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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Link between RKHS reconstruction and SVM

Simply put, my question is the following : I know Reproducing Kernel Hilbert Space Reconstruction (RKHS)-type methods like RBF reconstruction and I've used them in the past. I understand Support ...
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Interpolation of Hessian matrix

I have a model where hessian matrices are calculated along a path. Since the calculation is done using finite differences, this is very time consuming. I have tried to calculate only every second ...
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Is a spline interpolation considered to be a nonparametric model?

I am aware of the basic differences between nonparametric and parametric statistics. In parametric models, we assume the data follows a distribution and fit it onto it using a fixed number of ...
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27 views

Is it possible (and even correct) to calculate a confidence interval from an interpolated value?

I am using a probit model to calculate the limit of detection of a diagnostic test. For this, in R, I used glm(): ...
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Bilinear Interpolation Algorithm for up-sampling 2D images

In keras it is possible to use UpSampling2D layer to up-sample an image. You can use Bilinear Interpolation. Given an image ${h\times w}$ it is possible to increase its size in ${h*k\times w*l}$, ...
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How to calculate the z-score to an interpolated 2-dimensional point?

I have many 2-dimensional data-points (x,y) and I know that there is a correlation between x and y. Now, for a certain point P, I want to calculate something like a z-score (in y), given its x-value. ...
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26 views

Interpolating between points of known uncertainty

I have a large but finite set of objects (phylogenetic trees), each of which is assigned an integer value 0 ≤ v ≤ x. x varies from set to set, but is small (≪ 100). For a given set, I wish to ...
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Average sales of last three years using interpolation/extrapolation

I have average sales value for the last three years of a company, e.g. year avg. sales 2017 100 2018 150 2019 200 Is it possible to somehow come up with an estimate of total average sales value ...
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GDP and multipoint interpellation

I'm trying to interpolate multiple points between two points in time. I'm trying to convert an annual forecast to quarterly to fill in the missing data points. My data: Historical quarterly GDP ...
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How to get the number of deaths per month in this dataset?

This dataset shows the number of deaths (of all causes) in the US in 2019. It's labeled in weeks. What is the right interpretation of this for getting the number of deaths in January? Should I add ...
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standard deviation of two constant noised signals related through interpolation

Let us say say we have a noised constant signal and want to evaluate the standard deviation (std) of the noise. We calculate the std of the said noised signal and call it σ1. Now we process the signal,...
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Does ordinary kriging assumes a random field with zero drift?

The question is actually the above one. I'm a beginner in spatial stats and just trying to fit many puzzle pieces together. So I just wondered if ordinary kriging, in contrast to universal kriging, ...
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What's the difference between modpolyfit and peak.Detection functions in R baseline package in terms of interpolation?

I want to use these functions to subtract the baseline off the spectrum. The first one, the modpolyfit I guess just interpolates every nth point of the spectrum. But how about the baseline....
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In linear regression, we have 0 training error if data dimension is high, but are there similar results for other supervised learning problems?

P.S. I just posted this question on MathOverflow, as I didn't seem to get an answer here. Let's consider a supervised learning problem where $\{(x_1,y_1) \dots (x_n,y_n)\} \subset \mathbb{R}^p \times \...
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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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Combining kriging variance and observation measurement error

I have a set of point/areal data that I would like to interpolate in missing locations using kriging. The kriging prediction variance does not normally depend on the measurement itself, but rather on ...
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190 views

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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Inverse Distance Weighting for interpolation/gap-filling with bivariate data?

I'm in two minds about this and none of the resources I find online seem to give a clear answer on this. I understand the premise of IDW and have used it before. However, is this method valid (or in ...
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How to add residuals to model to improve fitting?

I performed a GAM in R for temperature from meteorological stations. My goal is to have a well-fitted model to predict temperature to a bigger territory. When I do that, I can see that residuals of ...
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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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Must an interpolator exist with linearly independent basis functions?

I have data $(x_1,y_1), \dots, (x_n, y_n) \in \mathbb R^2$ and the $x_i$ are distinct and increasing. I want to interpolate the $y_i$ with a function $$ f(x) = \sum_{i=1}^Na_i h_i(x) $$ where the $...
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Necessary conditions for Lagrange polynomial positive on interval

Given a Lagrange polynomial of degree $k$ in second form of the barycentric interpolation formula $p(x) = \frac{\sum_{j=0}^k \frac{w_j}{x - x_j} y_j}{\sum_{j=0}^k \frac{w_j}{x - x_j}}$ with $x_j = \...
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181 views

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 ...
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72 views

Intuition Behind Correlation Function in Kriging Models

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)) ...
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How can I interpolate bewteen probability distributions?

