Related papers: The Signature Kernel
Signature-based methods have recently gained significant traction in machine learning for sequential data. In particular, signature kernels have emerged as powerful discriminators and training losses for generative models on time-series,…
We introduce a similarity function on formulae of signal temporal logic (STL). It comes in the form of a kernel function, well known in machine learning as a conceptually and computationally efficient tool. The corresponding kernel trick…
The sequential data observed in earth science can be regarded as paths in multidimensional space. To read the path effectively, it is useful to convert it into a sequence of numbers called the signature, which can faithfully describe the…
The use of kernel functions is a common technique to extract important features from data sets. A quantum computer can be used to estimate kernel entries as transition amplitudes of unitary circuits. Quantum kernels exist that, subject to…
Signcryption is a cryptographic primitive which performs encryption and signature in a single logical step. In conventional signcryption only receiver of the signcrypted text can verify the authenticity of the origin i.e. signature of the…
The sequence of moments of a vector-valued random variable can characterize its law. We study the analogous problem for path-valued random variables, that is stochastic processes, by using so-called robust signature moments. This allows us…
In this article a surprising result is demonstrated using the neural tangent kernel. This kernel is defined as the inner product of the vector of the gradient of an underlying model evaluated at training points. This kernel is used to…
The signature of a parametric curve is a sequence of tensors whose entries are iterated integrals. This construction is central to the theory of rough paths in stochastic analysis. It is here examined through the lens of algebraic geometry.…
Sequential and temporal data arise in many fields of research, such as quantitative finance, medicine, or computer vision. A novel approach for sequential learning, called the signature method and rooted in rough path theory, is considered.…
Stern's diatomic sequence is a well-studied and simply defined sequence with many fascinating characteristics. The binary signed-digit representation of integers is an alternative representation of integers with much use in efficient…
We derive the optimal signed variable in general case kernels for the classical statistic density estimation, which are some generalization of the famous Epanechnikov's ones.
We discuss how to define a kernel for Signal Temporal Logic (STL) formulae. Such a kernel allows us to embed the space of formulae into a Hilbert space, and opens up the use of kernel-based machine learning algorithms in the context of STL.…
Strictly proper kernel scores are well-known tool in probabilistic forecasting, while characteristic kernels have been extensively investigated in the machine learning literature. We first show that both notions coincide, so that insights…
Building on the interpretation of a recurrent neural network (RNN) as a continuous-time neural differential equation, we show, under appropriate conditions, that the solution of a RNN can be viewed as a linear function of a specific feature…
We consider a kernel based harmonic analysis of "boundary," and boundary representations. Our setting is general: certain classes of positive definite kernels. Our theorems extend (and are motivated by) results and notions from classical…
Signature verification is an authentication technique that considers handwritten signature as a biometric. From a biometric perspective this project made use of automatic means through an integration of intelligent algorithms to perform…
The development of machine learning algorithms in the cyber security domain has been impeded by the complex, hierarchical, sequential and multimodal nature of the data involved. In this paper we introduce the notion of a streaming tree as a…
Recently a new formulation of quantum mechanics has been suggested which describes systems by means of ensembles of classical particles provided with a sign. This novel approach mainly consists of two steps: the computation of the Wigner…
We propose a new kernel for biological sequences which borrows ideas and techniques from information theory and data compression. This kernel can be used in combination with any kernel method, in particular Support Vector Machines for…
In topological data analysis, persistent homology characterizes robust topological features in data and it has a summary representation, called a persistence diagram. Statistical research for persistence diagrams have been actively…