Questions tagged [constraint]

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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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18 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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33 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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35 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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6 views

Fisher Scoring for Constrained optimization

Suppose I am estimating a parameter vector using the usual Fisher Scoring updates; \begin{equation} \theta_{s+1} = \theta_{s} + \lambda\mathcal{I}(\theta_{s})^{-1}\frac{dl}{d\theta}\bigg|_{\theta=\...
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1answer
41 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
68 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
44 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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19 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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23 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
38 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
52 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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21 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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21 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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43 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
32 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
80 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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11 views

Speed of transition parameter constraints

Given a logistic smooth transition regression \begin{equation} y_{t}=x_{t}^{\prime }\beta _{1}(1-{g}(z_{t};\gamma ,\delta ))+x_{t}^{\prime }\beta _{2}{g}(z_{t};\gamma ,\delta )+\varepsilon _{t}% \text{...
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32 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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50 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
199 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
79 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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28 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
78 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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15 views

Timeseries space consumption optimization for machine learning model

I need to train machine learning model that can run on device with low memory. My features come from aggregations of time-series so I need to store all data in this time-series until it leaves the ...
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43 views

GMM: can a constrained regression perform better than an unconstrained regression?

I have one linear regression with a set of explanatory variables and an other set of instrument variables. In my constrained regression, one of the coefficient for a given variable is constrained to ...
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2answers
206 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
22 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
60 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
29 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
410 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
29 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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117 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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28 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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47 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
805 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
596 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 ...
2
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1answer
132 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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198 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
82 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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172 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 ...
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1answer
45 views

How to compute a non linear mix model with links between the parameters and their variance in R?

I'm working on a biological problem where we want to modelize the impact of a treatment and a chemical modification on the measured quantity of a molecule (peptides). We will note $x_{ijk}$ the ...
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77 views

Constrained classification - how to classify a set of related items

I need to classify a set of elements into a few categories. Example: ...
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1answer
49 views

Primal constrained (not on $\xi_i$, but on $\mathbf{w}$!) formulation of L2 SVM

I recently came across a statement that the unconstrained primal L2-regularized SVM formulation $$ \min_\mathbf{w} \lambda \|\mathbf{w}\|^2_2 + \sum_i \max (0, \; 1 - y_i \mathbf{w}^T\mathbf{x}_i) $$ ...
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1answer
291 views

Monotonic constraints in regression model with interaction

I'm trying to figure out what constraints I need to use to have monotonicity (both on $x$ and $z$) on the regression model with interaction. My model is: $$\mathbb{E}[Y|x,z]= \beta_0+\beta_1x+\...
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1answer
173 views

R: Genetic Algorithm supporting dynamic constraints

Is there any package available or some other approach to implement constraints like (x1 < x2) or even more complex relationships provided by some function. Another desired option would be a ...
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1answer
716 views

Reinforcement learning (Q-learning) under constraint

I want know how to add a constraint to Q-learning. I have an action resulting in two rewards every time (reward 1= delivery cost , reward 2= delivery time). I want to minimize the cost while ensuring ...
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396 views

How can I impose such constraints on regression coefficients in practice?

I am estimating a linear regression model with the dependent variable $y$ and $k$ explanatory variables $x_1, \ldots, x_k$: $$y=\beta_0+x_1\beta_1+ \ldots+ x_k\beta_k + \epsilon.$$ In the estimation ...