Questions tagged [constraint]

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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 ...
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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 ...
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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 ...
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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, ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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,...
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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. ...
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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 ...
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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 ...
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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 ...
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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 (...
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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 ...
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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 ...
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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 ...
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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. ...
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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?
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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 $f_{\text{fast}}$...
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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 ...
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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 ...
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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 $Y$, ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 &...
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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 ...
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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-...
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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 ...
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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 ...
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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 ...
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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, ...
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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
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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
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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}...
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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/...
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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 ...
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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 ...
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1answer
190 views

contraints on parameters in MCMC

I run a basic version of mcmc, based on example given in this Metropolis-Hasting tutorial ...
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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 ...
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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 ...
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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 $...
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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 ...
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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 ...
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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. ...
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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 ...