arXiv subjects

Joseph K. Chege

Publications and source records attributed to Joseph K. Chege.

3 recordsLinked to original sources

arXiv2025

A Unified MDL-based Binning and Tensor Factorization Framework for PDF Estimation

Reliable density estimation is fundamental for numerous applications in statistics and machine learning. In many practical scenarios, data are best modeled as mixtures of component densities that capture complex and multimodal patterns. However, conventional density estimators based on uniform histograms often fail to capture local variations, especially when the underlying distribution is highly nonuniform. Furthermore, the inherent discontinuity of histograms poses challenges for tasks requiring smooth derivatives, such as gradient-based optimization, clustering, and nonparametric discriminant analysis. In this work, we present a novel non-parametric approach for multivariate probability density function (PDF) estimation that utilizes minimum description length (MDL)-based binning with quantile cuts. Our approach builds upon tensor factorization techniques, leveraging the canonical polyadic decomposition (CPD) of a joint probability tensor. We demonstrate the effectiveness of our method on synthetic data and a challenging real dry bean classification dataset.

cs.LG↗

arXiv2025

Probabilistic Position-Aided Beam Selection for mmWave MIMO Systems

Millimeter-wave (mmWave) MIMO systems rely on highly directional beamforming to overcome severe path loss and ensure robust communication links. However, selecting the optimal beam pair efficiently remains a challenge due to the large search space and the overhead of conventional methods. This paper proposes a probabilistic position-aided beam selection approach that exploits the statistical dependence between user equipment (UE) positions and optimal beam indices. We model the underlying joint probability mass function (PMF) of the positions and the beam indices as a low-rank tensor and estimate its parameters from training data using Bayesian inference. The estimated model is then used to predict the best (or a list of the top) beam pair indices for new UE positions. The proposed method is evaluated using data generated from a state-of-the-art ray tracing simulator and compared with neural network-based and fingerprinting approaches. The results show that our approach achieves a high data rate with fewer training samples and a significantly reduced beam search space. These advantages render it a promising solution for practical mmWave MIMO deployments, reducing the beam search overhead while maintaining a reliable connectivity.

eess.SP↗

arXiv2024

Joint Bayesian Parameter and Model Order Estimation for Low-Rank Probability Mass Tensors

Obtaining a reliable estimate of the joint probability mass function (PMF) of a set of random variables from observed data is a significant objective in statistical signal processing and machine learning. Modelling the joint PMF as a tensor that admits a low-rank canonical polyadic decomposition (CPD) has enabled the development of efficient PMF estimation algorithms. However, these algorithms require the rank (model order) of the tensor to be specified beforehand. In real-world applications, the true rank is unknown. Therefore, an appropriate rank is usually selected from a candidate set either by observing validation errors or by computing various likelihood-based information criteria, a procedure that could be costly in terms of computational time or hardware resources, or could result in mismatched models which affect the model accuracy. This paper presents a novel Bayesian framework for estimating the low-rank components of a joint PMF tensor and simultaneously inferring its rank from the observed data. We specify a Bayesian PMF estimation model and employ appropriate prior distributions for the model parameters, allowing the rank to be inferred without cross-validation.We then derive a deterministic solution based on variational inference (VI) to approximate the posterior distributions of various model parameters. Numerical experiments involving both synthetic data and real classification and item recommendation data illustrate the advantages of our VI-based method in terms of estimation accuracy, automatic rank detection, and computational efficiency.

stat.ML↗