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Varying coefficient models (VCMs) are widely used for estimating nonlinear regression functions for functional data. Their Bayesian variants using Gaussian process priors on the functional coefficients, however, have received limited…
Recent economic events, including the global financial crisis and COVID-19 pandemic, have exposed limitations in linear Factor Augmented Vector Autoregressive (FAVAR) models for forecasting and structural analysis. Nonlinear dimension…
In addition to recent developments in computing speed and memory, methodological advances have contributed to significant gains in the performance of stochastic simulation. In this paper, we focus on variance reduction for matrix…
We utilize copulas to constitute a unified framework for constructing and optimizing variational proposals in hierarchical Bayesian models. For models with continuous and non-Gaussian hidden variables, we propose a semiparametric and…
Gaussian processes are rich distributions over functions, which provide a Bayesian nonparametric approach to smoothing and interpolation. We introduce simple closed form kernels that can be used with Gaussian processes to discover patterns…
This is a tutorial and survey paper on factor analysis, probabilistic Principal Component Analysis (PCA), variational inference, and Variational Autoencoder (VAE). These methods, which are tightly related, are dimensionality reduction and…
Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…
Gaussian processes are powerful models for probabilistic machine learning, but are limited in application by their $O(N^3)$ inference complexity. We propose a method for deriving parametric families of kernel functions with compact spatial…
This paper explores a federated learning approach that automatically selects the number of latent processes in multi-output Gaussian processes (MGPs). The MGP has seen great success as a transfer learning tool when data is generated from…
Conditional Autoencoders (CAEs) offer a flexible, interpretable approach for estimating latent asset-pricing factors from firm characteristics. However, existing studies usually limit the latent factor dimension to around K=5 due to…
We address the task of simultaneous feature fusion and modeling of discrete ordinal outputs. We propose a novel Gaussian process(GP) auto-encoder modeling approach. In particular, we introduce GP encoders to project multiple observed…
Variational Autoencoder (VAE)-based generative models offer flexible representation learning by incorporating meta-priors, general premises considered beneficial for downstream tasks. However, the incorporated meta-priors often involve…
Gaussian process regression is a well-established Bayesian machine learning method. We propose a new approach to Gaussian process regression using quantum kernels based on parameterized quantum circuits. By employing a hardware-efficient…
There has been considerable recent interest in Bayesian modeling of high-dimensional networks via latent space approaches. When the number of nodes increases, estimation based on Markov Chain Monte Carlo can be extremely slow and show poor…
Latent Gaussian models and boosting are widely used techniques in statistics and machine learning. Tree-boosting shows excellent prediction accuracy on many data sets, but potential drawbacks are that it assumes conditional independence of…
Gaussian processes are probabilistic models that are commonly used as functional priors in machine learning. Due to their probabilistic nature, they can be used to capture the prior information on the statistics of noise, smoothness of the…
We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent P\'olya--Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model's…
Locally weighted regression was created as a nonparametric learning method that is computationally efficient, can learn from very large amounts of data and add data incrementally. An interesting feature of locally weighted regression is…
An important property for deep neural networks is the ability to perform robust out-of-distribution detection on previously unseen data. This property is essential for safety purposes when deploying models for real world applications.…
With the rapid development of modern technology, massive amounts of data with complex pattern are generated. Gaussian process models that can easily fit the non-linearity in data become more and more popular nowadays. It is often the case…