The kernel tag has no wiki summary.
3
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0answers
28 views
Kernel density estimator that doesn't collapse in the tails
I have iid datapoints $x_1, \dots, x_n$, generated by an unknown density $f(x)$.
So far I have approximated $f(x)$ with a normal $N(\hat{\mu}, \hat{\sigma}^2 )$, where $\hat{\mu}$ and $\hat{\sigma}^2$ ...
1
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1answer
33 views
How to understand effect of RBF SVM
How can I understand what the RBF Kernel in SVM does? I mean I understand the maths, but is there a way to get a feeling when this kernel will be useful?
Would results from kNN be related to SVM/RBF ...
0
votes
1answer
55 views
The Lagrange multipliers of SVM
Actually the solve the SVM is to solve the following Lagrangian Equation:
If we don't use kernel function, $\langle x^{(i)},x^{(j)}\rangle$ is just the vector vector inner product. The ...
0
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0answers
19 views
Smoothing of log-distributed periodogram
I use the lomb-scargle periodogram to output information about chemical species in distinct time periods. This produces a distribution that is skewed heavily, with the majority of points and variance ...
1
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1answer
37 views
How to explain how I divided a bimodal distribution based on kernel density estimation
I have a dataset of bimodal population. It contains a smaller peak, which is considered to be "bad", and a bigger peak. I try to separate the bad part of data from the rest of data. What I did was: ...
1
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1answer
30 views
Evaluating features and similarity measures
I am currently developing a classificator, which is supposed to classify into a number of classes. For this purpose I am
designing some features and similarity measures which I might use for a later ...
0
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0answers
23 views
intersection kernel and distances between two histograms
intersection kernel can be given as $\sum_i min(x_i, y_i)$ . where x and y are histograms.
If two histograms are compeletely different the distance will be low.
If two histograms are similar what ...
-1
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0answers
23 views
kernels distances gram matrix classification
Could you please explain some thing about kernels? As I understand it is technique to map the feature space into a high dimensional feature space where we could separate two classes by a linear ...
4
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2answers
68 views
Why are these proper kernels and how to deduce that they are?
I am struggling to understand kernels and how to determine whether they are proper or not.
For these examples can anyone explain why an example is proper and why another example is not.
Given K1 and ...
0
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1answer
60 views
Is it legitimate to use a conditional PDF derived using kernel density estimation for hypothesis testing?
Suppose I have some sample $X$ drawn from some unknown multivariate distribution $F(A,B)$, and I want to test the null hypothesis that a particular point $x$ was drawn from $F$.
Would it be ...
0
votes
1answer
88 views
how to read y axis in kernel density graph [duplicate]
I need to understand how to read kernel density graphs. How do you come up with the values in y-axis?
1
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1answer
109 views
Number of kernel evaluations in SVM training
What is the typical number of kernel evaluations (between two training vectors) performed during a (kernelized) Support Vector Machine (SVM) training?
I am asking this question because I need to ...
1
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0answers
47 views
How to choose kernel functions for support vector regression
Are there any good resources regarding how to design kernels for regression problems, specifically time-series regression type of problem. I am finding the choice of a kernel for regression extremely ...
0
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0answers
48 views
Estimating probability density in Parzen windows
I came across an interesting paper about stability measure which can be used as evaluation metric for continuous data discretization.
The stability measure is constructed from a series of estimated ...
1
vote
1answer
110 views
How to determine if the data points are linearly separable from an SVM hyperplane
How to know the data points are linearly separable from an SVM hyperplane?
How to get the optimal classifier during iteration process?
How to calculate the complexity of the SVM model?
1
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0answers
83 views
Weighted covariance matrix using kernels
I would like to create a weighted covariance matrix (say 5 variables) using 3 different time points where the weights come from a kernel function (can be normal, triangular, etc) but I'm not ...
5
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1answer
89 views
Kernel density estimation on asymmetric distributions
Let $\{s_1,\ldots,s_N\}$ be a set of samples drawn from an unknown (but certainly asymmetric) probability distribution.
I would like to find the probability distribution by using the KDE approach:
$$
...
0
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0answers
29 views
What distribution to choose? Do Kernel estimations help?
