arXiv research

Paper learns meaningful state and action representations from MDP trajectories.

BKTR models spatiotemporal data with scalable tensor regression.

BKTF uses tensor factorization for Bayesian optimization of complex functions.

A low-rank tensor model simplifies multi-dimensional Markov chains.

New algorithm detects changes in Markov kernels with unknown post-change kernel.

A new kernel improves tensor classification accuracy and reduces computation time.

Proposes a new kernel technique for tensor data in SVM.

New method improves stochastic kriging for high-dimensional simulations.

A novel Laplace-approximated Bayesian Tensor Network Kernel Machine (LA-TNKM) provides principled uncertainty estimates.

Stochastic kernel based dimensionality reduction approaches have become popular in the last decade. The central component of many of these methods is a symmetric kernel that quantifies the vicinity between pairs of data points and a kernel-induced Markov chain on the data. Typically, the Markov chain is fully specified…

Estimates spatio-temporal Hawkes processes using tensor recovery.

Tensor networks constrain kernel machines to Gaussian processes.

KReTTaH uses tensor trains and Hadamard overparameterization for fast, interpretable multi-way data imputation.

KReTTaH uses tensor trains and Hadamard overparameterization for fast, interpretable multi-way data imputation.

In this paper we study the variational problem associated to support vector regression in Banach function spaces. Using the Fenchel-Rockafellar duality theory, we give explicit formulation of the dual problem as well as of the related optimality conditions. Moreover, we provide a new computational framework for solving…

A new method reduces Volterra kernel complexity and uncertainty quantification.

This work speeds up fHMM analysis by tensor algebra.

Identifies conditions for multiple invariant probabilities in Markov kernels.

Efficiently trains deep Gaussian processes with sparse approximations.

New method trains Markov kernels for efficient sampling.

A new HMM model captures kernel dependencies using context-specific Bayesian networks.

Study shows Bergman kernel quotient approaches one for punctured surfaces.

We consider a heat kernel approach for the development of stochastic pricing kernels. The kernels are constructed by positive propagators, which are driven by time-inhomogeneous Markov processes. We multiply such a propagator with a positive, time-dependent and decreasing weight function, and integrate the product over…

Bayesian tensor train kernel machine uses Laplace approximation for scalable GP regression.

Study asymptotics of extension and orthogonal Bergman kernels for high tensor powers of positive line bundles.

Maximum mean discrepancy (MMD), also called energy distance or N-distance in statistics and Hilbert-Schmidt independence criterion (HSIC), specifically distance covariance in statistics, are among the most popular and successful approaches to quantify the difference and independence of random variables, respectively. T…

New method detects changes in high-dimensional Markov processes without explicit likelihood evaluation.

This work improves fair tensor decomposition using a kernel criterion.

Bayesian Complementary Kernelized Learning models complex spatiotemporal data.

The paper improves Stein importance sampling for Markov chain samples.

Efficient tensor kernel method reduces memory usage and computational cost for sparse regression.

The X-ray transform on the periodic slab $[0,1]\times\mathbb T^n$, $n\geq0$, has a non-trivial kernel due to the symmetry of the manifold and presence of trapped geodesics. For tensor fields gauge freedom increases the kernel further, and the X-ray transform is not solenoidally injective unless $n=0$. We characterize t…

Bayesian TNKMs automatically infer model complexity and feature relevance.

KFT improves tensor forecasting by incorporating side information.

Theoretical studies have proven that the Hilbert space has remarkable performance in many fields of applications. Frames in tensor product of Hilbert spaces were introduced to generalize the inner product to high-order tensors. However, these techniques require tensor decomposition which could lead to the loss of infor…

The study establishes a curvature-dimension condition for discrete Markov chains.

We develop algorithms with low regret for learning episodic Markov decision processes based on kernel approximation techniques. The algorithms are based on both the Upper Confidence Bound (UCB) as well as Posterior or Thompson Sampling (PSRL) philosophies, and work in the general setting of continuous state and action …

Tensor-network techniques have enjoyed outstanding success in physics, and have recently attracted attention in machine learning, both as a tool for the formulation of new learning algorithms and for enhancing the mathematical understanding of existing methods. Inspired by these developments, and the natural correspond…

New concentration inequality for U-statistics of Markov chains.

In this paper, we discuss how a suitable family of tensor kernels can be used to efficiently solve nonparametric extensions of $\ell^p$ regularized learning methods. Our main contribution is proposing a fast dual algorithm, and showing that it allows to solve the problem efficiently. Our results contrast recent finding…

New method tunes SMC samplers efficiently without high costs.

Proposes a new method for high-dimensional density estimation.

Develops a new tensor classification method for high-dimensional data.

A new method reduces the complexity of tensor products from cubic to quadratic, improving both speed and accuracy.

Due to Čencov's theorem, there exists a unique family of invariant symmetric $(0,2)$-tensor fields on the space of positive probability measures on a set of $n$-points indexed by $n\in \mathbb{N}$ under Markov embeddings. We deform Markov embeddings keeping sufficiency, and prove existence and uniqueness of invariant f…

Paper improves generalization bounds for multi-kernel learning with mixed datasets.

Efficiently fine-tunes patient-independent seizure detection models with tensor kernel machine.

This paper develops tools for nonreversible MCMC with convergence guarantees.