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Questions tagged [kernel-functions]

Questions about the similarity functions used in machine learning to compare inputs in implicit higher-dimensional feature spaces.

Further reading:

21 questions
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Why are kernel methods with RBFs effective for handwritten digits (letters) classification?

The question emerged while reading Ch. 3 of Rasmussen & Williams http://www.gaussianprocess.org/gpml/. In the end of this chapter, the authors gave results for the problem of handwritten digits classification (16x16 greyscale pictures); features are…
ostrodmit
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Kernel Perceptron vs Polynomial Perceptron

I was looking at Support Vector machines (SVM) kernels. Looking at Polynomial Kernel and Kernel Perceptron I was curious how they differ? Work Done Polynomial Kernel: $d_{k+1}(x)=d_{k}(\bar{x})+\rho k(\bar{x}_{k}, \bar{x})\; \mbox{if}\;…
priyanka
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Support Vector Machines as Neural Nets?

This is more of a conceptual question. I have learned about Neural Nets, and I have some clue as to how Support Vector Machines work. I read somewhere however that given the appropriate kernel (is that right?), the SVM is identical to the Neural…
Josh F
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Some questions on kernels and Reinforcement Learning

I've a test in a few days and I've a few issues with some of the subjects. Let's start with kernels, basically I understood that a kernel needs to be positive semi-definite and symmetric in order to be valid. Is that enough? For example the…
Bar
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Calculating Contiguous String Kernel efficiently

I am given two strings, $\overline{a},\overline{b}$ in a finite alphabet, $\Sigma$, and a positive integer $k$. I want to compute the $k$-th order contiguous string kernel, which is defined to be the sum…
Twis7ed
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Paging only for user code. What about kernel code?

Why is paging done only for user code (user space)? I know that the basic intuition behind paging is for managing larger logical address space in smaller physical main memory space. Won't the kernel size also be large? If the kernel code is large…
Nascimento de Cos
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How can a classifier using Laplacian kernel achieve no error on the input samples?

If we have a sample dataset $S = \{(x_1, y_i),\dots,(x_n,y_n)\}$ where $y_i = \{0,1\}$, how can we tune $\sigma$ such that there is no error on $S$ from a classifier using the Laplacian kernel? Laplacian Kernel is $$ K(x,x') = \exp\left(-\dfrac{\|…
quarantineStudy
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Checking if a kernel is valid

The kernel is $K(x,z) = \sum_{i=1}^D (x_i+z_i)$ My approach was trying to express $K = \phi(x)^T\phi(z) = (x_1 x_2 ... x_D \quad 1 1 ...1)(1 1 ...1\quad z_1 z_2 ... z_D )^T$ where $\phi$ is 2Dx1 and thus a Kernel. The solution says: K is not a…
db18
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How do we mathematically figure out if a SVM kernel function overfits?

Looking at the kernel function (Gaussian, polynomial. chi-squared, etc) how do we figure out that changing which value will cause overfitting? In my perspective, if we increase (for example) the variance term in Gaussian kernel expression, bias…
Tashi
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Understanding gradient flow of a linearized wide neural network

I've been trying to fully understand the paper "Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent" (available here), but I'm stuck on the linearization part, specifically section 2.2. The idea is that in the infinite…
user161590
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Does flipping the kernel in image processing only help maintain mathematical symmetry?

So I've been really confused about the act of flipping a kernel in image processing. Is there any intuitive way to think about it or does it only help computing efficiently and maintain the mathematical symmetry? Do we necessarily flip a kernel in…
mamamoo
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Machine Learning algorithm to learn submodular set functions

I'm looking for some machine learning algorithm to train on data that are sampled from some submodular set function and I want the learned model predictions also obey submodularity. For example linear regression can do this (because it's linear…
Arash Jamshidi
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How could i create a multi-threading system in a kernel?

Im trying to figure out if there's an assembler instructions or a bios intruction to get multi-threading in a kernel. In the case that doesn't exist that, how could i set muti-threading in a kernel?
UserGuestIneedyourhelpguys2631
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How to understand mapping function of kernel?

For a kernel function, we have two conditions one is that it should be symmetric which is easy to understand intuitively because dot products are symmetric as well and our kernel should also follow this. The other condition is given below There…
christopher
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Vertex deletion to perfect matching

You are given a Graph G and an integer k. The question is: Does G contain a vertex set X of size at most k such that deleting X results in a graph of degree at most 1? Design an FPT (or a kernelization) algorithm for this problem and argue why it is…
ilirosmanaj
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