# Questions tagged [constraint]

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17 views

I'm trying to explore OR problems and wanted to know what algorithm fits here. Consider fuel stations with lithium ion battery that service replacing battery at each refuel ( you replace your batters ...
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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 ...
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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. ...
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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?
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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 ...
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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 ...
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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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### 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 ...
22 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
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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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
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### 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 ...
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### 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 ...
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 ...