Questions tagged [kernel]
Kernel functions are a class of functions which transform the original data into a new space in which the classes of the data are easier to separate by a kernel algorithm.
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SVM kernel for detecting if a substring appears in some given string
I'm trying to do the exercise in 16.1 in the book Understanding Machine Learning, Ben-David, et al. formulated as follows:
Consider the task of learning to find a sequence of characters
("...
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Why linear kernel regression is equivalent to plain linear regression?
I am trying to understand either intuitively/geometricaly and/or mathematicaly why the followings are equivalent:
Classic Ordinay Least Squares linear regression
Linear-kernelized Ordinary Least ...
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kernel methods and parameter updates
Background information:
(it might be helpful to read the first 5 pages of this:https://cs229.stanford.edu/summer2020/cs229-notes3.pdf before answering the question).
I’m currently learning machine ...
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Derivative of a KernelRidge regression model based on Coulomb Matrix descriptor
I am trying to take analytical derivatives of a KernelRidge regression model that takes as input a Coulomb Matrix descriptor. A Coulomb Matrix is a way of representing a molecular structure basically ...
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Why don't we increase the parameter from 64 to 128 in this CNN model?
I'm looking at an example lab from a coursera course titled Intro to Tensorflow. In this CNN model, they're gradually increasing the no. of filters from 16 to 32 and then 64. Why don't we increase it ...
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Epanechnikov kernel smoothing and Priestley-Chao (PC) kernel estimate
I wrote the Python code below to try to automate the application of kernel smoothing using the Epanechnikov kernel with a bandwidth of h = 0.4 calculating the Priestley-Chao kernel estimate of the ...
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Is the transformation implied by a positive-type kernel well-defined?
I’ve been trying to get my head around the particularity of the Hilbert space that a positive-type (equiv. positive definite) kernel represents an inner product on, and was hoping for some help in ...
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How to choose the optimal PCA kernel
In a chemometrics application, I need to reduce the dimensionality of a spectral scan. The standard PCA is linear. Not sure if the data is. How do I choose the most optimal PCA kernel?
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A mathematician from the outside looking in
I am wondering if anybody could give a survey of applications of approximation theory to data science. One application I am familiar with are, for example, wavelet neural networks. Does anybody know ...
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Kernel ridge regression (KRR), accuracy scale?
What does a good range for the accuracy score look like for the KRR model?
For example, RMSE produces a value between 0 and 1, where values closer to 0 represent better fitting models. What's the ...
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memory bound for kernel tricks in machine learning
Based on Andrew Ng's lecture on Kernel,
you use training samples (referred as landmarks l) and use them during prediction to construct the higher dimensional representation of the given sample.
This ...
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why layer of dimension 1 is outputting image of size n
I am studying a model where landmarks from an image are calculated. The work comes from Convolutional Experts Constrained Local Model for 3D Facial Landmark Detection.
I need to confirm why the ...
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What is custom SVM kernel?
What is custom kernel in the Support Vector Machine. How is it different from Polynomial kernel. How to implement a custom kernel. Can you provide a code to implement a custom kernel.
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What are the benefits of using spectral k-means over simple k-means?
I have understood why k-means can get stuck in local minima.
Now, I am curious to know how the spectral k-means helps to avoid this local minima problem.
According to this paper A tutorial on ...
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Bayesian Linear Regression using the Kernel Trick vs Constructing features using Kernels as Prototypes
How different is it to do Bayesian linear regression using the GP approach (kernel trick) versus constructing features using kernels to prototypes? As far as I know, this very basic question is ...
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Kernel trick derivation: why this simplification is incorrect?
I am trying to derive kernel trick from linear regression, and I have a mistake in the very end, which leads to an expression too simple.
Basic linear regression
For a basic linear regression (with no ...
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which type of machine learning algorithms perform better at extrapolation (in general)
Assuming that:
the problem lies in the field of natural science, i.e. relationships between variables are physics-based and does not change depending on context
its a regression based model
Would it ...
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Can a CNN have a different number of convolutional layers and kernel and what does it mean?
So if I have $3$ RGB channels, $6$ convolutional layers and $4$ kernels, does this mean that each kernel does a convolution on each channel and so the input for the next convolution will be $3 \times ...
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When should I use 'rbf' and 'polynomial' kernel trick in machine learning algo?
I have a problem about hate-speech classification using support-vector machine algorithm.
The task is to identify the sentence that contains 'positive' or 'negative' sentiment.
Which is the best ...
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Theoretical differences between KPCA and t-SNE?
I (think I) understand the underlying principles of most dimensionality reduction methods (MDS, IsoMap, t-SNE, Spectral Embedding, Diffusion maps, etc...).
Some of the algorithms I use the most are ...
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Radial Basis Function (Gaussian) kernel question
I have followed the mathematics of the RBF kernel and understand how to show that the input space is mapped into an infinite-dimensional feature space. However, I'm struggling to make sense of the ...
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Does linear kernel make SVM a linear model?
I have deleloped several SVR models for my case study using the linear kernel, and those models were optimized using the RMSE as criterion. Now Im searching for additional evaluation metrics and it ...
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Can someone clarify what the linear assumption of PCA is?
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For the past few hours I've been trying to search what this linear assumption is. Some of the articles states that that your independent variables have to be linear in relationship and need some ...
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Why are neural networks equivalent to kernel methods?
I read a recent paper by Pedro Domingos, claiming that Every Model Learned by Gradient Descent Is Approximately a Kernel Machine.
