Related papers: Gaussian-Mixture-Model Q-Functions for Policy Iter…

This paper presents a novel systematic methodology to obtain new simple and tight approximations, lower bounds, and upper bounds for the Gaussian Q-function, and functions thereof, in the form of a weighted sum of exponential functions.…

A longstanding problem in machine learning is to find unsupervised methods that can learn the statistical structure of high dimensional signals. In recent years, GANs have gained much attention as a possible solution to the problem, and in…

Machine Learning (ML) applications are proliferating in the enterprise. Relational data which are prevalent in enterprise applications are typically normalized; as a result, data has to be denormalized via primary/foreign-key joins to be…

We consider the analysis of continuous repeated measurement outcomes that are collected through time, also known as longitudinal data. A standard framework for analysing data of this kind is a linear Gaussian mixed-effects model within…

We derive closed-form expressions for the Bayes optimal decision boundaries in binary classification of high dimensional overlapping Gaussian mixture model (GMM) data, and show how they depend on the eigenstructure of the class covariances,…

We develop here a semiparametric Gaussian mixture model (SGMM) for unsupervised learning with valuable spatial information taken into consideration. Specifically, we assume for each instance a random location. Then, conditional on this…

This paper proposes a novel method for deep learning based on the analytical convolution of multidimensional Gaussian mixtures. In contrast to tensors, these do not suffer from the curse of dimensionality and allow for a compact…

This paper aims at presenting a new application of information geometry to reinforcement learning focusing on dynamic treatment resumes. In a standard framework of reinforcement learning, a Q-function is defined as the conditional…

Gaussian Mixture Models (GMMs) are a standard tool in data analysis. However, they face problems when applied to high-dimensional data (e.g., images) due to the size of the required full covariance matrices (CMs), whereas the use of…

The Group Relative Policy Optimization (GRPO), a reinforcement learning method used to fine-tune large language models (LLMs), has proved its effectiveness in practical applications such as DeepSeek-R1. It raises a question whether GRPO can…

Geometric data and purpose-built generative models on them have become ubiquitous in high-impact deep learning application domains, ranging from protein backbone generation and computational chemistry to geospatial data. Current geometric…

We study reinforcement learning with linear function approximation and finite-memory approximations for partially observed Markov decision processes (POMDPs). We first present an algorithm for the value evaluation of finite-memory feedback…

Multi-modal densities appear frequently in time series and practical applications. However, they cannot be represented by common state estimators, such as the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF), which…

Programming by demonstration has recently gained much attention due to its user-friendly and natural way to transfer human skills to robots. In order to facilitate the learning of multiple demonstrations and meanwhile generalize to new…

Spatial generalized linear mixed models (SGLMMs) are popular for analyzing non-Gaussian spatial data. These models assume a prescribed link function that relates the underlying spatial field with the mean response. There are circumstances,…

In learned image compression, probabilistic models play an essential role in characterizing the distribution of latent variables. The Gaussian model with mean and scale parameters has been widely used for its simplicity and effectiveness.…

The Gaussian Filter (GF) is one of the most widely used filtering algorithms; instances are the Extended Kalman Filter, the Unscented Kalman Filter and the Divided Difference Filter. GFs represent the belief of the current state by a…

Generalized additive models (GAMs) are flexible non-linear regression models, which can be fitted efficiently using the approximate Bayesian methods provided by the mgcv R package. While the GAM methods provided by mgcv are based on the…

Process reward models (PRMs) provide more nuanced supervision compared to outcome reward models (ORMs) for optimizing policy models, positioning them as a promising approach to enhancing the capabilities of LLMs in complex reasoning tasks.…

This paper focuses on reinforcement learning (RL) with clustered data, which is commonly encountered in healthcare applications. We propose a generalized fitted Q-iteration (FQI) algorithm that incorporates generalized estimating equations…