Questions tagged [constraint]
The constraint tag has no usage guidance.
136
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19
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Constrain loss function based on input variables
I'm doing a simple regression task using a neural network with two inputs (x1 and x2) and one output (...
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0
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31
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How to model the additive components of a random variable whose value is known
I would like to model the variables $Y_1, Y_2, …, Y_n$, which satisfy the constraint $Y_1 + Y_2 + … + Y_n = Y$; where $Y$ (or at least an accurate estimate $\hat{Y}$ thereof) is readily available. ...
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15
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Supervised classifier for nested interval data and ordinal classes
I'm having trouble formalizing the following classification problem:
Let $x_i$ denote univariate (scalar), continuous, real data points
Let $y_i \in \mathbb{N}$ be their corresponding labels
Classes ...
2
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1
answer
62
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Constrained, Supervised Classification
I am playing around with a classification model, and I would like to know if there are any known methods to achieve what I am looking to do.
The data looks something like this:
Class
id
$x_1$
$x_2$
.....
- 75
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20
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Defining parameters so that they obey multiple constraints
I'd like to define parameters $\beta_i$ for $i=1,\ldots,I$ for a problem so that they automatically obey some constraints. The constraints are:
$\sum_{i=1,\ldots,I} w_i \beta_i = c_1$ and
$\sum_{i=1,\...
- 30.4k
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1
answer
61
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Does every distribution family have a set of maximum entropy constraints?
I am reflecting on these examples of maximum entropy distributions. I am (pleasantly) surprised that various common distribution families have maximum entropy constraints.
It got me wondering if ...
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2
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248
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How can I fit a distribution to a dataset while forcing it through an exact point in r?
This code was kindly recommended to me in my original question. It returned the same parameter estimates as the software called CRAFT by Aon Benfield. I have also managed to replicate it for the ...
- 51
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Relaxed magic-square generator distribution
This question is about a magic square generator, "relaxed" because
it's only about one vector (row) in the square independent of all other rows;
the individual elements are continuous and ...
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1
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154
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LAVAAN modification indices for constrained parameters
I'm looking for a way to estimate the equivalent of modification indices for parameters that are not zero, but are constrained to be equal. See example below.
...
- 23
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18
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Least Squares with Positive Coefficients Restrictions [duplicate]
Consider the following linear model:
$$Y_i=\beta_0+\beta_1 X_{i1}+\cdots+\beta_k X_{ik}+\varepsilon_i$$
Here, I want to get the estimate with a positive value restriction $\hat{\beta}_1>0$.
That is,...
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3
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730
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Non negative least square on some coefficient
Non negative least square solves
$$
y = \alpha^T x \\
s.t. \forall i,~ \alpha_i \geq 0
$$
However, I would like to apply the non negativity constraint only on some coefficient, say only the $\alpha_i,~...
- 193
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101
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Estimate variables which sum to zero? [closed]
Assume we have $y_i$ such that $\sum y_i=0$.
Assume we have estimation machinery (some machine learning) which can estimate each $y_i$.
So we can forget constraint and eastimate each of them, or we ...
1
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32
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How to generate two matrices with given (constrained to) column-wise and row-wise correlations in R? [closed]
I would like to generate two matrices X and Y, of the same dimensions (n x ...
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Marginal density of dirichlet distribution
I'm studying BRML.
In this book, a Dirichlet distribution is defined as
$$
p(\alpha | u) = \frac{\Gamma(\sum_{q=1}^Q u_q)}{\prod_{q=1}^Q \Gamma(u_q)} \delta_0 \left( \sum_{q=1}^{Q} \alpha_q - 1 \right)...
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2
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Why is XOR not linearly separable?
Let the function $XOR:\{0,1\} \times \{0,1\} \to \{0,1\}$ be the function defined by
$$\begin{align}
XOR(0,0) &= 0, \\[6pt]
XOR(0,1) &= 1, \\[6pt]
XOR(1,0) &= 1, \\[6pt]
XOR(1,1) &= 0. ...
- 303
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Fitting Sparsed Constrained regression with non-negative coefficients adding to 1
I see a similar problem in How do I fit a constrained regression in R so that coefficients total = 1?
Specifically, my model is
$Y_i= \pi_1 X_1+\pi_2 X_2 +...+ \pi_K X_K +\epsilon_i$ with $\pi_k \ge 0$...
