Related papers: A Sparse Bayesian Learning Algorithm for Estimatio…
We develop a stochastic approximation framework for learning nonlinear operators between infinite-dimensional spaces utilizing general Mercer operator-valued kernels. Our framework encompasses two key classes: (i) compact kernels, which…
Research in modern data-driven dynamical systems is typically focused on the three key challenges of high dimensionality, unknown dynamics, and nonlinearity. The dynamic mode decomposition (DMD) has emerged as a cornerstone for modeling…
We develop a nonparametric Bayesian modeling framework for clustered ordinal responses in developmental toxicity studies, which typically exhibit extensive heterogeneity. The primary focus of these studies is to examine the dose-response…
We propose a general matrix-valued multiple kernel learning framework for high-dimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, including those that induce sparsity, to…
We propose a general matrix-valued multiple kernel learning framework for high-dimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, including those that induce sparsity, to…
Deep kernel learning provides an elegant and principled framework for combining the structural properties of deep learning algorithms with the flexibility of kernel methods. By means of a deep neural network, we learn a parametrized kernel…
Accurate uncertainty quantification is a critical challenge in machine learning. While neural networks are highly versatile and capable of learning complex patterns, they often lack interpretability due to their ``black box'' nature. On the…
This work presents a systematic analysis and extension of the sparse radial basis function network (SparseRBFnet) previously introduced for solving nonlinear partial differential equations (PDEs). Based on its adaptive-width shallow kernel…
Existing support vector machines(SVM) models are sensitive to noise and lack sparsity, which limits their performance. To address these issues, we combine the elastic net loss with a robust loss framework to construct a sparse…
Active policy search combines the trial-and-error methodology from policy search with Bayesian optimization to actively find the optimal policy. First, policy search is a type of reinforcement learning which has become very popular for…
Marginalising over families of Gaussian Process kernels produces flexible model classes with well-calibrated uncertainty estimates. Existing approaches require likelihood evaluations of many kernels, rendering them prohibitively expensive…
While tasks could come with varying the number of instances and classes in realistic settings, the existing meta-learning approaches for few-shot classification assume that the number of instances per task and class is fixed. Due to such…
We study Sparse Multiple Kernel Learning (SMKL), which is the problem of selecting a sparse convex combination of prespecified kernels for support vector binary classification. Unlike prevailing l1 regularized approaches that approximate a…
Nonlinear function estimation is core to modern machine learning applications. In this paper, to perform nonlinear function estimation, we reduce a nonlinear inverse problem to a linear one using a polynomial kernel expansion. These kernels…
We present CavePerception, a framework for the analysis of sparse data from sensor networks that incorporates elements of inverse modeling and forward modeling. By integrating machine learning with physical modeling in a hypotheses space,…
The article considers the nonlinear inverse problem of identifying the material parameters in viscoelastic structures based on a generalized Maxwell model. The aim is to reconstruct the model parameters from stress data acquired from a…
The problem of inferring pair-wise and higher-order interactions in complex systems involving large numbers of interacting variables, from observational data, is fundamental to many fields. Known to the statistical physics community as the…
Recent advances in computer vision and machine learning suggest that a wide range of problems can be addressed more appropriately by considering non-Euclidean geometry. In this paper we explore sparse dictionary learning over the space of…
We consider machine learning techniques to develop low-latency approximate solutions to a class of inverse problems. More precisely, we use a probabilistic approach for the problem of recovering sparse stochastic signals that are members of…
This work presents a distributed algorithm for nonlinear adaptive learning. In particular, a set of nodes obtain measurements, sequentially one per time step, which are related via a nonlinear function; their goal is to collectively…