# 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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### Uncertainty propagation for quadratic interpolation

I have timeseries data $(t_i, y_i)$ with uncertainties $\Delta y$. I need to interpolate this data to match the timestamps with the timestamps of another dataset. Theory To propagate the uncertainties,...
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### What advantage do sinusoidal positional encodings have over binary positional encodings in transformer LLMs?

I've recently come across an article that discusses the reasons why large language models use sinusoidal functions to generate positional encodings — as per the famous paper Attention Is All You Need (...
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### Interpolation: From age groups to specific age

I have a database contains 10 age groups ( [15;19], [20;24]... [+60) and number of individuals in every age group but it doesn't follow any distribution (once it decreases and other time it increases),...
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### splines: uniform knot positions

Suppose we have 8 uniformly distributed interpolation points x = 1 2 3 4 5 6 7 8 and want to define a bspline curve of order k=5, hence the knot vector has 8+5=13 ...
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### How to convert B-Spline to piecewise polynomials?

Suppose I have a basis spline $$S(x) = \sum\limits_i N_{i,k} a_i$$ defined on the interval $x \in [a,b]$ with control points $a_i$, degree $k$. $N_i$ are the basis spline functions. The knot vector ...
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### Best way to impute missing values in a time series

I have a camera that detects every time it views a car. Each detection is recorded in a database. I then simulate this behavior as a time series by doing an each hour count of the records. The problem ...
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### Interpolation on bond issuance data

I am currently working on an analysis on bond issuance during the COVID pandemic. I will run a linear regression of spread on multiple bond issuance characteristics but also on multiple firm key-...
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### Why does a triangular function not work as a radial basis function for interpolation?

This code is based on the example on https://en.wikipedia.org/wiki/Radial_basis_function_interpolation : ...
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### Computing coordinates of points of an image after elastic deformation

My task is: given an image and set of points of interest, elastically and randomly deform the image and save it with the modified aforementioned points. example: (blue points are the points of ...
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### How would you deal with sparse and scattered 2d data in a way that makes physical sense?

I am currently analyzing rainfall data which is in longitude/latitude/value format i.e. a 2d matrix. That is, I have a series of values x,y,z such that ...
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### Is polynomial interpolation with RKHS in some way more advantageous than simple Lagrange interpolation?

The reproducing kernel Hilbert space associated with the polynomial kernel $K(x,z)=(1+xz)^{d-1}$ (or other similar polynomials) can be used to interpolate a continuous function $f$ at by its value at ...
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### Alternative to hot deck imputation

I use hot deck imputation for a project that I work on. But I'm dissatisfied that it can't come up with new values. If my doner set had thousands of values in it, and they were nicely distributed, ...
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### Cubic spline with circular predictor [duplicate]

I have a set of observations $y_i$ for a set of values of the independent variable $x_i$. $x_i$ takes values of angles, so it is a circular variable. Is there some method to perform cubic splines or ...
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### Training error loss vs "classification loss"

From the paper To understand deep learning we need to understand kernel learning, three questions: In section 2 "Setup" there appears a definition of interpolated classifier as an algo that ...
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### How to perform inference on regression coefficients when some X values are interpolated?

This should be a simple question but I'm having a hard time finding an answer. Assume I have some data $y$ with covariates $X$. This set of data was obtained via a simple random sample. I want to ...
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### Best interpolating points for a Gaussian process regression

I have an unknown function $f(x)$, defined on a domain, that is modeling a perception function based on a human user response. I estimate it with a GP with mean $\mu$ and kernel $K$. I determine the ...
1 vote
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### Can kriging method be used for dataset that is not spatial?

Sorry if the question sounds stupid. I am new to this. Consider the following dataset: ...
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### How to deal with noisy observation in Survival Analysis

I'm new to Survival Analysis. Usually in survival analysis, we want to model the survival function progress w.r.t time. This is normally done through Cox model, or KM-model within a specific time ...
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### Natural Spline Interpolation in R [closed]

I am trying to construct a natural cubic spline interpolation using R and test it with a Runge test function. I have implemented the following code; however, the interpolation is not passing through ...
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### Kriging : when it is said kriging is an unbiaised estimator, is that synonymous with saying it is an exact interpolator?

I feel like they are not synonymous, but I cannot intuitively explain the difference between "unbiased" and "exact." In other words, I am asking about the difference between the ...
161 views

### What do the weights in the specaccum function actually do?

I am trying to create a species accumulation curve that accounts for different areas of each sample. For example, samples were obtained from different sized quadrats. I think the weights argument in ...
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### General question about interpolation and machine learning

I have a pooled data with two-monthly frequency. lets say response variable is y. I want monthly time series for y. Can someone please share link to methods through which I can better predict the ...
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### Effective way to down sample or up sample signals without losing information?

I have an edf data here that I got from this website. The data was supposed to be fed into an ML model. The data is taken from a sleep study (polysomnography). However, the data for some of the ...
1 vote
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### Algorithm for approximating linear-interpolated curve

Goal Given a curve defined by a set of (x, y) coordinates with linear interpolation, we want to find the best approximation using a smaller set of points (w/ linear interpolation) that fall along a ...
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### Interpolate / Impute time series (sparse measurements)

I observed a manufacturing process that yielded ~40,000 parts I sampled 200 of these parts (every 200th part) and measured their properties My ultimate goal is to show that sensor data, that ...
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### Statistical difference between curves

I have 12 curves (three replicates for each treatment), see attached picture. X=days; Y=percentage. The experiment has 2 variables: A: 4 cases; B: 3 cases. I would like to know, if there is a method ...
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### Correct approach for predicting new value based on similarity to other data points

relative rookie here so apologies if the answer to this is obvious. I am trying to find the correct approach/technique for this problem. I have object A and a data set. The data set contains 2 columns,...
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### Interpolation using LogNormal distributions in R

I want to interpolate the dataset below using lognormal distribution in R. As you can see from the data below, I have different land size classes (ha) and I would like to interpolate the data using ...
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### Can increasing dimentionality improve classification in Neural Networks?

I had a dataset where each data sample (pixel) had 7 features (reflectance at 7 wavelengths). However, running my neural network on the 7 features was not able to reach a high accuracy in classifying ...
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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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### 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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### 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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### 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 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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### 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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### 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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### 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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### 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 ...