed]
Suppose I have a set of points $S$ in the plane, which defines a curve in a discretized fashion. This could be $3\cdot 10^3$ points on the unit circle:
But also could be $3\cdot 10^3$ points ...
1
vote
0answers
13 views
Evaluating/defining CDF on a hypersphere/hypercube [closed]
I have a set of data defined on the positive orthant of the hypercube. I can project that data onto the positive orthant of the hypersphere, or the simplex.
I can then assign a distribution to that ...
0
votes
0answers
21 views
Comparing paired percentages with a constraint
I would like to compare two variables, which are paired and both contain percentages. The sample size shall be large enough (>100), so I do not consider applying any nonparametric method. However, ...
1
vote
0answers
22 views
Generate uniform distribution under multiple constraints
I have to acknowledge that my skill in statistics are really rusted.
I would like to implement in Python a uniform distribution that satisfies constraints on the mean, the median, the standard ...
2
votes
1answer
30 views
Resulting shapes when partitioning the constraint matrix $\boldsymbol{A}$ in linear programming
\begin{equation}
\boldsymbol{A} =
\begin{bmatrix}
{1}_n^\top \otimes \mathbb{I}_m \\ \mathbb{I}_n \otimes {1}_m^\top
\end{bmatrix} \in \mathbb{R}^{(m+n)\times mn}
\end{equation}
If the above matrix ...
0
votes
0answers
11 views
How to quantify a prior or information into a Fisher matrix?
I have 2 Fisher matrices of the same dimension, each one representing parameters that I have to constain by combining these 2 matrices in Fisher's formlism.
Firstly, I did a simple sum between both to ...
10
votes
2answers
989 views
Proving Ridge Regression is strictly convex
Definition of ridge regression
$$min_\beta||y-X\beta||_2^2+\lambda||\beta||_2^2, \lambda\ge0$$
you can prove a function is strictly convex if the 2nd derivative is strictly greater than 0 thus
But ...
1
vote
0answers
30 views
Clustering with constraints on group composition and size
Let's say that I know that in my data I have underlying clusters (if it helps, it may be reasonable to assume that I might even know how many) that are of a fixed size (let's say 4) and each cluster ...
2
votes
0answers
56 views
More on Fisher Information matrix with constraint
I have a similar Maximum Likelihood problem setup and a follow-up question to the question asked here
My constraints involve vector parameters $\vec{w}=\{w_1,w_2,\cdots,w_K\}$ and $\vec{\mu} = \{\mu_1,...
1
vote
0answers
27 views
How does glmnet put constraints on coefficient upper and lower bounds?
Based on glmnet documentation at https://web.stanford.edu/~hastie/glmnet/glmnet_alpha.html
Coefficient upper and lower bounds
These are recently added features that enhance the scope of the models. ...
1
vote
1answer
152 views
Minimize $f(A,B)$ s.t. $\text{exp}(A)^T \text{exp}(B)=J_K$
I have a function $f(A,B)$ that maps a pair of two (tall) matrices, $A$ and $B$, to a scalar cost that I want to minimize. $A$ and $B$ both have $K$ columns. I also want to impose a set of equality ...
0
votes
1answer
39 views
Constraining a parameter in a 4 level variable In a propensity score regression
I’m generating a propensity score using logistic regression in SAS. The model predicts compliance with a quality measure. I will match patients into groups who actually complied and not complied with ...
0
votes
0answers
23 views
Constrains on the coefficients of SARIMA
I am trying to generate synthetic time-series through SARIMA random process by defining the model coefficients manually. Could any one help me how to generate coefficients? What are the constraints on ...
0
votes
0answers
24 views
Prediction basis for ti() smooths in mgcv
How are the sum to zero constraints absorbed in a bivariate decomposition smooth, ti()? And more importantly, how can we recover the parameters in the original basis to make predictions with new data (...
2
votes
0answers
955 views
Convex multiple variables optimization problem with constraints in python [closed]
I am currently trying to implement the following optimization problem in python (in order to resolve it with scipy.optimize.minimize).
Please note that $\alpha$ is given, $T$ is the number of ...
1
vote
1answer
53 views
How can I shift the average probability keeping constraint (0.0:1.0)?
