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Significant recent work has studied the ability of gradient descent to recover a hidden planted direction $\theta^\star \in S^{d-1}$ in different high-dimensional settings, including tensor PCA and single-index models. The key quantity that…
We introduce a novel generative model for the representation of joint probability distributions of a possibly large number of discrete random variables. The approach uses measure transport by randomized assignment flows on the statistical…
Variational inference is a powerful tool for approximate inference, and it has been recently applied for representation learning with deep generative models. We develop the variational Gaussian process (VGP), a Bayesian nonparametric…
We introduce a Gaussian Prototype Layer for gradient-based prototype learning and demonstrate two novel network architectures for explainable segmentation one of which relies on region proposals. Both models are evaluated on agricultural…
In this paper, we study the problem of learning one-dimensional Gaussian mixture models (GMMs) with a specific focus on estimating both the model order and the mixing distribution from independent and identically distributed (i.i.d.)…
Hierarchical probabilistic models, such as Gaussian mixture models, are widely used for unsupervised learning tasks. These models consist of observable and latent variables, which represent the observable data and the underlying…
The commonly used latent space embedding techniques, such as Principal Component Analysis, Factor Analysis, and manifold learning techniques, are typically used for learning effective representations of homogeneous data. However, they do…
We consider probabilistic multinomial probit classification using Gaussian process (GP) priors. The challenges with the multiclass GP classification are the integration over the non-Gaussian posterior distribution, and the increase of the…
Complex computer codes or models can often be run in a hierarchy of different levels of complexity ranging from the very basic to the sophisticated. The top levels in this hierarchy are typically expensive to run, which limits the number of…
Obtaining high certainty in predictive models is crucial for making informed and trustworthy decisions in many scientific and engineering domains. However, extensive experimentation required for model accuracy can be both costly and…
Latent dynamics discovery is challenging in extracting complex dynamics from high-dimensional noisy neural data. Many dimensionality reduction methods have been widely adopted to extract low-dimensional, smooth and time-evolving latent…
We consider the problem of high-dimensional Gaussian graphical model selection. We identify a set of graphs for which an efficient estimation algorithm exists, and this algorithm is based on thresholding of empirical conditional…
In this work, we give efficient algorithms for privately estimating a Gaussian distribution in both pure and approximate differential privacy (DP) models with optimal dependence on the dimension in the sample complexity. In the pure DP…
We consider the classification problem of a high-dimensional mixture of two Gaussians with general covariance matrices. Using the replica method from statistical physics, we investigate the asymptotic behavior of a general class of…
We introduce fully scalable Gaussian processes, an implementation scheme that tackles the problem of treating a high number of training instances together with high dimensional input data. Our key idea is a representation trick over the…
We present a new subspace-based method to construct probabilistic models for high-dimensional data and highlight its use in anomaly detection. The approach is based on a statistical estimation of probability density using densities of…
We present a latent diffusion model over 3D scenes, that can be trained using only 2D image data. To achieve this, we first design an autoencoder that maps multi-view images to 3D Gaussian splats, and simultaneously builds a compressed…
We consider the problem of inferring a latent function in a probabilistic model of data. When dependencies of the latent function are specified by a Gaussian process and the data likelihood is complex, efficient computation often involve…
The Gaussian process latent variable model (GP-LVM) is a popular approach to non-linear probabilistic dimensionality reduction. One design choice for the model is the number of latent variables. We present a spike and slab prior for the…
In traditional models of supervised learning, the goal of a learner -- given examples from an arbitrary joint distribution on $\mathbb{R}^d \times \{\pm 1\}$ -- is to output a hypothesis that is competitive (to within $\epsilon$) of the…