I wanted to understand the key idea a little better. Why are neural ...
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How to evaluate KDE against histogram?
I am currently testing some approaches for density estimation, and I think the basic approach of histograms may not be the best option to me and KDE is certainly a good alternative to go. While ago I ...
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How do you choose a kernel for a discontinuous function in Gaussian Process Regression? [closed]
I'm doing Gaussian Process Regression and created a series of functions by gluing other functions together on random places. Here's an example:
Perhaps this one is to complicated, but all the ...
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Kernel Density in Scikit Learn
I'm trying to understand how does the KernelDensity class in scikit-learn work. Consider the following two cases which build a kernel from two different arrays (a). I'm wondering why the result of ...
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Should kernel size always be a prime number?
Should kernel size always be a prime number? E.g. (3,3) (5,5) (7,7).
While tinkering with sklearn.preprocessing.KernelCenterer(), I noticed that I could only get it ...
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what are the main differences between parametric and non-parametric machine learning algorithms?
I am interested in parametric and non-parametric machine learning algorithms, their advantages and disadvantages and also their main differences regarding computational complexities. In particular I ...
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In classical kernel regression, is there a task which responds almost exclusively to a single kernel choice?
I'm curious if there is any well-known kernel regression/classification task which can only be "solved" using a specific choice of kernel?
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Non semi positive definite kernel matrix
What happens if we run a support vector machine model using a kernel that does not satisfy requirements such as non-positive semi definite?
This is my flow of thought: In kernel methods $w.x$ is ...
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Has anyone succeeded in finding a good Scala/Spark kernel for Jupyter?
The ones I've tried so far
Almond: Works very well for just Scala, but you have to import dependencies, and it gets tedious after a while. And unfortunately can't run when using Spark with YARN ...
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KLMS in machine learning
As Least Mean Square is a very popular choice to be used in combination with neural networks topologies, what would be the most common machine learning algorithms (and easily) to combine with Kernel ...
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Why do we use 2D kernel for RGB data?
I have recently started kearning CNN and I coukdnt understand that why are we using a 2D kernel like of shape (3x3) for a RGB data in place of a 3D kernel like of shape (3x3x3)?
Are we sharing the ...
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PCA vs.KernelPCA: which one to use for high dimensional data?
I have a dataset which contains a lot of features (>>3). For computational reasons, I would like to apply a dimensionality reduction. At this point I could use different techniques:
standard PCA
...
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How to use a RBF kernel to create a "Kernel Space" using the similarity of each pair of point?
I am trying to use Semi-Unsupervised clustering using reinforcement learning following this paper.
Assume I have n data-points each of which has d dimensions. I also have c pairwise constraints of ...
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How to implement SVM from scratch?
I am trying to build a SVM from scrath and I would like to maximize this Lagrarian expression:
I know what variables means but I would like to know how this maximization is implemeted. Should I start ...
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Understanding SVM Kernels
Following Andrew Ng's machine learning course, he explains SVM kernels by manually selecting 3 landmarks and defining 3 gaussian function based on them. Then he says that we are actually defining 3 ...
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How to choose a kernel function and a feature mapping function?
Although, after extensive of reading, I know the concepts of support vector machines pretty well by now, I have trouble translating the concept of the kernel function $K$ and the feature mapping ...
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GP derivative in GpyTorch
I am working on a project using GP-regression models to model transition and measurements models in a Kalman Filter. This means I need to be able to sample from the derivative of the original GP model....
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What is the kernel matrix used for in the kernel trick?
I have $n$ linearly inseperable datapoints, $x_1 \dots , x_n$. I use the kernel trick to map and compute the dot product in higher dimensions (without actually mapping / transforming the data).
...
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Support Vector Machine (SVM) for classification problem based on Earth Mover's Distance (EMD)
I would like to run SVM for my classification problem using the Earth Mover's Distance (EMD) as a distance measurement. As I understood the documentation for Python scikit-learn (https://scikit-learn....
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Many separation line using RBF kernel in SVM
Below is my code, it take a range of a number, creates a new column label that contains either -1 or 1.
In case the number is ...
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What is a good method for detecting local minims and maxims?
I'm using kernel density estimation in order to compute
probability density function for item occurrence.
Using this output, i want to find all the local minims and maxims.
I'm interested in different ...
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Kernel engineering, valid kernels, multipliying by constant =0?
I am reading Bishop, Pattern Recognition and Machine Learning. In the chapter about kernels rules are given for constructing kernels from existing valid kernels.
The first one being let k(x,y) be a ...
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What are practical differences between kernel k-means and spectral clustering?
I've been lately wondering about kernel k-means and spectral clustering algorithms and their differences.
I know that spectral clustering is a more broad term and different settings can affect the ...
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Why spectral clustering results in disjointed cluster?
I'm working on a project where I have to dynamically cluster the position of objects with respect to one coordinate. So I'm essentially dealing with subsequent frames and each frame represents a one-...
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Implementing a Kernel Adaptive Filtering model explained in a paper
In this paper, Stock price prediction using kernel adaptive filtering
within a stock market interdependence approach, the authors propose a method for predicting stock prices by combining the ...
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Kernel Trick and Inner Product Preservation
I understand that the point of using the kernel trick is to project the problem onto a higher dimensional space, where the problem is linearly separable. In this explanation, https://www.quora.com/...
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Designing Custom Kernel from my Mathematical model
I derived a mathematical model for a porous system and the final function looks like this ,
after going through the Mercers Theorem and its condition for a kernel I would love to write an SVM kernel ...
