Questions tagged [kernel-smoothing]

Kernel smoothing techniques, such as kernel density estimation (KDE) and Nadaraya-Watson kernel regression, estimate functions by local interpolation from data points. Not to be confused with [kernel-trick], for the kernels used e.g. in SVMs.

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34 views

Reducing the dataset size for KDE

I have GPS data, so 2 coordinates, and I want to estimate the busiest places (i.e. the places with more data points). However, I have a lot of points: currently ~4 million for 12 days, and I will be ...
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Expected value and variance of KDE

I need to find the expected value and variance of KDE given that $$(i) E[u] = 0 \to \int u\phi(u)du=0\\ (ii)V[u] = \sigma^2 \to \int u^2\phi(u)du=\sigma^2$$ where $\phi$ is the kernel function. I've ...
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Computing a KDE and its point-wise error from data with measurement errors

I have a set of measurements and their associated errors. I would like to compute a kernel density estimate (KDE) and the error of the KDE at each point. The KDE and the KDE error should take into ...
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What is cross validation doing in my spatial ecology model, and how necessary is it to run?

I'm currently using the R latticeDensity package to estimate home ranges of animals. Within the documentation, The minimum uvc (Unbiased CrossValidation ...
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Kernel density estimate vs Dirichlet process mixture

Nowadays the Dirichlet process mixture (DPM) seems to be the default Bayesian approach for density estimation. My question is why not simply use the kernel density estimate (KDE) to model the density? ...
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Estimate size of each group with uncertainties from a KDE plot

I want to know the percentage of individuals in the "low-squeak" and "high-squeak" groups with uncertainties. How do I calculate it given the following bimodal distribution? For example, I need to ...
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How can probability be equal to pdf times volume of area?

I'm studying pattern recognition and I'm at the part about Kernel density estimators. During the introduction of the subject, the book I'm studying (Pattern Recognition & Machine Learning by ...
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1answer
19 views

What does it mean to “renormalize” the density of a kernel distribution?

I'm a marine spatial ecologist looking to remove land from some kernel density estimations of tagged sharks. I've seen numerous methods for this approach, with one such method described succinctly in ...
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42 views

Naive Bayes + KDE = Lazy?

If I in Naive Bayes use Kernel Density Estimation to estimate logarithms of the conditional probabilities of the attributes in each class $\ln p(x_j|C_k)$ can we consider this classifier to be an ...
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1answer
14 views

t test and kde plot does not match

I cannot understand the results of scipy independent two samples tests on my my dataset. the results of the test as I understand it suggest there is a significant difference between the means of the ...
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Interpolating Regression Models Across Geographical Space

I have 50 timeseries datasets from 50 cities across the United States (1 for each city). The timeseries are of different lengths (they are daily timeseries anywhere from 3-30 years long), but they are ...
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Behavior of kernel density estimation

Consider the random variable $X=YZ$, where $Y\sim\text{Normal}(0,1)$ and $Z\sim\text{log-Normal}(0,1)$ are independent. I wanted to assess the accuracy of kernel density estimates for the density ...
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Density estimation as an optimization problem

Density estimation is the estimation of a probability density function from observed data. Can some of the common approaches to density estimation, such as kernel density estimation, be formulated as ...
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58 views

Sampling from transformed KDE representation

Let's say that I have a random variable $X$ distributed according to some prior distribution $p(x)$, for simplicity assume that it's a Log Normal distribution. I then sample $N$ elements from this ...
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21 views

“Simple” boundary correction method in kernel density estimation

I'm new to kernel density estimation and have a rough idea on boundary bias. When correcting for boundaries, I tried to use boundary correction method as "simple" which is available in R. Once I ...
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How does one choose the bandwidth for the confidence intervals of a kernel density estimate?

My lecturer estimated a kernel density, then wanted to give confidence intervals for it. So, he used a bandwidth $$h_c = h_g \times \frac 1{n^{0.05}}$$ where $h_g$ was the bandwidth of the original ...
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Demmler-Reinsch basis for smoothing splines

I have seen some papers about using the so-called Demmler-Reinsch basis for smoothing spline because it is a basis for natural spline space and also Sobolev space. For example, these papers: A ...
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1answer
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How to generate random samples from a 2D dataset?

