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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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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58 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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Best supervised regression algorithms for purposes of smoothness and interpolation

Suppose I have a dataset -- in this case a time series dataset of dimension $m$ -- which is causal. When I say causal, I mean that, given a $t_0$, no data from time $t_i > t_0$ may be used to ...
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Interpolation & Curve-Fitting of Hyperbolic Functions

So this may be somewhat odd, but I have a set of points (x,y) that are then fit to various distributions by transforming these distributions to have a linear form. I also have values of adjusted 'x' (...
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Understanding interpolation results in a sigmoid regression

I have a doubt about the results I got from an interpolation even though it was performed by a statistical software (SigmaPlot). I have the variable X that is the time expressed in hours and the ...
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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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Time series error progagation with linear interpolation?

So I have different data points in time, each data point has its own standard error of estimation. If I want to interpolate linearly between the data points to calculate the area under curve, how ...
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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 machine learning suitable for predicting a country's yearly statistical data?

My data consists of 55 years of around 200 different indicators for 200 different countries. The data is around 80% complete. Some indicators are dependent within the data(E.g. yearly meat spoilage ...
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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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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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307 views

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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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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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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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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115 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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Converting extrapolation point to interpolation point

Just wondering if this is possible via mathematical conversion. I thought some Kernels might do this in the kernel space. I got curious whether it's possible to create a general method that ...
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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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SAS Proc expand, how does it go from lower to higher frequencies [closed]

Proc Expand is quite useful for interpolating values, however sas help is not clear how it does when we want to spread the time series from a lower frequency (say year) to a higher frequency (say ...
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270 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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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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How to handle multiple points at the same location in spatial interpolation?

I am new to the topic of spatial interpolation and would appreciate your opinion on a general question which has arisen. Suppose I have a data set containing rental rates for different apartments in ...
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62 views

Regression for curve fitting

For a curve generated from dataset points, split the curve into parts and obtain the best-fit degree of polynomial,coeffcients and the interval/range of the split through implementation in python.I am ...
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Piece wise Polynomial Regression [duplicate]

It's wide known that for polynomial interpolation Chebyshev sites (as knots) are almost optimal, we can show that using those the Lebesgue constant is near to the lower bound. Is that claim also ...
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Estimating Spline curve by OLS. Is a good idea to fix the knots at Chebyshev sites?

I am writing my master's degree thesis on a novel method for fixing knots in an adaptive way and while reading the literature I've found many references to the so-called Chebyshev sites. This sites or ...
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Estimation of function using Spline Interpolation

My problem is the following: Estimate the function from given data (below) and show that the estimated function has the following properties: (i) $f(0)=0$ (ii) $f(x)>0, x>0$ and $f(x)<0, x<...
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How to interpolate/resample both dense and sparse points?

Suppose I have data like red points below I would like to interpolate/resample these points at black ticks. At right the points are sparse and it is obvious to interpolate them linearly or with ...
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361 views

How does Excel interpolate / imputate missing values in time-series when fitting a line to a plot?

I have a scatter plot in Excel (upper part of the screenshot) of time-series data. In-between the values that I plot (to the left), are some missings. I fit a (linear) line to those values and display ...
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Interpolating between consecutive weather radar images

I have a series of rainfall intensity images from a weather radar taken every 10 minutes. My goal is to generate intermediate frames in order to create a slow motion video. I've tried using the ...
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Looking for an unbiased version of the empirical cumulative distribution function that I can interpolate

Most definitions of the ECDF define it as (#elements <= threshold) / #elements. Matlab and R both implement their ecdf() functions using this formula. In my testing, however, I find that there is ...
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Difference between extrapolation and interpolation in higher dimensions

The most common distinction I've seen made between interpolation and extrapolation is that interpolation is within the range of the data, whereas extrapolation is outside the range of the data. This ...
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233 views

Poor regression results of neural networks on 2d benchmark data (compared to spline interpolation)

I try to understand for which regression tasks neural networks might be useful. One benchmark for me is to reproduce the ability of scipy.interpolate.griddata: ...
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Can I say Holt-Winters Method is an example of interpolation?

I believe it fits under the definition from wiki: In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of ...
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Minimize function curve 'length'

Given a set of points $(x_i, y_i)$, how can I find the serie of $ C^\infty $-functions for which the sum passes through all points and for which the length of the resulting curve is minimal; i.e. if ...
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Interpolate covariance matrix

I have measurements $z_i$ and associated covariance matrices $R_i$ separated in time by some sampling interval, and I want to interpolate between measurements. For example, I have a measurement at ...
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1answer
34 views

Estimating distribution of sound features based on speed

I am currently working on creating a model of sound of inside of a car based on speed. To be specific, making a Gaussian distribution of MFCC(13 dim) for each speed, i.e. car running at 30kmph, 60kmph,...
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reducing 2 variables of a function into one

I have an experiment where I'm measuring some physical quantity Q as a function of 3 variables which I can physically control (x,y,z). I'm collecting many samples of Q and (x,y,z) and then I can ...
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Obtain function that models strange oscillating data points

I've collected some interesting data from a fairly complex Python program I've written and I'm curious to figure out the mathematics behind it; or, at least, the empirical mathematics. Analyzing the ...
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Confidence intervals for bilinear interpolation

I have 4 data points which I am using to interpolate a query point using bilinear interpolation. Each of the 4 data points is obtained from the average of several observations (typically 10-16 for ...
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Replacing missing wind speed data from a nearby site

I am doing a project that is looking at testing various imputation methods for estimating missing wind speed at a site in Trinidad. The dataset consist of hourly wind speeds for 15 years. I have tried ...
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941 views

'Amelia' command returns error message: 'matrix is singular or not positive definite'

I've followed the instructions laid out in this thread, and created 'group' and 'time' variables. Below is a small subsample of my data. The set is longitudinal and in long format. ...

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