I recently did some maximum likelihood estimations where the dependent variable justified the use of a normal distribution. Now, however, the dependent variable has a skewness of 0.4 and a kurtosis of ...
5
votes
1answer
152 views
Kernel Ridge Regression Efficiency
Ridge Regression can be expressed as $$\hat{y} = (\mathbf{X'X} + a\mathbf{I}_d)^{-1}\mathbf{X}x$$ where $\hat{y}$ is the predicted label, $\mathbf{I}_d$ the $d \times d$ identify matrix, $\mathbf{x}$ ...
0
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2answers
224 views
Which SVM kernel to use for a binary classification problem?
I'm a beginner when it comes to support vector machines. Are there some guidelines that say which kernel (e.g. linear, polynomial) is best suited for a specific problem? In my case, I have to classify ...
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0answers
54 views
Computing weighted standard deviation using lowess mean values
I have two questions:
First question:
I want to compute the weighted standard deviation with tri-cubic kernel. I am using lowess function in R to compute the weighted mean using tri-cubic ...
1
vote
1answer
372 views
What does the y axis in a kernel density plot mean? [duplicate]
Possible Duplicate:
Probability distribution value exceeding 1 is OK?
I thought the area under the curve of a density function represents the probability of getting an x value between a ...
2
votes
1answer
42 views
How does a Daniell kernel differ from a two sided average?
As far as I can understand, the Daniell kernel, is simply $K(j/M)=\frac{1}{2M+1}1(|j|\leq M)$.
Namely, this is a two sided average. Why do people call this an untruncated kernel and differentiate ...
0
votes
1answer
64 views
SVM decision function
our decision function e.g. in SVMs for binary classification (where the response is labeld by $y_i \in \{-1,1\}$) has the form:
$f(\mathbf{x}) = \text{sgn}(\mathbf{w}^\top \mathbf{x} + b)$ where ...
1
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0answers
74 views
Sheather-Jones bandwidth algorithm implementation in java?
The Sheather-Jones method for selecting an appropriate bandwidth for kernel density estimation generally produces better results than simpler methods such as Silverman's rule of thumb and Scott's ...
0
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0answers
96 views
SVM with svm and svmpath function
I am trying to compare the R functions svm (library: e1071) and svmpath (library svmpath).
...
2
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1answer
83 views
Mixed SVM kernel of RBF and linear
I've read some introduction about different kernels for SVM. It seems RBF is a measure of point distance while the basic kernel (i.e. no kernel) splits the space by hyper-planes.
I could imagine that ...
3
votes
1answer
85 views
Regarding redundant training data in building SVM-based classifier
To build a SVM-based classifier, I have a training data set consisting of N data points. Some of them are redundant. For instance, there have 50 data points which are exactly the same, and there have ...
1
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1answer
170 views
Kernelised k Nearest Neighbour
I'm new to kernels and have hit a snag while trying to kernelise kNN.
Preliminaries
I'm using a polynomial kernel:
$K(\mathbf{x},\mathbf{y}) = (1 + \langle \mathbf{x},\mathbf{y} \rangle)^d$
Your ...
0
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1answer
458 views
About SVM cost and gamma parameters tuning
I am using R and e1071 package to tune a C-classification SVM.
My question is: regardless of the kernel type (linear, ...
2
votes
1answer
125 views
What practical application is there for the Asymptotic Mean Integrated Squared Error in kernel density estimation?
Introduction
For some time now I have been struggling to understand how theoretical results can be applied in practice. Fortunately in most cases the link between theory and practice is not hard to ...
0
votes
1answer
101 views
How do I access or compute the posterior covariance matrix returned by kernlab::gausspr R function?
I am looking to compute the covariance matrix of an inferred Gaussian process in R. Below I outline how I would do this manually, but I realize that the kernlab ...
1
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0answers
41 views
what can I say about the following kernel estimation?
I have a discrete random variable $X$ and two random vectors $\vec{Y}$ and $\vec{Z}$.
For a given $x$ (i.e. an instance of $X$), I am interested in estimating:
$$E[\vec{Y} \vec{Z}^{\top} | X = x]$$
...
