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To gain insight into the mechanisms behind machine learning methods, it is crucial to establish connections among the features describing data points. However, these correlations often exhibit a high-dimensional and strongly nonlinear…
Dimensionality reduction (DR) algorithms compress high-dimensional data into a lower dimensional representation while preserving important features of the data. DR is a critical step in many analysis pipelines as it enables visualisation,…
It is widely believed that natural image data exhibits low-dimensional structure despite the high dimensionality of conventional pixel representations. This idea underlies a common intuition for the remarkable success of deep learning in…
The abundance of models of complex networks and the current insufficient validation standards make it difficult to judge which models are strongly supported by data and which are not. We focus here on likelihood maximization methods for…
Likelihood-based inferences have been remarkably successful in wide-spanning application areas. However, even after due diligence in selecting a good model for the data at hand, there is inevitably some amount of model misspecification:…
Diffusion models recently have been successfully applied for the visual synthesis of strikingly realistic appearing images. This raises strong concerns about their potential for malicious purposes. In this paper, we propose using the…
Accurate indoor positioning for wireless communication systems represents an important step towards enhanced reliability and security, which are crucial aspects for realizing Industry 4.0. In this context, this paper presents an…
We propose an efficient algorithm for approximate computation of the profile maximum likelihood (PML), a variant of maximum likelihood maximizing the probability of observing a sufficient statistic rather than the empirical sample. The PML…
Nearest neighbor classifier is arguably the most simple and popular nonparametric classifier available in the literature. However, due to the concentration of pairwise distances and the violation of the neighborhood structure, this…
In this paper, we develop a local rank correlation measure which quantifies the performance of dimension reduction methods. The local rank correlation is easily interpretable, and robust against the extreme skewness of nearest neighbor…
Divergence estimators based on direct approximation of density-ratios without going through separate approximation of numerator and denominator densities have been successfully applied to machine learning tasks that involve distribution…
Place recognition is a challenging problem in mobile robotics, especially in unstructured environments or under viewpoint and illumination changes. Most LiDAR-based methods rely on geometrical features to overcome such challenges, as…
Online statistical inference facilitates real-time analysis of sequentially collected data, making it different from traditional methods that rely on static datasets. This paper introduces a novel approach to online inference in…
Large language models (LLMs) demonstrate remarkable emergent abilities to perform in-context learning across various tasks, including time series forecasting. This work investigates LLMs' ability to estimate probability density functions…
Minimizing a convex risk function is the main step in many basic learning algorithms. We study protocols for convex optimization which provably leak very little about the individual data points that constitute the loss function.…
Method of parameterizing and smoothing the unknown underling distributions using Bernstein polynomials is proposed, verified and investigated. Any distribution with bounded and smooth enough density can be approximated by the proposed…
Reliable probability estimation is of crucial importance in many real-world applications where there is inherent (aleatoric) uncertainty. Probability-estimation models are trained on observed outcomes (e.g. whether it has rained or not, or…
The Local Learning Coefficient (LLC) is introduced as a novel complexity measure for deep neural networks (DNNs). Recognizing the limitations of traditional complexity measures, the LLC leverages Singular Learning Theory (SLT), which has…
Parametric density estimation, for example as Gaussian distribution, is the base of the field of statistics. Machine learning requires inexpensive estimation of much more complex densities, and the basic approach is relatively costly…
We consider non-parametric estimation and inference of conditional moment models in high dimensions. We show that even when the dimension $D$ of the conditioning variable is larger than the sample size $n$, estimation and inference is…