Questions tagged [constraint]

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4 votes
2 answers
145 views

Non negative least square on some coefficient

Non negative least square solves $$ y = \alpha^T x \\ s.t. \forall i,~ \alpha_i \geq 0 $$ However, I would like to apply the non negativity constraint only on some coefficient, say only the $\alpha_i,~...
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2 votes
0 answers
97 views

Estimate variables which sum to zero? [closed]

Assume we have $y_i$ such that $\sum y_i=0$. Assume we have estimation machinery (some machine learning) which can estimate each $y_i$. So we can forget constraint and eastimate each of them, or we ...
1 vote
0 answers
17 views

How to generate two matrices with given (constrained to) column-wise and row-wise correlations in R? [closed]

I would like to generate two matrices X and Y, of the same dimensions (n x ...
1 vote
0 answers
55 views

Marginal density of dirichlet distribution

I'm studying BRML. In this book, a Dirichlet distribution is defined as $$ p(\alpha | u) = \frac{\Gamma(\sum_{q=1}^Q u_q)}{\prod_{q=1}^Q \Gamma(u_q)} \delta_0 \left( \sum_{q=1}^{Q} \alpha_q - 1 \right)...
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0 votes
0 answers
21 views

Difference between ineqLB/ineqUB and LB/UB in the solnp() function in R

I'm trying the solnp() function of the {Rsolnp} package in R. I want to optimize an objective function which subjects to ...
19 votes
2 answers
5k views

Why is XOR not linearly separable?

Let the function $XOR:\{0,1\} \times \{0,1\} \to \{0,1\}$ be the function defined by $$\begin{align} XOR(0,0) &= 0, \\[6pt] XOR(0,1) &= 1, \\[6pt] XOR(1,0) &= 1, \\[6pt] XOR(1,1) &= 0. ...
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3 votes
0 answers
31 views

Fitting Sparsed Constrained regression with non-negative coefficients adding to 1

I see a similar problem in How do I fit a constrained regression in R so that coefficients total = 1? Specifically, my model is $Y_i= \pi_1 X_1+\pi_2 X_2 +...+ \pi_K X_K +\epsilon_i$ with $\pi_k \ge 0$...
0 votes
0 answers
130 views

What is the difference between constrained and unconstrained models

I have a question what is the difference between constrained and unconstrained model or freely estimated model. I am trying to test for chi square difference between them to determine discriminant ...
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0 votes
0 answers
11 views

Constraining reconstructed vectors to lie in a hyperplane ina VAE

I'm trying to add a linear constraint to my variational autoencoder model. Let's say that my input is made of two concatenated vectors: $\textbf{x} = \textbf{t} \oplus \textbf{y}$ where (for example) ...
0 votes
0 answers
81 views

Appropriate standardized solution for a CFA of one latent variable, and multiple ordinal indicators

I am currently working on a CFA in OpenMx, where a standardized latent variable is estimated by multiple ordinal indicators with means and variances restricted to 0 and 1, respectively. According to ...
1 vote
0 answers
53 views

Modeling a functional relationship with Constrained Gaussian Process regression

I searched the site for an answer to this question, but the closest I could find was: Gaussian process where the output is constrained to be 0 or greater which doesn't have an answer. So, I have a ...
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0 votes
0 answers
45 views

How to Model Constrained Outcome in Multivariate Regression Context

I have a problem in which the ratio of two different outcomes as a function of time $\frac{Y_{1t}}{Y_{2t}}$ is unknown constant $c$. I would like to estimate regression models of the following type: $$...
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0 votes
0 answers
17 views

Forecasting of ratios that need to addup to 100% [duplicate]

I intend to forecast 'shares' or ratios independently that need to add up to 100% . How can I do this especially when there are >2 ratios to predict. e.g. share of mdot, share of desktop and sahre ...
1 vote
1 answer
310 views

Fix second-order factor loadings to equal in all second-order factors with two first-order factor indicators? CFA / SEM

I am conducting a CFA followed up by a SEM analysis. In my original model I had 13 latent variables. As some of these were highly correlated, I created second-order factors, of which 3 are indicated ...
1 vote
1 answer
188 views

How can nuisance parameters in Fisher matrix can deteriorate the useful constraints?

I have a Fisher matrix $F$ which has the matrix blocks form like this : $$ F=\begin{bmatrix} A & B\\ C & D \end{bmatrix} $$ The block $A$ is the most important block, in the sense the ...
1 vote
0 answers
14 views

Cluster Analysis for data with preexisting cluster membership restrictions

I am trying to see if a particular set of plant morphological data (sepal dimensions, corolla dimensions, etc.) can, through cluster analysis, suggest a number of distinct species in the data set. ...
1 vote
1 answer
82 views

How to set a constraint for a non-linear least squares problem [closed]

I am trying to fit some data where the cost function is $ax^2 + bx + c$ and I need to have $a+b+c = 1$. How do I set such a constraint in MATLAB or Python?
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4 votes
3 answers
251 views

Adjusting round-off error so as to have percentages that sum up to $100$

I have non-negative numbers $x_1, \dots, x_n$. These numbers are all percentages rounded to the nearest tenth of a percentage. Unfortunately, I don't have any of the numerators or denominators driving ...
  • 4,063
4 votes
2 answers
199 views

In optimization, is there a distinction between "implicit/natural" and "explicit/designed" constraints?

