Kernel refers to weighting functions used in non-parametric estimation techniques.

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denoising using R or matlab [on hold]

How can I use R or matlab to denoise data using the following smoothers 1) wavelet 2) epanechnikov kernel 3) polynomial spline 4) logistic kernel.
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45 views

Cascade Combination of Kernel Functions

I have a question regarding machine learning and specifically kernel functions. Suppose we have a Kernel function, say $K(x)$, and also another distinct one, say $K'(x)$. I want to know is $K(K'(x))$ ...
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15 views

Difference between Primal, Dual and Kernel Ridge Regression

I would like to basically ask what the title says. What is the difference between Primal, Dual and Kernel Ridge Regression? People are using all three, and because of the different notation that ...
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1answer
38 views

Linear Kernel in Baysian Linear Regression

I came up with http://mlg.eng.cam.ac.uk/duvenaud/cookbook/index.html and it is actually very useful. At some point it says If you use just a linear kernel in a GP, you're simply doing Bayesian ...
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19 views

Derive squared exponential covariance function

In Gaussian Processes, SVMs, kernels are used (as to my understanding) as similarity measure. However, they have the constraint that any kernel has to be represented as a dot product. i.e. ...
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19 views

Prediction with scikit and an precomputed kernel (SVM)

I am kind of a newbie in the MachineLearning area and evaluating some tools etc. to get a feeling for it. For a project I am using a tool that creates a precomputed kernel (gram matrix) and also is ...
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1answer
20 views

Finding the cluster centers in kernel k-means clustering

I think this is the most easily understood topic in Kernel K Means Clustering. But assuming that I am not an expert in Machine Learning, can someone tell me how does someone calculate Kernel K means ...
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19 views

What's wrong with the intuition that kernel measures similarity between observations?

Near the middle of page 16 of Andrew Ng's notes on SVM, he explained an intuitive view of kernel as measuring similarity between observations, but then added the caveat that there are things wrong ...
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41 views

Need a working algorithm to find out optimal kernel bandwidth for density estimation

I am looking for a working algorithm for find out optimal kernel bandwidth for density estimation. I need to write my own program in pascal instead of using R or Matlab. So far all algorithms I ...
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9 views

Kernel PCA number of components

When using Kernel PCA for dimensionality reduction is there any simple criterion which can be used to determine the number of components to use? I am using Kernel PCA with linear kernel, which would ...
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1answer
62 views

SVM basic theory?

I have some questions about SVM: In SVM there is a nonlinear and linear SVM. What is the difference between them? To do classification in SVM, we will find the linearly separable boundary ...
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30 views

How to find out optimal KDE bandwidth via Bootstrap Aggregation

I am a programmer and trying to do some data analysis. Since I am very interested in statistics, and I have learned a lot of programming languages, learning how to use professional packages such as ...
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1answer
60 views

Kernel smoothing for Edgeworth expansion

Suppose I have an estimator which includes an indicator function in the objective function, then the objective function is not smooth. But if I want to approximate the behavior of this estimator in ...
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1answer
30 views

Calculating agreement between an ordinal and continuous scale

I'm having a bit of trouble wrapping my head around something. I have a data set which contains two columns that essentially attempt to measure the same thing, one on a 1-50 continuous scale and ...
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18 views

What is the difference between the metric window width and Nearest-neighbor's window in Kernel Smoothing methods?

I'm learning Kernel smoothing methods. I didn't really get the difference between the metric window width and Nearest-neighbor's window. For me both seem the same. Can anybody explain it to me? for ...
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19 views

how to prove this kernel function is positive semidefinite

How to prove $k(x_i,x_j)=e^{-(LR(x_i-x_j))^TLR(x_i-x_j)}$ is a valid kernel function or positive semi definite? $x=(\mu,\lambda)^T$ and R is a 2x2 rotation matrix, L is a 2x2 diagonal scaling matrix ...
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1answer
47 views

