相关论文: Joint Learning in the Gaussian Single Index Model
Understanding the advantages of deep neural networks trained by gradient descent (GD) compared to shallow models remains an open theoretical challenge. In this paper, we introduce a class of target functions (single and multi-index Gaussian…
Properties of data are frequently seen to vary depending on the sampled situations, which usually changes along a time evolution or owing to environmental effects. One way to analyze such data is to find invariances, or representative…
Learning an effective global model on private and decentralized datasets has become an increasingly important challenge of machine learning when applied in practice. Existing distributed learning paradigms, such as Federated Learning,…
This paper proposes a novel method for deep learning based on the analytical convolution of multidimensional Gaussian mixtures. In contrast to tensors, these do not suffer from the curse of dimensionality and allow for a compact…
This paper addresses the problem of regression to reconstruct functions, which are observed with superimposed errors at random locations. We address the problem in reproducing kernel Hilbert spaces. It is demonstrated that the estimator,…
The Gaussian graphical model is a widely used tool for learning gene regulatory networks with high-dimensional gene expression data. Most existing methods for Gaussian graphical models assume that the data are homogeneous, i.e., all samples…
This manuscript considers the problem of learning a random Gaussian network function using a fully connected network with frozen intermediate layers and trainable readout layer. This problem can be seen as a natural generalization of the…
A recent line of work has shown remarkable behaviors of the generalization error curves in simple learning models. Even the least-squares regression has shown atypical features such as the model-wise double descent, and further works have…
Gaussian graphical model selection is usually studied under independent sampling, but in many applications observations arise from dependent dynamics. We study structure learning when the data consist of a single trajectory of Gaussian…
This paper proposes a receding horizon active learning and control problem for dynamical systems in which Gaussian Processes (GPs) are utilized to model the system dynamics. The active learning objective in the optimization problem is…
We consider the problem of learning a one-hidden-layer neural network: we assume the input $x\in \mathbb{R}^d$ is from Gaussian distribution and the label $y = a^\top \sigma(Bx) + \xi$, where $a$ is a nonnegative vector in $\mathbb{R}^m$…
The success of machine learning methods heavily relies on having an appropriate representation for data at hand. Traditionally, machine learning approaches relied on user-defined heuristics to extract features encoding structural…
We provide a series of results for unsupervised learning with autoencoders. Specifically, we study shallow two-layer autoencoder architectures with shared weights. We focus on three generative models for data that are common in statistical…
Off-the-shelf Gaussian Process (GP) covariance functions encode smoothness assumptions on the structure of the function to be modeled. To model complex and non-differentiable functions, these smoothness assumptions are often too…
A computer model of the feed-forward neural network with the hidden layer is developed to reconstruct physical field investigated by the fiber-optic measuring system. The Gaussian distributions of some physical quantity are selected as…
Self-supervised learning attempts to learn representations from un-labeled data; it does so via a loss function that encourages the embedding of a point to be close to that of its augmentations. This simple idea performs remarkably well,…
In this paper we derive an efficient algorithm to learn the parameters of structured predictors in general graphical models. This algorithm blends the learning and inference tasks, which results in a significant speedup over traditional…
Multi-index models - functions which only depend on the covariates through a non-linear transformation of their projection on a subspace - are a useful benchmark for investigating feature learning with neural nets. This paper examines the…
Wasserstein gradient and Hamiltonian flows have emerged as essential tools for modeling complex dynamics in the natural sciences, with applications ranging from partial differential equations (PDEs) and optimal transport to quantum…
In computational reinforcement learning, a growing body of work seeks to construct an agent's perception of the world through predictions of future sensations; predictions about environment observations are used as additional input features…