Characteristic and Universal Tensor Product Kernels

نویسندگان

  • Zoltán Szabó
  • Bharath K. Sriperumbudur
چکیده

Kernel mean embeddings provide a versatile and powerful nonparametric representation of probability distributions with several fundamental applications in machine learning. Key to the success of the technique is whether the embedding is injective. This characteristic property of the underlying kernel ensures that probability distributions can be discriminated via their representations. In this paper, we consider kernels of tensor product type and various notions of characteristic property (including the one that captures joint independence of random variables) and provide a complete characterization for the corresponding embedding to be injective. This has applications, for example in independence measures such as Hilbert-Schmidt independence criterion (HSIC) to characterize the joint independence of multiple random variables.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Trellis Properties of Product Codes

In this paper, we study trellis properties of the tensor product (product code) of two linear codes, and prove that the tensor product of the lexicographically first bases for two linear codes in minimal span form is exactly the lexicographically first basis for their product code in minimal span form, also the tensor products of characteristic generators of two linear codes are the characteris...

متن کامل

Automatic Generation of Sparse Tensor Kernels with Workspaces

Recent advances in compiler theory describe how to compile sparse tensor algebra. Prior work, however, does not describe how to generate efficient code that takes advantage of temporary workspaces. These are often used to hand-optimize important kernels such as sparse matrix multiplication and the matricized tensor times Khatri-Rao product. Without this capability, compilers and code generators...

متن کامل

Arens-irregularity of tensor product of Banach algebras

We introduce Banach algebras arising from tensor norms. By these Banach algebras we make Arensregular Banach algebras such that tensor product becomes irregular, where is tensor norm. Weillustrate injective tensor product, does not preserve bounded approximate identity and it is notalgebra norm.

متن کامل

Decomposition of spaces of distributions induced by tensor product bases

Rapidly decaying kernels and frames (needlets) in the context of tensor product Jacobi polynomials are developed based on several constructions of multivariate C∞ cutoff functions. These tools are further employed to the development of the theory of weighted Triebel-Lizorkin and Besov spaces on [−1, 1]d. It is also shown how kernels induced by cross product bases can be constructed and utilized...

متن کامل

Universality, Characteristic Kernels and RKHS Embedding of Measures

Over the last few years, two different notions of positive definite (pd) kernels—universal and characteristic—have been developing in parallel in machine learning: universal kernels are proposed in the context of achieving the Bayes risk by kernel-based classification/regression algorithms while characteristic kernels are introduced in the context of distinguishing probability measures by embed...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • CoRR

دوره abs/1708.08157  شماره 

صفحات  -

تاریخ انتشار 2017