1
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4answers
225 views
comparing predictive model with hold out set
In Rapid Miner, I created a predictive model (SVM) with Kernel type = polynomial, c= 10, and obtained 80.77% accuracy using cross validation. When compared to hold out set my accuracy on the test ...
1
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0answers
167 views
Which non-parametric regression could I apply to fit a curve to this data set?
I have posted a similar question about the same problem, having been suggested to use a polynomial Robust Linear Model, which worked fine for most cases, as can be seen here:
Non-algebric ...
2
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1answer
166 views
Explain Kernel density chart
I'm running simulation on a linear model. I get 1000 results and the results are put into a density chart. I do understand that the xaxis is the dependent variable and yaxis represent the kernel ...
0
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1answer
165 views
Free data set for comparing kernel logistic regression and regular logistic regression [closed]
I'm looking for a data set that is easily accessible for comparing Kernel Logistic Regression (KLR) and regular logistic regression. All the paper that I find using KLR use synthetic data sets. I'm ...
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0answers
46 views
Given a kernel, how to find mapping phi?
I'm not clear about kernel.
How could I construct my own kernel that is valid? Is the only method Merce Theorem (positive semi-definite)? I mean if I know K is a valid kernel, do I know that ...
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0answers
54 views
Polynomial kernel in logistic regression?
So I have put together a nice logistic regression program that works quite well. Now, I have used two dimensions to test it and see how it works, and guided by some online tutorials, have increased ...
2
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0answers
38 views
How can I find the number of support vectors in an SVM, depending on kernel?
Here on slide 3 I see the claim that for linearly separable cases the number of support vectors will be d+1, where d is the dimension we are working on.
What if my data is not linearly separable and ...
2
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0answers
67 views
local polynomial regression standard errors
I am attempting to find a reference which explains how one computes standard errors for local polynomial regression? Specifically, in R one can use the loess ...
0
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0answers
54 views
Large data set for graph kernel benchmarking [closed]
I am doing a project on graph kernel, and to test the implementation we need a large data set (like graph about 10$^4$-10$^6$ nodes). Does anyone know of such a test which would be appropriate for ...
3
votes
2answers
165 views
Use of the Gamma parameter with support vector machines
When using libsvm, the parameter $\gamma$ is a parameter for the kernel function. Its default value is setup as $\frac{1}{Number Of Features}$
Is there any ...
5
votes
2answers
323 views
How to prove there is no finite-dimensional feature space for Gaussian RBF kernel?
How to prove that for the radial basis function $k(x, y) = \exp(-\frac{||x-y||^2)}{2\sigma^2})$ there is no finite-dimensional feature space $H$ such that for some $\Phi: \text{R}^n \to H$ we have ...
3
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0answers
47 views
Why we solve the dual problem in SVM? [duplicate]
Possible Duplicate:
Why bother with the dual problem when fitting SVM?
What advantages do we get from solving in the dual?
2
votes
1answer
103 views
Density estimation with scaled sinc-like kernels
Given data points $x_i$ in $\mathbb{R}^d$ with function values $f_i$,
one can estimate the function at a given $x$ by
$\ \ \ \ \text{f}_{est}( x ) = \frac {\sum { w_i f_i }} {\sum { w_i }}$
with $w_i ...
6
votes
2answers
344 views
How to prove that the radial basis function is a kernel?
How to prove that the radial basis function $k(x, y) = \exp(-\frac{||x-y||^2)}{2\sigma^2})$ is a kernel? As far as I understand, in order to prove this we have to prove either of the following:
For ...
2
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1answer
100 views
Representation within a RKHS framework
Given a p.s.d kernel $Q$, can minimization/maximization of $Tr(X^TQX)$ over X be represented within a reproducing kernel Hilbert space (RKHS) framework? If there is a primary concern with the trace ...
1
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1answer
99 views
Possible reason for failing to build a support vector machine
I was trying to build a classifier for a set of documents using a support vector machine. I choose to build the feature space using term occurrence. While experimenting, I found the following ...
8
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1answer
836 views
Is there an optimal bandwidth for a kernel density estimator of derivatives?
I need to estimate the density function based on a set of observations using the kernel density estimator. Based on the same set of observations, I also need to estimate the first and second ...
