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Questions tagged [constraint]

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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 ...
17 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, ...
20 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 ...
40 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 ...
29 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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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 ...
26 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 ...
32 views

Accelerated Projected SGD under box constraints

Are there generalizations of ADAM or Adagrad algorithm that allow box constraints for the parameters to be incorporated in the gradient descent step? Is it valid to simply run the algorithm as usual ...
23 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. ...
237 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 ...
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 ...
48 views

Multilabel classification problem where a number of output labels are in certain range

I am tackling a multi-label classification task. In this problem, we have 13 classes For one sample $x \in R^{20}$, $2 \leq |h(x)| \leq4$ Here, $h(x)$ means the prediction labels of sample x by ...
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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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"...
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 ...
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 ...
583 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, ...
464 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 ...
56 views

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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} ...
187 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 ...
74 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 ...
149 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 ...
44 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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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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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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Fitting a regression with constraints on the relationship between one independent variable and the dependent variable?

Let's say I have a dependent variable y (a rating of the pleasantness of shopping at a particular store from 0 to 100), and 10 independent variables ...
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Stan - find dimensions of an object - lower and upper question [closed]

I have a bunch of objects (roughly rectangular) , for some of which I know what their dimesions - x, y, and ...
102 views

Constraints on the moments of a bounded probability distribution

Consider a probability distribution with support on $[0,1]$. Suppose the first $n$ raw moments $m_1,...,m_n$ are given. What are the constraints on the $(n+1)^\text{th}$ moment? Obviously we have the ...
37 views

Algorithm that preserves the order of the predicted variable

Hi all, I need some advice on possible algorithms that I can apply to the following problem (if possible with pointers to implementations of these algorithms). The dataset: I have some dataset ...
575 views

Is there a clustering algorithm that can take a maximum distance from any mean as a constraint?

I am building an analytical tool that depends on being able to take a bunch of 1 dimensional numbers and group them into categories based on how close each number is to the mean of the group. However, ...
83 views

Zero restrictions in state-space models/ Kalman Filter

I am estimating a state space model using Kalman and the EM algorithm in Matlab, using Kevin Murphy's toolbox (http://www.cs.ubc.ca/~murphyk/Software/Kalman/kalman.html). My question should in ...
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Clustering with Parametric distance in terms of error

I want to solve a constraint-based clustering problem. The constraint is a function of the points in one cluster. In simpler terms, I want to divide the data points into two clusters (A and B), such ...
I have a dataset with two categorical predictors and a continuous response. Suppose the predictors have $a$ and $b$ levels, respectively, with group-specific parameters $\alpha_1, \dots, \alpha_a$ and ...