Related papers: Convergence rates for random feature neural networ…

Neural networks are regularly employed in adaptive control of nonlinear systems and related methods of reinforcement learning. A common architecture uses a neural network with a single hidden layer (i.e. a shallow network), in which the…

The dynamics of physical systems is often constrained to lower dimensional sub-spaces due to the presence of conserved quantities. Here we propose a method to learn and exploit such symmetry constraints building upon Hamiltonian Neural…

In recent years, functional linear models have attracted growing attention in statistics and machine learning, with the aim of recovering the slope function or its functional predictor. This paper considers online regularized learning…

The intrinsic Helmholtz free-energy functional, the centerpiece of classical density functional theory, is at best only known approximately for 3D systems. Here we introduce a method for learning a neuralnetwork approximation of this…

A Random Vector Functional Link (RVFL) network is a depth-2 neural network with random inner weights and biases. Only the outer weights of such an architecture are to be learned, so the learning process boils down to a linear optimization…

Random Feature (RF) models are used as efficient parametric approximations of kernel methods. We investigate, by means of random matrix theory, the connection between Gaussian RF models and Kernel Ridge Regression (KRR). For a Gaussian RF…

We identify various classes of neural networks that are able to approximate continuous functions locally uniformly subject to fixed global linear growth constraints. For such neural networks the associated neural stochastic differential…

Randomized Hadamard Transforms (RHTs) have emerged as a computationally efficient alternative to the use of dense unstructured random matrices across a range of domains in computer science and machine learning. For several applications such…

The random feature (RF) approach is a well-established and efficient tool for scalable kernel methods, but existing literature has primarily focused on kernel ridge regression with random features (KRR-RF), which has limitations in handling…

How many neurons are needed to approximate a target probability distribution using a neural network with a given input distribution and approximation error? This paper examines this question for the case when the input distribution is…

To accelerate kernel methods, we propose a near input sparsity time algorithm for sampling the high-dimensional feature space implicitly defined by a kernel transformation. Our main contribution is an importance sampling method for…

We study the approximation of a square-integrable function from a finite number of evaluations on a random set of nodes according to a well-chosen distribution. This is particularly relevant when the function is assumed to belong to a…

The performance of adaptive estimators that employ embedding in reproducing kernel Hilbert spaces (RKHS) depends on the choice of the location of basis kernel centers. Parameter convergence and error approximation rates depend on where and…

Consider the problem of predicting the next symbol given a sample path of length n, whose joint distribution belongs to a distribution class that may have long-term memory. The goal is to compete with the conditional predictor that knows…

High-dimensional functional data have become increasingly prevalent in modern applications such as high-frequency financial data and neuroimaging data analysis. We investigate a class of high-dimensional linear regression models, where each…

In this paper, we consider Hybrid Mixed Networks (HMN) which are Hybrid Bayesian Networks that allow discrete deterministic information to be modeled explicitly in the form of constraints. We present two approximate inference algorithms for…

We develop approximate estimation methods for exponential random graph models (ERGMs), whose likelihood is proportional to an intractable normalizing constant. The usual approach approximates this constant with Monte Carlo simulations,…

In this paper, we propose an adaptive group Lasso deep neural network for high-dimensional function approximation where input data are generated from a dynamical system and the target function depends on few active variables or few linear…

We study the connection between the highly non-convex loss function of a simple model of the fully-connected feed-forward neural network and the Hamiltonian of the spherical spin-glass model under the assumptions of: i) variable…

The aim of this paper is twofold: In the first part, we leverage recent results on scenario design to develop randomized algorithmsfor approximating the image set of a nonlinear mapping, that is, a (possibly noisy) mapping of a set via a…