# 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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### 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 ... 14 views

### Methods to approximate Area under Precision-Recall Curve

average_precision_score from sklearn uses formula: ap = sum( (recall[k+1] - recall[k]) * precision[k+1] ) But trapezoidal rule implies: ...
1 vote
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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 ...
14 views

### Best interpolation technique for ODE-data

Let's assume we have an ODE $\dot{x}=F(x)$ where $F: \mathbb{R}^n \rightarrow \mathbb{R}^n$ is a vector field. And we observe a trajectory $\gamma: [t_0,t_1] \rightarrow \mathbb{R}^n$ from this ODE ...
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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 ...
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### Error in linear interpolation of $n$-dimensional curves

Let's assume we are given an $n$-dimensional smooth curve $\gamma:[a,b] \rightarrow \mathbb{R}^n$ and $N$- sampled points $\{x_1,...,x_N\}$ of that curve. Now we use linear interpolation (or a higher ...
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: ...
146 views

### 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 ...
1 vote
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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 ...
76 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 ...
44 views

### What spatial interpolation is going on with interpolate_pw: population weighted or population-areal weighted?

After some feedback on my question, I am re-writing it: I think I want to use interpolate_pw from the tidycensus R package to interpolate data from 2000 to 2010 county boundaries. The R documentation ...
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### Lomb-Scargle or Periodogram for non-uniformly sampled data

I have non-uniformly sampled data and I'm trying to look at its Power Spectral Density (PSD). For that, I looked at the Periodogram PSD estimate of an interpolated (with uniform sampling period) ...
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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 ...
32 views

### Convex data modelling

I have convex real data and want to find the best model, say in MSE sense. Given i have some experience with this, I eyeballed some suitable 2-parameteical function. However, I would be interested in ...
119 views

### Chi square for comparing image and models

In this question, the data is a 2D array which represents an image. Each element in the array is the flux or brightness of a given pixel. As a second step, portions of the image are masked (pixel ...
181 views

### 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 ...
354 views

### 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 ...
101 views

### 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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### Estimating input demand elasticities with time series data pooling

I want to find input demand elasticities of Labor, seed, agro-chemicals and fertilizer of 5 vegetables. Time series data are available from 1991-2019 for each crop for two growing seasons. When I'm ...
193 views

### 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 ...
26 views

### 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 ...
27 views

### 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 ...
1 vote
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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 ...
102 views

### 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: ... 451 views

### 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 ...
8k views

### 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 ...
163 views

### 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....
1 vote
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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 ...
29 views

### 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 ...
1 vote
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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 ...
4k views

### 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 ...
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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 ...
197 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(): ...
1 vote
208 views

### 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 ${h*k\times w*l}$, ...
109 views

### 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. ...