# Questions tagged [interpolation]

Given a set of bivariate data (x, y), to impute a value of y corresponding to some value of x at which there is no measurement of y is called interpolation, if the value of x is within the range of the measured values of x.

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### How to predict single y target based on several X values? [duplicate]

I try to predict the result of an personality type test based on how people answered. My sample consists of the answers which range from 1 (strongly disagree) to 7 (strongly agree). Six answers lead ...
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### Arrange data so that two variables are linear

I have the following set of rainfall intensity data and I want to make a compilation of the rainfall intensities above some practical minimum as shown in the figure below. So the intensity and the ...
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### Best interpolation for strictly decreasing data

So I was using an interpolation for this curve and made the mistake of using Lagrange's polynomial interpolation: I wanted an interpolation that acts a that can vary depending on the data points, and ...
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### Which method is appropriate for using the pattern of a high frequency timeseries dataset to interpolate a low frequency timeseries dataset?

I have a low temporal frequency irregular dataset with a value available every 40 to 48 days. I have another set of time-series data over the same period at 12 day frequency. The pattern of the two ...
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### Number of points a one hidden layer neural-network can interpolate

We am trying to understand the number of points that a neural network of a particular size can interpolate. I think this may be isomorphic to its degree of freedom? We are not interested in whether ...
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### Can "Curve Fitting" be seen as an Alternative to Numerical Differentiation?

For a long time, the following point always confused me: If the "Fundamental Theorem of Calculus" tells us that all real and continuous functions are differentiable (i.e. have derivatives) - ...
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### Can we solve overfitting by adding more parameters?

What is the state of the art knowledge on how generalization in interpolating models looks with respect to the number of parameters? Does it look like this: (Picture from Mikhail Belkin's talk on ...
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### Interpolation using Gaussian processes

This is about Gaussian process interpolations, where the given data are f(0) = 1, f(0.4) = 3 and f(1) = 2. Assume that the covariance function used is the exponential covariance, where the expectation ...
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### How to expand weekly time series data from 38 weeks to 52 weeks format?

Recently I have been working with weekly data that has in total 52 weeks. Later I received data with an external variable and it is also in weekly format but the whole year has in total 38 weeks. The ...
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### Gaussian process - what am I doing wrong?

I have recently started to delve into Gaussian processes. During my review, I have found a book which states that one can interpret the mean of a Gaussian process as a combination of basis functions, ...
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### Imputation approaches for records with completely missing dimensions

I have two sets of data provided by the government - one spans the years 2016-2020, while the other only covers 2018-2020. Data from each dataset, for each year, are used to predict some outcome in ...
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### Types of data interpolation

Consider the following two "types" of interpolation. In one case, our model passes through all observed data, in the other one, it doesn't. Do these types of interpolations have a name? If ...
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### (Co)kriging / co-located kriging with heterogenous measurement errors

I have a large set of polygons on a map, some of which contain data on 2 count variables, say ($z_{1}$ and $z_{2}$) that are correlated. In fact, $z_{2}$ most likely causes $z_{1}$ without the ...
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### Should I use empirical or distribution-estimated quantiles for N=50?

I am building a custom value-at-risk platform at my job but have only 50 samples from which to draw. Because the stakeholders want to run the analysis for arbitrary confidence levels (not just ones in ...
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### Fitting a curve knowing points uncertainty

I have a set of points X and Y that represent a curve. It is not a linear curve but a model I cannot estimate analitically. I know the uncertainy on Y (1 sigma) and there is no uncertainty on X. Due ...
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### Interpolate or Extrapolate?

I've encountered a little problem with my research. My study is about the relationship between ICT Development and Service Trade from 1999-2018 (annually). Some of the missing data are located in the ...
I'm thinking and researching extensively to interpret the parameter $\theta$ (activeness parameter) in Gaussian correlation function in a Kriging model, namely as:  K(h;\theta)=exp(-h^2/(2\theta^2)) ...
I would like to implement a nearest-neighbor algorithm. The features are points in $\mathbb{R}^n$ and the labels I am trying to learn are probability distributions. So the label (probability ...