Related papers: The Kernel Trick for Nonlinear Factor Modeling

This paper introduces non-linear dimension reduction in factor-augmented vector autoregressions to analyze the effects of different economic shocks. I argue that controlling for non-linearities between a large-dimensional dataset and the…

Many estimation problems in astrophysics are highly complex, with high-dimensional, non-standard data objects (e.g., images, spectra, entire distributions, etc.) that are not amenable to formal statistical analysis. To utilize such data and…

Kernel methods give powerful, flexible, and theoretically grounded approaches to solving many problems in machine learning. The standard approach, however, requires pairwise evaluations of a kernel function, which can lead to scalability…

Score-based diffusion models in infinite-dimensional function spaces provide a mathematically principled framework for modelling function-valued data, offering key advantages such as resolution invariance and the ability to handle irregular…

Learning and forecasting stochastic time series is essential in various scientific fields. However, despite the proposals of nonlinear filters and deep-learning methods, it remains challenging to capture nonlinear dynamics from a few noisy…

High-dimensional data often exhibit variation that can be captured by lower dimensional factors. For high-dimensional data from multiple studies or environments, one goal is to understand which underlying factors are common to all studies,…

Kernels are key in machine learning for modeling interactions. Unfortunately, brute-force computation of the related kernel sums scales quadratically with the number of samples. Recent Fourier-slicing methods lead to an improved linear…

Statistical modeling of experimental physical laws is based on the probability density function of measured variables. It is expressed by experimental data via a kernel estimator. The kernel is determined objectively by the scattering of…

Feature learning in neural networks is crucial for their expressive power and inductive biases, motivating various theoretical approaches. Some approaches describe network behavior after training through a change in kernel scale from…

A key assumption in the theory of nonlinear adaptive control is that the uncertainty of the system can be expressed in the linear span of a set of known basis functions. While this assumption leads to efficient algorithms, it limits…

Distribution regression refers to the supervised learning problem where labels are only available for groups of inputs instead of individual inputs. In this paper, we develop a rigorous mathematical framework for distribution regression…

We introduce propagation kernels, a general graph-kernel framework for efficiently measuring the similarity of structured data. Propagation kernels are based on monitoring how information spreads through a set of given graphs. They leverage…

This paper investigates how to measure common market risk factors using newly proposed Panel Quantile Regression Model for Returns. By exploring the fact that volatility crosses all quantiles of the return distribution and using penalized…

As is known, factor analysis is a popular method to reduce dimension for high-dimensional data. For matrix data, the dimension reduction can be more effectively achieved through both row and column directions. In this paper, we introduce a…

Latent factor model estimation typically relies on either using domain knowledge to manually pick several observed covariates as factor proxies, or purely conducting multivariate analysis such as principal component analysis. However, the…

Predictive uncertainty estimation remains a challenging problem precluding the use of deep neural networks as subsystems within safety-critical applications. Aleatoric uncertainty is a component of predictive uncertainty that cannot be…

Nonnegative matrix factorization is a powerful technique to realize dimension reduction and pattern recognition through single-layer data representation learning. Deep learning, however, with its carefully designed hierarchical structure,…

Many algorithms for ranked data become computationally intractable as the number of objects grows due to the complex geometric structure induced by rankings. An additional challenge is posed by partial rankings, i.e. rankings in which the…

We propose a new estimator for nonparametric binary choice models that does not impose a parametric structure on either the systematic function of covariates or the distribution of the error term. A key advantage of our approach is its…

In this paper, we set up the theoretical foundations for a high-dimensional functional factor model approach in the analysis of large cross-sections (panels) of functional time series (FTS). We first establish a representation result…