Binary classification using radial basis kernel SVM with a single feature

Is there any interpretation (graphical or otherwise) of a radial basis kernel SVM being trained with a single feature? I can visualize the effect in 2 dimensions (the result being a separation ...
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43 views

Kernel estimation of hazard or density function

I am working with R package "muhaz" to get the kernel estimate of the hazard function. If we have the following example which is the sample of uncensored data: ...
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20 views

kernel for a (semi-) metric space

Let's say I have a metric space $(\mathcal{X}, d)$. Is there any kernel function that I can use with SVM? If we change the RBF kernel a little bit, we have $k(x,y) = e^{-d(x,y)^2}$. Is this a valid ...
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23 views

Optimal Kernel Size for Lanczos resampling

The kernel for Lanczos Resampling is defined by $$K(u) = \frac{a\text{sin}(\pi u)\text{sin}(\pi u/a)}{\pi^2u^2}.$$ How does one go about finding a value of $a$ to minimize the mean squared error, ...
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1answer
37 views

How does a linear SVM work? [duplicate]

I have a 2-class problem involving many features. Does a linear support vector machine (SVM) classifier only take into account the values of these features and nothing more? Does it see the ...
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1answer
128 views

How to draw random samples from a non-parametric estimated distribution?

I have a sample of 100 points which are continuous and one-dimensional. I estimated its non-parametric density using kernel methods. How can I draw random samples from this estimated distribution?
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3answers
197 views

Where is density estimation useful?

After going through some slightly terse mathematics, I think I have a slight intuition of kernel density estimation. But I am also aware that estimating multivariate density for more than three ...
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1answer
50 views

Integral of a function with uniform kernel

I am trying to understand question 9-1 on p.334 in Cameron & Trivedi (link) where I have to calculate the bias of a kernel density estimate at $x=1$ and $n=100$, where we assume that the ...
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11 views

scikit-learn SkewedChi2Sampler - meaning of skewedness parameter

I am trying to understand the meaning of the "skewedness" parameter for scikit-learn's SkewedChi2Sampler and figure out how this value affects the output of the sampler. I have looked at the docs ...
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1answer
37 views

SVM cost, kernel and dimension

Why is it SVM computation cost does not depend on kernel value, dimensions (when separating hyperplane )? Is it because all it does is just classifying and not much calculation involved?
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234 views

Ratio of probabilities vs ratio of PDFs

I'm using Bayes to solve a clustering problem. After doing some calculations I end up with the need to obtain the ratio of two probabilities: $$P(A)/P(B)$$ to be able to obtain $P(H|D)$. These ...
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1answer
61 views

SVM - Infinite dimensional feature space

What is the intuition behind the fact that an SVM with a Gaussian Kernel has infinite dimensional feature space?
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1answer
142 views

Gaussian RBF vs. Gaussian kernel

What is the difference between doing linear regression with a Gaussian RBF basis and doing linear regression with a Gaussian kernel?
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1answer
95 views

Poorness of Kernel methods on visual pattern recegnition?

I am currently reading the recent papers mainly written by Y. Bengio [1],[2],[3]. There are very strong claims about poorness of Kernel methods on recognizing handwritings in many general cases but ...
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21 views

Difference between Kernel classifier and linear classifier

I would just like to know what are the differences between kernel classifier and linear classifier? In what kind of problems the first is used and in what kind the second? What could be the ...
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56 views

What is the minimum number of data points required for kernel density estimation?

What is the minimum number of data points required for a kernel density estimation to be considered non-misleading/acceptable/adequate? Is there a some rule based on how dispersed the data is? For ...
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1answer
95 views

Applying kernel function to input data before giving it to algorithm

I have gene expression data, I do dimensionality reduction and clustering with self organizing maps, but self organizing maps do not perform well with my data. I want to map my data to feature space ...
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1answer
178 views

What are the limitations of Kernel methods and when to use kernel methods?

Kernel methods are very effective in many supervised classification tasks. So what are the limitations of kernel methods and when to use kernel methods? Especially in the large scale data era, what ...
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1answer
286 views

“Kernel density estimation” is a convolution of what?

