Questions tagged [nonlinear]

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6 views

Auto-correlation for irregular non-linear sample

I have irregular sampled residuals resulting from solving a non-linear optimization problem. Currently I am gridding them into a regular grid and calculating the auto-correlation to check the ...
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60 views

How to fit logistic regression to circular data?

I've made a script that can do normal logistic regression with sigmoid(linear model). However, I have data that has a circular decision boundary and looks like this. My question is how I can modify ...
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28 views

Degrees of freedom for a $\chi^2$ with non-linear polynomial model

I have a $\chi^2$ below for some model function $F$: $$ \chi^2 = \sum_{i=1}^{i=M} \frac{\left(y_{i}-F\left(x_i;\vec{a}\right)\right)^2}{\left(\Delta y_{i}\right)^2} $$ I know that non-linear model ...
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1answer
29 views

If X^2 is not significant but X is significant, do I have to remove X^2 and run again the regression analysis?

Model DV ~ W+PDSR+Corr+(FAGDP1+FAGDP2)+log(PCGDP)+Exp+Pop+Health FAGDP2=FAGDP1^2 Result: After removing FAGDP2(FAGDP1^2) from the model, FAGDP1 turns to be insignificant Am I right in removing FAGDP^...
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1k views

RMSE vs MSE loss function - the optimization solutions are equivalent?

If we optimize a function $f$ with respect to loss $L$, which is defined as RMSE; Are we going to get the same solution as optimizing MSE ? Even, if the function $f$ is non-linear (e.g. a neural ...
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14 views

Parameter estimation of a model with exponential almon lag structure

Suppose I have the following model: $$y_t = \beta_0\sum_{i=0}^p w(\delta;i)x_{t-i}$$ Where $\displaystyle w(\delta;i)=\frac{\exp(\delta_1 i+ \delta_2 i^2)}{\sum_{i=0}^p \exp(\delta_1 i+ \delta_2 i^2)}$...
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15 views

How to calculate the bandwidth of the Diks and Panchenko(2006) nonlinear granger causality test?

I am doing the nonlinear causality test of the crude oil futures and spot prices, and I want to use the method introduced by Diks and Panchenko(2006), but I am confused about how to choose the optimal ...
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122 views

Quantile regression with an exponential function

The following equation: y = a*x**b where y is a nonlinear function of x. By taking logs, the equation can be expressed as: ln(y) = ln(a) + bln(x). I would like to run a quantile regression instead of ...
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11 views

Non-linearly separable decision boundaries

This ANN uses tanh in the hidden layers and softmax activation in the output layer. I am trying to figure out if the network can learn nonlinearly separable decision boundaries and if so what ...
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17 views

standar error of non-linear regression

I'm trying to compute the standar error of a non-linear regression fit, I find the answer in this post Non-linear regression confidence interval But i did't find that formula in any other place,and I ...
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10 views

Candidate methods for maximizing multivariable constrained nonlinear loglikelihood function

I want to approximate the maximum value of a nonlinear loglikelihood function with 53 strictly positive variables via numerical methods that do not use derivatives. According to literature there are ...
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16 views

Problem with nonlinear regression with proportional data [closed]

I am trying to do a nonlinear regression with proportional data, but it doesn't work in Minitab or SPSS. The variables are independent and sum up to 100 but there seems to be a problem with variables ...
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0answers
13 views

"Nonlinear" random spatial field: an example

I want to generate a "nonlinear" random spatial field in the sense that the autocorrelation function in function of the lag/distance $h$, $\rho(h)$, should be not equal to the $R(h)$ ...
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2answers
107 views

Isn't ReLU just a linear function? [duplicate]

I am doing Andew Ng's Deep Learning course and he says that ReLU is better than Sigmoid, but it makes no sense to me at all. The biggest advantage of activation functions are too get a non-linear ...
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1answer
31 views

Proof of how to calculate the coefficient of variation of a nonlinear function

I'm struggling to find the proof of Eq. D.14b shown in the figure below: The variable $b$ represents the “Least Squares” best-fit to the slope between $r_e$ and $r_t$ which both depend on $X_1$ to $...
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7 views

Simultaneous linear and quadratic lm fit to different parts of the data

I have dependent variable x, indpendent variable y and group membership idx. There is a ...
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22 views

fitting non linear model with correlated data with R function

I've got correlated data and I want fit them with least-squares. For ex. $Y=(y_1,y_2... y_n)^t$ $ COV= \begin{vmatrix} c_{11} & c_{12} & ... & c_{1n} \\ c_{21} & c_{22} & ... & ...
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8 views

How to determine if a functional connectivity method can detect linear or nonlinear effects?