Suppose I'm given a data set consisting of many pairs of $(x,y)$ values which are correlated in some arbitrary complex way. How would I go about 'generating' more pairs of $(x,y)$ coordinates which ...
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Fitting KDE with scikitlearn and pandas to plot. However, distributions lie outside the range of data

I am fitting a distribution of scores ranging from 1-13 for a set of data using scikitlearns KDE functions and Pandas plot.kde. I have set the bandwidth with a gridsearchCV method. However, when the ...
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Gaussian Kernel and Feature Space [duplicate]

I have been reading this paper for a few days. There is one section (Section 3.3) that confuses me. We start by gathering local features from training images of a particular class into a single ...
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MSE for the kernel-based HAC long-run covariance matrix itself (in the Frobenius norm sense)

Consider the stationary multivariate time series $X_1, \ldots, X_T$ and the HAC-consistent long-run covariance matrix estimator $$\hat{\Gamma} = \hat{\Gamma}_0 + \sum_{l=1}^{T-1} K\left(\frac{l}{h_T}\...
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How does this algorithm converge?

From https://en.wikipedia.org/wiki/Kernel_density_estimation, we have this formula for the optimal bandwidth for a kernel density estimator. Note that we need $R(f'')$ which is unknown. An ...
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A comparison of the global optimal binwidth and local optimal binwidth of the histogram estimator

Suppose we have $X_1, \dots, X_n$ to be an i.i.d sample with unknown pdf $f(x)$ and cdf $F(x)$, and define $\hat{f} (x)$ to be the histogram estimator. We also define its Mean Integrated Square Error ...
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Gaussian Kernel density estimation by hand

I'm trying to understand the logic behind kernel density estimation. I found the explanation in wikipedia very useful, but I'm not capable yet, of having a full understanding of this method so I want ...
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Minimizing MISE to find consistent estimator

Consider kernel regression estimation of the mean function $m$ of the process $$y_t = m(x_t) + \epsilon_t,$$ where $\epsilon_t$' s are correlated with covariance function $R(s,t) = \exp \{-\lambda|s-...
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Does local linear regression include a weighting Kernel?

3 minutes ago 1 Hey, I am applying a Regression Discontinuity Design (RDD) to estimate the effect of a policy change. In RDD I can apply the parametric approach (polynomial regression) and the non-...
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state of the art in density estimation

I have seen density estimation methods which are pretty old. Specifically, I am referring to Parzen Window method. When I read the original Parzen's paper, I was amazed by it's beauty and I know that ...
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1answer
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Kernel density, why does my subset appear to have a larger spread than the original series?

I have a series that is 1500 observations long called alt_intercept. From it, I created a subset that contains values only if another series (called pvalue) is less ...
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1answer
39 views

why does y axis sometimes change from normal histogram to kernel density?

Consider the distributions I have plotted below. They are of the same variables, one in normal histogram form and another in kernel density (Epachanov). As far as I know, the auc of the kernel ...
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39 views

Kernel Density Estimation - Physical Interpretation?

I just read this article about the motivation for KDE. From what I understand, you are using Gaussian probability density distributions for each datapoint and then, depending on the selected kernel ...
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21 views

How can I estimate bivariate probability density for support restricted data?

I have a bivariate sample with the following kernel density estimation The issue is that there is actually a cutoff for log(Age) at about 2.5, so value greater than 2.5 has probability 0. The fitted ...
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25 views

Transformation of a random variable and KDEs — when is reweighting needed?

