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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.

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1 vote
33 views

### 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, ...
1 vote
36 views

### 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 ...
• 11
1 vote
57 views

### 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 ...
53 views

### How does the kernel sends information generated by an interrupt to the right process?

Andrew S. Tanenbaum, in his book Modern Operating Systems states that, When a hardware interrupt occurs while a user thread is running, the interrupted CPU switches into kernel mode. If the interrupt ...
20 views

### Radial Basis kernel producing the same decision boundary as a Linear kernel

The following question is from the MIT 6.034 2006 Final Exam paper. In answering part 6.5, I wasn't certain why the radial basis kernel would produce the same decision boundary as a linear kernel (...
• 1
55 views

### Connection between planar graph and vertex cover

I have two similar problems in which I'm trying to find a connection to help me solve one of them. In the first one I'm given a graph G = (V,E) , integer k, and vertex cover U of size k. The objective ...
1 vote
242 views

### 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?
101 views

### 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 ...
1 vote
67 views

### How to understand mapping function of kernel? [closed]

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 ...
• 121
1 vote
37 views

### 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? ...
1 vote
236 views

### 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 ...
• 113
1 vote
48 views

### 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 ...
• 11
300 views

### 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 ...
93 views

### 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 ...
• 21
213 views

### 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 ...
• 161
591 views

### 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})+\...
• 31
317 views

### Merging two disconnected graphs

Firstly, I'd like to apologize for any misused terms or ways I could have made the description much more succinct. It's been a while since I took machine learning during my bachelor's. I have two ...
• 101