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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Handling densely observed functional data with R package fda in reasonable time

I am trying to use the fda package to analyze functional data that is densely observed; for example, for one function I have ~25,000 samples of that function. (To be more precise, I observe $f(t_i), 1 ...
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Ideal Use Cases for Splines

In general, I have often heard of "splines" being referred to as "old models", criticized for being prone to overfit the data, and being considered to be only better than "...
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Interpolation to account for heaping effect in mortality time series for regression analysis

I am trying to estimate the relationship between daily temperature and daily number of deaths (from all causes) for a specific location using time series regression. More specifically, using a DLNM, i....
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Spearman Correlation on timeseries acquired at different resolutions in R

I am working in R, and I have got these two timeseries: ...
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Is Spline Interpolation suitable for Economic Data

I have GDP data recorded in quarterly and I wish to interpolate it for monthly data. Is the Spline Interpolation suitable for these type of economic data?
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Interpolation based on a known curve

I have 6 datasets, 1 of which has 20 points, the other five have only 2 (beginning and end points). I want to interpolate 18 intervening points into the 2 point datasets such that the resulting curves ...
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Why is the use of high order polynomials for regression discouraged?

I've read many times on this site that high order polynomials (generally more than third) shouldn't be used in linear regression, unless there is a substantial justification to do so. I understand the ...
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Interpolation: More advanced calculation than linear regression

I am currently modelling the customer growth of a company. I have assumed values for December 2020, 2021, 2022 and 2023 and want to estimate the values for the month in between. As you can see in the ...
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Estimation of covariance at a finer grid given observations at a coarse grid

I have some observed data at certain grid points on a sphere. I can calculate the empirical covariance at these points using the standard formula. Now I want to predict the covariance at a finer grid. ...
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For which dimensions do Neural Networks become favorable to multidimensional interpolation methods?

Say I have a high-dimensional function and I'm trying to approximate/interpolate it. The typical methods I've found were Gaussian Process, spline interpolation (and others here https://en.wikipedia....
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How to choose smoothing parameter in RBF interpolation

I'm using Scipy RBF interpolator to create a function that moves in between points of my multi-dimensional dataset (4 dimensions). The interpolator has a smoothing parameter that I'd like to use to ...
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How to create an ML training dataset from unevenly spaced multivariate timeseries?

I have a time series dataset with multiple features X_n from which I want to predict an output y. However, both the x and y values are unevenly spaced and were sometimes collected at different ...
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How do I interpolate a field that is divergence-free and curl-free at the same time?

A magnetic field is divergence free. At the points where there is no current, and no changing electric field, it is also curl free. There exist divergence-free and curl-free RBF kernels, and I could ...
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Interpolating curve equation from model data

I need to define an equation to represent a series of points from a model. As they are predictions from an already fit non-linear regression, noise shouldn't really be an issue. I have seen many ...
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Constrained interpolation/smoothing of multi-dimensional time series

Consider an $N$ dimensional time series $x_i(t),~i\in\{0,1,\cdots, N-1\}$ where $x_i(t)$ is smooth. It turns out that for all $t$: $x_i(t)>x_{i-1}(t)$. The multi-dimensional series is sampled at ...
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How to use a temperature raster (e.g., PRISM) to constrain temperature values in a thin plate spline regression and interpolation

I have point data with temperature, latitude, longitude, and elevation. I am interpolating across space to the extent of those points, and have been using elevation as a covariate in the ...
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18 votes
4 answers
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What does interpolating the training set actually mean?

I just read this article: Understanding Deep Learning (Still) Requires Rethinking Generalization In section 6.1 I stumbled upon the following sentence Specifically, in the overparameterized regime ...
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11 votes
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Modern machine learning and the bias-variance trade-off

I stumbled upon the following paper Reconciling modern machine learning practice and the bias-variance trade-off and do not completely understand how they justify the double descent risk curve (see ...
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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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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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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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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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6 votes
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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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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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9 votes
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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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2 votes
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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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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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2 votes
1 answer
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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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