相关论文: Information Theoretic Learning with Infinitely Div…

We propose a novel objective function for learning robust deep representations of data based on information theory. Data is projected into a feature-vector space such that the mutual information of all subsets of features relative to the…

Traditional machine learning relies on explicit models and domain assumptions, limiting flexibility and interpretability. We introduce a model-free framework using surprisal (information theoretic uncertainty) to directly analyze and…

Understanding the power of quantum data in machine learning is central to many proposed applications of quantum technologies. While access to quantum data can offer exponential advantages for carefully designed learning tasks and often…

A survey is given summarizing the state of the art of describing information processing in Quantum Decision Theory, which has been recently advanced as a novel variant of decision making, based on the mathematical theory of separable…

We introduce a novel kernel-based framework for learning differential equations and their solution maps that is efficient in data requirements, in terms of solution examples and amount of measurements from each example, and computational…

We study how iterated and composed completely positive maps act on operator-valued kernels. Each kernel is realized inside a single Hilbert space where composition corresponds to applying bounded creation operators to feature vectors. This…

Random matrix ensembles (RME) of quantal statistical Hamiltonian operators, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), had been applied in literature in study of following quantal…

Emergent learning transforms a disordered optical medium into a photonic device capable of storage, recognition, and classification of arbitrary memory patterns. First, we show that the intensity at the output of a multiply scattering…

Nonparametric feature selection in high-dimensional data is an important and challenging problem in statistics and machine learning fields. Most of the existing methods for feature selection focus on parametric or additive models which may…

We introduce an asymmetric distance in the space of learning tasks, and a framework to compute their complexity. These concepts are foundational for the practice of transfer learning, whereby a parametric model is pre-trained for a task,…

One of the most influential results in neural network theory is the universal approximation theorem [1, 2, 3] which states that continuous functions can be approximated to within arbitrary accuracy by single-hidden-layer feedforward neural…

This paper investigates the use of nonparametric kernel-regression to obtain a tasksimilarity aware meta-learning algorithm. Our hypothesis is that the use of tasksimilarity helps meta-learning when the available tasks are limited and may…

Kernel methods are powerful tools in machine learning. Classical kernel methods are based on positive-definite kernels, which map data spaces into reproducing kernel Hilbert spaces (RKHS). For non-Euclidean data spaces, positive-definite…

Recent research in the theory of overparametrized learning has sought to establish generalization guarantees in the interpolating regime. Such results have been established for a few common classes of methods, but so far not for ensemble…

As the size and richness of available datasets grow larger, the opportunities for solving increasingly challenging problems with algorithms learning directly from data grow at the same pace. Consequently, the capability of learning…

It is argued that deep learning is efficient for data that is generated from hierarchal generative models. Examples of such generative models include wavelet scattering networks, functions of compositional structure, and deep rendering…

In this paper, we establish a novel connection between the metric entropy growth and the embeddability of function spaces into reproducing kernel Hilbert/Banach spaces. Metric entropy characterizes the information complexity of function…

We present a general framework to learn functions in tensor product reproducing kernel Hilbert spaces (TP-RKHSs). The methodology is based on a novel representer theorem suitable for existing as well as new spectral penalties for tensors.…

In supervised learning with distributional inputs in the two-stage sampling setup, relevant to applications like learning-based medical screening or causal learning, the inputs (which are probability distributions) are not accessible in the…

Interpolation and approximation of functionals with conditionally positive definite kernels is considered on sets of centers that are not determining for polynomials. It is shown that polynomial consistency is sufficient in order to define…