Questions tagged [reproducing-kernel-hilbert-spaces]

Question 1

I wish to describe a problem encountered in my research and am seeking advice, or just pointers on where to look. My setting is as follows. Given a scatterplot of data in $\mathbb{R}^D$, we wish to ...

Question 2

I want to make sure that my understanding from these two papers, and whether we can provide an upper bound on the 1-Wasserstein by MMD is correct. Below $\gamma_k$ refers to maximum mean discrepancy (...

Question 3

Let $\Omega \subset \mathbb{R}^n$ be a domain, $I := [0,T)$ an interval and $s,r\in\mathbb{R}, r\geq 1$. The space $H^s_0(\Omega)$ denotes the standard zero-trace Sobolev space of $s$-times weakly ...

Question 4

Considering the space of continuous functions that vanishes at infinity $C_0^0(\mathbb{R}^d \times G_k(\mathbb{R}^d), \mathbb{R}) $ where $G_k$ denotes the k dimensional grassmannian, i want to find ...

Question 5

I'm trying to understand Reproducing Kernel Hilbert Spaces (RKHS). In particular I'm interested in the Kernel Mean Embedding (KME) operator $K$ s.t. $$ \mu(x) = \int k(x,y) p(y) dy $$ where $k(x,y)$ ...

Question 6

Suppose we have a generic (i.e. $\mathbf{x}_i = \mathbf{x}_j \implies y_i = y_j)$ dataset $(\mathbf{x}_i, y_i)_{i=1}^{n}$ where $\mathbf{x}_i\in \{0,1\}^n$ and $y_i\in\{0,1\}$. Define the kernel $K$ ...

Question 7

I'm working through the proof that the Hilbert transform maps $L^1(\mathbb{R})$ into weak-$L^1$, and I understand that the key step is the weak-$(1,1)$ estimate for the maximal Hilbert transform $H^*\...

Question 8

The continuous Hilbert matrix operator on analytic spaces of unit disk $\mathbb{D}:=\{z\in\mathbb{C}: |z|<1\}$ is easily derived to be $H(f)(z)=\int_0^1\frac{f(t)}{1-tz}dt$. It's known that the ...

Question 9

Given the characteristic kernels $k:\mathbb{R}^d \times \mathbb{R}^d \to \mathbb{R}$, $l:\mathbb{R}^p \times \mathbb{R}^p \to \mathbb{R}$, I know that the product kernel $r: (\mathbb{R}^d \times \...

Question 10

Given functions $f,g: \mathcal{X} \to \mathcal{H}$ lying in a vector-valued RKHS $\mathcal{H}_v$, i.e. outputting functions in the RKHS $\mathcal{H}$, what can we do about bounding the quantity $$ \...

Question 11

I admit - I have screwed up quite a bit here. When I went literature hunting for my thesis, I found a very neat paper talking about how you can complete your run-of-the-mill kernel pre-Hilbert space $(...

Question 12

I have a matrix valued kernel $K:\mathbb{R}^d\times \mathbb{R}^d \to \mathbb{R}^{d\times d}$. It will have a corresponding RKHS associated with it, say it is $H_k^d$. I want to know what will be the ...

Question 13

I am working on the paper titled "Generative models for financial time series with MMD using signature kernel". In this paper there is this particular sequential kernel: the signature kernel....

Question 14

I know that the reproducing kernel Hilbert space is a subspace of $L^2(X,\nu)$ space and is denser than it. A priori, we know the function $f\in L^2(X,\nu)$. I now want to add some conditions to $f$ ...

Question 15

Note: Also asked on Statistics Stack since I did not get an answer here. I am trying to understand a paper about regularization in non-parametric regression and I am struggling to understand the RKHS ...

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Questions tagged [reproducing-kernel-hilbert-spaces]

geodesic distance in embedded manifolds

upper bound on the 1-Wasserstein by maximum mean discrepancy (MMD) distance

Reproducing Kernel Hilbert Spaces with initial / boundary conditions

RKHS not stable under pullback by diffeomorphism

Why is a Gaussion kernel characteristic?

Proving that a special kernel can learn a generic binary dataset

Why is the Hilbert transform measurable for functions in $L^1(\mathbb{R})$?

Continuous Hilbert Matrix Operator on the upper Half-Plane

Are the product of characteristic kernels characteristic?

Cauchy-Schwarz for expected values of vector-valued functions

Literature Request: A specific paper about completion of Reproducing Kernel Hilbert Spaces (RKHS)

Inner product in Vector valued RKHS

Kernel Approximations (sequential kernel)

Conditions that make Hilbert space $L^2(X,\nu)$ become RKHS?

RKHS, Norms and Regularization

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