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Questions tagged [constraint]

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1answer
51 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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11 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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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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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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0answers
24 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
34 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
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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 ...
1
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1answer
17 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
20 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 ...
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0answers
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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
63 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
28 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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38 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 ...
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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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0answers
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Constraints on covariance matrix's correlation, and covariance matrix decomposition. [duplicate]

I have a $3 \times 3$ covariance matrix $\boldsymbol{\Sigma}$. I have two questions 1) which constraints on the correlations $\rho_{ij}$ must be satisfied to have a positive definite matrix? 2) does ...
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65 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
26 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
328 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
361 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
94 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
165 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
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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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0answers
135 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
38 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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0answers
34 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
149 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+\...
0
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1answer
103 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 ...
1
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1answer
485 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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0answers
284 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 ...
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1answer
114 views

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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1answer
41 views

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 ...
2
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0answers
81 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 ...
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0answers
34 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 ...
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2answers
448 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, ...
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1answer
77 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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0answers
22 views

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 ...
0
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1answer
178 views

Two-way ANOVA with modified sum-to-zero constraint

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 ...
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0answers
216 views

Understanding constraints in regression / maximum likelihood

There are many questions about implementing parameter constraints. My question is about understanding constraints. What follows is a very contrived example that I thought up on the spot. Feel free to ...
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0answers
62 views

What are some of the methods for constrained maximization?

This question is related to a question that I asked earlier. Since I am not able to decipher the algorithm in the original question, I would like to know whether there are other algorithms that can ...
1
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1answer
68 views

How can I add minimum and maximum constraints to a coefficient in a regression in R?

I have an array ($Y$) with a series of data to which I must fit the sum of some other arrays $(X_1,X_2,X_3)$. The expression is: $Y = c_1*X_1 + c_2*X_2 + c_3*X_3 + e$ I need to add some constraints (...
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0answers
26 views

Constrain multiple Regression for symmetric Stiffness

I want to do a 3-degree polynomial regression like $$y_i=a_0+\sum_{u=1}^{k} a_{u}x_{i,u}+\sum_{1\leq u \leq v \leq k} a_{u,v} x_{i,u}x_{i,v}+\sum_{1\leq u \leq v\leq w \leq k}a_{u,v,w}x_{i,u}x_{i,v}...
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0answers
35 views

Proposal distribution on a pair of ordered continous parameters

I'd like to sample a pair of continuous parameters which has the constraint that one has to be smaller than the other one. I understand one approach is by rejection sampling by rejecting the samples ...
3
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1answer
1k views

Fit logistic regression with linear constraints on coefficients in R

This is (I think) a routine question, but I haven't seen an answer here. In the past I had to fit logistic regression models with linear constraints on the coefficients, in the case when some of the ...
2
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1answer
2k views

Covariance matrix decomposition and coregionalization

The original question (that can be seen at the bottom of this post) was replaced by this first edit (below) EDIT I I give more details about my problem. First of all let suppose to have K vectors $\...
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2answers
85 views

normalization constraint in support vector machine

A support vector machine initially poses the following optimization problem: $$max_{\gamma, w, b} \gamma \\ s.t\ \\ y^{(i)}(w^Tx^{(i)} + b) \ge \gamma,\ \ i=1,\dots,m \\ ||w|| = 1$$ I understand the ...
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0answers
2k views

scipy optimization - 'Singular matrix C in LSQ subproblem' [closed]

I'm trying to do a fairly simple optimization, but I keep getting the error 'Singular matrix C in LSQ subproblem'. I've tried to search the internet, however I couldn't find anything about why this ...
3
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1answer
160 views

Regression with “proportionality constraints” on unknown parameters

Consider the following model: $${\bf y} = {\bf X}{\bf b} + {\bf e}$$ where ${\bf y}, {\bf n}\in {\cal R}^m$, ${\bf b}\in{\cal R}^n$, and ${\bf X}\in{\cal R}^{m \times n}$ where $m>n = {\rm rank}(...