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410
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What is the difference between constrained and unconstrained models
I have a question what is the difference between constrained and unconstrained model or freely estimated model.
I am trying to test for chi square difference between them to determine discriminant ...
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answers
138
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Modeling a functional relationship with Constrained Gaussian Process regression
I searched the site for an answer to this question, but the closest I could find was:
Gaussian process where the output is constrained to be 0 or greater
which doesn't have an answer. So, I have a ...
- 17.4k
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57
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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:
$$...
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17
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Forecasting of ratios that need to addup to 100% [duplicate]
I intend to forecast 'shares' or ratios independently that need to add up to 100% . How can I do this especially when there are >2 ratios to predict. e.g. share of mdot, share of desktop and sahre ...
1
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1
answer
618
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Fix second-order factor loadings to equal in all second-order factors with two first-order factor indicators? CFA / SEM
I am conducting a CFA followed up by a SEM analysis. In my original model I had 13 latent variables. As some of these were highly correlated, I created second-order factors, of which 3 are indicated ...
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1
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294
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How can nuisance parameters in Fisher matrix can deteriorate the useful constraints?
I have a Fisher matrix $F$ which has the matrix blocks form like this :
$$
F=\begin{bmatrix}
A & B\\
C & D
\end{bmatrix}
$$
The block $A$ is the most important block, in the sense the ...
user226073
1
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0
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16
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Cluster Analysis for data with preexisting cluster membership restrictions
I am trying to see if a particular set of plant morphological data (sepal dimensions, corolla dimensions, etc.) can, through cluster analysis, suggest a number of distinct species in the data set. ...
- 11
1
vote
1
answer
115
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How to set a constraint for a non-linear least squares problem [closed]
I am trying to fit some data where the cost function is $ax^2 + bx + c$ and I need to have $a+b+c = 1$. How do I set such a constraint in MATLAB or Python?
- 111
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3
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706
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Adjusting round-off error so as to have percentages that sum up to $100$
I have non-negative numbers $x_1, \dots, x_n$. These numbers are all percentages rounded to the nearest tenth of a percentage. Unfortunately, I don't have any of the numerators or denominators driving ...
- 4,294
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2
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340
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In optimization, is there a distinction between "implicit/natural" and "explicit/designed" constraints?
For example, I wish to optimization a function which has a log term $\log(x)$
Now the very presence of the log term induces a constraint which says $x > 0$. The case $x = 0 $ might be a bit ...
- 347
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How would you run a SUR with nonlinear constraints?
Chiappari et al (2012) estimate two Seemingly Unrelated Regressions like this:
$$
y_1 = a_1 + b_{11}x_1 + b_{12}x_2
$$
$$
y_2 = a_2 + b_{21}x_1 + b_{22}x_2
$$
Next, they want to test the hypothesis ...
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1
answer
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Sampling the inside of a curve [closed]
Suppose I have a set of points $S$ in the plane, which defines a curve in a discretized fashion. This could be $3\cdot 10^3$ points on the unit circle:
But also could be $3\cdot 10^3$ points ...
- 1,262
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29
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Comparing paired percentages with a constraint
I would like to compare two variables, which are paired and both contain percentages. The sample size shall be large enough (>100), so I do not consider applying any nonparametric method. However, ...
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Generate uniform distribution under multiple constraints
I have to acknowledge that my skill in statistics are really rusted.
I would like to implement in Python a uniform distribution that satisfies constraints on the mean, the median, the standard ...
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1
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Resulting shapes when partitioning the constraint matrix $\boldsymbol{A}$ in linear programming
\begin{equation}
\boldsymbol{A} =
\begin{bmatrix}
{1}_n^\top \otimes \mathbb{I}_m \\ \mathbb{I}_n \otimes {1}_m^\top
\end{bmatrix} \in \mathbb{R}^{(m+n)\times mn}
\end{equation}
If the above matrix ...
- 3,559
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Proving Ridge Regression is strictly convex
Definition of ridge regression
$$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 ...
- 710
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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 ...
- 30.4k
2
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260
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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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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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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 ...
- 7,049
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1
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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 ...
- 3
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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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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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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 ...
- 133
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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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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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111
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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 ...
- 11
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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$, ...
- 101
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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
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0
answers
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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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142
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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 ...
- 1,169
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133
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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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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 ...
- 241
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answer
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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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