Related papers: Kernel-Based Sparse Additive Nonlinear Model Struc…
Network modeling of high-dimensional time series data is a key learning task due to its widespread use in a number of application areas, including macroeconomics, finance and neuroscience. While the problem of sparse modeling based on…
Neural networks are predominantly trained using gradient-based methods, yet in many applications their final predictions remain far from the accuracy attainable within the model's expressive capacity. We introduce Linearized Subspace…
We propose a novel adaptive learning algorithm based on iterative orthogonal projections in the Cartesian product of multiple reproducing kernel Hilbert spaces (RKHSs). The task is estimating/tracking nonlinear functions which are supposed…
Kernel logistic regression (KLR) is a powerful classification method widely applied across diverse domains. In many real-world scenarios, indefinite kernels capture more domain-specific structural information than positive definite kernels.…
Modeling dynamical systems with ordinary differential equations implies a mechanistic view of the process underlying the dynamics. However in many cases, this knowledge is not available. To overcome this issue, we introduce a general…
Kernel-based methods enjoy powerful generalization capabilities in handling a variety of learning tasks. When such methods are provided with sufficient training data, broadly-applicable classes of nonlinear functions can be approximated…
Sparse additive models are an attractive choice in circumstances calling for modelling flexibility in the face of high dimensionality. We study the signal detection problem and establish the minimax separation rate for the detection of a…
The problem of structured matrix estimation has been studied mostly under strong noise dependence assumptions. This paper considers a general framework of noisy low-rank-plus-sparse matrix recovery, where the noise matrix may come from any…
We study the problem of estimating a temporally varying coefficient and varying structure (VCVS) graphical model underlying nonstationary time series data, such as social states of interacting individuals or microarray expression profiles…
We develop a novel framework for sparse multiscale kernel approximation of large scattered data problems based on a samplet representation. Samplets form a multiresolution analysis of localized discrete signed measures and enable…
Kernel-based methods for support vector machines (SVM) have shown highly advantageous performance in various applications. However, they may incur prohibitive computational costs for large-scale sample datasets. Therefore, data reduction…
Recently, tensor data (or multidimensional array) have been generated in many modern applications, such as functional magnetic resonance imaging (fMRI) in neuroscience and videos in video analysis. Many efforts are made in recent years to…
We study the problem of learning a sparse linear regression vector under additional conditions on the structure of its sparsity pattern. This problem is relevant in machine learning, statistics and signal processing. It is well known that a…
A dimension reduction method based on the "Nonlinear Level set Learning" (NLL) approach is presented for the pointwise prediction of functions which have been sparsely sampled. Leveraging geometric information provided by the Implicit…
We investigate the time-varying ARCH (tvARCH) process. It is shown that it can be used to describe the slow decay of the sample autocorrelations of the squared returns often observed in financial time series, which warrants the further…
We propose an efficient online dictionary learning algorithm for kernel-based sparse representations. In this framework, input signals are nonlinearly mapped to a high-dimensional feature space and represented sparsely using a virtual…
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…
Estimating the parameters of nonlinear block-oriented state-space models from input-output data typically involves solving a highly non-convex optimization problem, which is prone to poor local minima and slow convergence. This paper…
The classical approach to linear system identification is given by parametric Prediction Error Methods (PEM). In this context, model complexity is often unknown so that a model order selection step is needed to suitably trade-off bias and…
Recovering intrinsic data structure from corrupted observations plays an important role in various tasks in the communities of machine learning and signal processing. In this paper, we propose a novel model, named log-sum heuristic recovery…