I have a large datasets of values that range from 0 to n. I am interpreting the values as probabilities for a later pseudo-random selection process. To make the values serve as probabilities, I ...
1
vote
0answers
172 views
What analysis can I perform for constrained optimalization of coil parameters
I have about 20 discrete sets of variable coil parameters that I need to assign values to, satisfying given constraints. The objective is to minimize the manufacturing cost (and to satisfy the ...
0
votes
0answers
194 views
Learning Lagrangian multiplier for regularization term in the loss function
There is a method for imposing physical constraints on the neural networks, in which a physics-based loss is added to the loss function. This term is usually a function of the output of the network.
...
0
votes
0answers
14 views
Sparsity-inducing priors for non-negative random variables
Which priors could be used for inducing sparsity on a random variable with non-negativity constraints?
0
votes
0answers
40 views
Learn decision function for choosing between slow (accurate) and fast (inaccurate) networks
Suppose that we deal with a learning process (e.g., a retrieval task), for which we have learned two functions (typically implemented as neural networks), namely $f_{\text{slow}}$ and $f_{\text{fast}}$...
1
vote
0answers
36 views
Multiple Linear Regression with constraints that should satisfy a curve
I would like to estimate a multiple linear regression model with 15 coefficients like this:
Y=a1x1+a2x2+a3x3+.....+a15x15+e
I have a set of data that include Y(29x1) and X(29x15). I want ...
0
votes
0answers
10 views
How many parameters would the saturated model have if there were no constraints?
In a saturated log-linear model for three variables, the equation is
$\lambda+\lambda^A+\lambda^B+\lambda^C+\lambda^{AB}+\lambda^{BC}+\lambda^{AC}+\lambda^{ABC}$
I understand that we have to impose ...
0
votes
0answers
18 views
Is there an idiomatic way of setting constraints on parameters in R?
Let's say I have 2 categorical variables foo and bar that have the same 4 levels A, B, C and D
I have a response variable $Y$, ...
0
votes
0answers
48 views
How to impose a global constraint on cost function of a neural network?
I have a training set of time series samples. Each sample is composed of a noise process (input) and the corresponding trajectory (output) which is the solution of the stochastic differential equation ...
2
votes
0answers
56 views
How to update symmetric, positive definite matrix in the constrained Hamiltonian Monte Carlo algorithm?
original post
I'm working on the implementation of the Hamiltonian Monte Carlo (HMC) algorithm which includes a covariance matrix parameter, say $\Sigma$.
Let $\Phi$ be the (initialized) momentum ...
1
vote
0answers
27 views
Regression with Constrained fitted value
I would like to fit a (generalized) linear regression model such that that the predicted values must be greater than one of the input variables.
For example...
$\hat{age} =\beta_{1}*\text{age of ...
2
votes
0answers
50 views
Binary classification where I know only one candidate can be positive
I have a binary classification problem, where given a thing I need to determine whether it's of class A or class B. Now, I also have additional information: For each 30 examples for which I need to ...
4
votes
0answers
53 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 ...
2
votes
1answer
42 views
How to generate data such that an equation needs to hold?
Can I create or generate $\{y_i\}_{i=1}^{4}$ data set such that this equation holds
$$
\sum_{i=1}^{4}\sum_{j=1}^{4}m_{ij}y_{i}y_{j}=6
$$
where
$$
m=\left[
\begin{array}{cccc}
13 & 12 & 3 &...
4
votes
1answer
486 views
Machine learning with some constraints
I'm wondering how can machine learning approach solves a problem which has some restrictions.
Let's say we have a demand prediction problem (regression) and the demand must be less or equal than ...
2
votes
1answer
84 views
Spline basis function notation to include constraint for continuity at the knots
I know splines use basis functions to approximate a function locally, so that the function in one region is approximated with a weighted sum of these basis functions. Suppose the input is one-...
1
vote
0answers
21 views
How to compute statistical significance using a likelihood ratio?
The title really says it all. Suppose I have a change in log-likelihood (i.e., $\Delta LL = LL_{fitted} - LL_{null}$), and I would like to compute the $1\sigma$, $2\sigma$, etc. confidence region from ...
