Related papers: Kernel-independent adaptive construction of $\math…
Kernel ridge regression (KRR) is a widely used nonparametric method due to its strong theoretical guarantees and computational convenience. However, standard KRR does not distinguish between linear and nonlinear components in the signal,…
In this article we propose a new adaptive numerical quadrature procedure which includes both local subdivision of the integration domain, as well as local variation of the number of quadrature points employed on each subinterval. In this…
We consider the hashing mechanism for constructing binary embeddings, that involves pseudo-random projections followed by nonlinear (sign function) mappings. The pseudo-random projection is described by a matrix, where not all entries are…
Approximate Bayes Computations (ABC) are used for parameter inference when the likelihood function of the model is expensive to evaluate but relatively cheap to sample from. In particle ABC, an ensemble of particles in the product space of…
We construct compositional continuous approximations for an interconnection of infinitely many discrete-time switched systems. An approximation (known as abstraction) is itself a continuous-space system, which can be used as a replacement…
Hierarchical Archimedean copulas (HACs) are multivariate uniform distributions constructed by nesting Archimedean copulas into one another, and provide a flexible approach to modeling non-exchangeable data. However, this flexibility in the…
Traditional hidden Markov models have been a useful tool to understand and model stochastic dynamic data; in the case of non-Gaussian data, models such as mixture of Gaussian hidden Markov models can be used. However, these suffer from the…
Depth measures have gained popularity in the statistical literature for defining level sets in complex data structures like multivariate data, functional data, and graphs. Despite their versatility, integrating depth measures into…
This paper develops a parameter-free adaptive proximal bundle method with two important features: 1) adaptive choice of variable prox stepsizes that "closely fits" the instance under consideration; and 2) adaptive criterion for making the…
High-dimensional, heterogeneous data with complex feature interactions pose significant challenges for traditional predictive modeling approaches. While Projection to Latent Structures (PLS) remains a popular technique, it struggles to…
Markov Chain Monte Carlo (MCMC) methods, such as the Metropolis-Hastings (MH) algorithm, are widely used for Bayesian inference. One of the most important issues for any MCMC method is the convergence of the Markov chain, which depends…
This paper deals with non-parametric density estimation on $\bR^2$ from i.i.d observations. It is assumed that after unknown rotation of the coordinate system the coordinates of the observations are independent random variables whose…
Kernel-based hypothesis tests offer a flexible, non-parametric tool to detect high-order interactions in multivariate data, beyond pairwise relationships. Yet the scalability of such tests is limited by the computationally demanding…
We consider $L^2$-approximation on weighted reproducing kernel Hilbert spaces of functions depending on infinitely many variables. We focus on unrestricted linear information, admitting evaluations of arbitrary continuous linear…
We propose a scalable framework for the learning of high-dimensional parametric maps via adaptively constructed residual network (ResNet) maps between reduced bases of the inputs and outputs. When just few training data are available, it is…
With the development of machine learning and Big Data, the concepts of linear and non-linear optimization techniques are becoming increasingly valuable for many quantitative disciplines. Problems of that nature are typically solved using…
We consider the kernel partial least squares algorithm for non-parametric regression with stationary dependent data. Probabilistic convergence rates of the kernel partial least squares estimator to the true regression function are…
In most adaptive signal processing applications, system linearity is assumed and adaptive linear filters are thus used. The traditional class of supervised adaptive filters rely on error-correction learning for their adaptive capability.…
This paper proposes approaches for the analysis of multiple changepoint models when dependency in the data is modelled through a hierarchical Gaussian Markov random field. Integrated nested Laplace approximations are used to approximate…
This work presents a novel matrix-based method for constructing an approximation Hessian using only function evaluations. The method requires less computational power than interpolation-based methods and is easy to implement in matrix-based…