Questions tagged [constraint]

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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 (...
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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 ...
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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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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 ...
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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. ...
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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?
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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 $f_{\text{fast}}$...
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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 ...
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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 ...
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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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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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
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 ...
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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-...
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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 ...
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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 = \...
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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 ...
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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 ...
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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, ...
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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 ...
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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 ...
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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 ...
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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}...
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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/...
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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 ...
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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 ...
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1answer
124 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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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 ...
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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 ...
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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 $...
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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 ...
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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 ...
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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. ...
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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 ...
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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 ...
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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 $Y \sim D_y$ ...
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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"...
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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 ...
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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 ...
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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, ...
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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 ...
3
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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} ...
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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: $\frac{x_1*x_2}{x_3*x_4} ≡ 1$ $x \in (0,1)$ Please note that simply ...
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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 ...
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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 ...