1
vote
1answer
55 views
D-optimal DOE suggest repeated samples
I tried to generate a D optimal design but the design output sounds very weird to me. I have a (real) process and I`d like to explore 3 factors, but the process have a lot of constraints so I provide ...
0
votes
2answers
161 views
Parametrization of a skew-normal distribution such that negative part is constant
I was wondering, how the parameters of the skew-normal distribution (https://en.wikipedia.org/wiki/Skew_normal_distribution) would be constrained when I require that a constant part of its support is ...
3
votes
0answers
26 views
Sampling from Gaussian distribution subject to a quadratic inequality constraint
Would it be possible to generate samples $x \in \mathbb{R}^n$ from $\mathcal{N}(\mu, \Sigma)$ subject to an inequality constraint $x^\top Q x/2 + b^\top x \le c$, $Q = Q^\top \succeq 0$. We also know, ...
1
vote
0answers
23 views
Is there a way to run constrained EM?
I would like to run an EM (expectation maximization) algorithm to estimate hidden Markov model parameters except, in my case, I have an extra constraint on my start and final states in my HMM.
How do ...
2
votes
1answer
42 views
Confidence limits on a curve fit with algebraically related parameters
I suspect that the required techniques for my question already exist, but I don't know what the correct nomenclature is - if so apologies, and can someone point me at the right resources?
I have a ...
3
votes
1answer
354 views
multiple regression with constraints of independent variables
I'm running a regression analysis with independent variables $X_{1}, X_{2}, \cdots, X_{n}$ and dependent variable $Y$. There is a constraint among some of the independent variables, say, $X_{1} + X_{2}...
1
vote
0answers
70 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/...
2
votes
0answers
52 views
How to handle real-world (soft) constraints in an optimization problem? [closed]
I am working on a problem which involves optimizing for minimum power consumption in a large compressor network interconnected through pipelines (think of a connected graph with nodes as compressors ...
2
votes
1answer
632 views
How to implement constraints in a neural network for a regression problem?
Let's say I have different sensors in an engine, and I make a neural net which predicts the engine's temperature given different operating conditions measured by the sensors. I happen to know the ...
1
vote
1answer
190 views
contraints on parameters in MCMC
I run a basic version of mcmc, based on example given in this Metropolis-Hasting tutorial
...
1
vote
0answers
42 views
Sample subsets with distribution proportional to elementwise product
I have a set of $n$ elements, $x_1,x_2,\dots,x_n$, each with a weight $w_1, w_2,\dots, w_n$. I want to sample a subset of fixed size $k$ such that the probability of drawing $\{x_a,\dots,x_b\}$ is ...
0
votes
2answers
85 views
What are some of the approaches of defining joint pdf under sum constrain?
For example, we have three random variables,
$x_1 = Uniform(10,20)$
$x_2 = Uniform(20,40)$
$x_3 = Uniform(50,150)$
which follows the condition $x_1+x_2+x_3 = 100$
I am looking for a joint ...
2
votes
2answers
742 views
Normal distributed random variables with constraint?
Consider $n$ random variables $X_i$ with $i=1,2,...,n$, each drawing values from identical normal distributions with mean $\mu=0$ and standard deviation $\sigma=const.$ so that expectation values are $...
1
vote
0answers
29 views
Constraints on low dimensional representations of data
Is there literature discussing introduction of constraints to loss functions in order to specify certain structures on low dimensional representations? If so, how do they compare the efficacy of the ...
1
vote
1answer
210 views
Clustering with constraint on minimum size of cluster
I have dataset of $n$ objects, I want to cluster them according to correlation and I want to divide the dataset into groups of similar objects of sizes not less than 50 - because I use clustering for ...
2
votes
0answers
57 views
significance in linear regression with constraints
I have a problem which is similar to linear regression, but differs in two main points: 1) the number of regressors is equal to the number of observations and 2) I have constraints on the regressors.
...
1
vote
1answer
904 views
How do I design this multi-objective fitness function for use with genetic algorithm?
I have a multi-objective optimization problem that I am applying genetic algorithm (GA) to solve. Currently, there are only 2 objectives:
minimize cost
maximize validity
The cost minimization is ...
