# Questions tagged [nonlinearity]

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### Standardize Time Series Intervals in R

I have a time series that has data taken at irregular time intervals, and I would like to standardize the time intervals so that I can perform analysis such as detrended fluctuation analysis (which ...
1answer
38 views

### Modeling non-linear (short) time series and cross-validate them

beginner data scientist here. Time series analysis is a completly new area for me, so please correct me if i write something that makes no sense. I have many multivariante short time series, between ...
0answers
27 views

### Effects of Increasing number of neurons with relation to the activation function they have

I always thought that information which can be represented by using, say , 8 numbers (the output of 8 neurons in a layer) , need not be mapped onto a 9 or 10 dimensional space as it will occupy an 8-...
0answers
44 views

### Population Monte Carlo Algorithm using L2 Distance Measure/ Likelihood Distribution

I am currently struggling with some concepts of the Population Monte Carlo Framework. Initially, I came across this set of algorithms as I am currently trying to infer parameters from a 7D ...
0answers
28 views

### How to interpret plot residuals vs fitted values?

I run a ols regression and want now check the linearity assumption. I found out that i have to plot the residuals vs the fitted values and if there is no non linear pattern the linearity assumption ...
2answers
30 views

### How to address nonlinearities among covariates when modelling?

Generally, it is recommended to drop one variable from modelling when we found any collinearity among two variables. But what when two or more independent variables have nonlinear relationship. Can ...
2answers
45 views

### Would machine learning techniques help if the linear and nonlinear relationships is so weak?

I have a cross sectional data set at hand contains four predictors to predict one outcome, I employed bivariate analyses to check whether the relationship between the dependent and independent ...
1answer
28 views

### Effect on a Hidden Layer without Activation

I have a simple network for classifying MNIST digits using Fully Connected layers. However I cannot explain why a hidden layer without activation makes the network behave randomly. There are three ...
0answers
199 views

### Component Plus Residual Plot: How do they work?

How does component plus residual plot work? You create these plots by plotting: But how do they work? The books says that you want to get rid of the influences from other predictors. A linear ...
0answers
384 views

### Relu6 and vanishing gradients problem

In some recent machine learning papers (e.g. mobileNetV2), ReLU6, defined as $Relu(x)=\min(\max(0,x),6)$ is used instead of regular Relu non-linearities. Doesn't such a function result in the same ...
0answers
19 views

### Linear Unconditional X-Y, Non-Linear Conditional X-Y

Intuitively, I can imagine that an unconditional (i.e., unadjusted for any covariates) Y~X relation can present as a linear relation, whereas a conditional Y~X|Z relation can present as a non-linear ...
1answer
50 views

### Why do nonlinearities in deep neural nets give rise to very high derivatives?

In the book "Deep Learning" by Goodfellow, Bengio, and Courville, I do not understand the following statement about why nonlinearities in deep neural nets give rise to very high derivatives: The ...
2answers
482 views

### Cosine-Similarity vs non-linear measures

In NLP, people often use cosine similarity to measure how close two vector spaces are to each other. However, we know that cosine-similarity is the same thing as Pearson correlation, for centered ...
1answer
45 views

### Multiple Regression: Finding which variables are non linearly related to the outcome

I have a dataset with 10 predictors and 1 outcome variable. Looking at the Residual Vs Fitted Plot, I suspect a Non-Linearity that I am missing. But how can I check out of the 10 predictors, which ...
1answer
42 views

### How tanh has to do with nonlinearity

I was reading an article about image processing and I came across sigmoidal activation function and tanh like in this article: ...
1answer
38 views

### Interpreting coefficient from a nonlinear variable?

How do I interpret the coefficient from an equation that has a logged dependent variable and an inverted control variable? My model is of the form: \ln Y = \frac{\beta}{x} + \text{other terms} + \...
0answers
122 views

### Normalizing non-linearity

I have data on spot prices, inventory, and storage capacity. I want to regress spot prices on the inventory level but the relationship appears nonlinear. I believe that the non-linearity is created ...
0answers
141 views

### fitting a non-linear term in a logistic regression

I am running a logistic regression and I have run a box Tidwell test which seems to suggest that two of the IVs that I have in my model are non-linear. I have attempted to fit restricted cubic splines ...
0answers
302 views

### Non-linear Poisson Regression

I am trying to fit a count regression (rate model) of the form $y_{r,k}$ ~ $Poisson(N_k t_r^{-\alpha}exp(X_k\beta) + \delta)$. This looks complicated, so let me explain. (1) $y_{r,k}$ are the ...
1answer
116 views

### The effect of nonlinearity trends in the data on the cross correlation

Assume we have two datasets $X$ and $Y$ and I want to evaluate the cross correlation between them. What are the effects of nonlinearity trends within each dataset? That is, are there any relations ...
0answers
60 views

### What should I consider when determining the order of pooling-, non-linearity- and local-response-normalization-layers?

In convolutional neural networks (CNNs) it is common to intersperse convolutional layers with non-linearities, local-response-normalizations and possibly pooling-layers. In the literature I found ...
1answer
304 views

### Are there simple networks where a ReLu between convolutional layers has significant value?

At the moment I am studying the effect different non-linearities have on convolutional neural nets (CNNs). Since I'm not Google I am doing this by training simple nets (a few convolutional layers, ...
6answers
5k views

### Why is increasing the non-linearity of neural networks desired?

On the wikipedia page of convolutional neural networks, it is stated that rectified linear units are applied to increase the non-linearity of the decision function and of the overall network: https://...
0answers
77 views

### (How) can I validly impute data when I am using them to build derivative variables which I then use in spline regression?

As a minimal example of what I'm dealing with, let's say I have 4 continuous variables, $\textbf{x}_1$ through $\textbf{x}_4$. I'm ultimately performing a cubic spline regression with the dependent ...
0answers
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4answers
7k views

### How can I test a nonlinear vs a linear regression model?

I've got a panel regression model where the Ys assume a curved shape when plotted over time. A histogram of the residuals shows they are normally distributed but a residual-vs-fitted plot shows a ...
1answer
3k views

### How to interpret the direction of the Harvey-Collier test and Rainbow test for linearity?

I implemented both those tests with R, using the lmtest package. Both tests directionally say the same thing (I think) with a very similar p-value of very close to 0. But, are those tests saying ...