Related papers: Maximum Entropy Kernels for System Identification
Kernel Estimation provides an unbinned and non-parametric estimate of the probability density function from which a set of data is drawn. In the first section, after a brief discussion on parametric and non-parametric methods, the theory of…
3D action recognition was shown to benefit from a covariance representation of the input data (joint 3D positions). A kernel machine feed with such feature is an effective paradigm for 3D action recognition, yielding state-of-the-art…
In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization…
Coarse-grained (CG) models facilitate an efficient exploration of complex systems by reducing the unnecessary degrees of freedom of the fine-grained (FG) system while recapitulating major structural correlations. Unlike structural…
Maximum-Entropy Distributions offer an attractive family of probability densities suitable for moment closure problems. Yet finding the Lagrange multipliers which parametrize these distributions, turns out to be a computational bottleneck…
Kernels representing limiting cases of neural network architectures have recently gained popularity. However, the application and performance of these new kernels compared to existing options, such as the Matern kernel, is not well studied.…
This work addresses two main issues of the standard Kernel Entropy Component Analysis (KECA) algorithm: the optimization of the kernel decomposition and the optimization of the Gaussian kernel parameter. KECA roughly reduces to a sorting of…
Correlation matrices are a major type of multivariate data. To examine properties of a given correlation matrix, a common practice is to compare the same quantity between the original correlation matrix and reference correlation matrices,…
Identifying symmetries in quantum dynamics, such as identity or time-reversal invariance, is a crucial challenge with profound implications for quantum technologies. We introduce a unified framework combining group representation theory and…
In the past years statistical physics has been successfully applied for complex networks modelling. In particular, it has been shown that the maximum entropy principle can be exploited in order to construct graph ensembles for real-world…
As a novel similarity measure that is defined as the expectation of a kernel function between two random variables, correntropy has been successfully applied in robust machine learning and signal processing to combat large outliers. The…
In this paper we propose a new identification scheme for Hammerstein systems, which are dynamic systems consisting of a static nonlinearity and a linear time-invariant dynamic system in cascade. We assume that the nonlinear function can be…
Conformal prediction (CP) provides a comprehensive framework to produce statistically rigorous uncertainty sets for black-box machine learning models. To further improve the efficiency of CP, conformal correction is proposed to fine-tune or…
A nonparametric family of conditional distributions is introduced, which generalizes conditional exponential families using functional parameters in a suitable RKHS. An algorithm is provided for learning the generalized natural parameter,…
The information detection of complex systems from data is currently undergoing a revolution, driven by the emergence of big data and machine learning methodology. Discovering governing equations and quantifying dynamical properties of…
Designing categorical kernels is a major challenge for Gaussian process regression with continuous and categorical inputs. Despite previous studies, it is difficult to identify a preferred method, either because the evaluation metrics, the…
This paper studies the optimality of kernel methods in high-dimensional data clustering. Recent works have studied the large sample performance of kernel clustering in the high-dimensional regime, where Euclidean distance becomes less…
We study non-linear data-dimension reduction. We are motivated by the classical linear framework of Principal Component Analysis. In nonlinear case, we introduce instead a new kernel-Principal Component Analysis, manifold and feature space…
The characterization of network and biophysical properties from neural spiking activity is an important goal in neuroscience. A framework that provides unbiased inference on causal synaptic interaction and single neural properties has been…
Noisy intermediate-scale quantum processors have produced a quantum computation revolution in recent times. However, to make further advances new strategies to overcome the error rate growth are needed. One possible way out is dividing…