Related papers: Spectral Methods for Nonparametric Models
Multi-dimensional Hawkes process (MHP) is a class of self and mutually exciting point processes that find wide range of applications -- from prediction of earthquakes to modelling of order books in high frequency trading. This paper makes…
Spectral methods have greatly advanced the estimation of latent variable models, generating a sequence of novel and efficient algorithms with strong theoretical guarantees. However, current spectral algorithms are largely restricted to…
Recent advances in topic models have explored complicated structured distributions to represent topic correlation. For example, the pachinko allocation model (PAM) captures arbitrary, nested, and possibly sparse correlations between topics…
Spike-and-slab and horseshoe regression are arguably the most popular Bayesian variable selection approaches for linear regression models. However, their performance can deteriorate if outliers and heteroskedasticity are present in the…
This paper proposes a Hilbert space embedding for Dirichlet Process mixture models via a stick-breaking construction of Sethuraman. Although Bayesian nonparametrics offers a powerful approach to construct a prior that avoids the need to…
We introduce the Poisson Hierarchical Indian Buffet Process (PHIBP), a new class of species sampling models designed to address the challenges of complex, sparse count data by facilitating information sharing across and within groups. Our…
The spectral bundle method proposed by Helmberg and Rendl is well established for solving large-scale semidefinite programs (SDP) thanks to its low per iteration computational complexity and strong practical performance. In this paper, we…
Many high-dimensional data sets suffer from hidden confounding which affects both the predictors and the response of interest. In such situations, standard regression methods or algorithms lead to biased estimates. This paper substantially…
Latent feature models are a powerful tool for modeling data with globally-shared features. Nonparametric exchangeable models such as the Indian Buffet Process offer modeling flexibility by letting the number of latent features be unbounded.…
Accurately predicting infrared (IR) spectra in computational chemistry using ab initio methods remains a challenge. Current approaches often rely on an empirical approach or on tedious anharmonic calculations, mainly adapted to semi-rigid…
Feature allocation models are popular models used in different applications such as unsupervised learning or network modeling. In particular, the Indian buffet process is a flexible and simple one-parameter feature allocation model where…
Time-varying mixture densities occur in many scenarios, for example, the distributions of keywords that appear in publications may evolve from year to year, video frame features associated with multiple targets may evolve in a sequence. Any…
The Dirichlet process mixture (DPM) is a ubiquitous, flexible Bayesian nonparametric statistical model. However, full probabilistic inference in this model is analytically intractable, so that computationally intensive techniques such as…
Deep generative models (DGMs) have brought about a major breakthrough, as well as renewed interest, in generative latent variable models. However, DGMs do not allow for performing data-driven inference of the number of latent features…
Latent feature models are attractive for image modeling, since images generally contain multiple objects. However, many latent feature models ignore that objects can appear at different locations or require pre-segmentation of images. While…
Latent feature models are widely used to decompose data into a small number of components. Bayesian nonparametric variants of these models, which use the Indian buffet process (IBP) as a prior over latent features, allow the number of…
The spectral bundle method developed by Helmberg and Rendl is well-established for solving large-scale semidefinite programs (SDPs) in the dual form, especially when the SDPs admit $\textit{low-rank primal solutions}$. Under mild regularity…
The purpose of this work is to describe a unified, and indeed simple, mechanism for non-parametric Bayesian analysis, construction and generative sampling of a large class of latent feature models which one can describe as generalized…
Nonlinear spectral problems arise across a range of fields, including mechanical vibrations, fluid-solid interactions, and photonic crystals. Discretizing infinite-dimensional nonlinear spectral problems often introduces significant…
In this paper, we propose the unfitted spectral element method for solving elliptic interface and corresponding eigenvalue problems. The novelty of the proposed method lies in its combination of the spectral accuracy of the spectral element…