Suppose I have been given some data $X$ that I wish to resample according to their empirical distribution. For whatever reason, I decided to transform these variables to some other space $Y = f(X)$ ...
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How to choose sample size from probability density for computing mutual information based on continuous variables

I need to compute mutual information gain based two continuous variables $X$ and $Y$ $I(X|Y) = \int_X\int_Y p_{x.y}(x,y) \log(\frac{p_{x.y}(x,y)}{p_{x}(x)p_{y}(y)})$. I have used Kernel Density ...
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ksmooth function in R

I'm trying to understand how ksmooth function in R works (I haven't really taken much statistics other than an introductory one at college, so sorry if this is a ...
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1answer
46 views

Find PDF(X,Y) from PDF(X) and PDF(Y)

given that X and Y are not mutually exclusive, is there anyway to calculate PDF(X,Y) from PDF(X) and PDF(Y)? Following are a few plots made from the dataset. In above image i have to find how PDF(11,...
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27 views

Reading kernel distribution plot vs typical histogram

Tasked with showing the distribution of a certain data set in a different way, I wanted to try to plot a kernel density. After seeing it however, my co-worker advised against it saying that because ...
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21 views

What does alpha in smoothing stand for

I want to apply Gaussian smoothing to a dataset and came across the smth.gaussian function in R. That besides the numerical input data requires two parameters: ...
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22 views

ROC curve with symmetrical kernel

I am trying to use kernels with ROC curve, and 'm succeed to plot them but now my query is about theoretical grounds, i.e. its bias, var, etc. I want to evaluate the theorems (1 & 2) in Pulit (...
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Kernel Density estimation with guassian kernel function why don't have indicator function like other kernels [closed]

Kernel Density estimation with guassian kernel function why don't have indicator function like other kernels.
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When to use non-parametric regression such as kernel, generalized additive model, spline, and polynomial?

I understand that kernel regression is a form of non-linear/non-parametric regression. However, I know you can also use generalized additive models for non-linear regression, as well as polynomials ...
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3answers
970 views

Python: “Normalizing” kde, so it always lines up with histogram

In Python, I am attempting to find a way to plot/rescale kde's so that they match up with the histograms of the data that they are fitted to: The above is a nice example of what I am going for, but ...
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277 views

What kind of kernel is used by statsmodels.nonparametric.kernel_regression.KernelReg?

I am doing multivariate nonparametric kernel regression using the Python function as mentioned in the title. The documentation can be found here: https://www.statsmodels.org/stable/generated/...
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How to calculate Kernel Density for Bootstrap Likelihood

I am attempting to write R code to generate bootstrap likelihood as described in section 3 of this paper https://arxiv.org/pdf/1510.07287.pdf. I am confident that I performed the bootstraps correct, ...
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Reproducing kernels: how do I numerically compute the decomposition?

Suppose I'm given a kernel, $$ K(x,y) : \mathbb{R} \times \mathbb{R} \rightarrow \mathbb{R} $$ In order to describe/understand the (unique) associated RKHS, I seek its eigenfunctions, as per Mercer'...
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81 views

KDE that better-preserves percentile distributions

My understanding is that a Gaussian KDE, because the kernel is symmetric, preserves the statistical mean of a distribution. For my particular case, I'd really prefer a KDE that preserved the median, ...
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1answer
81 views

Density Estimation and Data Normalization

Is there any problem to first normalize data (for example, min-max one) then use kernel density estimation to get pdf of each sample? Thanks.
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Every point has the same probability?

I am reading "Pattern recognition and machine learning" by Cristopher Bishop. In Chapter 2.5.1 "Kernel density estimator", there is written that: Let us suppose that observations are being drawn ...
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1answer
42 views

Kernel Density Estimation for non-parametric

I'm writing an R function to get the fitted values of the kernel density estimate. For that I use the computational formula of summation of ({n-1 h-1 K{(x - Xi)/h}}?) $$ \hat{f}(x) = \frac1{n h}\sum_{...
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1answer
621 views

How to choose the bandwidth of a KDE in python

Python's Sklearn module provides methods to perform Kernel Density Estimation. One of the challenges in Kernel Density Estimation is the correct choice of the kernel-bandwidth. I have come across ...
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Group comparison for bivariate distributions

For two groups A and B that consist of n and m individual samples. Each individual sample has a unique 2-dimensional joint probability density functions (PDFs)of two variables. These PDFs are ...