I am currently calculating the functional connectivity of EEG data using cross-correlation, phase lag index (a phase synchronization method), and mutual information. From what I understand, cross-...
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26 views

How to fit a non-linear model to data using a predefined function

I tried to fit a Difference of Gaussians (DoG) function to my data that has a non-linear relationship. The DoG function is as follows: ...
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0answers
37 views

Why do we use Relu if it's mostly linear

We use activation functions in neural nets to introduce some non-linearity. Now I understand that Relu is a non-linear function and I had no problems with it. But today I learned that when the output ...
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0answers
16 views

Simultaneous interaction model with nonlinear equations

I observe many groups of 3 individuals, and I want to estimate an interaction model of the form: $$\begin{array}{rl} y_1&=f_1(x, y-1)+e_1\\ y_2&=f_2(x, y-2)+e_2\\ y_3&=f_3(x, y-3)+e_3 \end{...
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1answer
54 views

Non-normal data transformation - what does it imply exactly and what does my results mean?

I am missing some understanding here. I am inspecting the relationship between the heart rate variability (HRV) and errors in the Sustained Attention to Response Task. When I conduct a basic linear ...
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21 views

Using Monte Carlo to solve a system of non-linear equations

I'd like to use Monte Carlo (if it's useful to know, the Numpy Monte Carlo tools) to solve (arbitrary) nonlinear systems of equations where a solution might ...
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15 views

How to measure the degree of non-linearity between dependent and independent variables?

I have a dataset with some 10,000 independent features and 1 dependent feature, the target. The target is continuous, so the end model to predict the target should be a regression model. There are too ...
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1answer
60 views

Bayesian fitting of a nonlinear model [closed]

Some years ago I developed a nonlinear model and java fitting engine that performs well enough to be useful, but is definitely a hack. I would like to modernize and publish an open-source tool (...
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2answers
202 views

Regression with flexible functional form

I am assuming a model of the form $$Y_i=\alpha+\beta X_i+g(\mathbf{Z}_i)+\epsilon_i,$$ here $\mathbf{Z}_i$ is an $m$ dimensional vector and $\epsilon_i$ is i.i.d. white noise. I would like to ...
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1answer
260 views

Correlation is a symmetric measure, but scatter plot matrix shows asymmetric dependence

The correlation matrix demonstrates that correlation is a symmetric measure: $\rho(X,Y) = \rho(Y,X)$ since the lower off-diagonals are mirror images of the upper off-diagonals. The scatterplot matrix ...
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163 views

How to use a scatter plot to detect non-linear co-dependence between two variables?

A scatter plot matrix of 3 time series (financial returns data) are shown below. It is a multivariate representation of a scatter plot, with the individual pairs shown in the off-diagonals. The ...
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2answers
684 views

Can non-linear dependence be detected between two variables by regressing them?

Linear regression is meant for linear relationships right, so, if I don't trust linear correlation and want to find out if random variables $y$ and $x$ have a non-linear relationship, can't I just ...
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4answers
2k views

What is the best programmatic way for determining whether two variables are linearly or non-linearly or not even related

What is the best programmatic way for determining whether two predictor variables are linearly or non-linearly or not even related, maybe using any of the packages scipy/statsmodels or anything else ...
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0answers
22 views

Does a low correlation level warrant the need to try a different dependence measure?

