Questions tagged [constraint]
The constraint tag has no usage guidance.
103
questions
0
votes
0answers
17 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
50 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
152 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
36 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
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0answers
9 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
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0answers
38 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
33 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
5 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
30 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
46 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
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0answers
22 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
41 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 ...
3
votes
0answers
42 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
$$
m=\left[
\begin{array}{cccc}
13 & 12 & 3 &...
4
votes
1answer
166 views
Machine learning with some constraints
I'm wondering how can machine learning approach solves a problem which has some restrictions.
Let's say we have a demand prediction problem (regression) and the demand must be less or equal than ...
1
vote
1answer
59 views
Spline basis function notation to include constraint for continuity at the knots
I know splines use basis functions to approximate a function locally, so that the function in one region is approximated with a weighted sum of these basis functions. Suppose the input is one-...
1
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0answers
20 views
How to compute statistical significance using a likelihood ratio?
The title really says it all. Suppose I have a change in log-likelihood (i.e., $\Delta LL = LL_{fitted} - LL_{null}$), and I would like to compute the $1\sigma$, $2\sigma$, etc. confidence region from ...
0
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0answers
28 views
Multivariate regression with constraint
I would like to obtain beta estimators by regressing multiple output variables Y1, Y2 and Y3 on multiple independent variables X1,X2 and X3 by considering the constraint Y1*Y2 = Y3, i.e.
$$Y_1 = \...
1
vote
1answer
46 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
94 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
22 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
22 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 ...
0
votes
0answers
46 views
Solving ridge regression for p >> n case using dual algorithm with or without nonnegativity constraints
I was reading the paper
"Efficient Regularized Regression with
L0 Penalty for Variable Selection and Network Construction"
in which iterated ridge regression is used to solve L0 penalized regression ...
2
votes
1answer
38 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
179 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
45 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
51 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 ...
1
vote
1answer
332 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 ...
0
votes
1answer
124 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
34 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
81 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
380 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
23 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
121 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
46 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
580 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 ...
0
votes
1answer
32 views
Correlation of Vectors with Constrained Sum
Taking the correlation of vectors with a constrained, fixed sum (say, a simplex, where sum is always 1) will induce spurious negative correlations, since increasing one element always means decreasing ...
2
votes
0answers
37 views
Does this distribution family exist?
Let $D$ be a one-parameter distribution family whose support is the positive reals. Let $D_x$ be a distribution from this family parametrized by its mean $x \ge 0$, let $X \sim D_x$ and $Y \sim D_y$ ...
0
votes
0answers
122 views
How to penalize change of states in Hidden Markov model?
I'm trying to fit a HMM on a sequence of observations and I would like to introduce some constraints that would penalize an excessive number of changes of state in the complete sequence (where "change"...
1
vote
0answers
31 views
Minimal requirement for reaching a feasible solution in non-convex constrained gradient descent
The problem is as follows:
$\max_x f(x) \enspace , \enspace \text{s.t.} \enspace g(x) \leq \alpha $
We can not assume that either $f$ nor $g$ are convex, on the contrary - we can assume they are ...
0
votes
0answers
48 views
Restriction in bayesian likelihood expression
I'm doing MCMC simulation but I'm confused in some part of my model. I dont know which of my likelihood expression is right.
My model is as following.
$\gamma$ = $(\gamma_{1},\cdots,\gamma_{K})$ and ...
0
votes
2answers
1k views
How to use equalities as constrains with constrOptim in R
I want to solve a matrix system which have several solutions (infinite since it is overdetermined - 6 equations with 8 unknowns). However, the way I want to do it is to a criterion for the variables, ...
3
votes
2answers
770 views
Coordinate descent with constraints
When performing constrained optimization on a smooth, convex function using coordinate descent, for what types of constraints will the algorithm work ? (i.e. converge or reach an approximate optimum ...
1
vote
0answers
59 views
3
votes
1answer
163 views
L2 SVM (squared hinge) theory
The linear L2 SVM can be intuitively understood as
\begin{equation}
\text{minimize } f(\boldsymbol{w}) = \frac{1}{2} \Vert\boldsymbol{w}\Vert^2_2 + C \sum_{i=1}^m \xi_i^2 \tag{1}
\end{equation}
...
5
votes
3answers
208 views
Generating identically-distributed random variables with a constraint
Is there a way to generate identically-distributed random variables (eg $x_1,x_2,x_3,x_4$) with the following constraint:
$\frac{x_1*x_2}{x_3*x_4} ā” 1$
$x \in (0,1)$
Please note that simply ...
2
votes
0answers
96 views
Eigenvalue-constrained covariance estimation and AIC
I'm estimating a covariance matrix $\Sigma$ from datasets where the number of dimensions $p$ may be close to or larger than the number of data points. To obtain a well-conditioned estimate, I use the ...
0
votes
0answers
227 views
Maximizing profit, using GAMS?
I've been given the following optimization problem and this is what I have done so far:
Cuppa Coffee Company mixes specialty coffee blends to sell to SmartBux, a small
chain of coffee shops. The ...