For example, I wish to optimization a function which has a log term $\log(x)$ Now the very presence of the log term induces a constraint which says $x > 0$. The case $x = 0 $ might be a bit ...
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1 vote
0 answers
43 views

How would you run a SUR with nonlinear constraints?

Chiappari et al (2012) estimate two Seemingly Unrelated Regressions like this: $$ y_1 = a_1 + b_{11}x_1 + b_{12}x_2 $$ $$ y_2 = a_2 + b_{21}x_1 + b_{22}x_2 $$ Next, they want to test the hypothesis ...
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1 vote
1 answer
60 views

Sampling the inside of a curve [closed]

Suppose I have a set of points $S$ in the plane, which defines a curve in a discretized fashion. This could be $3\cdot 10^3$ points on the unit circle: But also could be $3\cdot 10^3$ points ...
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0 votes
0 answers
29 views

Comparing paired percentages with a constraint

I would like to compare two variables, which are paired and both contain percentages. The sample size shall be large enough (>100), so I do not consider applying any nonparametric method. However, ...
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1 vote
0 answers
130 views

Generate uniform distribution under multiple constraints

I have to acknowledge that my skill in statistics are really rusted. I would like to implement in Python a uniform distribution that satisfies constraints on the mean, the median, the standard ...
2 votes
1 answer
35 views

Resulting shapes when partitioning the constraint matrix $\boldsymbol{A}$ in linear programming

\begin{equation} \boldsymbol{A} = \begin{bmatrix} {1}_n^\top \otimes \mathbb{I}_m \\ \mathbb{I}_n \otimes {1}_m^\top \end{bmatrix} \in \mathbb{R}^{(m+n)\times mn} \end{equation} If the above matrix ...
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10 votes
2 answers
3k views

Proving Ridge Regression is strictly convex

Definition of ridge regression $$min_\beta||y-X\beta||_2^2+\lambda||\beta||_2^2, \lambda\ge0$$ you can prove a function is strictly convex if the 2nd derivative is strictly greater than 0 thus But ...
1 vote
0 answers
164 views

Clustering with constraints on group composition and size

Let's say that I know that in my data I have underlying clusters (if it helps, it may be reasonable to assume that I might even know how many) that are of a fixed size (let's say 4) and each cluster ...
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2 votes
0 answers
136 views

More on Fisher Information matrix with constraint

I have a similar Maximum Likelihood problem setup and a follow-up question to the question asked here My constraints involve vector parameters $\vec{w}=\{w_1,w_2,\cdots,w_K\}$ and $\vec{\mu} = \{\mu_1,...
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2 votes
0 answers
288 views

How does glmnet put constraints on coefficient upper and lower bounds?

Based on glmnet documentation at https://web.stanford.edu/~hastie/glmnet/glmnet_alpha.html Coefficient upper and lower bounds These are recently added features that enhance the scope of the models. ...
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1 vote
1 answer
169 views

Minimize $f(A,B)$ s.t. $\text{exp}(A)^T \text{exp}(B)=J_K$

I have a function $f(A,B)$ that maps a pair of two (tall) matrices, $A$ and $B$, to a scalar cost that I want to minimize. $A$ and $B$ both have $K$ columns. I also want to impose a set of equality ...
0 votes
1 answer
42 views

Constraining a parameter in a 4 level variable In a propensity score regression

I’m generating a propensity score using logistic regression in SAS. The model predicts compliance with a quality measure. I will match patients into groups who actually complied and not complied with ...
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0 votes
0 answers
36 views

Constrains on the coefficients of SARIMA

I am trying to generate synthetic time-series through SARIMA random process by defining the model coefficients manually. Could any one help me how to generate coefficients? What are the constraints on ...
2 votes
0 answers
3k 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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1 vote
1 answer
69 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
0 answers
174 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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0 votes
1 answer
956 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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1 vote
0 answers
77 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
0 answers
23 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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0 votes
0 answers
93 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
0 answers
85 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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1 vote
0 answers
66 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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2 votes
0 answers
98 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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4 votes
0 answers
69 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
1 answer
77 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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4 votes
1 answer
2k 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 ...
2 votes
1 answer
359 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 vote
0 answers
32 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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1 vote
1 answer
69 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 ...
1 vote
2 answers
250 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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3 votes
0 answers
39 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
0 answers
28 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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