I am trying to get a better understanding of kernel density estimation. Using the definition from Wikipedia: https://en.wikipedia.org/wiki/Kernel_density_estimation#Definition $ \hat{f_h}(x) = ...
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1answer
44 views

From half-circle to linear model

this is kinda homeworkish so I don't want a full solution I just want some input. I have this data set And I want to transform the data (with a rbf Kernel?) in order to be able to do a simple ...
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2answers
358 views

Linear kernel and non-linear kernel for support vector machine?

When using support vector machine, are there any guidelines on choosing linear kernel vs. nonlinear kernel, like RBF? I once heard that non-linear kernel tends not to perform well once the number of ...
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29 views

Kernel/Basis function design with regularizer

I am solving this problem: $$ \sum_i \parallel f(x_i)- y_i\parallel_2^2 + \lambda <\psi f, \psi f>_{L_2}^2 $$ where the second part $<\psi f, \psi f>_2^2$ is regularizer using the linear ...
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1answer
98 views

Relationship between the kernel and the value of C in SVM's

How exactly does the value of C relate across different kernels that we can use for SVM's? As in, how does it vary when changing the polynomial degree of a kernel or while using a Gaussian kernel?
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44 views

strange density plot of p-value [duplicate]

I computed the T-score and P-value using t.test() for my data, and finally I've plotted the density of my p-value and I've got strange plot. I don't know, why I see ...
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1answer
82 views

Kernel density estimation - application

What is the validity of using a kernel-density-estimation to compare model x observed data? In other words, if the KDE curve for the observed data looks like the KDE for the model forecast, can I use ...
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69 views

Where does the square root for a polynomial kernel mapping function come from?

I'm trying to understand how polynomial kernel functions work, in my textbook it shows an example with a degree of 2, with an input dimension of 2: $K(\vec{x}, \vec{y})$ = $(1 + x_1y_1 + x_2y_2)^2$ ...
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44 views

Kernel density estimation for a variable with lots of zeros [duplicate]

I am trying to estimate the kernel density for number of days a child is sick. Around 73% of children report not being sick, i.e. zero. How do I estimate a kernel density for this censored variable ...
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32 views

SVM kernel mapping, finding boundaries in projected space

I have a question about the support vector machine (SVM) kernel trick. How do you find the boundaries of the training data set in kernel projected space? Is that the same boundaries as you can obtain ...
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23 views

Value for Kernel Density Estimation is > 1 [duplicate]

I have 80 2D data points (located here) and am trying to estimate the pdf at a point $x$ by using a multivariate kernel density estimate. The mean vector is $\mu = [0.0368418, 0.0157501]$ and ...
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19 views

Local Kernel for Rate Data

Perhaps a naive question here. Is there a local kernel-based approach that is appropriate for modeling rate data of the form y/z, in which y can be 0 but z never is? Omitting z and measuring the mean ...
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131 views

I am still confused with Gaussian kernel in SVM

From the slides http://www.csie.ntu.edu.tw/~cjlin/talks/kuleuven_svm.pdf, $$\min \frac{1}{2}w^Tw $$ subject to $$y_i(w^T\phi(x_i)+b)\ge 1,i=1,\cdots,n$$ I think most people are very familiar with ...
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365 views

The Gaussian kernel

In SVM, the Gaussian kernel is defined as: $$K(x,y)=\exp\left({-\frac{\|x-y\|_2^2}{2\sigma^2}}\right)=\phi(x)^T\phi(y)$$ where $x, y\in \mathbb{R^n}$. I do not know the explicit equation of $\phi$. I ...
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4answers
246 views

Smooth a circular/periodic time series

I have data for motor vehicle crashes by hour of the day. As you would expect, they are high in the middle of the day and peak at rush-hour. ggplot2's default geom_density smooths it out nicely A ...
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2answers
72 views

Parameter selection in multiple kernel learning

I just got to apply multiple kernel learning to my data recently. I have data from three sources, so I want to learn three RBF kernels for each data source. But the MKL algorithms so far I know assume ...