Can it be determined somehow whether the correlation coefficient between two random variables would be insufficient for assessing the level and type of co-dependency between them, and that another ...
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1answer
47 views

Solving a system of nonlinear equations involving only products of unknowns

I would like to find the solution of a system of equations of the form: $A = w_1 F(x_k) + w_2 F(x_l) + w_3 F(x_m) +...$, where the unknowns are the $w_i$ and the function $F$, while my data are the $A$...
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0answers
33 views

Stopped by zero step from line search - R stops optimization early

I am trying to minimize an objective function, $J(\theta)$, with respect to $\theta$, a 19-dimensional parameter vector. $J(\theta)$ is a smooth nonlinear function so I have tried various gradient-...
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1answer
208 views

How come covariance can pick up non-linear relationships but correlation can't? [closed]

correlation is computed from covariance so how come covariance can pick up non-linear relationships between variables $X$ and $Y$ but (Pearson's) correlation can't?
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1answer
798 views

Neural Network: Matlab uses different activation functions for different layers - why?

I have trained on matlab an Artificial Neural Network with one input layer, one hidden layer and one output layer (my output is values between zero and one, which I turn into 0 or 1 according to a ...
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0answers
18 views

How to decompose entropy into linear and non-linear components?

Mutual information is the entropy between two random variables, $X$ and $Y$, based on their probabilities. It captures both the linear and non-linear interactions between $X$ and $Y$, whereas ...
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2answers
65 views

Non-Linear Time Series Book

I am looking for a book to study non linear time series for both univariate and multivariate topics. Your suggestions will be greatly appreciated. Thanks.
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0answers
54 views

Augmented Dickey Fuller and Nonlinear Time Series

Since the Augmented Dickey Fuller test assumes the time series to be an autoregressive-moving average model, I was wondering if it would be possible to explicitly construct a nonlinear time series ...
2
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0answers
79 views

How to determine the influence of a variable on the relationship between another two variables?

I have three continuous variables X, Y, and Z in the form of timeseries at several geographic locations. All variables have a skewed distribution because the timeseries mostly have zeros in them ...
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0answers
96 views

What are options if Rainbow test fails after Linear Regression

I tested with commonly available iris dataset and ran OLS with following formula: PW ~ SW + PL + SL + Species Output is as follows: ...
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2answers
605 views

Why not always use generalized estimating equations (GEE) instead of linear mixed models?

I read about generalized estimating equations (GEE) here, here and at other sites. It is mentioned in first of above links that "the parameter estimates are nearly identical" for linear ...
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0answers
21 views

Difference between sequential/simultaneous nonlinear partial least squares and NIPALS algorithm

I've been reading about nonlinear partial least squares, and according to the below study, there are two types of NLPLS: sequential NLPLS and simultaenous NLPLS. https://www.sciencedirect.com/science/...
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0answers
94 views

Nonlinear minimum Mean Square Error estimation

Let say I have the following parameter to estimate: $$ \theta = \frac{1}{\mu^2 - 1} \ .$$ The observed measurement is $x \sim \mathcal{N}(\mu,\sigma)$. The mean $\mu$ is unknown. There are two cases I ...
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0answers
35 views

When does a Linear regression stop being a good fit?

I'm testing a couple of hypotheses and I have a non normally distributed continuous response variable (residuals are not normally distributed as well). I have been given mixed suggestion on what model ...
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2answers
547 views

Effect of nonlinear transformations on the mean

Suppose I have a continuous random variable $X$ and a random variable $Z = f(X)$, where $f$ is a nonlinear monotonic transformation. How can I prove the following relation between the mean and the ...
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0answers
33 views

Statistical Testing of Non-linear Model Parameters

I have produced three non-linear 4-parameter logistic curves based on some experimental observations using three different measurement devices. Each curve shows the measurement of density decline ...
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2answers
124 views

How do I evaluate correlation, that appears non-linear

Directed here from StackOverflow Let's say I want to assess if there is a correlation between two fields, one of which I know to have a power distribution. A lot of the information I read assumes ...
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0answers
92 views

L-BFGS-B. Forces early stop with no 0 gradient

I am minimizing a non-linear function which is close to linear with L-BFGS-B with scipy.optimize. The issue is that I have a non zero jacobian, low levels of tolerance but the algorithm keeps early ...
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1answer
37 views

Granger causality test - What dependencies are being captured?

I'm currently reading on the Granger causality test but different sources seem to be contradicting. In the original paper Using the mutual information coefficient to identify lags in nonlinear models ...
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0answers
96 views

Q, method for non-linear mixed effect model using nlme?

I'm trying to apply non-linear mixed effect model in my data, but it does not work at all. My code is, ...

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