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 ...
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Difference between Gaussian Process Regression and Kriging - Regressive vs Interpolative?

I am using different machine learning models to model a noisy dataset for some study. I came across fitrgp model in MATLAB to model the data using gaussian process regression. I am also using dacefit ...
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How to use Interpolation in Neural Network?

I found some interpolation methods in time series data. For noisy or irrelevant data in time series, when I use simple interpolation (spline or linear) methods, my results are not bad. But, I want to ...
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How is vector arithmetic and interpolation possible in the latent space of GANs?

In the DCGAN paper (Alec Radford et al.), the authors were able to perform vector arithmetic for semantic analogies by averaging the latent vectors of generated images with the same class. They've ...
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“Jumping” among several interpolation techniques?

I am comparing several interpolation methods using monthly climatic data, through RMSE and a 10-fold cross-validation scheme. What I'm observing is that the performances vary from one month to ...
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Is there a non-arbitrary criterion to choose which points to use for interpolation?

Look at the image. I have to interpolate this experimental points with a voigt function to find the position of the center of the peak, I have to choose how many points and which points to use in the ...
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Shape preserving spline regression

There are shape-preserving, preserving especially positivity, monotonicity or convexity, spline interpolations such as described here and here. Are there similar shape-preserving spline regression ...
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1answer
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Vector Interpolation in Higher Dimensions

I have a collection of vectors $\mathbf{X}^{(i)}$ that live in a space of dimensionality $N$. I would like to construct a curve that interpolates through those points in a nearest neighbour fashion (i....
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Calculating percentile data points of a distribution give min,median, Max, mean and StDev

I am trying to populate 100 data points (equal percentiles) from 5 data points. I have Minimum,median,maximum and standard deviation. So the first of the 100 data points would be the minimum, and the ...
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Interpolating time ordered smooth function into space

I am using GAMs in R to generate daily weather variables, mainly precipitation and temperature. Currently, I am fitting a model for each weather station but I would like to use it in places where ...
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157 views

Interpolate/Impute Time Series Data from another Time Series

I have a dataset of multiple lakes with water level elevations through time. The observations are not regularly spaced and have many large gaps. Further, some of the older observations may be of lower ...
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170 views

Interpolation of uneven data in 2D using Gaussian Process

I have a dataset that is spacially distributed like the figure below. The function values of each point is plotted as the elevation in the 3rd dimension. Now, I want to find a kernel/and or method ...
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183 views

Handling non-uniform frequency data

I have some medical data (heart rates) at non-uniform intervals (usually readings every few min at the start of the study and several readings a minute toward the end). The timing and when the change ...
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440 views

Giving uncertainties to interpolated values in time series: application to mass balance reconciliation

My problem concerns a mass balance reconciliation in an industrial system. I have a node with several flows in-coming and one or several out-coming, what's incoming should equals what's out-coming (...
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Extrapolation v. Interpolation

What is the difference between extrapolation and interpolation, and what is the most precise way of using these terms? For example, I have seen a statement in a paper using interpolation as: "The ...
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Interpolation versus imputation for time series on chemical profiles of water wells

So I am working with some data on water wells and time series of chemical pollutant tests on those wells. There are 10 chemicals and 10 years in the data. My goal is to do some clustering on the wells ...
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how to select training and testing data for interpolation in 100 instances data?

I would like to divide my data of only 100 instances into training and testing an use the training data to fit a curve(interpolate) and use the testing data to calculate the error at the interpolated ...
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1k views

What is the best way to represent uncertainty from linear interpolation?

A little background to this question: Part of my job is to conduct flood risk appraisals to help determine the viability of flood defence construction. There is a standardised way to do this, which ...
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1answer
19 views

Word for data-series comprised from resampled, interpolated and merged data-series

Two series of data-points for a specific curve are given: $x$ as a function of $y$ (high resolution, low range) $y$ as a function of $x$ (low resolution, high range) The two series are merged and ...
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Is there a method to approximately predict a 3D curve given two plane view of the curve?

Let's say the original data contains three variables, so it is a list of (x,y,z). In the figure, the blue and red curves are the lists of (x,z1) and (y,z2), respectively. These two lists are obtained ...

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