相关论文: The Generative Leap: Sharp Sample Complexity for E…

Generative networks have shown remarkable success in learning complex data distributions, particularly in generating high-dimensional data from lower-dimensional inputs. While this capability is well-documented empirically, its theoretical…

Generalized additive model is a powerful statistical learning and predictive modeling tool that has been applied in a wide range of applications. The need of high-dimensional additive modeling is eminent in the context of dealing with high…

The Gaussian Process Latent Variable Model (GP-LVM) is a non-linear probabilistic method of embedding a high dimensional dataset in terms low dimensional `latent' variables. In this paper we illustrate that maximum a posteriori (MAP)…

This paper explores the interplay between statistics and generative artificial intelligence. Generative statistics, an integral part of the latter, aims to construct models that can generate efficiently and meaningfully new data across the…

In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…

A single-index model (SIM) is a function of the form $\sigma(\mathbf{w}^{\ast} \cdot \mathbf{x})$, where $\sigma: \mathbb{R} \to \mathbb{R}$ is a known link function and $\mathbf{w}^{\ast}$ is a hidden unit vector. We study the task of…

Few-shot segmentation is a challenging task, requiring the extraction of a generalizable representation from only a few annotated samples, in order to segment novel query images. A common approach is to model each class with a single…

We study the problem of learning general (i.e., not necessarily homogeneous) halfspaces with Random Classification Noise under the Gaussian distribution. We establish nearly-matching algorithmic and Statistical Query (SQ) lower bound…

Inference tasks in signal processing are often characterized by the availability of reliable statistical modeling with some missing instance-specific parameters. One conventional approach uses data to estimate these missing parameters and…

We study the problem of overcoming exponential sample complexity in differential entropy estimation under Gaussian convolutions. Specifically, we consider the estimation of the differential entropy $h(X+Z)$ via $n$ independently and…

We propose a geometric latent-subspace framework for generative modeling of discrete data. Specifically, we introduce latent subspaces in the exponential parameter space of product manifolds of categorical distributions as a novel method…

The complexity of learning a concept class under Gaussian marginals in the difficult agnostic model is closely related to its $L_1$-approximability by low-degree polynomials. For any concept class with Gaussian surface area at most…

We study gradient flow on the multi-index regression problem for high-dimensional Gaussian data. Multi-index functions consist of a composition of an unknown low-rank linear projection and an arbitrary unknown, low-dimensional link…

Deep Gaussian Processes (DGPs) are multi-layer, flexible extensions of Gaussian processes but their training remains challenging. Sparse approximations simplify the training but often require optimization over a large number of inducing…

We derive a novel generative model from iterative Gaussian posterior inference. By treating the generated sample as an unknown variable, we can formulate the sampling process in the language of Bayesian probability. Our model uses a…

Gaussian processes with derivative information are useful in many settings where derivative information is available, including numerous Bayesian optimization and regression tasks that arise in the natural sciences. Incorporating derivative…

Density estimation, which estimates the distribution of data, is an important category of probabilistic machine learning. A family of density estimators is mixture models, such as Gaussian Mixture Model (GMM) by expectation maximization.…

We propose an active learning method for discovering low-dimensional structure in high-dimensional Gaussian process (GP) tasks. Such problems are increasingly frequent and important, but have hitherto presented severe practical…

We introduce a new generative model where samples are produced via Langevin dynamics using gradients of the data distribution estimated with score matching. Because gradients can be ill-defined and hard to estimate when the data resides on…

We introduce a cluster-based generative image segmentation framework to encode higher-level representations of visual concepts based on one-shot learning inspired by the Omniglot Challenge. The inferred parameters of each component of a…