Related papers: Training Gaussian Mixture Models at Scale via Core…
We provide a new approach to approximate emulation of large computer experiments. By focusing expressly on desirable properties of the predictive equations, we derive a family of local sequential design schemes that dynamically define the…
We propose and analyze a new vantage point for the learning of mixtures of Gaussians: namely, the PAC-style model of learning probability distributions introduced by Kearns et al. Here the task is to construct a hypothesis mixture of…
Gaussian mixtures are a powerful and widely used tool to model non-Gaussian estimation problems. They are able to describe measurement errors that follow arbitrary distributions and can represent ambiguity in assignment tasks like point set…
In many machine learning tasks, a common approach for dealing with large-scale data is to build a small summary, {\em e.g.,} coreset, that can efficiently represent the original input. However, real-world datasets usually contain outliers…
Gaussian processes (GPs) are Bayesian nonparametric generative models that provide interpretability of hyperparameters, admit closed-form expressions for training and inference, and are able to accurately represent uncertainty. To model…
Gaussian mixture filters for nonlinear systems usually rely on severe approximations when calculating mixtures in the prediction and filtering step. Thus, offline approximations of noise densities by Gaussian mixture densities to reduce the…
A Bayesian coreset is a small, weighted subset of data that replaces the full dataset during Bayesian inference, with the goal of reducing computational cost. Although past work has shown empirically that there often exists a coreset with…
Gaussian mixture block models are distributions over graphs that strive to model modern networks: to generate a graph from such a model, we associate each vertex $i$ with a latent feature vector $u_i \in \mathbb{R}^d$ sampled from a mixture…
We provide statistical learning guarantees for two unsupervised learning tasks in the context of compressive statistical learning, a general framework for resource-efficient large-scale learning that we introduced in a companion paper.The…
We introduce a novel stochastic variational inference method for Gaussian process ($\mathcal{GP}$) regression, by deriving a posterior over a learnable set of coresets: i.e., over pseudo-input/output, weighted pairs. Unlike former free-form…
AI and data-driven models have large potential for data assimilation applications by creating fast and accurate forecasts. Their tendency to produce spurious inaccurate, nonphysical results -- hallucination -- however, raises a serious…
Fair clustering is a constrained variant of clustering where the goal is to partition a set of colored points, such that the fraction of points of any color in every cluster is more or less equal to the fraction of points of this color in…
In this note, we consider the problem of robust learning mixtures of linear regressions. We connect mixtures of linear regressions and mixtures of Gaussians with a simple thresholding, so that a quasi-polynomial time algorithm can be…
Bayesian methods provide an elegant framework for estimating parameter posteriors and quantification of uncertainty associated with probabilistic models. However, they often suffer from slow inference times. To address this challenge,…
The Gaussian mixture model is a classic technique for clustering and data modeling that is used in numerous applications. With the rise of big data, there is a need for parameter estimation techniques that can handle streaming data and…
By a "covering" we mean a Gaussian mixture model fit to observed data. Approximations of the Bayes factor can be availed of to judge model fit to the data within a given Gaussian mixture model. Between families of Gaussian mixture models,…
In order to scale standard Gaussian process (GP) regression to large-scale datasets, aggregation models employ factorized training process and then combine predictions from distributed experts. The state-of-the-art aggregation models,…
Gaussian processes are typically used for smoothing and interpolation on small datasets. We introduce a new Bayesian nonparametric framework -- GPatt -- enabling automatic pattern extrapolation with Gaussian processes on large…
Gaussian process (GP) is a Bayesian model which provides several advantages for regression tasks in machine learning such as reliable quantitation of uncertainty and improved interpretability. Their adoption has been precluded by their…
Gaussian processes (GPs) provide flexible distributions over functions, with inductive biases controlled by a kernel. However, in many applications Gaussian processes can struggle with even moderate input dimensionality. Learning a low…