A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Sum-of-norms clustering recovers mixtures of Gaussians even with infinite samples.
Study shows private learning of mixtures of Gaussians is possible with polynomial samples.
Robust learning mixtures of linear regressions improve robustness.
Proposes diffusion models using mixed Gaussian priors for better data representation.
Recently developed techniques have made it possible to quickly learn accurate probability density functions from data in low-dimensional continuous space. In particular, mixtures of Gaussians can be fitted to data very quickly using an accelerated EM algorithm that employs multiresolution kd-trees (Moore, 1999). In thi…
New algorithm learns mixtures of any constant number of Gaussians robustly.
This work improves Gaussian process inference using mixtures of experts and nested SMC samplers.
New method models multi-view noise as Mixture of Gaussians for robust MSL.
Autoencoders can learn generative models like mixtures of gaussians and sparse coding.
Improved sample efficiency for private learning of Gaussian mixtures.
We extend the mixtures of Gaussians (MOG) model to the projected mixture of Gaussians (PMOG) model. In the PMOG model, we assume that q dimensional input data points z_i are projected by a q dimensional vector w into 1-D variables u_i. The projected variables u_i are assumed to follow a 1-D MOG model. In the PMOG model…
This work approximates finite neural networks with Gaussian processes, providing error bounds and applications in prior selection.
Study learns Gaussian mixtures from censored data.
A mixture of Gaussians fit to a single curved or heavy-tailed cluster will report that the data contains many clusters. To produce more appropriate clusterings, we introduce a model which warps a latent mixture of Gaussians to produce nonparametric cluster shapes. The possibly low-dimensional latent mixture model allow…
A mixture of Gaussians fit to a single curved or heavy-tailed cluster will report that the data contains many clusters. To produce more appropriate clusterings, we introduce a model which warps a latent mixture of Gaussians to produce nonparametric cluster shapes. The possibly low-dimensional latent mixture model allow…
Transformers interpret as probabilistic mixtures, offering new insights.
Introduces a continuous version of LWE problem.
Algorithm learns mixtures of Gaussians efficiently using diffusion models.
Paper introduces deep structured mixtures of Gaussian processes for scalable GP approximations.
We propose a family of variational approximations to Bayesian posterior distributions, called -VB, with provable statistical guarantees. The standard variational approximation is a special case of -VB with . When , a novel class of variational inequalities are developed for linking the Bayes risk …
The paper develops efficient algorithms for variational inference with mixtures of isotropic Gaussians.
How can we train a statistical mixture model on a massive data set? In this work we show how to construct coresets for mixtures of Gaussians. A coreset is a weighted subset of the data, which guarantees that models fitting the coreset also provide a good fit for the original data set. We show that, perhaps surprisingly…
RAMBO optimizes multi-regime problems by discovering and modeling distinct energy basins.
Improved Gaussian process experts model for complex data.
Unified model for reducing dimensions and clustering high-dimensional data.
Study of deep neural networks with dependent weights leading to new model limits and properties.
The classical mixture of Gaussians model is related to K-means via small-variance asymptotics: as the covariances of the Gaussians tend to zero, the negative log-likelihood of the mixture of Gaussians model approaches the K-means objective, and the EM algorithm approaches the K-means algorithm. Kulis & Jordan (2012) us…
Graphical model has been widely used to investigate the complex dependence structure of high-dimensional data, and it is common to assume that observed data follow a homogeneous graphical model. However, observations usually come from different resources and have heterogeneous hidden commonality in real-world applicati…
New distances measure mixtures of Gaussians, useful in machine learning.
We develop a personalized real time risk scoring algorithm that provides timely and granular assessments for the clinical acuity of ward patients based on their (temporal) lab tests and vital signs. Heterogeneity of the patients population is captured via a hierarchical latent class model. The proposed algorithm aims t…
New algorithm clusters Gaussian mixtures with unknown covariance efficiently.
Paper proposes a VB method for TS-SBP mixture models with reduced computational cost.
Bayesian method identifies causal DAG structure from non-Gaussian errors.
A key task in Bayesian statistics is sampling from distributions that are only specified up to a partition function (i.e., constant of proportionality). However, without any assumptions, sampling (even approximately) can be #P-hard, and few works have provided "beyond worst-case" guarantees for such settings. For log-c…
Researchers developed a generic model to account for structural variability in SHM.
Markov Chain Monte Carlo (MCMC) algorithms are a workhorse of probabilistic modeling and inference, but are difficult to debug, and are prone to silent failure if implemented naively. We outline several strategies for testing the correctness of MCMC algorithms. Specifically, we advocate writing code in a modular way, w…
This paper proposes a variant of the method of Guédon and Verhynin for estimating the cluster matrix in the Mixture of Gaussians framework via Semi-Definite Programming. A clustering oriented embedding is deduced from this estimate. The procedure is suitable for very high dimensional data because it is based on pairwis…
We prove a central limit theorem for the components of the largest eigenvectors of the adjacency matrix of a finite-dimensional random dot product graph whose true latent positions are unknown. In particular, we follow the methodology outlined in \citet{sussman2012universally} to construct consistent estimates for the …
A software library for constructing and learning probabilistic models is presented. The library offers a set of building blocks from which a large variety of static and dynamic models can be built. These include hierarchical models for variances of other variables and many nonlinear models. The underlying variational B…
This study analyzes theoretical guarantees for VI with fixed-variance Gaussian mixtures.
A new method for Gaussian filtering using gradient flows and Wasserstein metrics.
DS-UI improves DNN uncertainty inference by combining a DNN classifier with MoGMM.
In this paper we show that very large mixtures of Gaussians are efficiently learnable in high dimension. More precisely, we prove that a mixture with known identical covariance matrices whose number of components is a polynomial of any fixed degree in the dimension n is polynomially learnable as long as a certain non-d…
Deep learning is a hierarchical inference method formed by subsequent multiple layers of learning able to more efficiently describe complex relationships. In this work, Deep Gaussian Mixture Models are introduced and discussed. A Deep Gaussian Mixture model (DGMM) is a network of multiple layers of latent variables, wh…
A mixture of factor analyzers is a semi-parametric density estimator that generalizes the well-known mixtures of Gaussians model by allowing each Gaussian in the mixture to be represented in a different lower-dimensional manifold. This paper presents a robust and parsimonious model selection algorithm for training a mi…
In this work we introduce a mixture of GPs to address the data association problem, i.e. to label a group of observations according to the sources that generated them. Unlike several previously proposed GP mixtures, the novel mixture has the distinct characteristic of using no gating function to determine the associati…
In recent years, a rich variety of shrinkage priors have been proposed that have great promise in addressing massive regression problems. In general, these new priors can be expressed as scale mixtures of normals, but have more complex forms and better properties than traditional Cauchy and double exponential priors. W…
In data-mining applications, we are frequently faced with a large fraction of missing entries in the data matrix, which is problematic for most discriminant machine learning algorithms. A solution that we explore in this paper is the use of a generative model (a mixture of Gaussians) to compute the conditional expectat…